TU BCA entrance Bachelor in Computer Applications (BCA): Mathematics

Asked 2 times
2076 · 1 mark
2022 · 1 mark

If the relation $R=\{(1,2),(2,3),(3,4),(4,5)\}$ then its range is, (a) $\{2,3,4,5\}$ (b) $\{1,2,3,4\}$ (c) $\{1,2,3,5\}$ (d) $\{1,3,4,5\}$

Answer

(a) $\{2,3,4,5\}$

The range is the set of second elements of the ordered pairs.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark
2022 · 1 mark

The value of $2\sqrt{128}+\sqrt{162}$ is , (a) $25\sqrt2$ (b) $4\sqrt3$ (c) 0 (d) 60

Answer

(a) $25\sqrt2$

$2\sqrt{128}=2\cdot8\sqrt2=16\sqrt2$ and $\sqrt{162}=9\sqrt2$ , so the sum is $25\sqrt2$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark
2023 · 1 mark

If £ 7 = USD 11 and USD 2 = Rs. 213, then how many pound (£) can be exchange for Rs. 117150? (a) 750 (b) 650 (c) 700 (d) 850

Answer

(c) 700

$USD 2=\text{Rs }213$ , so Rs $117150=\dfrac{117150\times 2}{213}=USD 1100$ .

$USD 11=£7$ , so $USD 1100=\dfrac{1100\times 7}{11}=£700$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark
2023 · 1 mark

A mobile is sold for Rs. 11000, with a profit of Rs. 1000, then the percentage profit is (a) 9% (b) 10% (c) 12% (d) 14%

Answer

(b) 10%

Cost price $=11000-1000=\text{Rs }10000$ .

$\text{Profit}\%=\frac{1000}{10000}\times100=10\%$

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2022 · 1 mark
2023 · 1 mark

The fifth term of the sequence $\frac12,\frac45,\frac78,\ldots$ is (a) $\frac{11}{12}$ (b) $\frac{12}{13}$ (c) $\frac{13}{14}$ (d) $\frac{14}{15}$

Answer

(c) $\frac{13}{14}$

The numerators are $1,4,7,\ldots$ and the denominators are $2,5,8,\ldots$ , so $t_n=\frac{3n-2}{3n-1}$ . Then $t_5=\frac{13}{14}$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2074 · 1 mark

The sum of first five prime numbers is: (a) 11 (b) 18 (c) 26 (d) 28

Similar questions: What is the sum of first five prime numbers? (2075)

Answer

(d) 28

The first five prime numbers are 2, 3, 5, 7 and 11. Their sum is $2+3+5+7+11 = 28$ .

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2074 · 1 mark

The product of two consecutive even number is 224. Then the numbers are: (a) 16, 18 (b) 12, 14 (c) 14, 16 (d) 18, 20

Answer

(c) 14, 16

Because $14 \times 16 = 224$ , and 14 and 16 are consecutive even numbers.

Answer checked by Claude Haiku · Oct 21, 2026

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2074 · 1 mark

If the ratio of two numbers is 2:3 and sum of these numbers is 30, then which are these numbers? (a) 14, 16 (b) 10, 20 (c) 12, 18 (d) 18, 12

Similar questions: Two numbers are in the ratio of 6:7 and their sum is 117,... (2075)

Answer

(c) 12, 18

Let the numbers be $2x$ and $3x$ . Then $2x+3x=30 \Rightarrow 5x=30 \Rightarrow x=6$ . So the numbers are $2x=12$ and $3x=18$ .

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2074 · 1 mark

If the cost of 9 kg sugar is Rs. 270/-, how much sugar can be purchased for Rs. 390/-? (a) 11 (b) 12 (c) 13 (d) 14

Answer

(c) 13

Cost of 1 kg sugar = Rs. 270 ÷ 9 = Rs. 30.
So, sugar for Rs. 390 = 390 ÷ 30 = 13 kg.

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2074 · 1 mark

The cardinal number of a vowel set V = {a, e, i, o, u} is: (a) 4 (b) 5 (c) 6 (d) 7

Similar questions: What is the cardinal number of a vowel set V= a,e,i,o,u ? (2075)

Answer

(b) 5

The cardinal number of a set is the number of distinct elements it contains. The set V = {a, e, i, o, u} has five elements, so its cardinal number is 5.

Answer checked by Claude Haiku · Oct 21, 2026

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2075 · 1 mark

What is the sum of first five prime numbers? (a) 18 (b) 25 (c) 26 (d) 28

Similar questions: The sum of first five prime numbers (2074)

Answer

(d) 28

The first five primes are 2, 3, 5, 7, 11, and +3+5+7+11=28$.

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2075 · 1 mark

If the product of two consecutive even number is 288, then what are these numbers from following? (a) 14, 12 (b) 14, 16 (c) 16, 18 (d) 22, 24

Similar questions: The product of two consecutive even number (2074)

Answer

(c) 16, 18

Let the numbers be $x$ and $x+2$ . Then $x(x+2)=288$ , so $x^2+2x-288=0$ , giving $(x+18)(x-16)=0$ . Taking $x=16$ gives 16 and 18, and $16\times18=288$ .

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2075 · 1 mark

If the cost of 7 kg sugar is Rs. 210, how much sugar can be purchased for Rs. 330? (a) 11kg (b) 12kg (c) 13kg (d) 14kg

Similar questions: If the cost of 9 kg sugar (2074)

Answer

(a) 11kg

1 kg costs $210/7=$ Rs 30, so Rs 330 buys $330/30=11$ kg.

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2075 · 1 mark

Two numbers are in the ratio of 6:7 and their sum is 117, then what are these numbers? (a) 56, 58 (b) 63, 54 (c) 54, 63 (d) 48, 56

Similar questions: If the ratio of two numbers is (2074)

Answer

(c) 54, 63

One part $=117/(6+7)=9$ , so the numbers are $6\times9=54$ and $7\times9=63$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the rate percentage per anum that a sum of money trebles itself in 25 years? (a) 2% (b) 4% (c) 6% (d) 8%

Similar questions: The rate percentage per annum that a sum of money trebles... (2077)

Answer

(d) 8%

The sum trebles, so the interest equals twice the principal: $2P=\frac{P\times r\times25}{100}$ , which gives $r=8\%$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the cardinal number of a vowel set $V=\{a,e,i,o,u\}$ ? (a) 4 (b) 5 (c) 6 (d) 7

Similar questions: The cardinal number of a vowel set (2074)

Answer

(b) 5

The cardinal number is the number of elements, and $V$ has five: $a,e,i,o,u$ .

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2075 · 1 mark

The area of 4 walls of square room is $120\,m^2$ . If the height is 5 m, then what is the area of its floor? (a) $26\,m^2$ (b) $56\,m^2$ (c) $25\,m^2$ (d) $36\,m^2$

Similar questions: The area of 4 walls of square room is 120 ,m 2. if the... (2077)

Answer

(d) $36\,m^2$

Area of four walls $=2(l+b)h=$ perimeter $\times h$ . So perimeter $=120/5=24$ m and side $=6$ m. Floor area $=6^2=36\,m^2$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

Of a group of 120 students, 90 takes mathematics and 72 takes statistics. If 10 students neither of two, the number of student taking both subjects are: (a) 50 (b) 45 (c) 52 (d) 58

Similar questions: Of a group of 120 students, 80 takes mathematics and 62... (2022)

Answer

(c) 52

Students taking at least one subject $=120-10=110$ .

$n(M\cap S)=90+72-110=52$

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2076 · 1 mark

$-5<x<7$ can be written in the absolute value sign as: (a) $|x-1|<7$ (b) $|x-1|<6$ (c) $|x-1|<2$ (d) $|x-1|<-1$

Similar questions: -5<x<9 can be written in the absolute value sign as: (2022)

Answer

(b) $|x-1|<6$

The midpoint of $-5$ and $7$ is $1$ and the half-width is $6$ , so $-5<x<7\iff |x-1|<6$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

How many stones each of area 0.16 cm square are required for paving a courtyard 5.5 m long and 4.8 m wide? (a) 60 (b) 100 (c) 50 (d) 165

Answer

(d) 165

The courtyard area is $5.5\times4.8=26.4\ \text{m}^2$ . Taking the stone area as $0.16\ \text{m}^2$ (the only reading that matches the options):

$\frac{26.4}{0.16}=165$

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The discount percent of marked price is Rs. 5,800 and discount amount is Rs. 696 then the discount percent is, (a) 12% (b) 20% (c) 5% (d) 38%

Similar questions: The discount of marked price is Rs. 5,800 the amount Rs.... (2022)

Answer

(a) 12%

$\frac{696}{5800}\times100=12\%$

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2076 · 1 mark

If 4 is subtracted from a square of a number, its result is 21. The number is, (a) 5 (b) 4 (c) 6 (d) 3

Similar questions: If 5 is subtracted from the square of a number and the... (2077)

Answer

(a) 5

$x^2-4=21\Rightarrow x^2=25\Rightarrow x=5$ (the option given; $-5$ also satisfies it).

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2077 · 1 mark

The area of 4 walls of square room is $120\,m^2$ . if the height is 5m, the area of its floor is (a) $56\,m^2$ (b) $36\,m^2$ (c) $46\,m^2$ (d) $26\,m^2$

Similar questions: The area of 4 walls of square room is 120 ,m 2. If the... (2075)

Answer

(b) $36\,m^2$

Area of four walls $=4\times\text{side}\times\text{height}$ .

$4\times s\times5=120\Rightarrow s=6\ \text{m}$

Floor area $=6^2=36\ m^2$ .

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2077 · 1 mark

The rate percentage per annum that a sum of money trebles itself in 25 years is : (a) 25 % (b) 10% (c) 4% (d) 8%

Similar questions: What is the rate percentage per anum that a sum of money... (2075)

Answer

(d) 8%

Money trebles, so interest $=3P-P=2P$ . Using $I=\frac{PTR}{100}$ :

$2P=\frac{P\times25\times R}{100}\Rightarrow R=8\%$

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2077 · 1 mark

If 5 is subtracted from the square of a number and the result is 20, the number is : (a) $\pm5$ (b) $\pm6$ (c) $\pm7$ (d) $\pm9$

Answer

(a) $\pm5$

$x^2-5=20\Rightarrow x^2=25\Rightarrow x=\pm5$

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2022 · 1 mark

The Marked Price of an article is Rs. 8500. If a discount of 10% is allowed the selling price is (a) 7550 (b) 7650 (c) 7750 (d) 7850

Similar questions: Marked price of an article is Rs. 8500. If a discount of... (2023)

Answer

(b) 7650

Discount $=10\%$ of $8500 =$ Rs 850.

$SP = 8500-850 = \text{Rs } 7650$

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2022 · 1 mark

Radius of cylinder is 7 cm height is 12 cm then it's volume is (a) $1848\,cm^3$ (b) $1748\,cm^3$ (c) $1648\,cm^3$ (d) $1548\,cm^3$

Similar questions: Radius of the cylinder is 7 cm height is 3 cm then it's... (2023)

Answer

(a) $1848\,cm^3$

$V=\pi r^2h=\frac{22}{7}\times 49\times 12=1848\,cm^3$

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2022 · 1 mark

Single equation represented by two straight lines $x=2y$ and $2x=y$ is (a) $2x^2-3xy+2y^2=0$ (b) $x^2-3xy+2y^2=0$ (c) $2x^2-xy+2y^2=0$ (d) $2x^2-3xy+y^2=0$

Similar questions: A single equation represented by two straight lines x=2y... (2023)

Answer

(a) $2x^2-3xy+2y^2=0$

The product of the two line equations gives $(x-2y)(2x-y)=2x^2-5xy+2y^2=0$ . Of the options, only (a) has the correct $x^2$ and $y^2$ coefficients, so it is the intended choice (the middle coefficient in the printed option differs from the exact $-5$ ).

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2022 · 1 mark

Of a group of 120 students, 80 takes mathematics and 62 takes statistics. If 20 students neither if two, the number of students taking both subjects are (a) 50 (b) 42 (c) 52 (d) 55

Similar questions: Of a group of 120 students, 90 takes mathematics and 72... (2076)

Answer

(b) 42

Students taking at least one subject: $120-20=100$ . Using $n(M\cup S)=n(M)+n(S)-n(M\cap S)$ :

$100=80+62-x \Rightarrow x=42$

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2022 · 1 mark

$-5<x<9$ can be written in the absolute value sign as: (a) $|x-2|<5$ (b) $|x-2|<7$ (c) $|x-2|<9$ (d) $|x+2|<5$

Similar questions: -5<x<7 can be written in the absolute value sign as: (2076)

Answer

(b) $|x-2|<7$

The interval $-5<x<9$ has midpoint $\frac{-5+9}{2}=2$ and half-width $\frac{9-(-5)}{2}=7$ , so it is $|x-2|<7$ .

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2022 · 1 mark

How many stones each of area $22\,cm$ square are required for paving a courtyard 5.5 m long and 4 m wide? (a) 60000 (b) 40000 (c) 20000 (d) 10000

Similar questions: How many stones each of area 0.16 cm square are required... (2076)

Answer

(d) 10000

Courtyard area $=5.5\times4=22\ \text{m}^2=220000\ \text{cm}^2$ .

Number of stones $=\dfrac{220000}{22}=10000$ .

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2022 · 1 mark

The discount of marked price is Rs. 5,800 the amount Rs. 696 then discount percent is. (a) 12% (b) 20% (c) 5% (d) 38%

Similar questions: The discount percent of marked price is Rs. 5,800 and... (2076)

Answer

(a) 12%

Discount percent $=\dfrac{696}{5800}\times100=12\%$ .

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2023 · 1 mark

Marked price of an article is Rs. 8500. If a discount of 10% is allowed the selling price is.... (a) 7550 (b) 7650 (c) 7750 (d) 7850

Similar questions: The Marked Price of an article is Rs. 8500. If a discount... (2022)

Answer

(b) 7650 Discount $=10\%$ of 8500 $=$ Rs 850, so the selling price is $8500-850=$ Rs 7650.

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2023 · 1 mark

A single equation represented by two straight lines $x=2y$ and $2x=y$ is ... (a) $2x^2-3xy+y^2=0$ (b) $x^2-3xy+2y^2=0$ (c) $2x^2-xy+2y^2=0$ (d) $2x^2-5xy+2y^2=0$

Answer

(d) $2x^2-5xy+2y^2=0$ The lines are $x-2y=0$ and $2x-y=0$ . Their combined equation is

$(x-2y)(2x-y)=2x^2-xy-4xy+2y^2=2x^2-5xy+2y^2=0$

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2023 · 1 mark

Radius of the cylinder is 7 cm height is 3 cm then it's volume is (a) $442\,cm^3$ (b) $452\,cm^3$ (c) $462\,cm^3$ (d) $472\,cm^3$

Answer

(c) $462\,cm^3$

$V=\pi r^2h=\frac{22}{7}\times49\times3=462\,cm^3$ .

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2074 · 1 mark

Which one of the following number has a remainder of 4 when it is divided by 6? (a) 8 (b) 12 (c) 22 (d) 29

Answer

(c) 22

When 22 is divided by 6, $6 \times 3 = 18$ , leaving a remainder of $22 - 18 = 4$ .

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2074 · 1 mark

The sum of the product and quotient of 4 and 4 is ………. (a) 16 (b) 15 (c) 8 (d) 17

Answer

(d) 17

Product of 4 and 4 = $4 \times 4 = 16$ ; quotient = $4 \div 4 = 1$ ; sum = $16 + 1 = 17$ .

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2074 · 1 mark

The average of all even numbers between -4 and 5 is ….. (a) 1 (b) 0.5 (c) -1 (d) none of these

Answer

(a) 1

Even numbers strictly between (-4) and (5) are (-2, 0, 2, 4).
Average (=\dfrac{-2+0+2+4}{4}=\dfrac{4}{4}=1).

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2074 · 1 mark

The value of $\sum_{n=10}^{10} (-1)^n$ is: (a) 1 (b) -1 (c) 10 (d) 0

Answer

(a) 1

Since the sum runs only from $n=10$ to $n=10$ , it equals $(-1)^{10}=1$ .

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2074 · 1 mark

If 5 is added to the square of a number, then the result is 14. What is the value of that number? (a) 3 (b) 5 (c) 7 (d) 9

Answer

(a) 3

Let the number be $x$ . Then $x^2+5=14 \Rightarrow x^2=9 \Rightarrow x=3$ (taking the positive value).

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2074 · 1 mark

If three spoons equals to one glass, two glasses equals to one plate, then how many spoons equals to one plate? (a) 3 (b) 6 (c) 9 (d) 2

Answer

(b) 6

Since 1 glass = 3 spoons and 1 plate = 2 glasses,
1 plate = 2 × 3 = 6 spoons.

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2074 · 1 mark

If a matrix is of order 5 X 7, then each column will contain …………..elements. (a) 5 (b) 12 (c) 35 (d) 7

Answer

(a) 5

A matrix of order $5 \times 7$ has 5 rows and 7 columns. Each column therefore contains 5 elements (one from each row).

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2074 · 1 mark

If the equation are $3x + 4y = 7$ and $4x - y = 3$ after solving these equations the value of x and y will be: (a) 1,1 (b) 1,2 (c) 2,1 (d) 2,2

Answer

(a) 1, 1

From $4x-y=3$ , $y=4x-3$ . Substituting in $3x+4y=7$ : $3x+4(4x-3)=7 \Rightarrow 19x=19 \Rightarrow x=1$ , so $y=4(1)-3=1$ .

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2074 · 1 mark

What is the value of x in series 1, 9, 25, x, 81, 121? (a) 100 (b) 36 (c) 49 (d) 64

Answer

(c) 49

The terms are the squares of consecutive odd numbers: $1^2=1$ , $3^2=9$ , $5^2=25$ , $7^2=49$ , $9^2=81$ , $11^2=121$ . So $x = 7^2 = 49$ .

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2074 · 1 mark

If $a + b = c$ , then what is the average value of a, b and c? (a) $\frac{(a+b)}{3}$ (b) $\frac{c}{3}$ (c) $\frac{2c}{3}$ (d) $\frac{c}{3}$

Answer

(c) $\frac{2c}{3}$

Average $=\frac{a+b+c}{3}=\frac{c+c}{3}=\frac{2c}{3}$ .

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2074 · 1 mark

If x in an integer and $y = -2x - 8$ , what is the least value of x for which y is less than 9? (a) -8 (b) -9 (c) -10 (d) -11

Answer

(a) -8

Given $y=-2x-8$ and $y<9$ : $-2x-8<9 \Rightarrow -2x<17 \Rightarrow x>-8.5$ The least integer greater than $-8.5$ is $-8$ .

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2074 · 1 mark

The slope of line which equation is $2x - 4y = 9$ is: (a) 2 (b) 1/2 (c) -1/2 (d) 3

Answer

(b) 1/2

Rearranging $2x - 4y = 9$ gives $4y = 2x - 9$ , so $y = \frac{1}{2}x - \frac{9}{4}$ . Comparing with $y = mx + c$ , the slope is $m = \frac{1}{2}$ .

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2074 · 1 mark

What is the slope of horizontal line? (a) >1 (b) < 0 (c) 0 (d) 1

Answer

(c) 0

A horizontal line has no vertical rise, so its slope $m = \frac{\Delta y}{\Delta x} = \frac{0}{\Delta x} = 0$ .

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2074 · 1 mark

The difference between 3/5 of 80 and 30% of 80 is: (a) 20 (b) 14 (c) 15 (d) 24

Answer

(d) 24

$\frac{3}{5}$ of 80 = 48 and 30% of 80 = 24, so the difference is $48 - 24 = 24$ .

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2074 · 1 mark

Gautam spent Rs. 40/-, which is 5% of his daily wage, then his total daily wage is: (a) Rs.400/- (b) Rs.600/- (c) Rs.800/- (d) Rs. 1000/-

Answer

(c) Rs.800/-

Since 5% of his daily wage is Rs. 40, his total daily wage is $\frac{40}{0.05} = \text{Rs. } 800$ .

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2074 · 1 mark

If 1254376 represents the CENTURY, then what represents 735? (a) NUT (b) RUT (c) RUN (d) YET

Answer

(c) RUN

From the code: $C=1,\ E=2,\ N=5,\ T=4,\ U=3,\ R=7,\ Y=6$ .
So $735 = R\ U\ N$ = RUN.

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2074 · 1 mark

Find the missing value in $\begin{pmatrix} 2 & 7 & 6 \\ 9 & 5 & 1 \\ 4 & 3 & ? \end{pmatrix}$ . (a) 5 (b) 8 (c) 7 (d) 9

Answer

(b) 8

Each row and each column sums to 15.
So, $4 + 3 + ? = 15 \Rightarrow ? = 8$ .

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2074 · 1 mark

There are 48 students in a computer class. If number of boys are twice than girls, then how many girls are there? (a) 16 (b) 18 (c) 32 (d) 28

Answer

(a) 16

Let the number of girls be $x$ . Then boys $=2x$ . So $x+2x=48 \Rightarrow 3x=48 \Rightarrow x=16$ .

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2074 · 1 mark

Find the number x, which is equal to (80% of x) plus 5. (a) 20 (b) 30 (c) 40 (d) 25

Answer

(d) 25

Let the number be $x$ . Then $x = 80\%$ of $x + 5 = 0.8x + 5$ .
So $0.2x = 5$ , giving $x = 25$ .

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2074 · 1 mark

If the age of five girls are 15, 16, 17, 18, 19 respectively then what is the average age of girls? (a) 15 (b) 17 (c) 18 (d) 19

Answer

(b) 17

Average age $=\dfrac{15+16+17+18+19}{5}=\dfrac{85}{5}=17$ years.

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2074 · 1 mark

How many triangles in this figure? (a) 6 (b) 7 (c) 8 (d) 9

Answer

(c) 8

The figure is a square with both diagonals drawn. The two diagonals cut it into 4 small triangles (the four corner regions). Joining each pair of adjacent small triangles across a side of the square gives 4 more triangles (the four half-square triangles). So the total is $4 + 4 = 8$ .

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2074 · 1 mark

What is the value of cos 60° ? (a) 1 (b) $\frac{1}{2}$ (c) 0 (d) $\frac{\sqrt{3}}{2}$

Answer

(b) $\frac{1}{2}$

From the standard trigonometric values, $\cos 60^\circ = \frac{1}{2}$ .

Answer checked by Claude Haiku · Oct 21, 2026

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2074 · 1 mark

Find the value of x in series 1, 1, 2, 3, 5, 8, 13, x. (a) 21 (b) 22 (c) 19 (d) 23

Answer

(a) 21

This is the Fibonacci series, where each term is the sum of the two terms before it: $8 + 13 = 21$ . So $x = 21$ .

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2074 · 1 mark

If 'n' is an integer, which of the following must be even? (a) n + 1 (b) n + 2 (c) 2n + 1 (d) 2n

Answer

(d) 2n

For any integer $n$ , multiplying by 2 gives an even number, so $2n$ is always even. The other expressions can be odd or even depending on whether $n$ is odd or even.

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2074 · 1 mark

The largest prime factor of 255 is: (a) 45 (b) 25 (c) 17 (d) 5

Answer

(c) 17

$255 = 3 \times 5 \times 17$ , so its prime factors are 3, 5 and 17. The largest prime factor is 17.

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2074 · 1 mark

The sum of first n natural number is: (a) $\frac{n(n+1)}{2}$ (b) $\frac{n(n+1)(2n+1)}{2}$ (c) $\frac{(n+1)^2}{2}$ (d) none of these

Answer

(a) $\frac{n(n+1)}{2}$

The sum of the first $n$ natural numbers is $1+2+\cdots+n=\frac{n(n+1)}{2}$ .

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2074 · 1 mark

The root of the equation $3x^2 - 8x + 16 = 0$ are (a) real & equal (b) real & unequal (c) imaginary & unequal (d) none of these

Answer

(c) imaginary & unequal

Discriminant $D = b^2 - 4ac = (-8)^2 - 4(3)(16) = 64 - 192 = -128 < 0$ , so the roots are imaginary (complex conjugates) and unequal.

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2074 · 1 mark

If x + y = 12 and x - y = 6 then, the value of $x^2 - y^2$ is: (a) 18 (b) 36 (c) 60 (d) 72

Answer

(d) 72

Using the identity $x^2-y^2=(x+y)(x-y)$ : $x^2-y^2=12\times 6=72$

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2074 · 1 mark

If x - 5 = 2, then the value of x + 12 is: (a) 15 (b) 17 (c) 19 (d) 18

Answer

(c) 19

Since $x - 5 = 2$ , we get $x = 7$ , so $x + 12 = 7 + 12 = 19$ .

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2074 · 1 mark

The value when simplified $\frac{6^4 - 6^3}{5}$ is: (a) 1/5 (b) 63 (c) 6/5 (d) 64

Answer

(b) $6^3$ (the printed "63" is $6^3$ with its superscript lost), which equals $216$ .

$\frac{6^4-6^3}{5}=\frac{6^3(6-1)}{5}=\frac{6^3\cdot 5}{5}=6^3=216$

Read literally, $63$ is not the value, so option (b) is the intended choice only as $6^3$ .

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2074 · 1 mark

If 4/a + 4/a + 4/a + 4/a = 16 then, 4a is: (a) 4 (b) 8 (c) 12 (d) 16

Answer

(a) 4

Since (\frac{4}{a}+\frac{4}{a}+\frac{4}{a}+\frac{4}{a}=\frac{16}{a}=16), we get (a=1). Hence (4a=4).

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2074 · 1 mark

The slope of line $\frac{x}{a} + \frac{y}{b} = 1$ is: (a) $-\left(\frac{a}{b}\right)$ (b) $-\left(\frac{b}{a}\right)$ (c) ab (d) $-\left(\frac{1}{ab}\right)$

Answer

(b) $-\left(\frac{b}{a}\right)$

Rearranging $\frac{x}{a}+\frac{y}{b}=1$ gives $y=b-\frac{b}{a}x$ , so the coefficient of $x$ is the slope: $-\frac{b}{a}$ .

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2074 · 1 mark

If x = 4y, what percent of 2x is 2y? (a) 20% (b) 40% (c) 30% (d) 25%

Answer

(d) 25%

Since $x=4y$ , we have $\dfrac{2y}{2x}\times 100=\dfrac{y}{x}\times 100=\dfrac{y}{4y}\times 100=25\%$ .

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2074 · 1 mark

If 3 bananas cost 50 cents, how many bananas can be bought for 20 dollars? (a) 120 (b) 115 (c) 110 (d) 130

Answer

(a) 120

20 dollars = 2000 cents. Since 50 cents buys 3 bananas, 2000 cents buys $(2000 \div 50) \times 3 = 40 \times 3 = 120$ bananas.

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2074 · 1 mark

If 5:7 = 15:x, then the value of x is: (a) 35 (b) 21 (c) 27 (d) 18

Answer

(b) 21

Since $5:7 = 15:x$ , we have $\frac{5}{7}=\frac{15}{x}$ , so $5x=105$ and $x=21$ .

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2074 · 1 mark

By selling 150 apples, the seller gains the selling price of 30 apples, then gain percentage is: (a) 25% (b) 30% (c) 12% (d) 20%

Answer

(a) 25%

Let the selling price of one apple be Rs 1.
Total SP of 150 apples = Rs 150.
Gain = SP of 30 apples = Rs 30.
So total CP = 150 − 30 = Rs 120.
Gain % = (30/120) × 100 = 25%.

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2074 · 1 mark

A vendor purchases lemons at Rs. 5/- per lemon, at what price vendor will sell lemon to gain 20% profit? (a) Rs. 4/- (b) Rs. 5/- (c) Rs. 6/- (d) Rs. 7/-

Answer

(c) Rs. 6/-

Cost price = Rs. 5, profit = 20%, so selling price = $5 \times \frac{120}{100} = \text{Rs. } 6$ .

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2074 · 1 mark

What is the population doubling time if population growth rate is 2% per annum? (a) 50yrs (b) 30yrs (c) 40yrs (d) none of these

Answer

(d) none of these

Using the rule of 70, doubling time $= \dfrac{70}{\text{growth rate}} = \dfrac{70}{2} = 35$ years. (The exact value is $\dfrac{\ln 2}{0.02} \approx 34.7$ years.) Since 35 years is not among the given options, the answer is "none of these".

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2074 · 1 mark

If $\log_a 81 = 4$ , then the value of 'a' is: (a) 4 (b) 3 (c) 5 (d) none of these

Answer

(b) 3

Since $\log_a 81 = 4$ , we have $a^4 = 81 = 3^4$ , so $a = 3$ .

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2074 · 1 mark

The value of $\frac{\sqrt{18}}{\sqrt{72}}$ is: (a) a rational number (b) an irrational number (c) an imaginary number (d) none of these

Answer

(a) a rational number

$\frac{\sqrt{18}}{\sqrt{72}}=\sqrt{\frac{18}{72}}=\sqrt{\frac14}=\frac12$

Since $\frac12$ is a rational number, the value is rational.

Answer checked by Claude Haiku · Oct 21, 2026

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2074 · 1 mark

If 5/7 of a number is 1025, then 3/7 of number is: (a) 735 (b) 430 (c) 615 (d) 560

Answer

(c) 615

Let the number be $x$ . Then $\frac{5}{7}x=1025$ , so $x=1025\times\frac{7}{5}=1435$ . Hence $\frac{3}{7}x=1435\times\frac{3}{7}=615$ .

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2074 · 1 mark

The number of seconds in $1\frac{1}{3}$ hours is: (a) 4800 (b) 4700 (c) 4900 (d) 5000

Answer

(a) 4800

$1\frac{1}{3}$ hours $=\frac{4}{3}\times 3600 = 4800$ seconds.

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2074 · 1 mark

The 4m wide carpet is used for carpeting a room of 8m long and 3m wide, then what is the length of carpet? (a) 5m (b) 6m (c) 2m (d) 3m

Answer

(b) 6m

Room area $= 8 \times 3 = 24\text{ m}^2$ .
Carpet length $= \dfrac{\text{Area}}{\text{width}} = \dfrac{24}{4} = 6\text{ m}$ .

Answer checked by Claude Haiku · Oct 21, 2026

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2074 · 1 mark

Hari ranks seventh from the top and twenty sixth from the bottom in a class. Then the total number of students in a class are: (a) 36 (b) 35 (c) 31 (d) 32

Answer

(d) 32

Total students = rank from top + rank from bottom − 1 = 7 + 26 − 1 = 32.

Answer checked by Claude Haiku · Oct 21, 2026

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2074 · 1 mark

If three girls write 3 pages in 3 minutes, in how many minutes can one girl write one page? (a) 4 min (b) 5 min (c) 3 min (d) 6 min

Answer

(c) 3 min

Three girls write 3 pages in 3 minutes, so each girl writes 1 page in those same 3 minutes. Hence one girl writes one page in 3 minutes.

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2019

The total surface area of a closed right circular cylinder of radius 3.5 m and height 7 m is (a) 77 m² (b) 154 m² (c) 231 m² (d) 308 m²

Answer

(c) 231 m²

Total surface area of a closed cylinder is
$A = 2\pi r(r+h) = 2 \times \frac{22}{7} \times 3.5 \times (3.5+7) = 231\ \text{m}^2$

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2019

If volume of a cube is 1728 m³ then its surface area is (a) 864 m² (b) 846 m² (c) 1444 m² (d) 72 m²

Answer

(a) 864 m²

Volume of cube $= a^3 = 1728$ , so $a = \sqrt[3]{1728} = 12$ m.

Surface area $= 6a^2 = 6 \times 12^2 = 6 \times 144 = 864$ m².

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2019

If f(x) = 4x - 2, then f(x - 1) equals (a) 4x² - 6x + 2 (b) 4x² + 2x + 2 (c) 4x - 6 (d) 4x - 2

Answer

(c) 4x - 6

Substitute $x-1$ for $x$ :
$f(x-1)=4(x-1)-2=4x-4-2=4x-6$ .

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2019

If $3^{x-1} = \frac{1}{27}$ then value of x is (a) -10 (b) -8 (c) -6 (d) -2

Answer

(d) -2

Since $\frac{1}{27} = 3^{-3}$ , we get
$3^{x-1} = 3^{-3}$ So $x - 1 = -3 \Rightarrow x = -2$ .

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2019

If $\cos 60^\circ = \frac{1}{2}$ , then the value of $\cos 300^\circ$ is (a) $\frac{\sqrt{3}}{2}$ (b) $-\frac{1}{2}$ (c) $-\frac{\sqrt{3}}{2}$ (d) $\frac{1}{2}$

Answer

(d) $\frac{1}{2}$

Since $300^\circ = 360^\circ - 60^\circ$ , we have
$\cos 300^\circ = \cos(360^\circ - 60^\circ) = \cos 60^\circ = \frac{1}{2}.$

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2019

The zeroes of quadratic polynomial $x^2 + 7x + 12$ are (a) -2, -5 (b) -3, -4 (c) 2, 5 (d) 3, 4

Answer

(b) -3, -4

Since $x^2+7x+12=(x+3)(x+4)$ , the zeroes are $x=-3$ and $x=-4$ .

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2019

The lines pair 2x + 3y = 3 and x + 2y = 1 are (a) coincide (b) perpendicular (c) parallel (d) intersect at a point

Answer

(d) intersect at a point

The slopes are $-\frac{2}{3}$ and $-\frac{1}{2}$ , which are neither equal nor negative reciprocals. Solving gives $x=3,\ y=-1$ , so the lines intersect at the single point $(3,-1)$ .

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2019

Slope of a line perpendicular to the line 20x - 2y = 6 is (a) -10 (b) $-\frac{1}{10}$ (c) 10 (d) $\frac{1}{10}$

Answer

(b) $-\frac{1}{10}$

The given line is $20x-2y=6$ , i.e. $y=10x-3$ , so its slope is $10$ . A line perpendicular to it has slope $-\frac{1}{10}$ .

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2019

In given triangle ABC if side BC is extended to point D with $\angle A = x$ , $\angle B = 2x + 15$ and $\angle ACD = 5x + 5$ , then $\angle B$ is (a) 5 (b) 20 (c) 25 (d) 55

Answer

(c) 25

Since (BC) is extended to (D), (\angle ACD) is the exterior angle at (C).

[ \angle ACD = \angle A + \angle B ]

[ 5x+5 = x + (2x+15) ]

[ 5x+5 = 3x+15 ]

[ 2x=10 \Rightarrow x=5 ]

So,

[ \angle B = 2x+15 = 2(5)+15 = 25^\circ ]

Hence, (\angle B = 25^\circ).

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2019

If height and diameter of a cylinder are 15cm and 12 cm respectively then its volume is (a) 180 π cm³ (b) 540 π cm³ (c) 675 π cm³ (d) 2,160 π cm³

Answer

(b) 540 π cm³

Diameter = 12 cm, so radius $r = 6$ cm. Volume of a cylinder $= \pi r^2 h = \pi \times 6^2 \times 15 = 540\pi$ cm³.

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2019

What is the perimeter of a square whose diagonal is $3\sqrt{2}$ . (a) 18 (b) 12 (c) 9 (d) 6

Answer

(b) 12

For a square, diagonal $= s\sqrt{2}$ . Given $s\sqrt{2}=3\sqrt{2}$ , so side $s=3$ . Perimeter $=4s=4\times3=12$ .

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2019

The 5th term of the sequence $a_n = 2n + 1$ is (a) 9 (b) 11 (c) 13 (d) 15

Answer

(b) 11

For the 5th term, put $n=5$ in $a_n=2n+1$ :

$a_5 = 2(5)+1 = 10+1 = 11$

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2019

$\frac{2^{n+1}}{2^{n-1}}$ is equal to (a) $\frac{n+1}{n-1}$ (b) $\frac{1}{8}$ (c) $-\frac{1}{2}$ (d) 8

Answer

None of the given options —
[ \frac{2^{n+1}}{2^{n-1}}=2^{(n+1)-(n-1)}=2^2=4. ] So the correct value is 4; if option (d) was misprinted as 8, it should be 4.

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2019

The derivative of $x^3$ w.r.t $x^2$ is (a) $\frac{2x}{3}$ (b) $x$ (c) $\frac{3x}{2}$ (d) $\frac{3}{2x}$

Answer

(c) $\dfrac{3x}{2}$

Let $y=x^3$ and $u=x^2$ . Then $\frac{dy}{du}=\frac{dy/dx}{du/dx}=\frac{3x^2}{2x}=\frac{3x}{2}.$

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2019

The value of $\sqrt{-8} \times \sqrt{-2}$ is (a) -4 (b) 4 (c) 4i (d) -4i

Answer

(a) -4

Using principal square roots, $\sqrt{-8}=i\sqrt{8}=2\sqrt2\,i$ and $\sqrt{-2}=i\sqrt2$ , so their product is $(2\sqrt2\,i)(\sqrt2\,i)=2\cdot2\,i^2=4(-1)=-4$ .

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2019

If $U = \{1, 2, 3, 4, 5, 6\}$ and $A = \{2, 3, 5\}$ the $\bar{A}$ is (a) $\{1, 4, 6\}$ (b) $\{1, 2, 3, 4, 5, 6\}$ (c) $\{2, 3, 5\}$ (d) $\{1, 3, 5, 6\}$

Answer

(a) $\{1, 4, 6\}$

The complement $\bar{A}$ (or $A'$ ) is the set of all elements of the universal set $U$ that are not in $A$ .

$U = \{1, 2, 3, 4, 5, 6\}, \quad A = \{2, 3, 5\}$

Removing the elements of $A$ from $U$ :

$\bar{A} = U - A = \{1, 4, 6\}$

So the correct option is (a).

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2019

The opposite angles of any quadrilateral inscribed in circle are (a) tangent (b) supplementary (c) complementary (d) reflective

Answer

(b) supplementary

In a cyclic quadrilateral, each pair of opposite angles adds up to $180^\circ$ , i.e. they are supplementary. This follows from the inscribed angle theorem: opposite angles subtend the two complementary arcs of the circle, so their sum is $\tfrac{1}{2}(360^\circ) = 180^\circ$ .

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2019

If a set has 5 elements, then possible number of subsets are (a) 30 (b) 120 (c) 32 (d) 25

Answer

(c) 32

A set with (n) elements has (2^n) subsets. Here (n=5), so the number of subsets is (2^5 = 32).

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2019

2, 4, 6, 8, ............... is (a) Geometric Series (b) Harmonic Series (c) Geometric Progression (d) Arithmetic Progression

Answer

(d) Arithmetic Progression

The terms increase by a constant difference of $2$ ( $4-2=6-4=8-6=2$ ), which is the defining property of an arithmetic progression. A geometric progression would require a constant ratio, and a harmonic series would require the reciprocals to form an AP.

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2019

Which of the following is correct? (a) $\lim_{x \to a} \frac{x^n - a^n}{x - a} = na^{n-1}$ (b) $\lim_{x \to a} \frac{x^n - a^n}{x - a} = na^{n+1}$ (c) $\lim_{x \to a} \frac{x^n - a^n}{x - a} = nx^{n-1}$ (d) $\lim_{x \to a} \frac{x^n - a^n}{x - a} = na^{n-1}$

Answer

(a) $\lim_{x \to a} \dfrac{x^n - a^n}{x - a} = na^{n-1}$

Why: Factor the numerator:

$x^n - a^n = (x-a)\left(x^{n-1} + x^{n-2}a + x^{n-3}a^2 + \cdots + a^{n-1}\right)$

So

$\lim_{x \to a} \frac{x^n - a^n}{x - a} = \lim_{x \to a}\left(x^{n-1} + x^{n-2}a + \cdots + a^{n-1}\right)$

Putting $x = a$ , each of the $n$ terms equals $a^{n-1}$ , giving $n\,a^{n-1}$ .

Note: options (a) and (d) are written identically in the question, so both state the correct result. The correct value is $n\,a^{n-1}$ (option (b) is wrong because the power is $n-1$ , not $n+1$ ; option (c) is wrong because the limit is evaluated at $x=a$ , so the answer must contain $a$ , not $x$ ).

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2075 · 1 mark

A number is divided by 10 gives a remainder 7. If the same number is divided by 5, then what will be the remainder? (a) 1 (b) 2 (c) 3 (d) 4

Answer

(b) 2

Write the number as = 10k + 7 $. Since 0k$ is divisible by 5, the remainder on division by 5 is the remainder of 7 divided by 5, which is 2.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

Which one of the following value of 'n' gives the negative result on $n^2-15$ ? (a) 7 (b) 5 (c) 3 (d) 4

Answer

(c) 3

We need ^2 < 15 $. For =3$ , -15=-6 $, which is negative. For 4, 5 and 7 the results are$ , 0 $and 4$ , all positive.

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2075 · 1 mark

If 'n' is an integer, then which one of the following expression must be even? (a) $n(n+1)$ (b) $n^2+1$ (c) $n(n+2)$ (d) $n(n+4)$

Answer

(a) (n+1)$

The product of two consecutive integers always contains one even factor, so it is always even. In the others, an odd $ makes both factors odd (or the sum odd), so they need not be even.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

If you save 1 paisa today, 2 paisa next day, 4 paisa the succeeding day and so on, then what is the total saving on the week? (a) 127 paisa (b) 64 paisa (c) 256 paisa (d) 128 paisa

Answer

(a) 127 paisa

The savings 1, 2, 4, ... form a GP with =1 $, =2$ , =7$.

6250S_7=\frac{2^7-1}{2-1}=1276250

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2075 · 1 mark

What is the value of $\sum_{n=10}^{10}(-1)^n$ ? (a) 0 (b) -1 (c) 1 (d) 10

Answer

(c) 1

The sum has a single term, $n=10$ , so it equals $(-1)^{10}=1$ .

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2075 · 1 mark

If 6 is subtracted from the cube of a number and the result is 21, then what is the value of that number? (a) 2 (b) 3 (c) 4 (d) 5

Answer

(b) 3

^3-6=21 $gives ^3=27$ , so =3$.

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2075 · 1 mark

The total of ages of A and B is 3:5, if B is 8 years elder to A, then what is the age of the A? (a) 12 yrs. (b) 15 yrs. (c) 18 yrs. (d) 21 yrs.

Answer

(a) 12 yrs.

The ratio of the ages is :B=3:5 $. The difference of 2 parts is 8 years, so one part is 4 years, and =3\times4=12$ years.

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2075 · 1 mark

If the root of the equation $x^2-6x+c=0$ is 3, then what is the value of c? (a) 3 (b) 6 (c) 8 (d) 9

Answer

(d) 9

Substitute =3 $: -18+c=0$ , so =9$.

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2075 · 1 mark

Which one of the following is true for the roots of the equation $x^2-8x+16=0$ ? (a) Imaginary & unequal (b) Rational & unequal (c) real & equal (d) real & unequal

Answer

(c) real & equal

The discriminant is =(-8)^2-4(1)(16)=64-64=0 $, so the roots are real and equal. Indeed ^2-8x+16=(x-4)^2$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

If the matrix is of order $5\times3$ , then how many elements will be single column? (a) 5 (b) 3 (c) 4 (d) 15

Answer

(a) 5

A \times3$ matrix has 5 rows and 3 columns, so each column has 5 elements.

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2075 · 1 mark

If $x-5=1$ , then what is the value of $x+7$ ? (a) 5 (b) 7 (c) 8 (d) 13

Answer

(d) 13

-5=1 $gives =6$ , so +7=13$.

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2075 · 1 mark

If $5x+13=31$ , what is the value of $\sqrt{(5x+31)}$ ? (a) 5 (b) 6 (c) 7 (d) 8

Answer

(c) 7

x+13=31 $gives x=18$ . Then x+31=49 $and$ \sqrt{49}=7$.

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2075 · 1 mark

What is the correct value of $\frac{5^4-5^3}{4}$ ? (a) $5^3$ (b) $\frac15$ (c) $5^4$ (d) $\frac54$

Answer

(a) ^3$

6250\frac{5^4-5^3}{4}=\frac{5^3(5-1)}{4}=\frac{5^3\cdot4}{4}=5^36250

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

If $a^x=b$ , $b^y=c$ and $c^z=a$ , then what is the value of xyz? (a) c (b) a (c) b (d) 1

Answer

(d) 1

Substituting, =c^z=(b^y)^z=((a^x)^y)^z=a^{xyz} $. Hence =1$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

If $6p+6q=36$ , then what is the average value of a and b? (a) 2 (b) 3 (c) 4 (d) 5

Answer

(b) 3

Dividing p+6q=36 $by 6 gives +q=6$ , so the average of the two quantities is $\frac{6}{2}=3$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

If $p+q=r$ , then what is the average value of p, q and r? (a) $\frac r3$ (b) $\frac{p+q}{3}$ (c) $\frac{2r}{3}$ (d) $\frac r2$

Answer

(c) $\frac{2r}{3}$

6250\text{Average}=\frac{p+q+r}{3}=\frac{r+r}{3}=\frac{2r}{3}6250

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the slope of the line whose equation is $2x-4y=9$ ? (a) 1 (b) $\frac12$ (c) 2 (d) 3

Answer

(b) $\frac12$

Rewrite as =\frac{2x-9}{4}=\frac12x-\frac94 $. The slope is$ \frac12 $(or hmtBc\frac{a}{b}=\frac{2}{4}$ ).

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

Which one of the following is correct for the acute angle of right angled triangle? (a) Complementary (b) supplementary (c) Adjacent (d) equal

Answer

(a) Complementary

The angles of a triangle sum to 80^\circ $and the right angle is 0^\circ$ , so the two acute angles add up to 0^\circ$, which makes them complementary.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

There are 60 students in a class. If 60% of them are girls, then how many boys in the class? (a) 24 (b) 36 (c) 18 (d) 40

Answer

(a) 24

Boys are 00%-60%=40% $of the class, and /bin/bash.4\times60=24$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

Last year Hari was 4 feet tall, and this year he is 5 feet tall. What is the percent increase of his height? (a) 10% (b) 15% (c) 20% (d) 25%

Answer

(d) 25%

6250\frac{5-4}{4}\times100%=25%6250

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the difference between $\frac35$ of 80 and 30% of 80? (a) 12 (b) 18 (c) 24 (d) 20

Answer

(c) 24

$\frac35\times80=48$ and $30\%$ of $80=24$ , so the difference is $48-24=24$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

The cost of 6 pens is equal to the cost of the 10 pencils. If the cost of 4 pencils is Rs. 120, then what is the cost of 4 pens? (a) 100 (b) 200 (c) 300 (d) 400

Answer

(b) 200

4 pencils cost Rs 120, so 1 pencil costs Rs 30 and 10 pencils cost Rs 300. This equals the cost of 6 pens, so 1 pen costs Rs 50 and 4 pens cost Rs 200.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

Ganga can read 48 pages per hour. At this rate, how many pages she can read in 80 minutes? (a) 60 (b) 72 (c) 48 (d) 64

Answer

(d) 64

80 minutes $=\frac43$ hour, so pages read $=48\times\frac43=64$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

If $5:7=15:x$ , then what is the value of x? (a) 18 (b) 21 (c) 24 (d) 35

Answer

(b) 21

$\frac57=\frac{15}{x}$ gives $x=\frac{7\times15}{5}=21$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

If cost price of 8 pens and selling price of 10 pens is equal, then what is loss percentage? (a) 20% (b) 15% (c) 10% (d) 25%

Answer

(a) 20%

Let each pen cost Rs 1 to buy. Then the cost of 10 pens is Rs 10, but they are sold for the cost price of 8 pens, Rs 8. Loss $=2$ , so loss $\%=\frac{2}{10}\times100=20\%$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

If the 20% discount is given on computer book costing Rs. 300, then what will be selling price? (a) Rs. 240 (b) Rs. 220 (c) Rs. 260 (d) Rs. 250

Answer

(a) Rs 240

Discount $=20\%$ of 300 $=$ Rs 60, so selling price $=300-60=$ Rs 240.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

A watch is bought at Rs. 250 and sold at Rs. 300, then what is the profit percentage? (a) 10% (b) 15% (c) 20% (d) 25%

Answer

(c) 20%

Profit $=300-250=$ Rs 50, so profit $\%=\frac{50}{250}\times100=20\%$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the population doubling time if the population growth rate is 2% per anum? (a) 60 yrs. (b) 50 yrs. (c) 40 yrs. (d) 30 yrs.

Answer

(b) 50 yrs.

Using simple growth, the population doubles when growth equals 100% of the original, so $t=\frac{100}{2}=50$ years.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the minimum value of $n(P\cap Q)$ ? When $n(U)=100$ , $n(P)=70$ , and $n(Q)=45$ ? (a) 15 (b) 55 (c) 30 (d) 45

Answer

(a) 15

$n(P\cup Q)\le100$ , so $n(P\cap Q)=n(P)+n(Q)-n(P\cup Q)\ge70+45-100=15$ . The minimum is 15.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

Which one of the following is true for prime number? (a) no factors (b) only one factor (c) only two factors (d) more than two factors

Answer

(c) only two factors

A prime number has exactly two factors, 1 and itself.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

Which one of the following interval notation is correct for $\{x: 5\leq x\leq15\}$ ? (a) $[5,\infty]$ (b) $[\infty,15]$ (c) $[6,14]$ (d) $[5,15]$

Answer

(d) $[5,15]$

Both end points are included ( $\le$ ), so the closed interval $[5,15]$ is used.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the value of 'x' when it is multiplied by 6 and added to 3 times its own number gives 63? (a) 6 (b) 7 (c) 8 (d) 9

Answer

(b) 7

$6x+3x=63\Rightarrow 9x=63\Rightarrow x=7$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the value of $\left(\sqrt5+\sqrt5\right)^2$ ? (a) 20 (b) 25 (c) 10 (d) 60

Answer

(a) 20

$(\sqrt5+\sqrt5)^2=(2\sqrt5)^2=4\times5=20$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the number of seconds in $1\frac13$ hour? (a) 1200 sec (b) 2400 sec (c) 3600 sec (d) 4800 sec

Answer

(d) 4800 sec

$1\frac13$ hour $=80$ minutes $=80\times60=4800$ seconds.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

In a kilometer race A beats B by 100 meters and B beats C by 150 meters. In the same race, by how many meters does A beats C? (a) 150 m (b) 100 m (c) 250 m (d) 200 m

Answer

(c) 250 m

A beats B by 100 m and B beats C by 150 m, so in the intended (additive) reading A beats C by $100+150=250$ m.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the probability of death? (a) 1 (b) $\frac12$ (c) 0 (d) $\infty$

Answer

(a) 1

Death is certain for every living being, so it is a sure event and its probability is 1.

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the chance to give the birth by a pregnant lady on Tuesday? (a) $\frac37$ (b) $\frac17$ (c) 1 (d) $\frac12$

Answer

(b) $\frac17$

There are 7 equally likely days in a week and Tuesday is one of them, so the probability is $\frac17$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2075 · 1 mark

What is the value of $\cos0^\circ$ ? (a) $\frac12$ (b) $\frac{1}{\sqrt2}$ (c) 0 (d) 1

Answer

(d) 1

$\cos0^\circ=1$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

If the slope of line joining $(1,2)$ and $(k,-5)$ is equally inclined with both the axes, then the value of $k$ is (a) 6 (b) -6 (c) 3 (d) -2

Answer

(b) $-6$

Equally inclined to both axes means the slope is $\pm1$ . The slope is $\frac{-5-2}{k-1}=\frac{-7}{k-1}$ .

For slope $1$ : $k-1=-7$ , so $k=-6$ (this is the option given; slope $-1$ would give $k=8$ , which is not listed).

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

What is the value of $\cot90^\circ$ ? (a) 3 (b) $\frac12$ (c) 0 (d) 1

Answer

(c) 0

$\cot 90^\circ=\frac{\cos90^\circ}{\sin90^\circ}=\frac{0}{1}=0$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

What is the probability of drawing a queen when one card is drawn randomly from a well shuffled pack of 52 cards? Find the probability of drawing a red queen? (a) $\frac{1}{26}$ (b) $\frac56$ (c) $\frac34$ (d) $\frac{15}{36}$

Answer

(a) $\frac{1}{26}$

There are 4 queens in 52 cards, so $P(\text{queen})=\frac{4}{52}=\frac1{13}$ . There are 2 red queens, so $P(\text{red queen})=\frac{2}{52}=\frac{1}{26}$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

If A, B, C are the subsets of a universal set U. Then $A-(B\cup C)$ is equal to, (a) $(A-B)\cup(A-C)$ (b) $(A-B)\cap(A-C)$ (c) $(A\cap B)-(A\cap C)$ (d) $(A\cup B)-(A\cup C)$

Answer

(b) $(A-B)\cap(A-C)$

By De Morgan's law, $A-(B\cup C)=A\cap(B\cup C)'=A\cap B'\cap C'=(A-B)\cap(A-C)$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The value of $\tan180^\circ$ is equal to, (a) 1 (b) -1 (c) 0 (d) $\infty$

Answer

(c) 0

$\tan180^\circ=\frac{\sin180^\circ}{\cos180^\circ}=\frac{0}{-1}=0$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

$1^2+2^2+3^2+\cdots+n^2$ is equal to, (a) $\frac{n(n+1)}{2}$ (b) $\frac{n(n+1)(2n+1)}{6}$ (c) $\left(\frac{n(n+1)}{2}\right)^2$ (d) None of the above

Answer

(b) $\frac{n(n+1)(2n+1)}{6}$

This is the standard formula for the sum of the first $n$ squares.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

If a matrix $A=\begin{pmatrix}0&5&-6\\-5&0&2\\6&-2&0\end{pmatrix}$ , then matrix A is known as (a) Symmetric Matrix (b) Skew-Symmetric Matrix (c) Diagonal Matrix (d) Triangular Matrix

Answer

(b) Skew-Symmetric Matrix

Here $A^T=-A$ : the diagonal entries are $0$ and $a_{ij}=-a_{ji}$ (for example $5$ and $-5$ , $-6$ and $6$ , $2$ and $-2$ ).

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The radius of the circle $x^2+y^2=9$ is equal to, (a) 4 (b) 3 (c) 5 (d) 9

Answer

(b) 3

$x^2+y^2=r^2$ with $r^2=9$ , so $r=3$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

If $A=\begin{bmatrix}1&2\\3&1\end{bmatrix}$ , then the value of $A^2-2A-5I$ is equal to, (a) 1 (b) -1 (c) 2 (d) 0

Answer

(d) 0

$A^2=\begin{bmatrix}7&4\\6&7\end{bmatrix},\quad 2A=\begin{bmatrix}2&4\\6&2\end{bmatrix},\quad 5I=\begin{bmatrix}5&0\\0&5\end{bmatrix}$

$A^2-2A-5I=\begin{bmatrix}0&0\\0&0\end{bmatrix}=0$

This is the null matrix, which is the option $0$ (consistent with the Cayley-Hamilton theorem).

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

What is the half of quarter of 400? (a) 200 (b) 100 (c) 50 (d) 90

Answer

(c) 50

A quarter of $400$ is $100$ , and half of $100$ is $50$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

Half percent, written as a decimal is, (a) 0.2 (b) 0.02 (c) 0.005 (d) 0.05

Answer

(c) 0.005

Half percent is $0.5\%=\frac{0.5}{100}=0.005$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The true discount on Rs. 2,562 due 4 months hence is Rs. 122. The rate percent is: (a) 12% (b) 13% (c) 14% (d) 15%

Answer

(d) 15%

Present worth $=2562-122=\text{Rs }2440$ . Using $TD=\frac{PW\times r\times t}{100}$ with $t=\frac13$ year:

$122=\frac{2440\times r}{100\times3}\Rightarrow r=\frac{122\times300}{2440}=15\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is: (a) 40% (b) 42% (c) 44% (d) 46%

Answer

(c) 44%

New area $=1.2\times1.2=1.44$ times the old area, so the increase is $44\%$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

AB and CD bisect each other at O. If AD = 6 cm, BC is: (a) 5.9 cm (b) 6 cm (c) 4.8 cm (d) 7 cm

Answer

(b) 6 cm

Since the diagonals bisect each other at $O$ , $OA=OB$ and $OD=OC$ , and the vertical angles are equal, so $\triangle AOD\cong\triangle BOC$ (SAS). Hence $BC=AD=6$ cm.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is: (a) 2 (b) 3 (c) 4 (d) 8

Answer

(a) 2

Amount $=30000+4347=34347$ .

$\left(1.07\right)^n=\frac{34347}{30000}=1.1449=(1.07)^2\Rightarrow n=2\text{ years}$

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

If a man were to sell his chair for Rs. 720, he would lose 25%. To gain 25%, he would sell it for: (a) Rs. 1,200 (b) Rs. 1,000 (c) Rs. 960 (d) Rs. 900

Answer

(a) Rs. 1,200

Cost price $=\frac{720}{0.75}=\text{Rs }960$ . To gain $25\%$ : $960\times1.25=\text{Rs }1200$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

Find the percentage gain or loss when the dot pens bought for Rs. 96 per dozen were sold at the rate of 10 for Rs. 90? (a) 13% (b) 20% (c) 4% (d) 12.5%

Answer

(d) 12.5%

Cost per pen $=\frac{96}{12}=\text{Rs }8$ . Selling price per pen $=\frac{90}{10}=\text{Rs }9$ .

$\text{Gain}\%=\frac{9-8}{8}\times100=12.5\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

What is the value of $\cos^230^\circ-\sin^230^\circ$ ? (a) $\frac12$ (b) $\frac{\sqrt3}{2}$ (c) $\frac{1}{\sqrt3}$ (d) $-\frac12$

Answer

(a) $\frac12$

$\cos^2\theta-\sin^2\theta=\cos2\theta$ , so the value is $\cos60^\circ=\frac12$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

Which one is the formula for area of equilateral triangle? (a) $\frac{\sqrt3}{4}a^2$ (b) $\frac12\times b\times h$ (c) $\sqrt{(s-a)(s-b)(s-c)}$ (d) None of these

Answer

(a) $\frac{\sqrt3}{4}a^2$

This is the area of an equilateral triangle of side $a$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The commission of Rs. 5,600 at the rate of 3.5% is: (a) Rs. 196 (b) Rs. 440 (c) Rs. 360 (d) Rs. 1,000

Answer

(a) Rs. 196

$5600\times\frac{3.5}{100}=\text{Rs }196$

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

What is the tax rate if original price is Rs. 2,000 and selling price is Rs. 2,400? (a) 20% (b) 17.39% (c) 35% (d) 10%

Answer

(a) 20%

Tax $=2400-2000=\text{Rs }400$ , so the rate is $\frac{400}{2000}\times100=20\%$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The sum of the ages of father and his son is 52 years. Eight years ago the father was eight times as old as his son, the present age of son is, (a) 10 years (b) 20 years (c) 12 years (d) 15 years

Answer

(c) 12 years

Let the son be $x$ years old, so the father is $52-x$ . Eight years ago: $52-x-8=8(x-8)$ .

$44-x=8x-64\Rightarrow9x=108\Rightarrow x=12$

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The radius of the circle $x^2+y^2-12x-4y=9$ is equal to, (a) 18 (b) 7 (c) 10 (d) 2

Answer

(b) 7

Complete the squares:

$(x-6)^2+(y-2)^2=9+36+4=49$

so $r=7$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The system of linear equation will be consistent and independent if they have, (a) exactly one solution (b) more than one solution (c) no solution (d) none of these

Answer

(a) exactly one solution

A consistent and independent system has exactly one (unique) solution; the lines intersect at a single point.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

Let a and b are two numbers on the real line. If $(a,b]=\{x: a<x\leq b\}$ is known as, (a) left open interval (b) right open interval (c) closed interval (d) open interval

Answer

(a) left open interval

$(a,b]$ excludes the left endpoint $a$ and includes the right endpoint $b$ , so it is open on the left.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

Let $f:R\to R$ and $g:R\to R$ be defined by $f(x)=2x^2-3$ , $g(x)=3x+2$ . Then the composite functions $g\circ f(x)$ is, (a) $9x+8$ (b) $2x+2$ (c) $2x+1$ (d) $6x^2-7$

Answer

(d) $6x^2-7$

$g\circ f(x)=g(f(x))=3(2x^2-3)+2=6x^2-9+2=6x^2-7$

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

A square matrix A is said to be singular if its determinant is equal to, (a) 1 (b) 0 (c) -1 (d) none of these

Answer

(b) 0

A square matrix is singular when $|A|=0$ , because it then has no inverse.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

The system of equations $4x-3y=-6$ , $-4x+2y=16$ is, (a) consistent and dependent (b) inconsistent and independent (c) inconsistent and dependent (d) consistent and independent

Answer

(d) consistent and independent

Adding the equations gives $-y=10$ , so $y=-10$ and $x=\frac{-6+3y}{4}=-9$ . A unique solution exists, so the system is consistent and independent.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

Ratio of 2 km to 600 m should be, (a) 2:7 (b) 2:8 (c) 2:3 (d) 10:3

Answer

(d) 10:3

$2\text{ km}=2000\text{ m}$ , so the ratio is $2000:600=10:3$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

In $a:b=c:d$ , then b and c are called, (a) antecedent (b) extreme (c) consequent (d) mean

Answer

(d) mean

In $a:b=c:d$ , $a$ and $d$ are the extremes, and $b$ and $c$ are the means.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

If $b^2-4ac<0$ then the roots of $ax^2+bx+c=0$ are: (a) equal (b) rational (c) irrational (d) imaginary

Answer

(d) imaginary

When the discriminant $b^2-4ac<0$ , the square root is of a negative number, so the roots are complex (imaginary) and unequal.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

A polygon having 10 sides is called, (a) decagon (b) heptagon (c) quadrilateral (d) hexagon

Answer

(a) decagon

A polygon with 10 sides is a decagon.

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2076 · 1 mark

Linear equation is also known as, (a) simultaneous equation (b) second degree equation (c) first degree equation (d) zero degree equation

Answer

(c) first degree equation

A linear equation has the highest power of the variable equal to 1.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

Two straight lines in same plane which never meet are called, (a) angles (b) transversal lines (c) vertex (d) parallel line

Answer

(d) parallel line

Coplanar lines that never meet, however far extended, are parallel.

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2076 · 1 mark

Degree of polynomial $f(x)=ax^2+2\ (a\neq0)$ (a) 2 (b) -2 (c) 1 (d) -3

Answer

(a) 2

The degree is the highest power of $x$ , which is 2 (since $a\neq0$ ).

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2076 · 1 mark

If A, G, H are arithmetic, geometric and harmonic means between a and b, then A, G, H are (a) in G.P (b) in A.P (c) real numbers (d) in H.P

Answer

(a) in G.P

$A=\frac{a+b}{2}$ , $H=\frac{2ab}{a+b}$ , so $AH=ab=G^2$ . Thus $\frac{A}{G}=\frac{G}{H}$ and A, G, H are in G.P.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

In selling an article for Rs. 76, a shopkeeper gain 52%. The gain by selling that for Rs. 74 is (a) 45% (b) 48% (c) 49% (d) 50%

Answer

(b) 48%

CP $=\frac{76}{1.52}=$ Rs 50. Gain at Rs 74 $=\frac{74-50}{50}\times100=48\%$ .

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2076 · 1 mark

Ram bought oranges at 6 for Rs. 10 and sold them at 4 for Rs. 6, find his loss percent (a) 12% (b) 8% (c) 6% (d) 10%

Answer

(d) 10%

Take 12 oranges. CP $=2\times10=$ Rs 20, SP $=3\times6=$ Rs 18. Loss $=\frac{2}{20}\times100=10\%$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

By giving a discount of 10% on the marked price of Rs. 1,100 of a mobile phone a dealer gains 10%, then the cost price is (a) Rs. 950 (b) Rs. 900 (c) Rs. 1,000 (d) Rs. 1,050

Answer

(b) Rs. 900

SP $=1100\times0.9=$ Rs 990. CP $=\frac{990}{1.10}=$ Rs 900.

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

Rama purchased a table in Rs. 1,260 and due to some damage on its top, she had to sell it for Rs. 1,197, her loss percent is (a) 20% (b) 15% (c) 10% (d) 5%

Answer

(d) 5%

Loss $=1260-1197=$ Rs 63. Loss percent $=\frac{63}{1260}\times100=5\%$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

A shopkeeper purchases 11 pens for Rs. 10 and sells them at of 10 for Rs. 11, then the profit is, (a) 18% (b) 19% (c) 20% (d) 21%

Answer

(d) 21%

For 110 pens: CP $=10\times10=$ Rs 100, SP $=11\times11=$ Rs 121. Profit $=21\%$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2076 · 1 mark

If $A=\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}$ , then A is (a) unit matrix (b) singular matrix (c) symmetric (d) all of them are true

Answer

(a) unit matrix

A is the $3\times3$ identity (unit) matrix. It is also symmetric but is non-singular ( $|A|=1$ ), so "all of them are true" is false.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The slope of the line passing through $(a,b)$ and $\left(\frac1a,b\right)$ is : (a) 0 (b) 4 (c) 3 (d) 2

Answer

(a) 0

$m=\frac{b-b}{\frac1a-a}=0$

The two points have the same $y$ -coordinate, so the line is horizontal.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $P(A\cup B)=1$ , two events A and B are (a) mutually exclusive (b) equally likely events (c) exhaustive (d) dependent events

Answer

(c) exhaustive

$P(A\cup B)=1$ means that at least one of $A$ or $B$ must occur, which is the definition of exhaustive events.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The set $\{X: X^2+X+1=0, X\in R\}$ is : (a) $\{1,\sqrt3\}$ (b) $\{-1,\sqrt3\}$ (c) $\{\}$ (d) $(-1,0)$

Answer

(c) $\{\}$

For $x^2+x+1=0$ the discriminant is $1-4=-3<0$ , so there is no real root. The set is empty.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

Every rational number is also (a) natural number (b) a whole number (c) an integer number (d) a real number

Answer

(d) a real number

Every rational number is a real number. Rationals like $\frac12$ need not be natural, whole or integer.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $f(u)=\frac{u}{u-1}$ , then $f(a)/f(a+1)$ is: (a) $f(-a)$ (b) $f\left(\frac1a\right)$ (c) $f(a^2)$ (d) $f\left(\frac{-a}{a+1}\right)$

Answer

(c) $f(a^2)$

$f(a)=\frac{a}{a-1},\quad f(a+1)=\frac{a+1}{a}$

$\frac{f(a)}{f(a+1)}=\frac{a^2}{(a-1)(a+1)}=\frac{a^2}{a^2-1}=f(a^2)$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

Average of even number between 20 to 100 (a) 60 (b) 40 (c) 50 (d) 70

Answer

(c) 60

The even numbers between 20 and 100 are $22,24,\dots,98$ , an arithmetic progression. The average is $\frac{22+98}{2}=60$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The value of $\cot30^\circ$ is : (a) $\frac12$ (b) $2/\sqrt3$ (c) $\sqrt3$ (d) 1

Answer

(c) $\sqrt3$

$\cot30^\circ=\frac{1}{\tan30^\circ}=\frac{1}{1/\sqrt3}=\sqrt3$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $AB=C$ exists, which of the following order of matrices is possible? (a) $A_{2\times3}, B_{3\times2}, C_{2\times3}$ (b) $A_{3\times2}, B_{2\times3}, C_{2\times2}$ (c) $A_{3\times2}, B_{2\times3}, C_{3\times3}$ (d) $A_{2\times3}, B_{3\times2}, C_{3\times3}$

Answer

(c) $A_{3\times2}, B_{2\times3}, C_{3\times3}$

The product $AB$ needs columns of $A$ equal to rows of $B$ , and the result has rows of $A$ and columns of $B$ . Here $(3\times2)(2\times3)=3\times3$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The value of $\begin{vmatrix}48&1&6\\32&5&4\\16&3&2\end{vmatrix}$ is: (a) 1 (b) 2 (c) 0 (d) 4

Answer

(c) 0

Expanding along the first row:

$48(10-12)-1(64-64)+6(96-80)=-96-0+96=0$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

Raman salary was decreased by 50% and subsequently increased by 50%. He has a loss of : (a) 0% (b) 25% (c) 0.25% (d) 2.5%

Answer

(b) 25%

Let the salary be $100$ . After a 50% decrease it is $50$ , and after a 50% increase it is $75$ . The loss is $25$ , i.e. 25%.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $a=4b$ , what percent of $2a$ is $2b$ ? (a) 10% (b) 20% (c) 25% (d) 26%

Answer

(c) 25%

$\frac{2b}{2a}\times100=\frac{b}{4b}\times100=25\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

What 3 percent is 250 out of 1 kg? (a) 25% (b) 35% (c) 24% (d) 30%

Answer

(a) 25%

$1\ \text{kg}=1000\ \text{g}$ , so

$\frac{250}{1000}\times100=25\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The equation of the straight line passing through $(2,4)$ and having slope -2 is : (a) $2x+y=8$ (b) $2x-y=4$ (c) $x+2y=8$ (d) $x-2y=4$

Answer

(a) $2x+y=8$

$y-4=-2(x-2)\Rightarrow y=-2x+8\Rightarrow 2x+y=8$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

A sum reckoned at 12% SI amounts to Rs. 2409 in 4 years, the sum is : (a) 1625 (b) 1635 (c) 1640 (d) 1652

Answer

(a) 1625

$A=P\left(1+\frac{12\times4}{100}\right)=1.48P$

$P=\frac{2409}{1.48}\approx1627.7$

The nearest option is 1625 (it gives an amount of 2405).

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

Ram gains the cost price of 10 books by selling 50 books. His profit percentage is : (a) Rs 30% (b) 25% (c) 20% (d) 16%

Answer

(c) 20%

Let the cost of one book be $1$ . Then $SP_{50}=CP_{50}+CP_{10}=50+10=60$ .

$\text{Profit}\%=\frac{10}{50}\times100=20\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

$\cos45^\circ=$ (a) 1 (b) 0 (c) $\sqrt2$ (d) $\frac12$

Answer

(c) $\sqrt2$ (read as $\frac{\sqrt2}{2}$ )

The true value is $\cos45^\circ=\frac{1}{\sqrt2}=\frac{\sqrt2}{2}\approx0.707$ . Among the options, this is the only one involving $\sqrt2$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The area of a triangular field whose three sides are 300, 400 and 500m (in $m^2$ ) is : (a) 6000 (b) 5000 (c) 400 (d) 200

Answer

(a) 6000

$300^2+400^2=500^2$ , so it is a right triangle.

$\text{Area}=\tfrac12\times300\times400=60000\ m^2$

The value 60000 is the intended one, and option (a) is it with a digit dropped.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The number of bricks, each 4cm x 3cm x 2cm are required to construct a wall having the dimension 11cm x 96cm x 64cm is : (a) 2815 (b) 281600 (c) 218500 (d) 2185

Answer

(a) 2815 (nearest option; exact count is 2816)

Number of bricks = volume of wall / volume of one brick.

$\frac{11\times96\times64}{4\times3\times2}=\frac{67584}{24}=2816$

The given option closest to this is 2815.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The value of $\sec60^\circ$ is : (a) $\frac12$ (b) $\frac{\sqrt3}{2}$ (c) 2 (d) $\frac{1}{\sqrt3}$

Answer

(c) 2

$\sec60^\circ=\frac{1}{\cos60^\circ}=\frac{1}{1/2}=2$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The ages of mother and her daughter are 30 years and 14 years respectively. The number of years ago that the product of their age was 192 is : (a) 5 (b) 6 (c) 7 (d) 9

Answer

(b) 6

Let the ages be reduced by $x$ years: $(30-x)(14-x)=192$ .

$x^2-44x+228=0\Rightarrow (x-6)(x-38)=0$

So $x=6$ (38 is impossible since the daughter was not yet born).

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

A rope is 40 ft. long is cut into two pieces, if one piece is 18 ft. longer than the other . What is the length , in feet, of the shorter piece ? (a) 11 (b) 12 (c) 13 (d) 14

Answer

(a) 11

Let the shorter piece be $x$ ft. Then $x+(x+18)=40\Rightarrow 2x=22\Rightarrow x=11$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $M=\begin{pmatrix}1&2\\2&3\end{pmatrix}$ , $M^2-rM-I=0$ , the value of r is : (a) -2 (b) -4 (c) 4 (d) 2

Answer

(c) 4

$M^2=\begin{pmatrix}5&8\\8&13\end{pmatrix},\quad M^2-rM-I=\begin{pmatrix}5-r-1&8-2r\\8-2r&13-3r-1\end{pmatrix}=0$

Each entry gives $r=4$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $f(x)=3x+5$ , then value of $\frac{f(x+h)-f(x)}{h}$ is : (a) 2 (b) 3 (c) 4 (d) 5

Answer

(b) 3

$\frac{f(x+h)-f(x)}{h}=\frac{3(x+h)+5-3x-5}{h}=\frac{3h}{h}=3$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The difference of two irrational number is : (a) always an irrational number (b) always a rational number (c) always a real number (d) All of above

Answer

(c) always a real number

The difference of two irrational numbers may be rational (e.g. $\sqrt2-\sqrt2=0$ ) or irrational (e.g. $\sqrt3-\sqrt2$ ), so (a) and (b) are false. It is always a real number.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $p-q+r=4$ and $p+q+r=8$ , the value of $p+q=$ (a) 2 (b) 4 (c) 6 (d) 8

Answer

(c) 6

Subtracting the equations gives $2q=4$ , so $q=2$ . Adding gives $2(p+r)=12$ , so $p+r=6$ . The intended value of the sum in the options is 6.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $\frac a4=\frac b5=\frac c9$ then $\frac{a+b+c}{c}$ is : (a) 4 (b) 2 (c) 7 (d) none

Answer

(b) 2

Let $a=4k,\ b=5k,\ c=9k$ . Then

$\frac{a+b+c}{c}=\frac{18k}{9k}=2$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If 60% of 450=15x, the value of x is : (a) 6 (b) 18 (c) 36 (d) 72

Answer

(b) 18

$60\%$ of $450=270$ , so $15x=270\Rightarrow x=18$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The system of equation $-4x+6y+2z=8$ and $2x-3y-z=-14$ have : (a) unique solution (b) no solution (c) infinity many solutions (d) none of these

Answer

(b) no solution

Multiplying the second equation by $-2$ gives $-4x+6y+2z=28$ , while the first says $-4x+6y+2z=8$ . The two are contradictory, so the system is inconsistent.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The area of rectangle field is $493\,m^2$ and its perimeter is 92 meter. The length and breadth (in m) are : (a) 7,4 (b) 9,7 (c) 29,17 (d) 19,13

Answer

(c) 29, 17

$l+b=46$ and $lb=493$ . Since $29+17=46$ and $29\times17=493$ , the length is 29 m and the breadth is 17 m.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

While solving the value of x is $X^3-3x^2+3x-1=0$ . (a) 2 (b) 1 (c) both (d) none

Answer

(b) 1

$x^3-3x^2+3x-1=(x-1)^3=0\Rightarrow x=1$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The side of triangle are 3cm, 4cm and 5cm. it is : (a) a right angle triangle (b) an isosceles triangle (c) an equilateral triangle (d) none of these

Answer

(a) a right angle triangle

$3^2+4^2=9+16=25=5^2$ , so the Pythagorean relation holds.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

Which of the following represents all solutions of the inequality $x^2<2x$ ? (a) $-1<x<1$ (b) $1<x<3$ (c) $0<x<2$ (d) $4<x<6$

Answer

(c) $0<x<2$

$x^2-2x<0\Rightarrow x(x-2)<0\Rightarrow 0<x<2$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If the term $2x$ , $x+10$ and $3x+2$ be in AP , the value of x is (a) 7 (b) 10 (c) 6 (d) 5

Answer

(c) 6

For an AP, $2(x+10)=2x+(3x+2)$ .

$2x+20=5x+2\Rightarrow 3x=18\Rightarrow x=6$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $t_n=3n-2$ , the value of $S_5$ is : (a) 35 (b) 40 (c) 45 (d) 50

Answer

(a) 35

The terms are 1, 4, 7, 10, 13, so $S_5=\frac52(1+13)=35$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $S_n=1+2+3+\ldots+n=20$ the sum of the series $S_n=1^3+2^3+3^3+\cdots+n^3$ is : (a) 400 (b) 500 (c) 450 (d) 1000

Answer

(a) 400

$1^3+2^3+\cdots+n^3=\left(\frac{n(n+1)}{2}\right)^2=(1+2+\cdots+n)^2=20^2=400$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

While selling a pen for Rs. 50, there is a loss of 5%, for what price should it be sold to gain 5%? (a) 55.26 (b) 52.63 (c) 55 (d) 56.32

Answer

(a) 55.26

Cost price $=\frac{50}{0.95}=52.63$ .

Selling price for 5% gain $=1.05\times52.63=55.26$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

A man sold 250 chairs and had gain equal to the selling price of 50 chairs. His profit percent is: (a) 5% (b) 10% (c) 25% (d) 50%

Answer

(c) 25%

Let the selling price of one chair be $s$ . Total SP $=250s$ , gain $=50s$ , so cost $=200s$ .

$\text{Profit}\,\%=\frac{50s}{200s}\times100=25\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

A watch is bought at Rs.250 and sold at Rs. 300, the gain percent is : (a) 25% (b) 20% (c) 50% (d) none

Answer

(b) 20%

$\text{Gain}\,\%=\frac{300-250}{250}\times100=20\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The list of price of an article is 25% above the selling price and cost price is 40% below the list price, then rate of discount is : (a) 15 % (b) 20% (c) 25% (d) 40%

Answer

(b) 20%

Let the selling price be 100. List price $=125$ and cost price $=0.6\times125=75$ .

The article is sold at 100 from a list price of 125, so

$\text{Discount}\,\%=\frac{125-100}{125}\times100=20\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $A=\begin{pmatrix}n&0\\0&1\end{pmatrix}$ and $A^2$ is identity matrix, the value of n is : (a) 1 (b) 2 (c) 0 (d) 3

Answer

(a) 1

$A^2=\begin{pmatrix}n^2&0\\0&1\end{pmatrix}=I\Rightarrow n^2=1\Rightarrow n=\pm1$

Of the options, $n=1$ is listed.

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If $A=\begin{pmatrix}1&2\\3&-4\end{pmatrix}$ , $Q=\begin{pmatrix}x&3\\2&-1\end{pmatrix}$ , determinant of $2p-3q$ is -5, the value of x is equal to : (a) $\frac{-1}{2}$ (b) $\frac12$ (c) $\frac{-1}{3}$ (d) $\frac{-1}{4}$

Answer

(c) $\frac{-1}{3}$ (nearest option; computed value is $\frac13$ )

Taking $P=A$ :

$2P-3Q=\begin{pmatrix}2-3x&-5\\0&-5\end{pmatrix},\quad \det=-5(2-3x)=-5\Rightarrow 2-3x=1\Rightarrow x=\tfrac13$

The nearest listed option is $-\frac13$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

The simple interest on Rs. 1250 for 5 years at 8% p.a is : (a) 480 (b) 1000 (c) 500 (d) 625

Answer

(c) 500

$SI=\frac{PTR}{100}=\frac{1250\times5\times8}{100}=500$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If a sum of money doubles itself in 8 years at simple interest, the rate percent per annum is : (a) 10. 5% (b) 11. 5% (c) 12. 5% (d) 13. 5%

Answer

(c) 12.5%

Interest after 8 years equals the principal: $P=\frac{P\times8\times R}{100}\Rightarrow R=12.5\%$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If two numbers are in the ratio 5:7 and their least common multiple is 315, their product is : (a) 2385 (b) 2538 (c) 2358 (d) 2835

Answer

(d) 2835

Let the numbers be $5k$ and $7k$ . LCM $=35k=315\Rightarrow k=9$ . The numbers are 45 and 63, and the product is $45\times63=2835$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

If 0.75:x::5:8, then x is equal to... (a) 1.12 (b) 1.2 (c) 1.25 (d) 1.30

Answer

(b) 1.2

$0.75:x::5:8\Rightarrow \frac{0.75}{x}=\frac58\Rightarrow x=\frac{0.75\times8}{5}=1.2$

Answer checked by Claude Sonnet · Oct 21, 2026

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2077 · 1 mark

A container contains 40l of milk from this container 4l of milk taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container? (a) 26.34l (b) 27.36l (c) 28l (d) 29.16l

Answer

(d) 29.16l

Milk left after $n$ replacements: $40\left(1-\frac{4}{40}\right)^3 = 40\times(0.9)^3 = 40\times0.729 = 29.16$ l.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If A and B are two subset of a universal set U. State the condition for $n(A\cup B)=n(A)+n(B)$ (a) If A and B are disjoint (b) If A and B are intersecting (c) $A\subset B$ (d) $A\supset B$

Answer

(a) If A and B are disjoint

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$ , so the formula reduces to $n(A)+n(B)$ only when $n(A\cap B)=0$ , that is, when A and B are disjoint.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The cost of an electric item is Rs. 4,250. How much should a customer pay for it with 13% VAT? (a) 5520.50 (b) 525.5 (c) 4802.5 (d) 3697.5

Answer

(c) 4802.5

Price with VAT $=4250\times1.13 = \text{Rs } 4802.50$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If US USD 1=NPR 115 convert NPR. 67275 dollar (a) 585 (b) 580 (c) 590 (d) 600

Answer

(a) 585

$67275 \div 115 = 585$ dollars.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If $f(x)=2x$ & $g(x)=x+1$ then $fog(2)$ (a) 4 (b) 6 (c) 8 (d) 10

Answer

(b) 6

$fog(2)=f(g(2))=f(3)=2\times3=6$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

A man earn Rs.720 a month. If he spends 80% of it in each month, how much he will save in a year (a) Rs. 1528 (b) Rs. 1628 (c) Rs. 1728 (d) Rs. 1828

Answer

(c) Rs. 1728

Monthly saving is $20\%$ of Rs 720, which is Rs 144. Yearly saving is $144\times12=\text{Rs } 1728$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If a selling price of 12 cycle is equal to cost price of 15 cycles. find gain % (a) 20% (b) 25% (c) 30% (d) 15%

Answer

(b) 25%

Let the cost of one cycle be Rs 1. Then $12\,SP = 15\,CP$ , so $SP = 15/12 = 1.25$ .

$\text{Gain}\% = \frac{1.25-1}{1}\times100 = 25\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

Circumference of a circle whose area is equal to half that of rectangle 44cm by 28 cm is, (a) 84 cm (b) 86 cm (c) 88 cm (d) 90 cm

Answer

(c) 88 cm

Rectangle area $=44\times28=1232$ cm². Circle area $=616$ cm².

$\pi r^2=616 \Rightarrow r^2=616\times\frac{7}{22}=196 \Rightarrow r=14$

Circumference $=2\pi r = 2\times\frac{22}{7}\times14 = 88$ cm.

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2078 · 1 mark

If a tank with capacity $96m^3$ have base are $24m^2$ then its height is equal to the (a) 1m (b) 2m (c) 3m (d) 4m

Answer

(d) 4m

$h=\frac{V}{A}=\frac{96}{24}=4\text{ m}$

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If $154000cm^3$ of water is taken out from a cylindrical well of diameter 3.5m, then decrease in height in cm is equal to , (a) 8/3cm (b) 8/5cm (c) 8/7 cm (d) 1cm

Answer

(b) 8/5 cm

Radius $=1.75$ m $=175$ cm. Volume removed $=\pi r^2 h$ .

$h=\frac{154000}{\frac{22}{7}\times175^2}=\frac{154000}{96250}=1.6=\frac{8}{5}\text{ cm}$

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If a surface area of a hemisphere is 32m3 then its radius is equal to (a) 3m (b) 4m (c) 5m (d) 6m

Answer

(b) 4m Taking the curved surface area $2\pi r^2 = 32\pi$ gives $r^2=16$ , so $r=4$ m.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

Two number are in the ratio 2:5 and their sum is 35 then the smaller number is (a) 10 (b) 12 (c) 14 (d) 16

Answer

(a) 10 Parts: $2+5=7$ , so the smaller number is $\frac{2}{7}\times 35 = 10$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The numerical value of $(343)^{-\frac23}$ is equal to (a) 1/49 (b) 1/7 (c) 1/25 (d) 1/29

Answer

(a) 1/49 $(343)^{-2/3}=(7^3)^{-2/3}=7^{-2}=\frac{1}{49}$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If $3^{2x+1}=9^{2x-1}$ then the value of x is equal to (a) 1/2 (b) 3/2 (c) 5/2 (d) 1

Answer

(b) 3/2 $3^{2x+1}=3^{2(2x-1)}$ , so $2x+1=4x-2$ , giving $2x=3$ and $x=\frac32$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

In a single throw of a dice, find the probability of getting a number divisible by 3 is (a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3

Answer

(b) 1/3 Numbers divisible by 3 on a die are 3 and 6, so $P=\frac{2}{6}=\frac13$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

In a three -dimensional space the three axes divide the space into (a) 4 parts (b) 6 parts (c) 8 parts (d) 3 parts

Answer

(c) 8 parts The three coordinate planes (formed by the axes) divide space into 8 octants.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

Half of the product of diagonals indicates the area of (a) parallelogram (b) rectangular (c) square (d) rhombus

Answer

(d) rhombus Area of a rhombus $=\frac12 d_1 d_2$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

A parallelogram having it's area $24cm^2$ and base 6cm then it's height is equal to , (a) 2cm (b) 3cm (c) 4 cm (d) 6 cm

Answer

(c) 4 cm Area = base × height, so $h=\frac{24}{6}=4$ cm.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If the area of triangle 56sq.cm and the altitude 8cm then the base is , (a) 7cm (b) 8cm (c) 14 cm (d) 28cm

Answer

(c) 14 cm Area $=\frac12 \times b \times h$ , so $b=\frac{2\times 56}{8}=14$ cm.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If $A=\begin{bmatrix}3&2\\4&3\end{bmatrix}$ , then the inverse of A is equal to (a) $\begin{bmatrix}3&-2\\-4&3\end{bmatrix}$ (b) $\begin{bmatrix}-3&2\\4&-3\end{bmatrix}$ (c) $\begin{bmatrix}-3&2\\-4&3\end{bmatrix}$ (d) $\begin{bmatrix}1&0\\0&1\end{bmatrix}$

Answer

(a) $\begin{bmatrix}3&-2\\-4&3\end{bmatrix}$ $|A|=9-8=1$ , so $A^{-1}=\frac{1}{1}\begin{bmatrix}3&-2\\-4&3\end{bmatrix}$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If $|A|=0$ , then A is called (a) singular matrix (b) zero matrix (c) non-singular matrix (d) identify matrix

Answer

(a) singular matrix A square matrix with zero determinant is called singular.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The famous mathematicians associated with finding the sum of the natural number is, (a) Pythagoras (b) newton (c) Gauss (d) Euclid

Answer

(c) Gauss Carl Friedrich Gauss is famed for the quick method of summing the natural numbers, $\frac{n(n+1)}{2}$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

Sum of the series $1+\frac12+\frac1{2^2}+\frac1{2^3}+\ldots$ (a) 1 (b) 2 (c) 1.555 (d) 1.7555

Answer

(b) 2 Infinite G.P. with $a=1$ , $r=\frac12$ : $S_\infty=\frac{a}{1-r}=\frac{1}{1/2}=2$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The A.M. between $x-3$ & $x+5$ is , (a) $2x+2$ (b) $x-1$ (c) $x+1$ (d) $2x+1$

Answer

(c) x+1 $A.M.=\frac{(x-3)+(x+5)}{2}=\frac{2x+2}{2}=x+1$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The value of $\sin75^\circ$ is (a) $\frac{\sqrt3+1}{2\sqrt2}$ (b) $\frac{\sqrt3-1}{2\sqrt2}$ (c) $\frac{\sqrt3+2}{2\sqrt2}$ (d) $\frac{\sqrt3+1}{\sqrt2}$

Answer

(a) $\frac{\sqrt3+1}{2\sqrt2}$ $\sin75^\circ=\sin(45^\circ+30^\circ)=\frac{1}{\sqrt2}\cdot\frac{\sqrt3}{2}+\frac{1}{\sqrt2}\cdot\frac12=\frac{\sqrt3+1}{2\sqrt2}$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The mean of the data 4,6,8,10,12,14 is (a) 7 (b) 8 (c) 9 (d) 10

Answer

(c) 9 Sum $=54$ , number of terms $=6$ , mean $=\frac{54}{6}=9$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The angle between two straight line $2x-3y+1=0$ & $3x+2y-2=0$ is (a) $45^\circ$ (b) $60^\circ$ (c) $75^\circ$ (d) $90^\circ$

Answer

(d) $90^\circ$ Slopes are $m_1=\frac23$ and $m_2=-\frac32$ . Since $m_1m_2=-1$ , the lines are perpendicular.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The value of $\lim_{x\to a}\frac{\sin(x-a)}{x-a}$ is (a) 0 (b) 1 (c) -1 (d) 1/2

Answer

(b) 1 This is the standard limit $\lim_{\theta\to0}\frac{\sin\theta}{\theta}=1$ with $\theta=x-a$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The derivatives of $\tan x$ is (a) $\sec^2x$ (b) $\sec x$ (c) $\sec x\tan x$ (d) $\cot$

Answer

(a) $\sec^2x$ $\frac{d}{dx}\tan x=\sec^2x$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The limit value of $\lim_{x\to3}\frac{x^2-9}{x-3}$ is (a) 9 (b) 0 (c) 6 (d) 1

Answer

(c) 6 $\frac{x^2-9}{x-3}=x+3$ for $x\ne3$ , which tends to $6$ as $x\to3$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

Reflection of a point $(-1,2)$ about the line $y=x$ is (a) $(1,2)$ (b) $(2,1)$ (c) $(-2,1)$ (d) $(2,-1)$

Answer

(d) $(2,-1)$ Reflection about $y=x$ swaps the coordinates: $(x,y)\to(y,x)$ , so $(-1,2)\to(2,-1)$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The value of $(i)^{101}$ is (a) $i$ (b) -1 (c) 1 (d) $-i$

Answer

(a) $i$ $i^{101}=i^{4\times25+1}=i^1=i$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The number of subset of a set containing n element is (a) $2^{2n}$ (b) $2n$ (c) $2^n$ (d) $n^2$

Answer

(c) $2^n$ Each of the $n$ elements is either in or out of a subset, giving $2^n$ subsets.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If $A=60^\circ$ value of $\sin3A$ is (a) 1/2 (b) 0 (c) -1/2 (d) 3/2

Answer

(b) 0 $\sin3A=\sin180^\circ=0$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If equation of circle is $x^2+y^2-4x+2y-11=0$ , then it's center is (a) $(-4,2)$ (b) $(-2,1)$ (c) $(2,-1)$ (d) $(2,1)$

Answer

(c) $(2,-1)$ For $x^2+y^2+2gx+2fy+c=0$ the centre is $(-g,-f)$ . Here $2g=-4$ , $2f=2$ , so $g=-2$ , $f=1$ and the centre is $(2,-1)$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If an equilateral triangle has side length a then it's area is (a) $\frac{\sqrt3}{2}a^2$ (b) $\frac{\sqrt3}{4}a^2$ (c) $\frac34a^2$ (d) $\frac14a^2$

Answer

(b) $\frac{\sqrt3}{4}a^2$ Height is $\frac{\sqrt3}{2}a$ , so area $=\frac12\cdot a\cdot\frac{\sqrt3}{2}a=\frac{\sqrt3}{4}a^2$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

Exterior angle of a regular hexagon is (a) $45^\circ$ (b) $60^\circ$ (c) $75^\circ$ (d) $30^\circ$

Answer

(b) $60^\circ$ Exterior angle of a regular $n$ -gon is $\frac{360^\circ}{n}=\frac{360^\circ}{6}=60^\circ$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If an angle is $270^\circ$ then it's value in grade system is (a) 100g (b) 200g (c) 300g (d) 400g

Answer

(c) 300g $100^g=90^\circ$ , so $270^\circ=\frac{270\times10}{9}=300^g$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

A man looks at the top of the tree which is at a distance of 1000m and makes angle of $45^\circ$ then height of the tree is (a) 100m (b) 75m (c) 50m (d) 40m

Answer

(a) 100m $\tan45^\circ=1$ , so height equals the horizontal distance to the tree. Of the options, 100 m is the intended value (distance 100 m).

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If $\sin\theta-\cos\theta=0$ then the value of $\theta$ is, (a) $0^\circ$ (b) $90^\circ$ (c) $60^\circ$ (d) $45^\circ$

Answer

(d) $45^\circ$ $\sin\theta=\cos\theta$ gives $\tan\theta=1$ , so $\theta=45^\circ$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

If $x>0$ then $|x|$ is equal to (a) -x (b) x (c) 0 (d) 1

Answer

(b) x For $x>0$ , $|x|=x$ by definition.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The range of the function $f(x)=\frac{x}{|x|}$ is (a) $\{1\}$ (b) $\{1,-1\}$ (c) $\{0\}$ (d) $\{-\infty,\infty\}$

Answer

(b) $\{1,-1\}$ For $x>0$ , $f(x)=\frac{x}{x}=1$ ; for $x<0$ , $f(x)=\frac{x}{-x}=-1$ . The function is undefined at 0, so the range is $\{1,-1\}$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

For set A, $(A')'$ is (a) $U-A$ (b) $A'$ (c) $A$ (d) $U'$

Answer

(c) $A$ The complement of the complement of a set is the set itself (double complement law).

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

Geometric mean between two number 4 and 6 is (a) 6 (b) 8 (c) 10 (d) 12

Answer

(a) 6 G.M. $=\sqrt{ab}$ . The intended numbers are 4 and 9, giving $\sqrt{36}=6$ ; for exactly 4 and 6 the value would be $\sqrt{24}\approx4.9$ , which is not listed, so 6 is the nearest listed choice.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The 6th term of the series 3,9,27,... is (a) 81 (b) 243 (c) 729 (d) 2187

Answer

(c) 729 G.P. with $a=3$ , $r=3$ : $t_6=3\cdot3^5=3^6=729$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

For some integers n which of the following is odd integer (a) n (b) n+1 (c) 2n (d) 2n+1

Answer

(d) $2n+1$ $2n$ is always even, so $2n+1$ is always odd for any integer $n$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The centroid of a triangle is a point where (a) the perpendicular from vertex to opposite sides meets (b) medians meet (c) bisectors of each angle meet (d) perpendicular bisectors of each sides meet

Answer

(b) medians meet The centroid is the point of concurrence of the three medians, dividing each in the ratio 2:1.

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The set $A=\{x: x\in N\ \&\ x^2+3x+2=0\}$ is (a) Null set (b) Finite set (c) Infinite set (d) set with two elements

Answer

(a) Null set $x^2+3x+2=(x+1)(x+2)=0$ gives $x=-1,-2$ , neither of which is a natural number, so $A=\varnothing$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2078 · 1 mark

The H.C.F of the algebraic expressions $a^2-b^2$ & $a^2+2ab+b^2$ is (a) a+b (b) $(a+b)^2(a-b)$ (c) a-b (d) $a^2-b^2$

Answer

(a) a+b $a^2-b^2=(a+b)(a-b)$ and $a^2+2ab+b^2=(a+b)^2$ , so the H.C.F. is $a+b$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Set of natural number is (a) Finite set (b) Infinite set (c) Null set (d) Singleton set

Answer

(b) Infinite set

The natural numbers $\{1,2,3,\ldots\}$ never end, so the set is infinite.

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

If $n(A)=26$ , $n(B)=32$ , then maximum value of $n(A\cup B)$ is (a) 26 (b) 58 (c) 32 (d) 6

Answer

(b) 58

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

This is largest when $n(A\cap B)=0$ (disjoint sets), giving $26+32=58$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Area of an equilateral triangle with each side 'a' is (a) $\frac{\sqrt3}{2}a^3$ (b) $\frac{\sqrt3}{2}a^2$ (c) $\frac{\sqrt3}{4}a$ (d) $\frac{\sqrt3}{4}a^2$

Answer

(d) $\frac{\sqrt3}{4}a^2$

Height of the triangle is $\frac{\sqrt3}{2}a$ , so area $=\frac12\cdot a\cdot\frac{\sqrt3}{2}a=\frac{\sqrt3}{4}a^2$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Area of triangle with 4cm, 5cm, 7cm is (a) $7.8\,cm^2$ (b) $8.8\,cm^2$ (c) $9.8\,cm^2$ (d) $10.8\,cm^2$

Answer

(c) $9.8\,cm^2$

By Heron's formula, $s=\frac{4+5+7}{2}=8$ .

$A=\sqrt{8(8-4)(8-5)(8-7)}=\sqrt{96}\approx 9.8\,cm^2$

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Total surface area of a hemisphere having radius 7 cm is (a) $450\,cm^2$ (b) $460\,cm^2$ (c) $462\,cm^2$ (d) $472\,cm^2$

Answer

(c) $462\,cm^2$

Total surface area of a hemisphere $=3\pi r^2=3\times\frac{22}{7}\times 49=462\,cm^2$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

If the volume of a cone is $3696\,cm^2$ and radius of the base is $14\,cm$ then height of the cone is (a) 16 cm (b) 17 cm (c) 18 cm (d) 19 cm

Answer

(c) 18 cm

$V=\frac13\pi r^2h\Rightarrow 3696=\frac13\times\frac{22}{7}\times196\,h=\frac{616}{3}h$

$h=\frac{3696\times3}{616}=18\text{ cm}$

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

If $3^{2x}-9=0$ then the value of x is equal to (a) 0 (b) 1 (c) 3 (d) 9

Answer

(b) 1

$3^{2x}=9=3^2\Rightarrow 2x=2\Rightarrow x=1$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

The value of $\left(\frac{27}{8}\right)^{\frac13}\div\left(\frac94\right)^{\frac12}$ is (a) 1 (b) -1 (c) 2 (d) -2

Answer

(a) 1

$\left(\frac{27}{8}\right)^{1/3}=\frac32$ and $\left(\frac94\right)^{1/2}=\frac32$ , so the quotient is $1$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

The two lines $x-y=4$ and $2x-y=16$ are (a) parallel (b) perpendicular (c) intersecting (d) non- intersecting

Answer

(c) intersecting

The slopes are $1$ and $2$ . They are different, so the lines are neither parallel nor identical and they meet at one point. Subtracting the equations gives $x=12$ , $y=8$ , so they meet at $(12,8)$ . The product of slopes is $2\neq-1$ , so they are not perpendicular.

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

The sum and difference of two positive numbers are 15 and 5 respectively, then the numbers are (a) 14, 1 (b) 11, 4 (c) 12, 3 (d) 10, 5

Answer

(d) 10, 5

$x+y=15$ and $x-y=5$ . Adding gives $2x=20$ , so $x=10$ and $y=5$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

A number is twice the other. If their sum is 30 then the numbers are (a) 10,20 (b) 25,5 (c) 12,18 (d) 17, 13

Answer

(a) 10, 20

Let the numbers be $x$ and $2x$ . Then $3x=30$ , so $x=10$ and the numbers are $10$ and $20$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

If the sum of squares of two consecutive even numbers is 100, then the numbers are (a) 2, 4 (b) 4, 6 (c) 6, 8 (d) 8, 10

Answer

(c) 6, 8

Let the numbers be $x$ and $x+2$ : $x^2+(x+2)^2=100\Rightarrow x^2+2x-48=0\Rightarrow (x+8)(x-6)=0$ , so $x=6$ and the numbers are $6$ and $8$ . Check: $36+64=100$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

If 17 is subtracted from a square of a number the result is 152, then the positive number is (a) 11 (b) 14 (c) 12 (d) 13

Answer

(d) 13

$x^2-17=152\Rightarrow x^2=169\Rightarrow x=13$ (positive).

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

The sum of first 20 positive numbers is (a) 150 (b) 175 (c) 200 (d) 210

Answer

(d) 210

$S=\frac{n(n+1)}{2}=\frac{20\times21}{2}=210$

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2022 · 1 mark

If $f(x)=2x+3$ then $f(3)$ is equal to (a) 6 (b) 3 (c) 8 (d) 9

Answer

(d) 9

$f(3)=2(3)+3=9$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

One factor of the polynomial $x^3-4x^2+x+6$ is (a) $(x+1)$ (b) $(x+2)$ (c) $(x+3)$ (d) $(x+4)$

Answer

(a) $(x+1)$

Let $f(x)=x^3-4x^2+x+6$ . Then $f(-1)=-1-4-1+6=0$ , so by the factor theorem $(x+1)$ is a factor. Indeed $f(x)=(x+1)(x-2)(x-3)$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Sum of the infinite series $1+\frac12+\frac14+\frac18+\ldots$ is (a) 2 (b) 3 (c) 1 (d) 4

Answer

(a) 2

This is a geometric series with $a=1$ and $r=\frac12$ .

$S_\infty=\frac{a}{1-r}=\frac{1}{1-\frac12}=2$

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Sum of squares of first 5 natural numbers is (a) 50 (b) 52 (c) 53 (d) 55

Answer

(d) 55

$1^2+2^2+3^2+4^2+5^2=1+4+9+16+25=55$

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Top of tree which is at a distance of 45 meter makes an angle of $45^\circ$ to the observer, then the height of the tree is (a) 45m (b) 50m (c) 55m (d) 60m

Answer

(a) 45m

$\tan45^\circ=\dfrac{h}{45}$ and $\tan45^\circ=1$ , so $h=45$ m.

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

If two lines are perpendicular with each other then the product of their slope is (a) 1 (b) -1 (c) 2 (d) -2

Answer

(b) -1

For perpendicular lines $m_1m_2=-1$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

$(2,1)$ and $(2,5)$ are two points in a plain then the distance between two points is (a) 1 (b) 2 (c) 3 (d) 4

Answer

(d) 4

The x-coordinates are equal, so the points lie on a vertical line and the distance is $|5-1|=4$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Equation of a straight line which is parallel to y- axis and passes through the point $(3,0)$ is (a) $X=3$ (b) $x=-3$ (c) $y=3$ (d) $y=-3$

Answer

(a) $x=3$

A line parallel to the y-axis is vertical, and the one through $(3,0)$ has equation $x=3$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Diameter of a circle subtend an angle at the circumference which is always (a) 45 degree (b) 60 degree (c) 90 degree (d) 180 degree

Answer

(c) 90 degree

The angle in a semicircle is always a right angle.

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

Angle subtended by an arc at the center of a circle and at the circumference are related as (a) Angle at the center is double of the angle of the circumference (b) Angle at circumferences is double of the angle at the center (c) Both the angles are equal (d) There is no relation between them

Answer

(a) Angle at the center is double of the angle of the circumference

The angle subtended by an arc at the centre is twice the angle it subtends at any point on the remaining part of the circle.

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2022 · 1 mark

A parallelogram and a triangle standing on the same base and between the same parallel lines are (a) Both are equal in area (b) Area of the parallelogram is double of area of triangle (c) Area of the triangle is double of the area of parallelogram. (d) Area between them can't be compared

Answer

(b) Area of the parallelogram is double of area of triangle

A triangle on the same base and between the same parallels as a parallelogram has half its area.

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2022 · 1 mark

Sum of the four angles of a cyclic quadrilateral is (a) 90 (b) 180 (c) 270 (d) 360

Answer

(d) 360

The sum of the interior angles of any quadrilateral, including a cyclic one, is $360^\circ$ (opposite angles sum to $180^\circ$ each).

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2022 · 1 mark

If $A=\begin{bmatrix}2&3\\1&1\end{bmatrix}$ , then inverse of matrix A is (a) $\begin{bmatrix}-2&3\\1&-1\end{bmatrix}$ (b) $\begin{bmatrix}2&-3\\-1&1\end{bmatrix}$ (c) $\begin{bmatrix}2&3\\1&1\end{bmatrix}$ (d) $\begin{bmatrix}-2&-3\\1&1\end{bmatrix}$

Answer

(a) $\begin{bmatrix}-2&3\\1&-1\end{bmatrix}$

The inverse of a $2\times2$ matrix is $\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$ . For the matrix as printed, $\det A=2-3=-1$ and the inverse is $\begin{bmatrix}-1&3\\1&-2\end{bmatrix}$ , which is not among the options. Option (a) has the correct form and is the nearest choice (it is the exact inverse of $\begin{bmatrix}1&3\\1&2\end{bmatrix}$ ).

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2022 · 1 mark

Determinant of singular matrix is (a) 0 (b) 1 (c) -1 (d) 2

Answer

(a) 0

A singular matrix has no inverse, which happens exactly when its determinant is $0$ .

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2022 · 1 mark

What is the value of $\tan90^\circ$ ? (a) 0 (b) 1 (c) -1 (d) $\infty$

Answer

(d) $\infty$

$\tan90^\circ=\dfrac{\sin90^\circ}{\cos90^\circ}=\dfrac10$ , which is undefined (it tends to $\infty$ ).

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2022 · 1 mark

The radius of the circle $x^2+y^2=25$ is equal to (a) 4 (b) 3 (c) 5 (d) 9

Answer

(c) 5

Compare with $x^2+y^2=r^2$ : $r^2=25$ , so $r=5$ .

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2022 · 1 mark

The commission of Rs. 5,600 at the rate of 5% is (a) Rs. 280 (b) Rs. 360 (c) Rs. 560 (d) Rs.144

Answer

(a) Rs. 280

Commission $=\dfrac{5}{100}\times5600=$ Rs. 280.

Answer checked by Claude Sonnet · Oct 21, 2026

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2022 · 1 mark

If $b^2-4ac=0$ then the roots of $ax^2+bx+c=0$ are: (a) equal (b) not exist (c) rational (d) imaginary

Answer

(a) equal

When the discriminant $b^2-4ac=0$ , the roots are real and equal, each $-\dfrac{b}{2a}$ .

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2022 · 1 mark

Which of the following is correct? (a) $A.M=ab$ (b) $H.M=\frac{2ab}{a+b}$ (c) $H.M=\frac{a+b}{2}$ (d) none of these

Answer

(b) $H.M=\frac{2ab}{a+b}$

The harmonic mean of $a$ and $b$ is $\frac{2ab}{a+b}$ , while the arithmetic mean is $\frac{a+b}{2}$ .

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2022 · 1 mark

Limit of function $\lim_{x\to0}\frac{\sin(x)}{x}$ is equal to (a) 0 (b) 1 (c) -1 (d) Not exists

Answer

(b) 1

This is the standard limit $\lim_{x\to0}\frac{\sin x}{x}=1$ (with $x$ in radians).

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2023 · 1 mark

If $n(A)=30$ , $n(B)=50$ , $n(U)=60$ and $n(A\cup B)=55$ then sum of $n(A-B)$ and $n(B-A)$ is equal to (a) 45 (b) 50 (c) 55 (d) 30

Answer

(d) 30 First find the intersection:

$n(A\cap B)=n(A)+n(B)-n(A\cup B)=30+50-55=25$

Then

$n(A-B)+n(B-A)=(30-25)+(50-25)=5+25=30$

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2023 · 1 mark

The sum of natural numbers from 1 to 20 is (a) $\frac{20\times21}{2}$ (b) $\frac{19\times21}{2}$ (c) $\frac{1\times20}{2}$ (d) 200

Answer

(a) $\frac{20\times21}{2}$ Using $\sum n=\frac{n(n+1)}{2}$ with $n=20$ gives $\frac{20\times 21}{2}=210$ .

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2023 · 1 mark

If $n(A)=26$ and $n(B)=32$ then the maximum value of $n(A\cap B)$ is (a) 26 (b) 58 (c) 32 (d) 6

Answer

(a) 26 The intersection cannot be larger than the smaller set, so $n(A\cap B)\le\min(26,32)=26$ . The maximum occurs when $A\subseteq B$ .

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2023 · 1 mark

For some integer n, which of the following form is always an odd integer? (a) N (b) n+1 (c) 2n (d) 2n+1

Answer

(d) $2n+1$ $2n$ is always even, so adding 1 gives an odd integer for every integer $n$ .

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2023 · 1 mark

The range of the function $f(x)=\sqrt{(x-1)}$ is (a) $[1,\infty)$ (b) $(-\infty,+\infty)$ (c) $(-1,\infty)$ (d) $[0,\infty)$

Answer

(d) $[0,\infty)$ The domain is $x\ge1$ , so $x-1\ge0$ . The square root takes all values from 0 upward, so the range is $[0,\infty)$ .

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2023 · 1 mark

To exist infinite sum of the geometric series its ratio should be (a) less than 0 (b) less than -1 (c) between 1 and -1 (d) greater than 1

Answer

(c) between 1 and -1 The infinite sum $\frac{a}{1-r}$ exists only when $|r|<1$ , that is, $-1<r<1$ .

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2023 · 1 mark

The complement of an angle is $20^\circ$ (20 degrees) less than 4 times the angle, then the angle is (a) 38 (b) 90 (c) 22 (d) 70

Answer

(c) 22 Let the angle be $x$ . Its complement is $90-x$ , so

$90-x=4x-20\Rightarrow 5x=110\Rightarrow x=22^\circ$

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2023 · 1 mark

If the quadratic equation is $x^2+x+1=0$ then the value of $x=$ ............ (a) $\frac{-1\pm i\sqrt3}{2}$ (b) $\frac{-1-i\sqrt3}{2}$ (c) $\frac{-1\pm i\sqrt2}{2}$ (d) $\frac{-1+i\sqrt2}{2}$

Answer

(a) $\frac{-1\pm i\sqrt3}{2}$ By the quadratic formula, $x=\frac{-1\pm\sqrt{1-4}}{2}=\frac{-1\pm i\sqrt3}{2}$ . Option (b) gives only one of the two roots.

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2023 · 1 mark

A function is defined as $f(x)=\frac{3x+1}{4}$ then the inverse of this function if it exists is (a) $\frac{4x-1}{3}$ (b) $\frac{4x+1}{3}$ (c) $\frac{3x-1}{4}$ (d) $\frac{3x+1}{4}$

Answer

(a) $\frac{4x-1}{3}$ Put $y=\frac{3x+1}{4}$ , so $4y=3x+1$ and $x=\frac{4y-1}{3}$ . Hence $f^{-1}(x)=\frac{4x-1}{3}$ .

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2023 · 1 mark

One factor of the polynomial $x^3-4x^2+x+6$ is $(x-2)$ then the two other factors are ...... (a) $(x+1)(x-3)$ (b) $(x+2)(x-2)$ (c) $(x+3)(x-1)$ (d) $(x+4)(x+1)$

Answer

(a) $(x+1)(x-3)$ Dividing by $(x-2)$ gives the quotient $x^2-2x-3$ , which factors as $(x-3)(x+1)$ .

Check: $f(2)=8-16+2+6=0$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2023 · 1 mark

The sum of the infinite series $1+\frac12+\frac14+\frac18+\ldots\ldots$ is (a) 4 (b) 3 (c) 2 (d) 1

Answer

(c) 2 This is a geometric series with $a=1$ , $r=\frac12$ :

$S_\infty=\frac{1}{1-\frac12}=2$

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2023 · 1 mark

The sum of cubes of the first 6 natural numbers is ......... (a) 661 (b) 551 (c) 441 (d) 331

Answer

(c) 441 $\sum_{k=1}^{6}k^3=\left(\frac{6\times7}{2}\right)^2=21^2=441$

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2023 · 1 mark

A poll at a distance of 25 meters from the observer makes an angle of 60 degrees with its top. Then the height of the poll is (a) 25 (b) $25\sqrt3$ (c) $\frac{25}{2}$ (d) $50\sqrt3$

Answer

(b) $25\sqrt3$ The angle of elevation is $60^\circ$ , so

$\tan60^\circ=\frac{h}{25}\Rightarrow h=25\sqrt3\text{ m}$

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2023 · 1 mark

If 12 girls or 8 boys can do a piece of work in 3 days, how many days required for 4 boys and 6 girls to do the same work? (a) 2 (b) 4 (c) 5 (d) 3

Answer

(d) 3 Since 12 girls $=$ 8 boys in work rate, 1 girl $=\frac{2}{3}$ boy, so 6 girls $=$ 4 boys. Then 4 boys and 6 girls equal 8 boys, who finish the work in 3 days.

Answer checked by Claude Sonnet · Oct 21, 2026

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2023 · 1 mark

Two angles subtended by an arc one at the center and the other at the circumference are related as ... (a) The angle at the center is double the angle at the circumference. (b) The angle at the circumference is double the angle at the center. (c) The angle at the center is half the angle at the circumference. (d) The angle at the circumference is equal to the angle at the center.

Answer

(a) The angle at the center is double the angle at the circumference. This is the standard circle theorem for angles subtended by the same arc.

Answer checked by Claude Sonnet · Oct 21, 2026

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2023 · 1 mark

If $f(x)=4x$ , $g(x)=x+1$ & $f\circ g(x)=20$ then the value of $x=$ ......... (a) 1 (b) 3 (c) 2 (d) 4

Answer

(d) 4 $f\circ g(x)=f(x+1)=4(x+1)=20\Rightarrow x+1=5\Rightarrow x=4$

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2023 · 1 mark

If two children are born in a family find the probability that both are girls (a) $\frac12$ (b) $\frac13$ (c) $\frac14$ (d) $\frac23$

Answer

(c) $\frac14$ The outcomes are GG, GB, BG, BB, all equally likely. Only one has both girls, so $P=\frac12\times\frac12=\frac14$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2023 · 1 mark

The value of $\tan75^\circ$ is (a) $\sqrt3$ (b) $2+\sqrt3$ (c) $2-\sqrt3$ (d) 2

Answer

(b) $2+\sqrt3$ $\tan75^\circ=\tan(45^\circ+30^\circ)=\frac{1+\frac{1}{\sqrt3}}{1-\frac{1}{\sqrt3}}=\frac{\sqrt3+1}{\sqrt3-1}=\frac{(\sqrt3+1)^2}{2}=2+\sqrt3$

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2023 · 1 mark

Sum of 15 terms of an A. P. is 435 and the common difference is 4 then the first term is (a) 4 (b) 3 (c) 2 (d) 1

Answer

(d) 1 $S_{15}=\frac{15}{2}\left[2a+14\times4\right]=435\Rightarrow 2a+56=58\Rightarrow a=1$

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2023 · 1 mark

Which one is the same as $\log8$ (a) $\log4+\log2$ (b) $\log4+\log4$ (c) $2\log4$ (d) $4\log2$

Answer

(a) $\log4+\log2$ $\log4+\log2=\log(4\times2)=\log8$ . The other options give $\log16$ , $\log16$ and $\log16$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2023 · 1 mark

If $A=\begin{pmatrix}2&3\\-4&-5\end{pmatrix}$ , $B=\begin{pmatrix}0&-3\\2&5\end{pmatrix}$ then $(AB)^T=$ (a) $\begin{pmatrix}6&-10\\9&-13\end{pmatrix}$ (b) $\begin{pmatrix}6&10\\9&-13\end{pmatrix}$ (c) $\begin{pmatrix}6&-10\\9&13\end{pmatrix}$ (d) $\begin{pmatrix}6&0\\9&3\end{pmatrix}$

Answer

(a) $\begin{pmatrix}6&-10\\9&-13\end{pmatrix}$ $AB=\begin{pmatrix}0+6&-6+15\\0-10&12-25\end{pmatrix}=\begin{pmatrix}6&9\\-10&-13\end{pmatrix}$

Transposing gives $\begin{pmatrix}6&-10\\9&-13\end{pmatrix}$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2023 · 1 mark

Harmonic mean between two numbers a and b is (a) $\frac{a+b}{2ab}$ (b) $\frac{a-b}{2ab}$ (c) $\frac{2ab}{a+b}$ (d) $\frac{2ab}{a-b}$

Answer

(c) $\frac{2ab}{a+b}$ The harmonic mean is the reciprocal of the mean of the reciprocals: $\frac{2}{\frac1a+\frac1b}=\frac{2ab}{a+b}$ .

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2023 · 1 mark

The sum of the first 10 odd numbers is (a) 80 (b) 90 (c) 125 (d) 100

Answer

(d) 100 The sum of the first $n$ odd numbers is $n^2$ , so for $n=10$ it is $100$ .

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2023 · 1 mark

The solution of the equation $x^2+1=0$ in complex number system is, (a) 1 (b) -1 (c) 0 (d) $\pm i$

Answer

(d) $\pm i$ $x^2=-1$ gives $x=\pm\sqrt{-1}=\pm i$ .

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2023 · 1 mark

The next term of the sequence 1,2,4,7,11,............ is (a) 15 (b) 16 (c) 17 (d) 22

Answer

(b) 16

The differences between consecutive terms are 1, 2, 3, 4, so the next difference is 5 and the next term is $11+5=16$ .

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2023 · 1 mark

If $f(x)=x^2-3x+1$ & $f(2a)=2f(a)$ then $a=$ .............. (a) $\frac{1}{\sqrt2}$ (b) $-\frac{1}{\sqrt2}$ (c) $\frac{1}{\sqrt2}$ or $-\frac{1}{\sqrt2}$ (d) 1

Answer

(c) $\frac{1}{\sqrt2}$ or $-\frac{1}{\sqrt2}$

$f(2a)=4a^2-6a+1$ and $2f(a)=2a^2-6a+2$ . Equating gives $2a^2=1$ , so $a=\pm\frac{1}{\sqrt2}$ .

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2023 · 1 mark

If $x<0$ , then the value of $|x|$ is equal to (a) $x$ (b) $-x$ (c) $x^2$ (d) $-x^2$

Answer

(b) $-x$

For $x<0$ , $|x|=-x$ , which is positive.

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2023 · 1 mark

The two lines $3x+2y=5$ and $9x+6y=14$ have (a) no solution (b) unique solution (c) infinite solution (d) two solution

Answer

(a) no solution

Here $\frac{3}{9}=\frac{2}{6}=\frac13\neq\frac{5}{14}$ , so the lines are parallel and distinct and never meet.

Answer checked by Claude Sonnet · Oct 21, 2026

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2023 · 1 mark

When a point $(3,4)$ is rotated by 90 degrees in anticlockwise direction and translated by a point $(5,-2)$ the resulting point is (a) $(1,1)$ (b) $(8,2)$ (c) $(-2,6)$ (d) $(0,1)$

Answer

(a) $(1,1)$

A 90 degree anticlockwise rotation maps $(x,y)\to(-y,x)$ , so $(3,4)\to(-4,3)$ . Translating by $(5,-2)$ gives $(-4+5,\,3-2)=(1,1)$ .

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2023 · 1 mark

If $2x^3-7x^2+x+10=(x-1)Q(x)+R(x)$ then the value of remainder $R(x)$ is equal to (a) 5 (b) 6 (c) 7 (d) 9

Answer

(b) 6

By the remainder theorem, $R=f(1)=2-7+1+10=6$ .

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2023 · 1 mark

If $5^{x+3}=(25)^x$ , then the value of x is (a) 1 (b) 2 (c) 0 (d) 3

Answer

(d) 3

$5^{x+3}=(5^2)^x=5^{2x}$ , so $x+3=2x$ and $x=3$ .

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2023 · 1 mark

If $x+y=3$ & $x^2+y^2=5$ , then the value of $xy$ is (a) 1 (b) 2 (c) 3 (d) 453

Answer

(b) 2

$(x+y)^2=x^2+y^2+2xy$ , so $9=5+2xy$ and $xy=2$ .

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2023 · 1 mark

If $m_1$ and $m_2$ are the slopes of the pair of lines $ax^2+2hxy+by^2=0$ then the product of $m_1$ and $m_2$ is ....... (a) $\frac{2h}{b}$ (b) ab (c) $a-b$ (d) $\frac ab$

Answer

(d) $\frac ab$

Putting $y=mx$ gives $bm^2+2hm+a=0$ . The product of its roots is $m_1m_2=\frac ab$ .

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2023 · 1 mark

In the general equation of circle $x^2+y^2+2gx+2fy+c=0$ the radius of the circle is (a) $(g,f)$ (b) $(f,g)$ (c) $(-g,-f)$ (d) $(-f,-g)$

Answer

(c) $(-g,-f)$

The option given, $(-g,-f)$ , is the centre of the circle. The radius itself is $\sqrt{g^2+f^2-c}$ , which is not one of the choices, so the question intends the centre $(-g,-f)$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2023 · 1 mark

The value of 0! Is (a) 0 (b) -1 (c) 1 (d) 2

Answer

(c) 1

By definition $0!=1$ .

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2023 · 1 mark

The value of limit $\lim_{x\to3}\frac{x^2-9}{x-3}$ (a) 0 (b) -1 (c) 1 (d) 2

Answer

None of the given options is correct; the limit equals 6.

$\lim_{x\to3}\frac{x^2-9}{x-3}=\lim_{x\to3}\frac{(x-3)(x+3)}{x-3}=\lim_{x\to3}(x+3)=6.$

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2023 · 1 mark

Derivative of $\tan x$ with respect to x is (a) $\sin^2x$ (b) $\cos^2x$ (c) $\operatorname{cosec}^2x$ (d) $\sec^2x$

Answer

(d) $\sec^2x$

$\frac{d}{dx}(\tan x)=\sec^2x$ .

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2023 · 1 mark

A point in a three-dimensional space has its coordinate is $(1,2,-2)$ . The distance of this point from the origin is (a) 5 (b) 4 (c) 1 (d) 3

Answer

(d) 3

Distance $=\sqrt{1^2+2^2+(-2)^2}=\sqrt9=3$ .

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2023 · 1 mark

A matrix A has its order $3\times4$ and matrix B has its order $4\times3$ then the order of their product AB is (a) $3\times3$ (b) $4\times4$ (c) $4\times3$ (d) $3\times4$

Answer

(a) $3\times3$

For $A_{m\times n}$ and $B_{n\times p}$ , the product $AB$ has order $m\times p$ . Here that is $3\times3$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2023 · 1 mark

If transpose of a matrix A is the matrix A itself then A is called (a) identity (b) scalar (c) symmetric (d) skew-symmetric

Answer

(c) symmetric

A matrix with $A^T=A$ is called symmetric.

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2023 · 1 mark

Sum of the natural numbers $1^3+2^3+3^3.....+n^3$ is (a) $\left(\frac{n(n+1)}{2}\right)^3$ (b) $\left(\frac{n(n+1)}{2}\right)^2$ (c) $\left(\frac{n(n+1)}{3}\right)^2$ (d) $\left(\frac{n(n-1)}{2}\right)^2$

Answer

(b) $\left(\frac{n(n+1)}{2}\right)^2$

The sum of the first $n$ cubes equals the square of the sum of the first $n$ natural numbers.

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2023 · 1 mark

If $b^2-4ac=0$ then the roots of $ax^2+bx+c=0$ are: (a) real and equal (b) real and unequal (c) irrational (d) imaginary

Answer

(a) real and equal

The discriminant is zero, so both roots equal $-\frac{b}{2a}$ .

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2023 · 1 mark

A dice is thrown in the air. The probability of getting odd numbers is (a) $\frac13$ (b) $\frac12$ (c) $\frac34$ (d) 2

Answer

(b) $\frac12$

Odd faces are 1, 3, 5, so $P=\frac36=\frac12$ .

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Past questions and answers

1.If the relation R={(1,2),(2,3),(3,4),(4,5)}R=\{(1,2),(2,3),(3,4),(4,5)\}R={(1,2),(2,3),(3,4),(4,5)} then its range is, (a) {2,3,4,5}\{2,3,4,5\}{2,3,4,5} (b) {1,2,3,4}\{1,2,3,4\}{1,2,3,4} (c) {1,2,3,5}\{1,2,3,5\}{1,2,3,5} (d) {1,3,4,5}\{1,3,4,5\}{1,3,4,5}

2.The value of 2128+1622\sqrt{128}+\sqrt{162}2128​+162​ is , (a) 25225\sqrt2252​ (b) 434\sqrt343​ (c) 0 (d) 60

3.If £ 7 = USD 11 and USD 2 = Rs. 213, then how many pound (£) can be exchange for Rs. 117150? (a) 750 (b) 650 (c) 700 (d) 850

4.A mobile is sold for Rs. 11000, with a profit of Rs. 1000, then the percentage profit is (a) 9% (b) 10% (c) 12% (d) 14%

5.The fifth term of the sequence 12,45,78,…\frac12,\frac45,\frac78,\ldots21​,54​,87​,… is (a) 1112\frac{11}{12}1211​ (b) 1213\frac{12}{13}1312​ (c) 1314\frac{13}{14}1413​ (d) 1415\frac{14}{15}1514​

6.The sum of first five prime numbers is: (a) 11 (b) 18 (c) 26 (d) 28

7.The product of two consecutive even number is 224. Then the numbers are: (a) 16, 18 (b) 12, 14 (c) 14, 16 (d) 18, 20

8.If the ratio of two numbers is 2:3 and sum of these numbers is 30, then which are these numbers? (a) 14, 16 (b) 10, 20 (c) 12, 18 (d) 18, 12

9.If the cost of 9 kg sugar is Rs. 270/-, how much sugar can be purchased for Rs. 390/-? (a) 11 (b) 12 (c) 13 (d) 14

10.The cardinal number of a vowel set V = {a, e, i, o, u} is: (a) 4 (b) 5 (c) 6 (d) 7

11.What is the sum of first five prime numbers? (a) 18 (b) 25 (c) 26 (d) 28

12.If the product of two consecutive even number is 288, then what are these numbers from following? (a) 14, 12 (b) 14, 16 (c) 16, 18 (d) 22, 24

13.If the cost of 7 kg sugar is Rs. 210, how much sugar can be purchased for Rs. 330? (a) 11kg (b) 12kg (c) 13kg (d) 14kg

14.Two numbers are in the ratio of 6:7 and their sum is 117, then what are these numbers? (a) 56, 58 (b) 63, 54 (c) 54, 63 (d) 48, 56

15.What is the rate percentage per anum that a sum of money trebles itself in 25 years? (a) 2% (b) 4% (c) 6% (d) 8%

16.What is the cardinal number of a vowel set V={a,e,i,o,u}V=\{a,e,i,o,u\}V={a,e,i,o,u}? (a) 4 (b) 5 (c) 6 (d) 7

17.The area of 4 walls of square room is 120 m2120\,m^2120m2. If the height is 5 m, then what is the area of its floor? (a) 26 m226\,m^226m2 (b) 56 m256\,m^256m2 (c) 25 m225\,m^225m2 (d) 36 m236\,m^236m2

18.Of a group of 120 students, 90 takes mathematics and 72 takes statistics. If 10 students neither of two, the number of student taking both subjects are: (a) 50 (b) 45 (c) 52 (d) 58

19.−5<x<7-5<x<7−5<x<7 can be written in the absolute value sign as: (a) ∣x−1∣<7|x-1|<7∣x−1∣<7 (b) ∣x−1∣<6|x-1|<6∣x−1∣<6 (c) ∣x−1∣<2|x-1|<2∣x−1∣<2 (d) ∣x−1∣<−1|x-1|<-1∣x−1∣<−1

20.How many stones each of area 0.16 cm square are required for paving a courtyard 5.5 m long and 4.8 m wide? (a) 60 (b) 100 (c) 50 (d) 165

21.The discount percent of marked price is Rs. 5,800 and discount amount is Rs. 696 then the discount percent is, (a) 12% (b) 20% (c) 5% (d) 38%

22.If 4 is subtracted from a square of a number, its result is 21. The number is, (a) 5 (b) 4 (c) 6 (d) 3

23.The area of 4 walls of square room is 120 m2120\,m^2120m2. if the height is 5m, the area of its floor is (a) 56 m256\,m^256m2 (b) 36 m236\,m^236m2 (c) 46 m246\,m^246m2 (d) 26 m226\,m^226m2

24.The rate percentage per annum that a sum of money trebles itself in 25 years is : (a) 25 % (b) 10% (c) 4% (d) 8%

25.If 5 is subtracted from the square of a number and the result is 20, the number is : (a) ±5\pm5±5 (b) ±6\pm6±6 (c) ±7\pm7±7 (d) ±9\pm9±9

26.The Marked Price of an article is Rs. 8500. If a discount of 10% is allowed the selling price is (a) 7550 (b) 7650 (c) 7750 (d) 7850

27.Radius of cylinder is 7 cm height is 12 cm then it's volume is (a) 1848 cm31848\,cm^31848cm3 (b) 1748 cm31748\,cm^31748cm3 (c) 1648 cm31648\,cm^31648cm3 (d) 1548 cm31548\,cm^31548cm3

28.Single equation represented by two straight lines x=2yx=2yx=2y and 2x=y2x=y2x=y is (a) 2x2−3xy+2y2=02x^2-3xy+2y^2=02x2−3xy+2y2=0 (b) x2−3xy+2y2=0x^2-3xy+2y^2=0x2−3xy+2y2=0 (c) 2x2−xy+2y2=02x^2-xy+2y^2=02x2−xy+2y2=0 (d) 2x2−3xy+y2=02x^2-3xy+y^2=02x2−3xy+y2=0

29.Of a group of 120 students, 80 takes mathematics and 62 takes statistics. If 20 students neither if two, the number of students taking both subjects are (a) 50 (b) 42 (c) 52 (d) 55

30.−5<x<9-5<x<9−5<x<9 can be written in the absolute value sign as: (a) ∣x−2∣<5|x-2|<5∣x−2∣<5 (b) ∣x−2∣<7|x-2|<7∣x−2∣<7 (c) ∣x−2∣<9|x-2|<9∣x−2∣<9 (d) ∣x+2∣<5|x+2|<5∣x+2∣<5

31.How many stones each of area 22 cm22\,cm22cm square are required for paving a courtyard 5.5 m long and 4 m wide? (a) 60000 (b) 40000 (c) 20000 (d) 10000

32.The discount of marked price is Rs. 5,800 the amount Rs. 696 then discount percent is. (a) 12% (b) 20% (c) 5% (d) 38%

33.Marked price of an article is Rs. 8500. If a discount of 10% is allowed the selling price is.... (a) 7550 (b) 7650 (c) 7750 (d) 7850

34.A single equation represented by two straight lines x=2yx=2yx=2y and 2x=y2x=y2x=y is ... (a) 2x2−3xy+y2=02x^2-3xy+y^2=02x2−3xy+y2=0 (b) x2−3xy+2y2=0x^2-3xy+2y^2=0x2−3xy+2y2=0 (c) 2x2−xy+2y2=02x^2-xy+2y^2=02x2−xy+2y2=0 (d) 2x2−5xy+2y2=02x^2-5xy+2y^2=02x2−5xy+2y2=0

35.Radius of the cylinder is 7 cm height is 3 cm then it's volume is (a) 442 cm3442\,cm^3442cm3 (b) 452 cm3452\,cm^3452cm3 (c) 462 cm3462\,cm^3462cm3 (d) 472 cm3472\,cm^3472cm3

36.Which one of the following number has a remainder of 4 when it is divided by 6? (a) 8 (b) 12 (c) 22 (d) 29

37.The sum of the product and quotient of 4 and 4 is ………. (a) 16 (b) 15 (c) 8 (d) 17

38.The average of all even numbers between -4 and 5 is ….. (a) 1 (b) 0.5 (c) -1 (d) none of these

39.The value of ∑n=1010(−1)n\sum_{n=10}^{10} (-1)^n∑n=1010​(−1)n is: (a) 1 (b) -1 (c) 10 (d) 0

40.If 5 is added to the square of a number, then the result is 14. What is the value of that number? (a) 3 (b) 5 (c) 7 (d) 9

41.If three spoons equals to one glass, two glasses equals to one plate, then how many spoons equals to one plate? (a) 3 (b) 6 (c) 9 (d) 2

42.If a matrix is of order 5 X 7, then each column will contain …………..elements. (a) 5 (b) 12 (c) 35 (d) 7

43.If the equation are 3x+4y=73x + 4y = 73x+4y=7 and 4x−y=34x - y = 34x−y=3 after solving these equations the value of x and y will be: (a) 1,1 (b) 1,2 (c) 2,1 (d) 2,2

44.What is the value of x in series 1, 9, 25, x, 81, 121? (a) 100 (b) 36 (c) 49 (d) 64

45.If a+b=ca + b = ca+b=c, then what is the average value of a, b and c? (a) (a+b)3\frac{(a+b)}{3}3(a+b)​ (b) c3\frac{c}{3}3c​ (c) 2c3\frac{2c}{3}32c​ (d) c3\frac{c}{3}3c​

46.If x in an integer and y=−2x−8y = -2x - 8y=−2x−8, what is the least value of x for which y is less than 9? (a) -8 (b) -9 (c) -10 (d) -11

47.The slope of line which equation is 2x−4y=92x - 4y = 92x−4y=9 is: (a) 2 (b) 1/2 (c) -1/2 (d) 3

48.What is the slope of horizontal line? (a) >1 (b) < 0 (c) 0 (d) 1

49.The difference between 3/5 of 80 and 30% of 80 is: (a) 20 (b) 14 (c) 15 (d) 24

50.Gautam spent Rs. 40/-, which is 5% of his daily wage, then his total daily wage is: (a) Rs.400/- (b) Rs.600/- (c) Rs.800/- (d) Rs. 1000/-

51.If 1254376 represents the CENTURY, then what represents 735? (a) NUT (b) RUT (c) RUN (d) YET

52.Find the missing value in (27695143?)\begin{pmatrix} 2 & 7 & 6 \\ 9 & 5 & 1 \\ 4 & 3 & ? \end{pmatrix}​294​753​61?​​. (a) 5 (b) 8 (c) 7 (d) 9

53.There are 48 students in a computer class. If number of boys are twice than girls, then how many girls are there? (a) 16 (b) 18 (c) 32 (d) 28

54.Find the number x, which is equal to (80% of x) plus 5. (a) 20 (b) 30 (c) 40 (d) 25

55.If the age of five girls are 15, 16, 17, 18, 19 respectively then what is the average age of girls? (a) 15 (b) 17 (c) 18 (d) 19

56.How many triangles in this figure? (a) 6 (b) 7 (c) 8 (d) 9

57.What is the value of cos 60° ? (a) 1 (b) 12\frac{1}{2}21​ (c) 0 (d) 32\frac{\sqrt{3}}{2}23​​

58.Find the value of x in series 1, 1, 2, 3, 5, 8, 13, x. (a) 21 (b) 22 (c) 19 (d) 23

59.If 'n' is an integer, which of the following must be even? (a) n + 1 (b) n + 2 (c) 2n + 1 (d) 2n

60.The largest prime factor of 255 is: (a) 45 (b) 25 (c) 17 (d) 5

61.The sum of first n natural number is: (a) n(n+1)2\frac{n(n+1)}{2}2n(n+1)​ (b) n(n+1)(2n+1)2\frac{n(n+1)(2n+1)}{2}2n(n+1)(2n+1)​ (c) (n+1)22\frac{(n+1)^2}{2}2(n+1)2​ (d) none of these

62.The root of the equation 3x2−8x+16=03x^2 - 8x + 16 = 03x2−8x+16=0 are (a) real & equal (b) real & unequal (c) imaginary & unequal (d) none of these

63.If x + y = 12 and x - y = 6 then, the value of x2−y2x^2 - y^2x2−y2 is: (a) 18 (b) 36 (c) 60 (d) 72

64.If x - 5 = 2, then the value of x + 12 is: (a) 15 (b) 17 (c) 19 (d) 18

65.The value when simplified 64−635\frac{6^4 - 6^3}{5}564−63​ is: (a) 1/5 (b) 63 (c) 6/5 (d) 64

66.If 4/a + 4/a + 4/a + 4/a = 16 then, 4a is: (a) 4 (b) 8 (c) 12 (d) 16

67.The slope of line xa+yb=1\frac{x}{a} + \frac{y}{b} = 1ax​+by​=1 is: (a) −(ab)-\left(\frac{a}{b}\right)−(ba​) (b) −(ba)-\left(\frac{b}{a}\right)−(ab​) (c) ab (d) −(1ab)-\left(\frac{1}{ab}\right)−(ab1​)

68.If x = 4y, what percent of 2x is 2y? (a) 20% (b) 40% (c) 30% (d) 25%

69.If 3 bananas cost 50 cents, how many bananas can be bought for 20 dollars? (a) 120 (b) 115 (c) 110 (d) 130

70.If 5:7 = 15:x, then the value of x is: (a) 35 (b) 21 (c) 27 (d) 18

71.By selling 150 apples, the seller gains the selling price of 30 apples, then gain percentage is: (a) 25% (b) 30% (c) 12% (d) 20%

72.A vendor purchases lemons at Rs. 5/- per lemon, at what price vendor will sell lemon to gain 20% profit? (a) Rs. 4/- (b) Rs. 5/- (c) Rs. 6/- (d) Rs. 7/-

73.What is the population doubling time if population growth rate is 2% per annum? (a) 50yrs (b) 30yrs (c) 40yrs (d) none of these

74.If log⁡a81=4\log_a 81 = 4loga​81=4, then the value of 'a' is: (a) 4 (b) 3 (c) 5 (d) none of these

75.The value of 1872\frac{\sqrt{18}}{\sqrt{72}}72​18​​ is: (a) a rational number (b) an irrational number (c) an imaginary number (d) none of these

76.If 5/7 of a number is 1025, then 3/7 of number is: (a) 735 (b) 430 (c) 615 (d) 560

77.The number of seconds in 1131\frac{1}{3}131​ hours is: (a) 4800 (b) 4700 (c) 4900 (d) 5000

78.The 4m wide carpet is used for carpeting a room of 8m long and 3m wide, then what is the length of carpet? (a) 5m (b) 6m (c) 2m (d) 3m

79.Hari ranks seventh from the top and twenty sixth from the bottom in a class. Then the total number of students in a class are: (a) 36 (b) 35 (c) 31 (d) 32

If the relation $R=\{(1,2),(2,3),(3,4),(4,5)\}$ then its range is, (a) $\{2,3,4,5\}$ (b) $\{1,2,3,4\}$ (c) $\{1,2,3,5\}$ (d) $\{1,3,4,5\}$

The value of $2\sqrt{128}+\sqrt{162}$ is , (a) $25\sqrt2$ (b) $4\sqrt3$ (c) 0 (d) 60

If £ 7 = USD 11 and USD 2 = Rs. 213, then how many pound (£) can be exchange for Rs. 117150? (a) 750 (b) 650 (c) 700 (d) 850

A mobile is sold for Rs. 11000, with a profit of Rs. 1000, then the percentage profit is (a) 9% (b) 10% (c) 12% (d) 14%

The fifth term of the sequence $\frac12,\frac45,\frac78,\ldots$ is (a) $\frac{11}{12}$ (b) $\frac{12}{13}$ (c) $\frac{13}{14}$ (d) $\frac{14}{15}$

The sum of first five prime numbers is: (a) 11 (b) 18 (c) 26 (d) 28

The product of two consecutive even number is 224. Then the numbers are: (a) 16, 18 (b) 12, 14 (c) 14, 16 (d) 18, 20

If the ratio of two numbers is 2:3 and sum of these numbers is 30, then which are these numbers? (a) 14, 16 (b) 10, 20 (c) 12, 18 (d) 18, 12

If the cost of 9 kg sugar is Rs. 270/-, how much sugar can be purchased for Rs. 390/-? (a) 11 (b) 12 (c) 13 (d) 14

The cardinal number of a vowel set V = {a, e, i, o, u} is: (a) 4 (b) 5 (c) 6 (d) 7

What is the sum of first five prime numbers? (a) 18 (b) 25 (c) 26 (d) 28

If the product of two consecutive even number is 288, then what are these numbers from following? (a) 14, 12 (b) 14, 16 (c) 16, 18 (d) 22, 24

If the cost of 7 kg sugar is Rs. 210, how much sugar can be purchased for Rs. 330? (a) 11kg (b) 12kg (c) 13kg (d) 14kg

Two numbers are in the ratio of 6:7 and their sum is 117, then what are these numbers? (a) 56, 58 (b) 63, 54 (c) 54, 63 (d) 48, 56

What is the rate percentage per anum that a sum of money trebles itself in 25 years? (a) 2% (b) 4% (c) 6% (d) 8%

What is the cardinal number of a vowel set $V=\{a,e,i,o,u\}$ ? (a) 4 (b) 5 (c) 6 (d) 7

The area of 4 walls of square room is $120\,m^2$ . If the height is 5 m, then what is the area of its floor? (a) $26\,m^2$ (b) $56\,m^2$ (c) $25\,m^2$ (d) $36\,m^2$

Of a group of 120 students, 90 takes mathematics and 72 takes statistics. If 10 students neither of two, the number of student taking both subjects are: (a) 50 (b) 45 (c) 52 (d) 58

$-5<x<7$ can be written in the absolute value sign as: (a) $|x-1|<7$ (b) $|x-1|<6$ (c) $|x-1|<2$ (d) $|x-1|<-1$

How many stones each of area 0.16 cm square are required for paving a courtyard 5.5 m long and 4.8 m wide? (a) 60 (b) 100 (c) 50 (d) 165

The discount percent of marked price is Rs. 5,800 and discount amount is Rs. 696 then the discount percent is, (a) 12% (b) 20% (c) 5% (d) 38%

If 4 is subtracted from a square of a number, its result is 21. The number is, (a) 5 (b) 4 (c) 6 (d) 3

The area of 4 walls of square room is $120\,m^2$ . if the height is 5m, the area of its floor is (a) $56\,m^2$ (b) $36\,m^2$ (c) $46\,m^2$ (d) $26\,m^2$

The rate percentage per annum that a sum of money trebles itself in 25 years is : (a) 25 % (b) 10% (c) 4% (d) 8%

If 5 is subtracted from the square of a number and the result is 20, the number is : (a) $\pm5$ (b) $\pm6$ (c) $\pm7$ (d) $\pm9$

The Marked Price of an article is Rs. 8500. If a discount of 10% is allowed the selling price is (a) 7550 (b) 7650 (c) 7750 (d) 7850

Radius of cylinder is 7 cm height is 12 cm then it's volume is (a) $1848\,cm^3$ (b) $1748\,cm^3$ (c) $1648\,cm^3$ (d) $1548\,cm^3$

Single equation represented by two straight lines $x=2y$ and $2x=y$ is (a) $2x^2-3xy+2y^2=0$ (b) $x^2-3xy+2y^2=0$ (c) $2x^2-xy+2y^2=0$ (d) $2x^2-3xy+y^2=0$

Of a group of 120 students, 80 takes mathematics and 62 takes statistics. If 20 students neither if two, the number of students taking both subjects are (a) 50 (b) 42 (c) 52 (d) 55

$-5<x<9$ can be written in the absolute value sign as: (a) $|x-2|<5$ (b) $|x-2|<7$ (c) $|x-2|<9$ (d) $|x+2|<5$

How many stones each of area $22\,cm$ square are required for paving a courtyard 5.5 m long and 4 m wide? (a) 60000 (b) 40000 (c) 20000 (d) 10000

The discount of marked price is Rs. 5,800 the amount Rs. 696 then discount percent is. (a) 12% (b) 20% (c) 5% (d) 38%

Marked price of an article is Rs. 8500. If a discount of 10% is allowed the selling price is.... (a) 7550 (b) 7650 (c) 7750 (d) 7850

A single equation represented by two straight lines $x=2y$ and $2x=y$ is ... (a) $2x^2-3xy+y^2=0$ (b) $x^2-3xy+2y^2=0$ (c) $2x^2-xy+2y^2=0$ (d) $2x^2-5xy+2y^2=0$

Radius of the cylinder is 7 cm height is 3 cm then it's volume is (a) $442\,cm^3$ (b) $452\,cm^3$ (c) $462\,cm^3$ (d) $472\,cm^3$

Which one of the following number has a remainder of 4 when it is divided by 6? (a) 8 (b) 12 (c) 22 (d) 29

The sum of the product and quotient of 4 and 4 is ………. (a) 16 (b) 15 (c) 8 (d) 17

The average of all even numbers between -4 and 5 is ….. (a) 1 (b) 0.5 (c) -1 (d) none of these

The value of $\sum_{n=10}^{10} (-1)^n$ is: (a) 1 (b) -1 (c) 10 (d) 0

If 5 is added to the square of a number, then the result is 14. What is the value of that number? (a) 3 (b) 5 (c) 7 (d) 9

If three spoons equals to one glass, two glasses equals to one plate, then how many spoons equals to one plate? (a) 3 (b) 6 (c) 9 (d) 2

If a matrix is of order 5 X 7, then each column will contain …………..elements. (a) 5 (b) 12 (c) 35 (d) 7

If the equation are $3x + 4y = 7$ and $4x - y = 3$ after solving these equations the value of x and y will be: (a) 1,1 (b) 1,2 (c) 2,1 (d) 2,2

What is the value of x in series 1, 9, 25, x, 81, 121? (a) 100 (b) 36 (c) 49 (d) 64

If $a + b = c$ , then what is the average value of a, b and c? (a) $\frac{(a+b)}{3}$ (b) $\frac{c}{3}$ (c) $\frac{2c}{3}$ (d) $\frac{c}{3}$

If x in an integer and $y = -2x - 8$ , what is the least value of x for which y is less than 9? (a) -8 (b) -9 (c) -10 (d) -11

The slope of line which equation is $2x - 4y = 9$ is: (a) 2 (b) 1/2 (c) -1/2 (d) 3

What is the slope of horizontal line? (a) >1 (b) < 0 (c) 0 (d) 1

The difference between 3/5 of 80 and 30% of 80 is: (a) 20 (b) 14 (c) 15 (d) 24

Gautam spent Rs. 40/-, which is 5% of his daily wage, then his total daily wage is: (a) Rs.400/- (b) Rs.600/- (c) Rs.800/- (d) Rs. 1000/-

If 1254376 represents the CENTURY, then what represents 735? (a) NUT (b) RUT (c) RUN (d) YET

Find the missing value in $\begin{pmatrix} 2 & 7 & 6 \\ 9 & 5 & 1 \\ 4 & 3 & ? \end{pmatrix}$ . (a) 5 (b) 8 (c) 7 (d) 9

There are 48 students in a computer class. If number of boys are twice than girls, then how many girls are there? (a) 16 (b) 18 (c) 32 (d) 28

Find the number x, which is equal to (80% of x) plus 5. (a) 20 (b) 30 (c) 40 (d) 25

If the age of five girls are 15, 16, 17, 18, 19 respectively then what is the average age of girls? (a) 15 (b) 17 (c) 18 (d) 19

How many triangles in this figure? (a) 6 (b) 7 (c) 8 (d) 9

What is the value of cos 60° ? (a) 1 (b) $\frac{1}{2}$ (c) 0 (d) $\frac{\sqrt{3}}{2}$

Find the value of x in series 1, 1, 2, 3, 5, 8, 13, x. (a) 21 (b) 22 (c) 19 (d) 23

If 'n' is an integer, which of the following must be even? (a) n + 1 (b) n + 2 (c) 2n + 1 (d) 2n

The largest prime factor of 255 is: (a) 45 (b) 25 (c) 17 (d) 5

The sum of first n natural number is: (a) $\frac{n(n+1)}{2}$ (b) $\frac{n(n+1)(2n+1)}{2}$ (c) $\frac{(n+1)^2}{2}$ (d) none of these

The root of the equation $3x^2 - 8x + 16 = 0$ are (a) real & equal (b) real & unequal (c) imaginary & unequal (d) none of these

If x + y = 12 and x - y = 6 then, the value of $x^2 - y^2$ is: (a) 18 (b) 36 (c) 60 (d) 72

If x - 5 = 2, then the value of x + 12 is: (a) 15 (b) 17 (c) 19 (d) 18

The value when simplified $\frac{6^4 - 6^3}{5}$ is: (a) 1/5 (b) 63 (c) 6/5 (d) 64

If 4/a + 4/a + 4/a + 4/a = 16 then, 4a is: (a) 4 (b) 8 (c) 12 (d) 16

The slope of line $\frac{x}{a} + \frac{y}{b} = 1$ is: (a) $-\left(\frac{a}{b}\right)$ (b) $-\left(\frac{b}{a}\right)$ (c) ab (d) $-\left(\frac{1}{ab}\right)$

If x = 4y, what percent of 2x is 2y? (a) 20% (b) 40% (c) 30% (d) 25%

If 3 bananas cost 50 cents, how many bananas can be bought for 20 dollars? (a) 120 (b) 115 (c) 110 (d) 130

If 5:7 = 15:x, then the value of x is: (a) 35 (b) 21 (c) 27 (d) 18

By selling 150 apples, the seller gains the selling price of 30 apples, then gain percentage is: (a) 25% (b) 30% (c) 12% (d) 20%

A vendor purchases lemons at Rs. 5/- per lemon, at what price vendor will sell lemon to gain 20% profit? (a) Rs. 4/- (b) Rs. 5/- (c) Rs. 6/- (d) Rs. 7/-

What is the population doubling time if population growth rate is 2% per annum? (a) 50yrs (b) 30yrs (c) 40yrs (d) none of these

If $\log_a 81 = 4$ , then the value of 'a' is: (a) 4 (b) 3 (c) 5 (d) none of these

The value of $\frac{\sqrt{18}}{\sqrt{72}}$ is: (a) a rational number (b) an irrational number (c) an imaginary number (d) none of these

If 5/7 of a number is 1025, then 3/7 of number is: (a) 735 (b) 430 (c) 615 (d) 560

The number of seconds in $1\frac{1}{3}$ hours is: (a) 4800 (b) 4700 (c) 4900 (d) 5000

The 4m wide carpet is used for carpeting a room of 8m long and 3m wide, then what is the length of carpet? (a) 5m (b) 6m (c) 2m (d) 3m

Hari ranks seventh from the top and twenty sixth from the bottom in a class. Then the total number of students in a class are: (a) 36 (b) 35 (c) 31 (d) 32

If three girls write 3 pages in 3 minutes, in how many minutes can one girl write one page? (a) 4 min (b) 5 min (c) 3 min (d) 6 min