+2 college entrance (after SEE) +2 Management entrance: model and practice sets (English, Maths, GK/IQ, Nepali): Mathematics

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2019 Management Sample Test Set A · 1 mark
2082 · United Academy Management Model Set 2 · 1 mark

What is 10 % of 20 % of 30? (a) 0.006 (b) 0.6 (c) 6 (d) 60

Answer

(b) 0.6

$20\%\text{ of }30=6,\qquad 10\%\text{ of }6=0.6.$

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

If f(x) = (x+1)/(x−1), x ≠ 1, then f(f(x) )= (a) (x−1)/(x+1) (b) 1/x (c) x (d) none

Answer

(c) x

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

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

The quadratic equation having roots 2 and 3 is (a) x² − 5x + 6 (b) x² + 5x + 6 (c) x² + 5x – 6 (d) x² − 5x − 6

Answer

(a) $x^2-5x+6$

Sum of roots $=2+3=5$ and product $=2\times3=6$ , so the equation is $x^2-(\text{sum})x+\text{product}=x^2-5x+6=0$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

Orders of matrices A and B are m×n and n×p. Which of the following statements is not true? (a) AB is defined (b) BA is defined (c) order of AB is m×p (d) A + B is not defined

Answer

(b) BA is defined

$A$ is $m\times n$ and $B$ is $n\times p$ . $AB$ is defined and has order $m\times p$ . $BA$ needs the columns of $B$ ( $p$ ) to equal the rows of $A$ ( $m$ ), which is not guaranteed. $A+B$ needs equal orders, which is not the case in general. So the statement that is not true is (b).

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

Angle between the lines represented by x² − 2xy cotθ − y² = 0 is (a) 30° (b) 45° (c) 60° (d) 90°

Answer

(d) $90^\circ$

Comparing with $ax^2+2hxy+by^2=0$ : $a=1$ , $b=-1$ , $h=-\cot\theta$ . Since $a+b=0$ , the lines are perpendicular:

$\tan\phi=\frac{2\sqrt{h^2-ab}}{a+b}\to\infty\Rightarrow \phi=90^\circ$

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

Find the value of K in order that the point (K, 1), (5, 5) and (10, 7) may be collinear. (a) -3 (b) -4 (c) -6 (d) -5

Answer

(d) $-5$

Slope of the line through $(5,5)$ and $(10,7)$ is $\frac{7-5}{10-5}=\frac25$ . For collinearity, the slope from $(K,1)$ to $(5,5)$ must also be $\frac25$ :

$\frac{5-1}{5-K}=\frac25\Rightarrow 20=2(5-K)\Rightarrow 5-K=10\Rightarrow K=-5$

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

If 80% of the adult population of a village is registered to vote, and 60% of those registered actually voted in a particular election, what percent of the adults in the village did not vote in that election? (a) 40% (b) 48% (c) 50% (d) 52%

Answer

(d) 52%

Voters $=80\%\times60\%=48\%$ of adults. Did not vote $=100\%-48\%=52\%$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

If 3⁄4 of a number is 7 more than 1⁄6 of the number, what is the number? (a) 20 (b) 12 (c) 18 (d) 15

Answer

(b) 12

$\frac34x-\frac16x=7\Rightarrow\frac{9x-2x}{12}=7\Rightarrow 7x=84\Rightarrow x=12$

Check: $\frac34(12)=9$ and $\frac16(12)=2$ , and $9-2=7$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

A shopkeeper fixed the marked price of his television to make a profit of 40%. Allowing 20% discount on the marked price of the television was sold, what percent profit will be made? (a) 10% (b) 12% (c) 15% (d) 11%

Answer

(b) 12%

Let cost price $=$ Rs 100. Marked price $=$ Rs 140. Selling price after 20% discount $=0.8\times140=$ Rs 112. Profit $=112-100=$ Rs 12, which is 12%.

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

Value of x in x − 2 = √x is (a) 1 or 4 (b) 1 only (c) 4 only (d) none

Answer

(c) 4 only

Put $\sqrt x=t$ , so $t^2-2=t\Rightarrow t^2-t-2=0\Rightarrow(t-2)(t+1)=0$ . Since $t\ge0$ , $t=2$ and $x=4$ . Check: $4-2=2=\sqrt4$ . For $x=1$ : $1-2=-1\ne1$ , so it is extraneous.

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

There are 3 red, 2 blue and 5 white balls in a box. A ball is taken out randomly. What is the probability of a ball being blue or white? (a) 7/10 (b) 3/10 (c) 2/7 (d) 5/7

Answer

(a) $\dfrac{7}{10}$

Total balls $=3+2+5=10$ . Blue or white $=2+5=7$ , so $P=\dfrac{7}{10}$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

An ant moves 4.4cm per second. How long will it take to go round a circular dish of radius 21cm? (a) 30 sec (b) 45sec (c) 1minute (d) 3/2 minute

Answer

(a) 30 sec

Distance round the dish is the circumference: $2\pi r = 2\times\frac{22}{7}\times 21 = 132$ cm. Time $=\frac{132}{4.4}=30$ seconds.

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

Simplify 4√28 − √63 (a) 8√7 (b) 7√7 (c) 6√7 (d) 5√7

Answer

(d) $5\sqrt7$

$4\sqrt{28}=4\cdot2\sqrt7=8\sqrt7$ and $\sqrt{63}=3\sqrt7$ , so $8\sqrt7-3\sqrt7=5\sqrt7$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

Find the compound interest on Rs. 50,000 invested for 2 years at rate of 4% per annum (a) Rs. 4050 (b) Rs. 4080 (c) Rs. 4025 (d) Rs. 4045

Answer

(b) Rs. 4080

$A=50000\left(1+\frac{4}{100}\right)^2=50000\times1.0816=\text{Rs. }54080$

Compound interest $=54080-50000=$ Rs. 4080.

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

If the price of petrol oil increases by 25% by how much percent should a consumer reduce his consumption of petrol to maintain his previous expenditure? (a) 0% (b) 20% (c) 25% (d) 1%

Answer

(b) 20%

Let old price be 100 and consumption $C$ . New price is 125, so new consumption $=\frac{100C}{125}=0.8C$ . The reduction is $20\%$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

What is the relation between the central angle with the angle at the circumference standing on the same arc? (a) equal (b) double (c) three times (d) four times

Answer

(b) double

The angle at the centre is twice the angle at the circumference standing on the same arc.

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

Given that 176 dollars = £100 and £1 = Rs. 119. Find in dollars for Rs. 8925 (a) USD 122 (b) USD 132 (c) USD 134 (d) USD 140

Answer

(b) $132

Rs. 8925 $=\frac{8925}{119}=\pounds75$ . Then $\pounds75=\frac{176}{100}\times75=USD 132$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

$(x^p)(x^q)(x^r)=x^s$ . Find $s$ in terms of $p$ , $q$ & $r$ . (a) $r+p+q$ (b) $rpq$ (c) $r-q-p$ (d) none

Answer

(a) $r+p+q$

By the law of indices, $x^p\cdot x^q\cdot x^r=x^{p+q+r}$ , so $s=p+q+r$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

The two ends of a diameter are (-4,1) and (2,1). Find area of the circle (a) 3π (b) 9π (c) 6π (d) 36π

Answer

(b) $9\pi$

Centre $=\left(\frac{-4+2}{2},\frac{1+1}{2}\right)=(-1,1)$ . Diameter $=|2-(-4)|=6$ , so $r=3$ and area $=\pi r^2=9\pi$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

After paying an income tax of 5% a man has Rs. 7600 left. What is his income? (a) Rs.800 (b) Rs. 8000 (c) Rs.4000 (d) Rs.16000

Answer

(b) Rs. 8000

After tax he keeps $95\%$ of income: $0.95I=7600$ , so $I=\frac{7600}{0.95}=$ Rs. 8000.

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

If 5x + 13 = 31. Find √(5x + 31) (a) 7 (b) √173/5 (c) 15 (d) √13

Answer

(a) 7

$5x+13=31\Rightarrow5x=18$ . Then $5x+31=49$ and $\sqrt{49}=7$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

The price of 50 books is Rs. 4000. If the price is increased by 25%, what will be the price of 36 books? (a) 3500 (b) 2500 (c) 3600 (d) 4000

Answer

(c) 3600

Old price per book $=\frac{4000}{50}=$ Rs. 80. After a $25\%$ rise it is Rs. 100. Price of 36 books $=36\times100=$ Rs. 3600.

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

12p + 3q = 1 and 7q − 2p = 9. What is the average of p and q? (a) 0.1 (b) 1 (c) 0.5 (d) 2.5

Answer

(c) 0.5

Multiply $7q-2p=9$ by 6: $-12p+42q=54$ . Adding to $12p+3q=1$ gives $45q=55$ , so $q=\frac{11}{9}$ .

Then $12p=1-3q=1-\frac{11}{3}=-\frac83$ , so $p=-\frac29$ .

Average $=\frac{p+q}{2}=\frac{-2/9+11/9}{2}=\frac{1}{2}=0.5$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

If x − y = 5, and xy = 6. Find the value of x³ − y³ (a) 219 (b) 129 (c) 215 (d) 228

Answer

(c) 215

$x^3-y^3=(x-y)^3+3xy(x-y)=5^3+3(6)(5)=125+90=215$

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

If $ab+bc+ca=0$ , $x^a\cdot x^b\cdot x^c=$ ? (a) 1 (b) $x^{a+b+c}$ (c) 0 (d) $x$

Answer

(b) $x^{a+b+c}$

By the law of indices, $x^a\cdot x^b\cdot x^c=x^{a+b+c}$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

What percentage of 1 km 20m is 720m? (a) 71% (b) 70.58% (c) 70% (d) 85%

Answer

(b) 70.58%

$1\text{ km }20\text{ m}=1020$ m. Required percentage $=\frac{720}{1020}\times100\approx70.58\%$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

x(x − 3) = x, then x = (a) 0, −4 (b) 0, 4 (c) −4, 4 (d) 0, 3

Answer

(b) 0, 4

$x(x-3)=x\Rightarrow x^2-4x=0\Rightarrow x(x-4)=0$ , so $x=0$ or $x=4$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

ax + b² = a² + bx, then solve for x (a) a² − b² (b) a + b (c) a – b (d) 1

Answer

(b) $a+b$

$ax-bx=a^2-b^2\Rightarrow x(a-b)=(a-b)(a+b)$ , so $x=a+b$ (for $a\ne b$ ).

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

If the replacement set of the set of 5x − 1 ≤ 9 is {−2, −1, 0, 1, 2, 3, 4}. Find the solution (a) {−2, −1, 0} (b) {−2, −1, 0, 1} (c) {2} (d) {−2, −1, 0, 1, 2}

Answer

(d) $\{-2,-1,0,1,2\}$

$5x-1\le9\Rightarrow5x\le10\Rightarrow x\le2$ . Elements of the replacement set satisfying this are $-2,-1,0,1,2$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

The locus of the point whose abscissa and ordinate are always equal is (a) x + y = 0 (b) x − y = 0 (c) x + y = 1 (d) x − y = 1

Answer

(b) $x-y=0$

Abscissa $x$ equals ordinate $y$ , so $x=y$ , that is $x-y=0$ .

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2082 · United Academy Management Model Set 1 · 1 mark
2082 · United Academy Management Model Set 5 · 1 mark

The point of intersection of perpendicular bisectors of the sides of a triangle is known as (a) centre (b) incentre (c) orthocenter (d) circumcenter

Answer

(d) circumcenter

The perpendicular bisectors of the sides meet at the circumcentre, which is equidistant from the three vertices.

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2082 · United Academy Management Model Set 2 · 1 mark
2082 · United Academy Management Model Set 3 · 1 mark

If a-b=1, b-c=2 and c-a=d, what is the value of d (a) -3 (b) -1 (c) 1 (d) 3

Answer

(a) -3

Adding the three equations:

$(a-b)+(b-c)+(c-a)=0 \implies 1+2+d=0 \implies d=-3.$

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2082 · United Academy Management Model Set 2 · 1 mark
2082 · United Academy Management Model Set 3 · 1 mark

If f(x)=2x² -7 and g(x)=9x+2, then fog(x)= (a) 2(9x+2)² -7 (b) 9(2x² -7)+2 (c) 6x² -11 (d) None

Answer

(a) 2(9x+2)² -7

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

This is option (a) as written; it expands to $162x^2+72x+1$ , so it is not equal to option (c).

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2019 Management Sample Test Set A · 1 mark

What is the probability of getting 2 in a roll of a dice? (a) $\frac12$ (b) $\frac16$ (c) $\frac13$ (d) $\frac23$

Similar questions: What is the probability of getting a 2 or a 6 in (2018 Practice MCQs (Mathematics))

Answer

(b) $\frac16$

A die has 6 equally likely outcomes and only one of them is 2, so

$P(2)=\frac16$

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2019 Management Sample Test Set A · 1 mark

The area of square field is 144 m $^2$ then its perimeter is …… (a) 12 m (b) 48 m (c) 144 m (d) 150 m

Similar questions: The area of square field is 144m², then its peri (2018 Practice MCQs (Mathematics))

Answer

(b) 48 m

Side $=\sqrt{144}=12$ m, so perimeter $=4\times12=48$ m.

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2082 · United Academy Management Model Set 2 · 1 mark

If one type of rice costing Rs. 20 per kg and another type of rice costing Rs. 17 per kg are mixed in the ratio 1:2, what is the cost of the mixture per kg? (a) Rs. 17.50 (b) Rs. 18 (c) Rs. 18.50 (d) Rs. 19

Similar questions: If one type of rice costing Rs. 20 per kg and an (2082 · United Academy Management Model Set 3)

Answer

(b) Rs. 18

Cost per kg $=\dfrac{1\times20+2\times17}{1+2}=\dfrac{54}{3}=$ Rs. 18.

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2082 · United Academy Management Model Set 2 · 1 mark

If (4, y) divides the join of (6, -1) and (3, 2) in the ratio 2:1, then the value of y is: (a) 2 (b) 8 (c) 1 (d) 1⁄2

Similar questions: If (4, y) divides the join of (6, -1) and (3, 2) (2018 Practice MCQs (Mathematics))

Answer

(c) 1

Using the internal section formula with ratio $2:1$ from $(6,-1)$ to $(3,2)$ :

$y=\frac{2(2)+1(-1)}{2+1}=\frac{3}{3}=1$

Check: $x=\dfrac{2(3)+1(6)}{3}=4$ , which matches.

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2082 · United Academy Management Model Set 3 · 1 mark

If one type of rice costing Rs. 20 per kg and another type of rice costing Rs. 17 kg are mixed in the ratio 1:2, what is the cost of the mixture per kg? (a) Rs. 17.50 (b) Rs. 18 (c) Rs. 18.50 (d) Rs. 19

Similar questions: If one type of rice costing Rs. 20 per kg and an (2082 · United Academy Management Model Set 2)

Answer

(b) Rs. 18

$\text{Cost per kg}=\frac{1\times 20+2\times 17}{1+2}=\frac{54}{3}=\text{Rs. }18$

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2018 Practice MCQs (Mathematics) · 1 mark

The area of square field is 144m², then its perimeter is ... (a) 12m (b) 48m (c) 144m (d) 150m

Similar questions: The area of square field is 144 m^2 then its per (2019 Management Sample Test Set A)

Answer

(b) 48 m

Side $=\sqrt{144}=12$ m, so perimeter $=4\times12=48$ m.

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2018 Practice MCQs (Mathematics) · 1 mark

If (4, y) divides the join of (6, -1) and (3, 2) in the ratio of 2:1 then the value of y is: (a) 2 (b) 8 (c) 1 (d) 1/2

Similar questions: If (4, y) divides the join of (6, -1) and (3, 2) (2082 · United Academy Management Model Set 2)

Answer

(c) 1

Section formula for internal division in the ratio $2:1$ : $y=\frac{2(2)+1(-1)}{2+1}=\frac{3}{3}=1$ Check on $x$ : $\frac{2(3)+1(6)}{3}=4$ , which matches the given point.

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2018 Practice MCQs (Mathematics) · 1 mark

What is the probability of getting a 2 or a 6 in a roll of a dice? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6

Similar questions: What is the probability of getting 2 in a roll o (2019 Management Sample Test Set A)

Answer

(b) $\tfrac{1}{3}$

Favourable outcomes are $\{2,6\}$ out of $6$ equally likely outcomes: $P=\frac{2}{6}=\frac{1}{3}$

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2019 Management Sample Test Set A · 1 mark

If $2^{x+3}=32$ , then value of $3^{x+2}$ is …….. (a) 5 (b) 9 (c) 27 (d) 81

Answer

(d) 81

$2^{x+3}=32=2^5 \Rightarrow x+3=5 \Rightarrow x=2$

$3^{x+2}=3^{4}=81$

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2019 Management Sample Test Set A · 1 mark

If $y-\frac1y=3$ , then the value of $y^2+\frac1{y^2}$ is …… (a) 12 (b) 11 (c) 9 (d) 8

Answer

(b) 11

Square both sides of $y-\frac1y=3$ :

$y^2-2+\frac1{y^2}=9 \Rightarrow y^2+\frac1{y^2}=11$

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2019 Management Sample Test Set A · 1 mark

If $a=b^x$ , $b=c^y$ and $c=a^z$ then $xyz=$ …….. (a) 2 (b) 1 (c) 0 (d) abc

Answer

(b) 1

Substitute successively: $a=b^x=(c^y)^x=c^{xy}=(a^z)^{xy}=a^{xyz}$ .

So $a^1=a^{xyz}$ , hence $xyz=1$ .

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2019 Management Sample Test Set A · 1 mark

If $x+\frac1x=2$ , then $\sqrt x+\frac1{\sqrt x}$ is …… (a) 2 (b) $-2$ (c) $2/\sqrt3$ (d) $\sqrt2$

Answer

(a) 2

$x+\frac1x=2 \Rightarrow x^2-2x+1=0 \Rightarrow (x-1)^2=0 \Rightarrow x=1$

Then $\sqrt x+\frac1{\sqrt x}=1+1=2$ .

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2019 Management Sample Test Set A · 1 mark

The mode of the data 1, 2, 2, 3, 3, 3, 4, 5 is ………. (a) 1 (b) 2 (c) 3 (d) 4

Answer

(c) 3

The mode is the value that occurs most often. In 1, 2, 2, 3, 3, 3, 4, 5 the value 3 occurs three times, more than any other.

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2019 Management Sample Test Set A · 1 mark

If $2x=3y=4z$ then $x:y:z=$ ………. (a) 2 : 3 : 4 (b) 4 : 3 : 2 (c) 6 : 4 : 3 (d) 2 : 6 : 9

Answer

(c) 6 : 4 : 3

Let $2x=3y=4z=12k$ (12 is the LCM of 2, 3, 4). Then $x=6k$ , $y=4k$ , $z=3k$ , so $x:y:z=6:4:3$ .

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2019 Management Sample Test Set A · 1 mark

Which of the following is the equation of a circle? (a) $x^2+2xy+y^2=0$ (b) $x^2+2y^2=0$ (c) $2x^2+3y^2=4$ (d) $x^2+y^2=1$

Answer

(d) $x^2+y^2=1$

A circle has the form $x^2+y^2=r^2$ , with equal coefficients of $x^2$ and $y^2$ and no $xy$ term. Here $r=1$ . The other options are a pair of lines, a point, and an ellipse respectively.

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2019 Management Sample Test Set A · 1 mark

Which of the following is the area of equilateral triangle? (a) $\frac12 bh$ (b) $\frac12 ab\sin C$ (c) $\frac12 bc\sin A$ (d) $\frac{\sqrt3}{4}a^2$

Answer

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

For an equilateral triangle of side $a$ , the height is $\frac{\sqrt3}{2}a$ , so

$\text{Area}=\frac12\cdot a\cdot\frac{\sqrt3}{2}a=\frac{\sqrt3}{4}a^2$

The other options are general triangle formulas, not specific to the equilateral triangle.

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2019 Management Sample Test Set A · 1 mark

If circumference of a circle is $4\pi$ then its area is ………. (a) $\pi$ (b) $2\pi$ (c) $3\pi$ (d) $4\pi$

Answer

(d) $4\pi$

$2\pi r = 4\pi \Rightarrow r = 2$ , so area $= \pi r^2 = \pi(2)^2 = 4\pi$ .

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2019 Management Sample Test Set A · 1 mark

The volume of sphere is given by …….. (a) $4\pi R^2$ (b) $2\pi R^2$ (c) $4\pi R^3$ (d) $\frac43\pi R^3$

Answer

(d) $\frac43\pi R^3$

The volume of a sphere of radius $R$ is $\frac43\pi R^3$ . ( $4\pi R^2$ is its surface area.)

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2019 Management Sample Test Set A · 1 mark

Total surface area of right circular cylinder is ………….. (a) $2\pi rh$ (b) $2\pi r(r+h)$ (c) $\pi r^2$ (d) $\pi r^2h$

Answer

(b) $2\pi r(r+h)$

Total surface area = curved surface $2\pi rh$ + two circular ends $2\pi r^2$ $= 2\pi r(r+h)$ .

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2019 Management Sample Test Set A · 1 mark

If A = {1, 2, 3, 4}, then number of possible subsets are ……. (a) 8 (b) 6 (c) 16 (d) 9

Answer

(c) 16

A set with $n$ elements has $2^n$ subsets. Here $n=4$ , so $2^4 = 16$ .

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2019 Management Sample Test Set A · 1 mark

Which of the following is the symbol of null set? (a) {0} (b) {1} (c) {∅} (d) ∅

Answer

(d) $\varnothing$

The null (empty) set is written $\varnothing$ or $\{\ \}$ . $\{0\}$ and $\{\varnothing\}$ each contain one element, so they are not null.

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2019 Management Sample Test Set A · 1 mark

Which of the following is the irrational number? (a) $\frac{11}{15}$ (b) $\pi$ (c) $0.333\ldots$ (d) 4.5679

Answer

(b) $\pi$

$\pi = 3.14159\ldots$ is non-terminating and non-recurring, so it cannot be written as $\frac pq$ . The others are rational: $\frac{11}{15}$ is a fraction, $0.333\ldots=\frac13$ and $4.5679$ terminates.

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2019 Management Sample Test Set A · 1 mark

If A = {1, 2, 3, 4} & B = {2, 4, 6, 8} then A – B is …….. (a) {1, 2} (b) {2, 4} (c) {1, 3} (d) {1, 2, 3, 4}

Answer

(c) $\{1, 3\}$

$A-B$ contains the elements of $A$ that are not in $B$ . Since $2$ and $4$ are in $B$ , $A-B=\{1,3\}$ .

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2019 Management Sample Test Set A · 1 mark

The degree of polynomial $x^3+2xy+y^2$ is …….. (a) 1 (b) 2 (c) 3 (d) 4

Answer

(c) 3

The degree of a polynomial is the highest total power in any term: $x^3$ has degree $3$ , $2xy$ has degree $2$ , $y^2$ has degree $2$ . So the degree is $3$ .

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2019 Management Sample Test Set A · 1 mark

A boy is 3 years older than his sister. Two years ago, the sum of their ages was 19. How old is the boy now? (a) 13 years (b) 12 years (c) 11 years (d) 10 years

Answer

(a) 13 years

Let the boy be $b$ years old, so his sister is $b-3$ . Two years ago their ages were $b-2$ and $b-5$ :

$(b-2)+(b-5)=19 \Rightarrow 2b=26 \Rightarrow b=13.$

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2019 Management Sample Test Set A · 1 mark

Arithmetic mean of the data: 2, 5, 10, 12, 6 is (a) 7 (b) 10 (c) 12 (d) 11

Answer

(a) 7

$\text{Mean}=\frac{2+5+10+12+6}{5}=\frac{35}{5}=7.$

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2019 Management Sample Test Set A · 1 mark

Each angle of a regular polygon having number of sides 6 is ………. (a) $90^\circ$ (b) $120^\circ$ (c) $135^\circ$ (d) $60^\circ$

Answer

(b) $120^\circ$

Each interior angle of a regular $n$ -gon is $\frac{(n-2)\times180^\circ}{n}=\frac{4\times180^\circ}{6}=120^\circ$ .

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2019 Management Sample Test Set A · 1 mark

The sum of 1 + 2 + 3 + 4 + ……… + 100 is (a) 2000 (b) 5000 (c) 5500 (d) 5050

Answer

(d) 5050

$S_n=\frac{n(n+1)}{2}=\frac{100\times101}{2}=5050.$

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2019 Management Sample Test Set A · 1 mark

The median of the data: 8, 12, 35, 15, 10, 11, 14 is …….. (a) 4.5 (b) 12 (c) 13 (d) 14

Answer

(b) 12

Arrange in order: $8, 10, 11, 12, 14, 15, 35$ . There are $7$ values, so the median is the $\frac{7+1}{2}=4^{\text{th}}$ value, which is $12$ .

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2019 Management Sample Test Set A · 1 mark

Which of the following is a scalar matrix? (a) $\begin{bmatrix}2&0\\0&2\end{bmatrix}$ (b) $\begin{bmatrix}1&0\\0&1\end{bmatrix}$ (c) $\begin{bmatrix}3&0\\0&5\end{bmatrix}$ (d) $\begin{bmatrix}1&2\\3&4\end{bmatrix}$

Answer

(a) $\begin{bmatrix}2&0\\0&2\end{bmatrix}$

A scalar matrix is a diagonal matrix whose diagonal elements are all equal and non-zero, with all other elements zero. Option (c) has unequal diagonal entries and (d) is not diagonal. (The identity matrix in (b) is the special scalar matrix with scalar $1$ ; (a) is the general scalar matrix with scalar $2$ .)

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2019 Management Sample Test Set A · 1 mark

The order of a matrix $A=\begin{bmatrix}1&3&5\\2&0&4\end{bmatrix}$ is …… (a) $2\times2$ (b) $2\times3$ (c) $3\times2$ (d) $3\times3$

Answer

(b) $2\times3$

The matrix has $2$ rows and $3$ columns, so its order is $2\times3$ .

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2019 Management Sample Test Set A · 1 mark

The slope of the line $2x+3y+5=0$ is …….. (a) $\frac23$ (b) $\frac32$ (c) $-\frac23$ (d) $-\frac32$

Answer

(c) $-\frac23$

Rewrite as $y=-\frac23x-\frac53$ . For $ax+by+c=0$ the slope is $-\frac ab=-\frac23$ .

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2019 Management Sample Test Set A · 1 mark

What will be the next number in the sequence 1, 4, 7, 10, ……..? (a) 11 (b) 12 (c) 13 (d) 14

Similar questions: What will be the next number in the sequence 1, (2019 Management Sample Test Set A)

Answer

(c) 13

This is an arithmetic sequence with common difference $3$ , so the next term is $10+3=13$ .

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2019 Management Sample Test Set A · 1 mark

What will be the next number in the sequence 1, 2, 6, 22, ……….? (a) 58 (b) 85 (c) 86 (d) 87

Similar questions: What will be the next number in the sequence 1, (2019 Management Sample Test Set A)

Answer

(c) 86

The differences are $1, 4, 16$ , each $4$ times the previous. The next difference is $64$ , so the next term is $22+64=86$ .

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2019 Management Sample Test Set A · 1 mark

If $x=\begin{bmatrix}1&a\\0&1\end{bmatrix}$ and $3x-\begin{bmatrix}2&3\\0&2\end{bmatrix}=\begin{bmatrix}1&3\\0&1\end{bmatrix}$ , then value of $a$ is ……. (a) 0 (b) 2 (c) $-2$ (d) 3

Answer

(b) 2

$3x=\begin{bmatrix}1&3\\0&1\end{bmatrix}+\begin{bmatrix}2&3\\0&2\end{bmatrix}=\begin{bmatrix}3&6\\0&3\end{bmatrix}\Rightarrow x=\begin{bmatrix}1&2\\0&1\end{bmatrix}.$

Comparing with $x=\begin{bmatrix}1&a\\0&1\end{bmatrix}$ gives $a=2$ .

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2019 Management Sample Test Set A · 1 mark

Which of the following is the formula to find compound amount? (a) $P\left(1-\frac{R}{100}\right)^T$ (b) $P\left(1+\frac{R}{100}\right)^T$ (c) $P\left(1-\frac{R}{200}\right)^T$ (d) $P\left(1-\frac{R}{100}\right)^{2T}$

Answer

(b) $P\left(1+\frac{R}{100}\right)^T$

With principal $P$ , rate $R\%$ per year and time $T$ years (compounded yearly), the compound amount is $A=P\left(1+\frac{R}{100}\right)^T$ .

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2019 Management Sample Test Set A · 1 mark

If $p=q^r$ , $q=r^p$ and $r=p^q$ then $pqr=$ ………. (a) 1 (b) 2 (c) 3 (d) 4

Answer

(a) 1

The values $p=q=r=1$ satisfy all three equations: $1=1^1$ in each case. Indeed, if $p=1$ then $r=p^q=1$ , and then $q=r^p=1$ . Hence $pqr=1\times1\times1=1$ .

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2019 Management Sample Test Set A · 1 mark

What is the root of $x^2-36=0$ ? (a) 6 (b) $-6$ (c) $\pm6$ (d) 36

Answer

(c) $\pm6$

$x^2-36=0\Rightarrow x^2=36\Rightarrow x=\pm6.$

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2019 Management Sample Test Set A · 1 mark

The rate of interest at the rate of Re. 1 per Rs. 50 per month is ….. (a) 12 % (b) 6 % (c) 18 % (d) 24 %

Answer

(d) 24 %

Interest is Re. 1 on Rs 50 per month, i.e. $\frac{1}{50}\times100=2\%$ per month. Per year this is $2\times12=24\%$ .

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2019 Management Sample Test Set A · 1 mark

30 m long pole is broken at a height of 10 m then the angle made by the end of the pole to the ground is ….. (a) $60^\circ$ (b) $30^\circ$ (c) $45^\circ$ (d) $75^\circ$

Answer

(b) $30^\circ$

The pole breaks at $10$ m, so the broken part has length $30-10=20$ m and forms the hypotenuse. If $\theta$ is the angle with the ground:

$\sin\theta=\frac{10}{20}=\frac12\Rightarrow\theta=30^\circ.$

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2082 · United Academy Management Model Set 2 · 1 mark

The point (a,0), (0,b) and (1,1) are collinear if (a) a + b = ab (b) a − b = ab (c) b − a = ab (d) a + b + ab = 0

Answer

(a) a + b = ab

The line through $(a,0)$ and $(0,b)$ is $\dfrac{x}{a}+\dfrac{y}{b}=1$ . If $(1,1)$ lies on it, then

$\frac{1}{a}+\frac{1}{b}=1 \implies a+b=ab.$

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2082 · United Academy Management Model Set 2 · 1 mark

The area of circle centred at (1,2) and passing through (4,6) is (a) 5π (b) 25π (c) 10π (d) 15π

Answer

(b) 25π

The radius is the distance from $(1,2)$ to $(4,6)$ :

$r=\sqrt{(4-1)^2+(6-2)^2}=\sqrt{9+16}=5.$

Area $=\pi r^2=25\pi$ .

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2082 · United Academy Management Model Set 2 · 1 mark

Angle between the two lines x = 0 and y = 0 is (a) 45° (b) 90° (c) 180° (d) α

Answer

(b) 90°

The line $x=0$ is the y-axis and $y=0$ is the x-axis. They are perpendicular, so the angle between them is $90^\circ$ .

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2082 · United Academy Management Model Set 2 · 1 mark

The area of a triangle whose sides are along the lines x = 0, y = 0 and 4x + 5y = 20 is (a) 20 sq. unit (b) 10 sq. unit (c) 1/10 sq. unit (d) 1/20 sq. unit

Answer

(b) 10 sq. unit

The line $4x+5y=20$ is $\dfrac{x}{5}+\dfrac{y}{4}=1$ , so its intercepts are $5$ and $4$ . With the axes it forms a right triangle of area

$\tfrac12\times5\times4=10 \text{ sq. unit}.$

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2082 · United Academy Management Model Set 2 · 1 mark

The set of male student in United Universal school is (a) singleton set (b) empty set (c) super set (d) sub set

Answer

(d) sub set

All male students of the school are also students of the school, so the set of male students is contained in the set of all students. It is therefore a subset.

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2082 · United Academy Management Model Set 2 · 1 mark

The distance between the parallel lines 5x − 12y + 65 = 0 and 10x − 24y − 78 = 0 is (a) 2 (b) 8 (c) 16 (d) 0

Answer

(b) 8

Rewrite the second line by dividing by 2: $5x-12y-39=0$ . For $ax+by+c_1=0$ and $ax+by+c_2=0$ the distance is

$d=\frac{|c_1-c_2|}{\sqrt{a^2+b^2}}=\frac{|65-(-39)|}{\sqrt{25+144}}=\frac{104}{13}=8.$

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2082 · United Academy Management Model Set 2 · 1 mark

Ram sells 10 articles for the same money he paid for 12 articles. What is his gain percent? (a) 12% (b) 20% (c) 25% (d) 30%

Answer

(b) 20%

Let the cost of one article be Rs $c$ . Then the selling price of 10 articles is $12c$ , and their cost is $10c$ .

$\text{Gain \%}=\frac{12c-10c}{10c}\times100=20\%.$

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2082 · United Academy Management Model Set 2 · 1 mark

If x is 300 percent of 25 and y is 25 percent more than 40, the x is what percent of y? (a) 50% (b) 75% (c) 66.5% (d) 150%

Answer

(d) 150%

$x=3\times25=75$ and $y=40\times1.25=50$ . Then

$\frac{x}{y}\times100=\frac{75}{50}\times100=150\%.$

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2082 · United Academy Management Model Set 2 · 1 mark

The sum of two numbers is 16 and sum of their squares is 130. Find the numbers? (a) 9, 7 (b) 8, 8 (c) 10, 6 (d) 11, 5

Answer

(a) 9, 7

Let the numbers be $x,y$ with $x+y=16$ and $x^2+y^2=130$ . Then $2xy=(x+y)^2-(x^2+y^2)=256-130=126$ , so $xy=63$ . The numbers are roots of $t^2-16t+63=0$ , i.e. $(t-9)(t-7)=0$ , giving 9 and 7.

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2082 · United Academy Management Model Set 2 · 1 mark

If √2 sinθ = 1, which of the followings is not the value of θ? (a) 45° (b) 135° (c) 225° (d) 405°

Answer

(c) 225°

$\sqrt2\sin\theta=1$ gives $\sin\theta=\tfrac{1}{\sqrt2}$ , so $\theta=45^\circ,135^\circ$ (and $405^\circ=45^\circ+360^\circ$ ). At $225^\circ$ , $\sin 225^\circ=-\tfrac1{\sqrt2}$ , so it is not a solution.

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2082 · United Academy Management Model Set 2 · 1 mark

The population of a village was 7200. 5% of the population was migrated and 2% died due to different causes within a year. What would be the population of the village after a year? (a) 6669 (b) 6966 (c) 6696 (d) 9666

Answer

(c) 6696

Total decrease $=5\%+2\%=7\%$ , so the population is $93\%$ of 7200:

$7200\times0.93=6696$

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2082 · United Academy Management Model Set 2 · 1 mark

If x² – y² = 28 and x – y = 8, what is the average of x and y? (a) 1.75 (b) 3.5 (c) 7 (d) 8

Answer

(a) 1.75

$x^2-y^2=(x+y)(x-y)$ , so $x+y=\dfrac{28}{8}=3.5$ . Average $=\dfrac{x+y}{2}=1.75$ .

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2082 · United Academy Management Model Set 2 · 1 mark

0 < a < b < 1. If x = √(a + b) and y = √a + √b, then (a) x > y (b) x < y (c) x = y (d) none

Answer

(b) $x<y$

$x^2=a+b$ , while $y^2=a+b+2\sqrt{ab}$ . Since $a,b>0$ , $2\sqrt{ab}>0$ , so $y^2>x^2$ . Both are positive, hence $x<y$ .

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2082 · United Academy Management Model Set 2 · 1 mark

If sin θ +cosec θ = 2 then sin² θ+ cosec² θ is equal to (a) 1 (b) 4 (c) 2 (d) 9

Answer

(c) 2

For $\sin\theta>0$ , $\sin\theta+\dfrac1{\sin\theta}\ge2$ with equality only when $\sin\theta=1$ . So $\sin\theta=1$ , $\operatorname{cosec}\theta=1$ , and $\sin^2\theta+\operatorname{cosec}^2\theta=1+1=2$ .

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2082 · United Academy Management Model Set 2 · 1 mark

If the equation x² + 2(k+2)x + 9k = 0 has equal roots, then the value of k is (a) 1 (b) 2 (c) 3 (d) 0

Answer

(a) 1

For equal roots, $D=0$ : $[2(k+2)]^2-4(9k)=0$ , so $(k+2)^2=9k$ , i.e. $k^2-5k+4=0$ , giving $(k-1)(k-4)=0$ , $k=1$ or $4$ . Only $k=1$ is among the options.

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2082 · United Academy Management Model Set 2 · 1 mark

If $A\cap B=\emptyset$ , then: (a) $A\subset\overline B$ (b) $A\subset B$ (c) $B\subset A$ (d) $\overline B\subset\overline A$

Answer

(a) $A\subset\overline B$

If $A$ and $B$ have no common element, every element of $A$ lies outside $B$ , so $A\subset\overline B$ .

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2082 · United Academy Management Model Set 2 · 1 mark

The compound interest on a sum of money in 2 years at 5% p.a will be Rs. 120 more than the simple interest. Find the sum. (a) Rs. 40,000 (b) Rs. 45,000 (c) Rs. 48,000 (d) Rs. 50,000

Answer

(c) Rs. 48,000

For 2 years, $CI-SI=P\left(\dfrac{r}{100}\right)^2=P\times\dfrac{25}{10000}=\dfrac{P}{400}$ . Setting $\dfrac{P}{400}=120$ gives $P=$ Rs. 48,000.

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2082 · United Academy Management Model Set 2 · 1 mark

If the equation x² + (k + 2)x + 2k = 0 has equal roots, find k. (a) 1 (b) 2 (c) 3 (d) 4

Answer

(b) 2

Equal roots need $D=0$ : $(k+2)^2-8k=0$ , so $k^2-4k+4=0$ , i.e. $(k-2)^2=0$ , giving $k=2$ .

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2082 · United Academy Management Model Set 2 · 1 mark

Geometric mean between $a$ and $b$ is: (a) $ab$ (b) $\sqrt{ab}$ (c) $a^2b^2$ (d) None

Answer

(b) $\sqrt{ab}$

If $a,G,b$ are in G.P., then $G^2=ab$ , so $G=\sqrt{ab}$ .

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2082 · United Academy Management Model Set 2 · 1 mark

Sum of the squares of first 'n' natural numbers is: (a) n(n+1)(2n+1)/6 (b) n(n+1)(2n+1) (c) n(n²+1)/(n+1) (d) n/2 [2a+(n-1)d]

Answer

(a) $\dfrac{n(n+1)(2n+1)}{6}$

This is the standard formula: $1^2+2^2+\dots+n^2=\dfrac{n(n+1)(2n+1)}{6}$ .

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2082 · United Academy Management Model Set 2 · 1 mark

Two lines $y=m_1x+c_1$ and $y=m_2x+c_2$ will be co-incident if: (a) $m_1/m_2 : m_2 = 1$ (b) $m_1/m_2=c_1/c_2=1$ (c) $m_1/m_2=1$ (d) $m_1m_2=-1$

Answer

(b) $m_1/m_2=c_1/c_2=1$

Two lines are coincident when they have the same slope and the same intercept: $m_1=m_2$ and $c_1=c_2$ , i.e. $\dfrac{m_1}{m_2}=\dfrac{c_1}{c_2}=1$ .

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2082 · United Academy Management Model Set 2 · 1 mark

If 2x³ = 54, what is the value of 3x²? (a) 9 (b) 6 (c) 27 (d) 81

Answer

(c) 27

$2x^3=54$ gives $x^3=27$ , so $x=3$ . Then $3x^2=3\times9=27$ .

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2082 · United Academy Management Model Set 2 · 1 mark

The value of $\alpha^2\beta+\alpha\beta^2$ if $\alpha$ and $\beta$ are the roots of the equation $3x^2-2x-6=0$ . (a) $-5/2$ (b) $-4/3$ (c) $-7/2$ (d) $-9/2$

Answer

(b) $-4/3$

$\alpha^2\beta+\alpha\beta^2=\alpha\beta(\alpha+\beta)$ . For $3x^2-2x-6=0$ : $\alpha+\beta=\dfrac23$ , $\alpha\beta=-2$ . So the value is $-2\times\dfrac23=-\dfrac43$ .

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2082 · United Academy Management Model Set 2 · 1 mark

If A and B are mutually exclusive events, then: (a) P(A ∪ B) = P(A) + P(B) - P(A ∩ B) (b) P(A ∪ B) = P(A) + P(B) (c) P(A ∪ B) = P(A) × P(B/A) (d) None

Answer

(b) $P(A\cup B)=P(A)+P(B)$

Mutually exclusive events cannot occur together, so $P(A\cap B)=0$ and the general addition rule reduces to $P(A\cup B)=P(A)+P(B)$ .

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2082 · United Academy Management Model Set 2 · 1 mark

If a sum of money will be half much again as it is in 10 years the rate of interest is... (a) 5% (b) 10% (c) 15% (d) neither one

Answer

(a) 5%

"Half as much again" means the amount becomes $1.5$ times the principal, so interest $=0.5P$ in 10 years:

$r=\frac{I\times100}{P\,t}=\frac{0.5P\times100}{P\times10}=5\%$

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2082 · United Academy Management Model Set 3 · 1 mark

There would be a loss of 15% if a pen is sold for Rs.51. What should be selling price to gain 20%? (a) Rs.84 (b) Rs.80 (c) Rs.72 (d) Rs.60

Answer

(c) Rs.72 Selling at a 15% loss gives Rs.51, so the cost price is $CP=\frac{51}{0.85}=\text{Rs }60.$ For a 20% gain: $SP=60\times1.2=\text{Rs }72.$

Answer checked by Claude Sonnet · Oct 21, 2026

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2082 · United Academy Management Model Set 3 · 1 mark

A certain fraction becomes 2 when 7 is added to its numerator and 1 when 2 is subtracted from denominator. What is the fraction? (a) 4/5 (b) 3/5 (c) 4/7 (d) 3/7

Answer

(b) 3/5 Let the fraction be $\frac{n}{d}$ . Then $n+7=2d$ and $n=d-2$ . Substituting, $d-2+7=2d$ , so $d=5$ and $n=3$ . Check: $\frac{3+7}{5}=2$ and $\frac{3}{5-2}=1$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2082 · United Academy Management Model Set 3 · 1 mark

If a, b, c are three mutually perpendicular unit vectors, then |a + b + c| is equal to: (a) 1 (b) 3 (c) 2√3 (d) √3

Answer

(d) $\sqrt{3}$ For perpendicular unit vectors, $a\cdot a=1$ and $a\cdot b=0$ etc. So $|a+b+c|^2=1+1+1+0=3,$ giving $|a+b+c|=\sqrt{3}$ .

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2082 · United Academy Management Model Set 3 · 1 mark

If two circles touch, the point of contact lies on a: (a) circle (b) square (c) parallelogram (d) None

Answer

(d) None When two circles touch, the point of contact lies on the straight line joining their centres, not on a circle, square or parallelogram.

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2082 · United Academy Management Model Set 3 · 1 mark

A sum of money is divided between Mary and David in the ratio 5:8. If Mary's share is Rs. 225, then the total amount of money will be: (a) 300 (b) 400 (c) 585 (d) None

Answer

(c) 585 Mary's 5 parts are Rs.225, so one part is Rs.45. The total is $13\times45=585$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2082 · United Academy Management Model Set 3 · 1 mark

A dealer gains the selling price of 10 radio sets by selling 6 sets. His percentage profit will be (a) 10% (b) 15% (c) 20% (d) None

Answer

(d) None As worded, the profit cannot be a positive percentage. The standard problem is a gain equal to the selling price of 6 sets on selling 10 sets. Taking SP per set as 1: SP of 10 sets = 10, profit = 6, so CP = 4 and $\text{profit}\%=\frac{6}{4}\times100=150\%,$ which matches none of the given options.

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2082 · United Academy Management Model Set 3 · 1 mark

A father is 2 times as old as his son. 16 years ago the age of the father was three times the age of the son what is the present age of the father? (a) 64 years (b) 10 years (c) 80 years (d) None

Answer

(a) 64 years Let the son be $x$ years and the father $2x$ . Sixteen years ago, $2x-16=3(x-16)$ , so $2x-16=3x-48$ , giving $x=32$ . The father is $2\times32=64$ years old.

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2082 · United Academy Management Model Set 3 · 1 mark

The cost of carpeting a room at Rs. 50 per square meter is Rs. 1000. Find the breath of the room, if it's length is 5 m. (a) 2 m (b) 3 m (c) 2.5 m (d) 4 m

Answer

(d) 4 m Area of carpet $=\frac{1000}{50}=20\ \text{m}^2$ . So $b=\frac{20}{5}=4\ \text{m}.$

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2082 · United Academy Management Model Set 3 · 1 mark

The market price of a watch is Rs. 640. What is the selling price if a discount of 15% is allowed? (a) Rs. 736 (b) Rs. 544 (c) Rs. 625 (d) Rs. 525

Answer

(b) Rs. 544 $SP=640\times\left(1-\frac{15}{100}\right)=640\times0.85=\text{Rs }544.$

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2082 · United Academy Management Model Set 3 · 1 mark

The angle of elevation of the top of a tree at a point 15 m from the tree is 30°. Find the foot of the tree (a) 8.25 m (b) 8.66 m (c) 9.2 m (d) 9.6 m

Answer

(b) 8.66 m Height of the tree: $\tan30^\circ=\frac{h}{15}$ , so $h=15\times\frac{1}{\sqrt3}=5\sqrt3\approx8.66\ \text{m}.$

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2082 · United Academy Management Model Set 3 · 1 mark

A garden is 25.50m wide and 35 m long. What is its perimeter? (a) 892.5 m (b) 121 m (c) 105m (d) 70 m

Answer

(b) 121 m $P=2(l+b)=2(35+25.5)=2\times60.5=121\ \text{m}.$

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2082 · United Academy Management Model Set 3 · 1 mark

A quadrilateral with all sides equal is: (a) parallelogram (b) square (c) rectangle (d) rhombus

Answer

(d) rhombus

A rhombus is the quadrilateral whose four sides are all equal. A square also has equal sides, but it additionally has four right angles, so "all sides equal" alone describes the rhombus in general.

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2082 · United Academy Management Model Set 3 · 1 mark

What is the probability of drawing a heart or an ace from a deck of 52 cards? (a) 26/52 (b) 4/13 (c) 1/52 (d) 2/13

Answer

(b) 4/13

There are 13 hearts and 4 aces, and the ace of hearts is counted twice, so favourable cases are $13+4-1=16$ .

$P=\frac{16}{52}=\frac{4}{13}$

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2082 · United Academy Management Model Set 3 · 1 mark

Unit matrix is not (a) Scalar matrix (b) Diagonal matrix (c) Square matrix (d) Null matrix

Answer

(d) Null matrix

A unit (identity) matrix is a square, diagonal and scalar matrix, since its diagonal entries are all equal to 1 and the rest are 0. It has non-zero entries, so it is not a null matrix.

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2082 · United Academy Management Model Set 3 · 1 mark

If A and B are square matrices of the same order, which of the following statements may not be true? (a) AB is defined (b) BA is defined (c) Order of AB and BA are same (d) AB = BA

Answer

(d) $AB = BA$

For square matrices of the same order, both $AB$ and $BA$ are defined and have the same order, but matrix multiplication is not commutative in general, so $AB=BA$ may not hold.

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2082 · United Academy Management Model Set 3 · 1 mark

If the point (x,2) is equidistant from (8,-2) and (2,-2), find the value of x. (a) 3 (b) 4 (c) 5 (d) 6

Answer

(c) 5

Equidistance gives:

$(x-8)^2+(2+2)^2=(x-2)^2+(2+2)^2$ $x^2-16x+64=x^2-4x+4\Rightarrow -12x=-60\Rightarrow x=5$

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2082 · United Academy Management Model Set 3 · 1 mark

If the range and co-domain of a function are equal, then the function is called (a) onto (b) one-to one (c) into (d) None

Answer

(a) onto

When the range equals the co-domain, every element of the co-domain has a pre-image, which is the definition of an onto (surjective) function.

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2082 · United Academy Management Model Set 3 · 1 mark

If 120% of 'a' is equal to 80% of 'b', which of the following is equal to a+b? (a) 1.5a (b) 2a (c) 2.5a (d) 3a

Answer

(c) 2.5a

$1.2a=0.8b\Rightarrow b=1.5a$ $a+b=a+1.5a=2.5a$

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2082 · United Academy Management Model Set 3 · 1 mark

From 1980 to 1990, Michael's weight increased by 25%. If his weight was 80 kilograms in 1990. What was it in 1980? (a) 1.75W (b) 1.25 W (c) 1.20W (d) 0.80 W

Answer

(b) 1.25 W

Let $W$ be his weight in 1980. A 25% increase gives the 1990 weight $=W+0.25W=1.25W$ . Since this is 80 kg, $W=80/1.25=64$ kg.

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2082 · United Academy Management Model Set 3 · 1 mark

The average of 10 numbers is -10. If the sum of six of them is 100, what is the average of the other four? (a) -100 (b) -50 (c) 0 (d) 50

Answer

(b) $-50$

$\text{Total}=10\times(-10)=-100$ $\text{Sum of other four}=-100-100=-200$ $\text{Average}=\frac{-200}{4}=-50$

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2082 · United Academy Management Model Set 3 · 1 mark

What is the largest prime factor of 255? (a) 5 (b) 15 (c) 17 (d) 51

Answer

(c) 17

$255=3\times 5\times 17$

The prime factors are 3, 5 and 17, so the largest is 17.

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2082 · United Academy Management Model Set 3 · 1 mark

Father is 5 times the son. In 5 years time he will be thrice as much as his son. Find the son age (a) 6 (b) 5 (c) 8 (d) 10

Answer

(b) 5

Let the son be $x$ years old, so the father is $5x$ . After 5 years:

$5x+5=3(x+5)\Rightarrow 2x=10\Rightarrow x=5$

Check: father 25, son 5; after 5 years 30 and 10, and $30=3\times10$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2082 · United Academy Management Model Set 3 · 1 mark

When an article is sold for Rs. 2,000 there is a loss of 10%. To earn a gain of 10% the article must be sold for (a) Rs. 2444.44 (b) Rs. 2420 (c) Rs. 300 (d) Rs. 60

Answer

(a) Rs. 2444.44

At a 10% loss, $SP=0.9\,CP=2000$ , so

$CP=\frac{2000}{0.9}=\text{Rs. }2222.22$

For a 10% gain:

$SP=1.1\times 2222.22=\text{Rs. }2444.44$

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2082 · United Academy Management Model Set 3 · 1 mark

The simple interest on Rs. 600 at 6% for six month is (a) Rs. 218 (b) Rs. 21.80 (c) Rs. 35 (d) Rs. 18

Answer

(d) Rs. 18

$I=\frac{PTR}{100}=\frac{600\times 0.5\times 6}{100}=\text{Rs. }18$

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2082 · United Academy Management Model Set 3 · 1 mark

In sum of Rs. 5000 became Rs. 6000 in 3 years at a certain te of compound interest, what will the sum be in 6 years (a) Rs. 7200 (b) Rs.1100 (c) Rs. 7000 (d) Rs. 6600

Answer

(a) Rs. 7200

Over 3 years the sum grows by the factor $6000/5000=1.2$ . In 6 years (two such periods) the factor is $1.2^2=1.44$ .

$5000\times 1.44=\text{Rs. }7200$

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2082 · United Academy Management Model Set 3 · 1 mark

Salary was first increased by 10% and then decreased by 10%. What is the total percentage change in salary? (a) 2.2% (b) 1.5% (c) 1% (d) 3%

Answer

(c) 1% (a decrease)

Take the salary as 100. After a 10% increase it is 110; after a 10% decrease it is $110\times0.9=99$ . The net change is $-1$ , i.e. a 1% decrease.

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2082 · United Academy Management Model Set 4 · 1 mark

$\sin3A=\frac{\sqrt3}{2}$ , the value of $\sin3A$ is (a) $\frac12$ (b) 0 (c) 1 (d) $\frac{\sqrt3}2$

Answer

(d) $\frac{\sqrt3}{2}$ The question states $\sin 3A=\frac{\sqrt3}{2}$ , so that is its value.

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2082 · United Academy Management Model Set 4 · 1 mark

$\tan\theta=\cot\theta$ when the value of $\theta$ is (a) 0° (b) 30° (c) 45° (d) 90°

Answer

(c) 45° $\tan\theta=\cot\theta \Rightarrow \tan^2\theta=1 \Rightarrow \tan\theta=1$ , so $\theta=45^\circ$ .

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2082 · United Academy Management Model Set 4 · 1 mark

The value of $\vec a\cdot\vec b$ when $\vec a=\begin{pmatrix}3\\2\end{pmatrix}$ , $\vec b=\begin{pmatrix}-2\\3\end{pmatrix}$ is (a) 0 (b) 12 (c) -12 (d) 10

Answer

(a) 0 $\vec a\cdot\vec b=(3)(-2)+(2)(3)=-6+6=0$

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2082 · United Academy Management Model Set 4 · 1 mark

When Standard Deviation = 10, mean = 40, then the coefficient of variation is (a) 40% (b) 25% (c) 50% (d) 100%

Answer

(b) 25% $CV=\frac{\sigma}{\bar x}\times100=\frac{10}{40}\times100=25\%$

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2082 · United Academy Management Model Set 4 · 1 mark

If f (x) = 2x and g (x) = 3x + 2, the value of fog (1) is (a) 20 (b) 15 (c) 5 (d) 10

Answer

(d) 10 $g(1)=3(1)+2=5$ , then $fog(1)=f(5)=2\times5=10$ .

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2082 · United Academy Management Model Set 4 · 1 mark

The sum of two numbers is 40 and difference is 10. Find the ratio of two numbers. (a) 5:4 (b) 5:3 (c) 3:2 (d) 2:5

Answer

(b) 5:3 Let the numbers be $x$ and $y$ : $x+y=40$ , $x-y=10$ , so $x=25$ , $y=15$ . $x:y=25:15=5:3$

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2082 · United Academy Management Model Set 4 · 1 mark

Matrix $\begin{pmatrix}-1&0\\0&1\end{pmatrix}$ is associated with (a) reflection of x = y (b) reflection on x – axis (c) reflection on line x = 0 (d) reflection on y = 1

Answer

(c) reflection on line $x=0$ The matrix sends $(x,y)\to(-x,y)$ , which reflects points in the $y$ -axis, i.e. the line $x=0$ .

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2082 · United Academy Management Model Set 4 · 1 mark

Slope of line $px+qy+c=0$ is (a) $\frac pq$ (b) $\frac qp$ (c) $-\frac pq$ (d) $-\frac qp$

Answer

(c) $-\frac pq$ Writing $qy=-px-c$ gives $y=-\frac pq x-\frac cq$ , so the slope is $-\frac pq$ .

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2082 · United Academy Management Model Set 4 · 1 mark

If the third term of A.P. is 3, sum of first five terms is (a) 8 (b) 12 (c) 15 (d) 18

Answer

(c) 15 For an A.P., $S_5=\frac52(a_1+a_5)=5a_3=5\times3=15$ .

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2082 · United Academy Management Model Set 4 · 1 mark

If $\cos A=\frac12$ and $\cos B=\frac{\sqrt3}2$ , the value of $\cos(A+B)$ is (a) 0 (b) 1 (c) $\frac1{\sqrt2}$ (d) -1

Answer

(a) 0 $A=60^\circ$ and $B=30^\circ$ , so $\cos(A+B)=\cos90^\circ=0$ . Check: $\cos A\cos B-\sin A\sin B=\frac12\cdot\frac{\sqrt3}{2}-\frac{\sqrt3}{2}\cdot\frac12=0$ .

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2082 · United Academy Management Model Set 4 · 1 mark

If n (A) = 11, n (B) = 20, what is the possible maximum value of n (A ∩ B)? (a) 0 (b) 11 (c) 18 (d) 29

Answer

(b) 11 $A\cap B\subseteq A$ , so $n(A\cap B)\le \min(11,20)=11$ , attained when $A\subseteq B$ .

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2082 · United Academy Management Model Set 4 · 1 mark

The interest compounded semi-annually on Rs. P for T years at R% p.a. is (a) $P\left[\left(1+\frac R{100}\right)^T-1\right]$ (b) $P\left[\left(1+\frac R{200}\right)^{2T}-1\right]$ (c) $P\left[\left(1+\frac R{200}\right)^T-1\right]$ (d) $P\left[\left(1+\frac R{100}\right)^{2T}-1\right]$

Answer

(b) $P\left[\left(1+\frac R{200}\right)^{2T}-1\right]$ Semi-annually the rate per period is $\frac R2\%$ and there are $2T$ periods, so amount $=P\left(1+\frac R{200}\right)^{2T}$ ; interest is amount minus $P$ .

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2082 · United Academy Management Model Set 4 · 1 mark

Ganesh bought a mobile for Rs. 40,000 last year but this year its value has been depreciated to Rs. 37,600. What is the rate of depreciation? (a) 5% (b) 6% (c) 7% (d) 10%

Answer

(b) 6% Depreciation $=40000-37600=\text{Rs }2400$ . $\text{Rate}=\frac{2400}{40000}\times100=6\%$

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2082 · United Academy Management Model Set 4 · 1 mark

The exchange rate of 1 Euro is NPR 130.40. What will be the new rate if the Nepali currency is devaluated by 5% in comparison to Euro? (a) NPR 123.88 (b) NPR 117.36 (c) NPR 143.44 (d) NPR 136.92

Answer

(d) NPR 136.92 Devaluation of the rupee means more NPR per Euro: $130.40\times1.05=136.92$

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2082 · United Academy Management Model Set 4 · 1 mark

The relationship among the radius a, height h and slant height l in a cone is? (a) a² + h² = l² (b) a² - h² = l² (c) h² - a² = l² (d) l² + a² = h²

Answer

(a) $a^2+h^2=l^2$ The radius, height and slant height form a right-angled triangle with $l$ as hypotenuse.

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2082 · United Academy Management Model Set 4 · 1 mark

The last mean or nth mean ( $g_n$ ) of a G.P. is given by (a) $ar^n$ (b) $br$ (c) $ar^{n-1}$ (d) Both (a) and (b)

Answer

(a) $ar^n$

If $n$ geometric means are inserted between $a$ and $b$ , then $b=ar^{n+1}$ , so the last mean is $g_n=ar^n=\frac{b}{r}$ .

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2082 · United Academy Management Model Set 4 · 1 mark

In a two digit number, the sum of digits is 5 & the product of the digits is 6, the number is (a) 56 (b) 32 (c) 23 (d) Both (b) and (c)

Answer

(d) Both (b) and (c)

Digits with sum 5 and product 6 are 2 and 3 ( $2+3=5$ , $2\times3=6$ ), so the number is 23 or 32.

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2082 · United Academy Management Model Set 4 · 1 mark

What value of x makes the expression $\frac{x^2-4}{x^2-8x+12}$ undefined? (a) 2 (b) 6 (c) 4, 6 (d) 2, 6

Answer

(d) 2, 6

The expression is undefined where the denominator is zero: $x^2-8x+12=(x-2)(x-6)=0$ , so $x=2$ or $x=6$ .

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2082 · United Academy Management Model Set 4 · 1 mark

The length of sides of a triangle are $\frac2x$ , $\frac3{2x}$ & $\frac1{x+1}$ . The perimeter of the triangle is (a) $\frac{7x+9}{2x(x+1)}$ (b) $\frac{7x+10}{2x(x+1)}$ (c) $\frac{9x+7}{2x(x+1)}$ (d) $\frac{9x+5}{2x(x+1)}$

Answer

(c) $\frac{9x+7}{2x(x+1)}$

$P=\frac2x+\frac3{2x}+\frac1{x+1}=\frac{7}{2x}+\frac1{x+1}=\frac{7(x+1)+2x}{2x(x+1)}=\frac{9x+7}{2x(x+1)}$

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2082 · United Academy Management Model Set 4 · 1 mark

For what value of $y$ the equation $6^{y-2}$ equals to 1? (a) 0 (b) 1 (c) 1/2 (d) 1/3

Answer

$y=2$ , which is not among the listed options.

$6^{y-2}=1=6^0$ , so $y-2=0$ and $y=2$ .

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2082 · United Academy Management Model Set 4 · 1 mark

Which of the following values of $x$ satisfy the equation $2^{x+1}+2^x=24$ ? (a) 1 (b) 2 (c) 3 (d) 4

Answer

(c) 3

$2^{x+1}+2^x=2^x(2+1)=3\cdot2^x=24$ , so $2^x=8=2^3$ and $x=3$ .

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2082 · United Academy Management Model Set 4 · 1 mark

∆ABC & ∆BCD lying between the lines AD & BC have equal area, the relation between AD & BC is (a) AD = BC (b) AD II BC (c) AD ⊥ BC (d) AD ≤ BC

Answer

(b) AD II BC

Triangles on the same base BC with equal areas have equal heights, so A and D are at the same distance from BC. Hence AD is parallel to BC.

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2082 · United Academy Management Model Set 4 · 1 mark

The degree measure of an angle at the centre of a circle is _________ the degree measures of its opposites arc (a) equal to (b) half of (c) less than (d) greater than

Answer

(a) equal to

The central angle subtends an arc whose degree measure is equal to the angle itself.

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2082 · United Academy Management Model Set 4 · 1 mark

The average which divides the arranged data into two equal parts is (a) mean (b) median (c) mode (d) first quartile

Answer

(b) median

The median is the middle value, which divides the arranged data into two equal halves.

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2082 · United Academy Management Model Set 4 · 1 mark

The first quartile divides the data in the ratio of (a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 2 : 3

Answer

(b) 1 : 3

$Q_1$ has 25% of the data below it and 75% above, so it divides the data in the ratio 1 : 3.

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2082 · United Academy Management Model Set 4 · 1 mark

The empirical relationship between mean, median & mode is: (a) Mean > Median > Mode (b) Mean = Median = Mode (c) Mode = 3 Median - 2 Mean (d) Mode = 3 Mean - 2 Median

Answer

(c) Mode = 3 Median - 2 Mean

This is the empirical (Pearson) relation for moderately skewed distributions.

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2082 · United Academy Management Model Set 4 · 1 mark

The probability scale of any event E is (a) 0 < P (E) < 1 (b) 1 < P (E) < 0 (c) 0 ≤ P (E) ≤ 1 (d) 1 ≤ P (E) ≤ 0

Answer

(c) $0 \le P(E) \le 1$

Probability is 0 for an impossible event and 1 for a certain event, so both end values are allowed.

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2082 · United Academy Management Model Set 4 · 1 mark

For any event E, P (E′) is equal to (a) - P (E) (b) 1 - P (E) (c) P (E) - 1 (d) P (E)

Answer

(b) $1 - P(E)$

An event and its complement are exhaustive and mutually exclusive, so $P(E)+P(E')=1$ .

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2082 · United Academy Management Model Set 4 · 1 mark

What is the altitude of the sun when the length of shadow of a vertical pole is equal to its height? (a) 30° (b) 45° (c) 60° (d) None of above

Answer

(b) 45°

If shadow length equals height, then $\tan\theta=\frac{\text{height}}{\text{shadow}}=1$ , so $\theta=45^\circ$ .

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2082 · United Academy Management Model Set 4 · 1 mark

A tree 18 m high is broken by the wind. So, its top touches the ground. If the length of broken part of the tree is 12 m, the angle made by the top of the tree with the ground is (a) 45° (b) 30° (c) 60° (d) 75°

Answer

(b) 30°

The tree breaks 6 m above the ground (18 - 12 = 6 m remains standing), and the broken part of 12 m is the hypotenuse. Then $\sin\theta=\frac{6}{12}=\frac12$ , so $\theta=30^\circ$ .

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2018 Practice MCQs (Mathematics) · 1 mark

Let A = {1, 2, 3}, the possible numbers of non-empty proper subset for the set A is ..... (a) 8 (b) 7 (c) 6 (d) 9

Answer

(c) 6

A set with $n$ elements has $2^n$ subsets. Non-empty proper subsets exclude the empty set and the set itself, so the number is $2^n-2$ .

$2^3-2=8-2=6$

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2018 Practice MCQs (Mathematics) · 1 mark

Which one of the following is the multiplicative inverse of -a? (a) -1/a (b) a (c) 1 (d) 1/a

Answer

(a) $-1/a$

The multiplicative inverse of $x$ is $1/x$ . For $x=-a$ it is $\dfrac{1}{-a}=-\dfrac{1}{a}$ , since $(-a)\left(-\dfrac1a\right)=1$ .

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2018 Practice MCQs (Mathematics) · 1 mark

If A = (-2, 3] and B = (0, 5) then B – A = ..... (a) (0, 5) (b) (3, 5) (c) [3, 5) (d) None

Answer

(b) (3, 5)

$B-A$ contains the elements of $B=(0,5)$ that are not in $A=(-2,3]$ . Removing $(0,3]$ from $(0,5)$ leaves $(3,5)$ .

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2018 Practice MCQs (Mathematics) · 1 mark

Let A and B are any two sets such that n(A) = 3, n(B) = 4, then the number of all possible relations from set A to B is ....... (a) 12 (b) 64 (c) 81 (d) 63

Answer

None of the options is correct. The correct number is $4096$ .

A relation from $A$ to $B$ is any subset of $A\times B$ . Since $n(A\times B)=3\times4=12$ , the number of relations is

$2^{12}=4096.$

The option 12 is only $n(A\times B)$ , not the number of relations.

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2018 Practice MCQs (Mathematics) · 1 mark

If R = {(3, 2), (4, 2), (3, 1), (7, 1), (2, 3)} is to be a function. Then which one of the following must be removed from the set? (a) (3, 2) (b) (4, 2) (c) (2, 3) (d) (7, 1)

Answer

(a) (3, 2)

In a function each first element has exactly one image. Here $3$ has two images, $2$ and $1$ , from $(3,2)$ and $(3,1)$ . Removing $(3,2)$ leaves $\{(4,2),(3,1),(7,1),(2,3)\}$ , in which every first element appears once.

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2018 Practice MCQs (Mathematics) · 1 mark

If p(x) = 4x – 6 and p(a) = 0, then a = ....... (a) 3/2 (b) –6 (c) 2/3 (d) -3/2

Answer

(a) 3/2

$p(a)=4a-6=0\Rightarrow a=\frac{6}{4}=\frac32.$

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2018 Practice MCQs (Mathematics) · 1 mark

If g(x) = 3x + 2 and g(f(x)) = x, then f(2) = ........... (a) 6 (b) 3 (c) –1 (d) 0

Answer

(d) 0

$g(f(x))=3f(x)+2=x$ , so $f(x)=\dfrac{x-2}{3}$ . Then

$f(2)=\frac{2-2}{3}=0.$

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2018 Practice MCQs (Mathematics) · 1 mark

If a motor car is driven at the rate of 66km/hr. Each of its wheel makes 500 revolution per minute. What is the radius of wheel? (a) 0.35m (b) 0.67m (c) 0.7m (d) 0.87m

Answer

(a) 0.35 m

Speed $=66$ km/hr $=\dfrac{66000}{60}=1100$ m/min. With 500 revolutions per minute, the distance per revolution is $\dfrac{1100}{500}=2.2$ m, which is the circumference.

$2\pi r=2.2\Rightarrow r=\frac{2.2\times7}{2\times22}=0.35\text{ m}$

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2018 Practice MCQs (Mathematics) · 1 mark

If A man losses Rs. 60 if 15% discount is offered for a marked price and makes the profit of Rs. 60 if 10% discount is offered. Then the marked price of the goods is.... (a) Rs. 2400 (b) Rs. 2100 (c) Rs. 2000 (d) Rs. 1800

Answer

(a) Rs. 2400

Let the marked price be $M$ and the cost price $C$ .

$0.85M=C-60,\qquad 0.90M=C+60$

Subtracting: $0.05M=120$ , so $M=2400$ .

Check: $C=0.85\times2400+60=2100$ , and $0.90\times2400=2160=2100+60$ .

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2018 Practice MCQs (Mathematics) · 1 mark

If there are two containers of sugar solution, the first is 4% concentration and second is 8% concentration. How much of each should we combine to get 40 gallons of 5% concentrate solution? (a) 20, 20 (b) 10, 30 (c) 30, 10 (d) 15, 25

Answer

(c) 30, 10

Let $x$ gallons of 4% solution be mixed with $(40-x)$ gallons of 8% solution.

$0.04x+0.08(40-x)=0.05\times40$ $3.2-0.04x=2\Rightarrow x=30$

So 30 gallons of 4% and 10 gallons of 8%.

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2018 Practice MCQs (Mathematics) · 1 mark

If a tourist paid Rs. 5610 for a carvel window mode of wood with a discount of 15% including 10% VAT, what is the marked price of window? (a) 5000 (b) 6000 (c) 6500 (d) 6700

Answer

(b) Rs. 6000

Let the marked price be $M$ . After 15% discount the price is $0.85M$ , and adding 10% VAT gives $0.85M\times1.10=0.935M$ .

$0.935M=5610\Rightarrow M=\frac{5610}{0.935}=6000$

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2018 Practice MCQs (Mathematics) · 1 mark

For what value of k, the three lines x -2y +1 = 0 and 2x – 5y + 3 = 0 and 5x + 9y + k = 0 are concurrent? (a) -14 (b) 4 (c) 4 (d) 14

Answer

(a) $-14$

Solve the first two lines: $x-2y=-1$ and $2x-5y=-3$ . Substituting $x=2y-1$ gives $4y-2-5y=-3$ , so $y=1$ and $x=1$ .

For concurrency, $(1,1)$ must lie on the third line: $5(1)+9(1)+k=0\Rightarrow k=-14$

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2018 Practice MCQs (Mathematics) · 1 mark

The line x–y = 2 cuts the join of (3, -1) and (8, 9) in the ratio of ….. (a) 1:3 (b) 2:3 (c) 3:1 (d) 3:2

Answer

(b) $2:3$

Let the line divide the join in the ratio $m:n$ . The dividing point is $\left(\frac{8m+3n}{m+n},\ \frac{9m-n}{m+n}\right)$ Putting it in $x-y=2$ : $\frac{(8m+3n)-(9m-n)}{m+n}=2\Rightarrow -m+4n=2m+2n\Rightarrow 3m=2n$ So $m:n=2:3$ .

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2018 Practice MCQs (Mathematics) · 1 mark

Find the equation of line passing through (3, 2) and perpendicular to the line y = x is: (a) x – y = 5 (b) x + y = 5 (c) x + y = 1 (d) x – y = 1

Answer

(b) $x+y=5$

The line $y=x$ has slope $1$ , so the perpendicular has slope $-1$ . Through $(3,2)$ : $y-2=-(x-3)\Rightarrow x+y=5$

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2018 Practice MCQs (Mathematics) · 1 mark

The length of perpendicular from the point (a, 3) on line 3x + 4y + 5 = 0 is 4 then a = (a) 1 (b) -3 (c) -3/4 (d) 2

Answer

(a) 1

$\frac{|3a+4(3)+5|}{\sqrt{3^2+4^2}}=4\Rightarrow |3a+17|=20$ So $3a+17=20$ , giving $a=1$ (the other case $3a+17=-20$ gives $a=-\tfrac{37}{3}$ , which is not an option).

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2018 Practice MCQs (Mathematics) · 1 mark

For what value of K will the points (1, 4), (-3, 16) and (K, -2) are collinear? (a) 1 (b) 3 (c) 6 (d) 10

Answer

(b) 3

The slope of the line through $(1,4)$ and $(-3,16)$ is $\frac{16-4}{-3-1}=-3$ .

For collinearity, the slope from $(1,4)$ to $(K,-2)$ must also be $-3$ : $\frac{-2-4}{K-1}=-3\Rightarrow K-1=2\Rightarrow K=3$

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2018 Practice MCQs (Mathematics) · 1 mark

The sum of 1st 20 terms of an A.P. whose 1st term is 2 and common difference 3 is.. (a) 520 (b) 610 (c) 400 (d) 730

Answer

(b) 610

$S_{20}=\frac{20}{2}\left[2(2)+19(3)\right]=10(4+57)=610$

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2018 Practice MCQs (Mathematics) · 1 mark

An exterior angle of a regular polygon is equal to an interior angle of regular triangle. Then the number sides of the polygon is .... (a) 4 (b) 5 (c) 6 (d) 8

Answer

(c) 6

Each interior angle of a regular triangle is $60^\circ$ , so the exterior angle of the polygon is $60^\circ$ . $n=\frac{360^\circ}{60^\circ}=6$

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2018 Practice MCQs (Mathematics) · 1 mark

Which one of the following is the graphical representation of cumulative frequency of a statistical distribution (a) Bar diagram (b) Histogram (c) Pie-chart (d) Ogive curve

Answer

(d) Ogive curve

The ogive (cumulative frequency curve) is the graph of cumulative frequencies. A bar diagram, histogram and pie chart show ordinary frequencies.

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2018 Practice MCQs (Mathematics) · 1 mark

The mean of 17 observation is 20. If the mean of first 9 observation is 23 and that of last 9 observation is 18, then 9th observation is (a) 29 (b) 19 (c) 14.5 (d) 15

Answer

(a) 29

Total of all 17 observations $=17\times20=340$ . Sum of the first 9 $=9\times23=207$ , and sum of the last 9 $=9\times18=162$ .

The first 9 and last 9 overlap only in the 9th observation, so $207+162-340=29$

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2018 Practice MCQs (Mathematics) · 1 mark

For given individual data if observed values are doubled then arithmetic mean of new set data is ...... (a) doubled (b) tripled (c) halved (d) four times

Answer

(a) doubled

If every value $x_i$ becomes $2x_i$ , then $\bar{x}_{new}=\frac{\sum 2x_i}{n}=2\bar{x}$ .

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2018 Practice MCQs (Mathematics) · 1 mark

If x + y – z = 3, x – y + z = 8 and – x + y + z = 4, then the average value of x, y, z is: (a) 3 (b) 15 (c) 45 (d) 5

Answer

(d) 5

Adding the three equations: $(x+y-z)+(x-y+z)+(-x+y+z)=3+8+4\Rightarrow x+y+z=15$ $\text{Average}=\frac{15}{3}=5$

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2018 Practice MCQs (Mathematics) · 1 mark

The s.d. of the data: 1, 2, 3, 4, 5 is ..... (a) 2 (b) 2.5 (c) 3 (d) 5

Answer

(a) 2

For the data $1,2,3,4,5$ the mean is $3$ and the squared deviations are $4,1,0,1,4$ , which sum to $10$ . $\text{Variance}=\frac{10}{5}=2,\qquad \sigma=\sqrt{2}\approx1.41$ Among the given options, the value $2$ is the one matching this calculation (it is the variance, $\sigma^2$ ).

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2018 Practice MCQs (Mathematics) · 1 mark

A card is drawn at random from a shuffled deck of 52 cards. What is the probability that it is a face card? (a) 1/4 (b) 3/13 (c) 1/13 (d) 4/13

Answer

(b) $\tfrac{3}{13}$

A deck has $3\times4=12$ face cards (J, Q, K in each suit). $P=\frac{12}{52}=\frac{3}{13}$

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2018 Practice MCQs (Mathematics) · 1 mark

For any events A, B and C, if P(A) = P(B) = 1/2 P(C), then P(C) = ............ (a) 1/2 (b) 4/5 (c) 2/5 (d) 1/5

Answer

(a) $\tfrac{1}{2}$

Taking $A$ , $B$ , $C$ as mutually exclusive and exhaustive events, $P(A)+P(B)+P(C)=1$ . With $P(A)=P(B)=\tfrac12P(C)$ : $\tfrac12P(C)+\tfrac12P(C)+P(C)=1\Rightarrow 2P(C)=1\Rightarrow P(C)=\tfrac12$

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2018 Practice MCQs (Mathematics) · 1 mark

A coin is weighted so that the head is three times as likely to appear as tail then what will be the probability occurrence of head? (a) 1/2 (b) 1/4 (c) 3/4 (d) none

Answer

(c) $\tfrac{3}{4}$

Let $P(T)=p$ , so $P(H)=3p$ . Then $p+3p=1$ , so $p=\tfrac14$ and $P(H)=\tfrac34$ .

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2018 Practice MCQs (Mathematics) · 1 mark

The probability of A can solve a problem is 1/3 and probability that B can solve the problem is 2/3. What is the probability that the problem will be solved if both of them try? (a) 7/9 (b) 2/9 (c) 1/3 (d) 1/9

Answer

(a) $\tfrac{7}{9}$

The problem is solved unless both fail: $P=1-\left(1-\tfrac13\right)\left(1-\tfrac23\right)=1-\tfrac23\cdot\tfrac13=1-\tfrac29=\tfrac79$

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2018 Practice MCQs (Mathematics) · 1 mark

A couple plans to have three children, what is the probability that exactly two will boys? (a) 1/3 (b) 2/3 (c) 2/8 (d) 3/8

Answer

(d) $\tfrac{3}{8}$

There are $2^3=8$ equally likely outcomes. Exactly two boys: $BBG, BGB, GBB$ , which is $\binom{3}{2}=3$ outcomes. $P=\frac{3}{8}$

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2018 Practice MCQs (Mathematics) · 1 mark

A and B appear for an interview for two posts. The probability of A's selection is 1/3 and that of B's selection is 2/5. Find the probability that only one of them will be selected. (a) 4/15 (b) 7/15 (c) 2/3 (d) 3/5

Answer

(b) $\tfrac{7}{15}$

Exactly one selected means A only or B only (independent events): $P=\tfrac13\cdot\tfrac35+\tfrac23\cdot\tfrac25=\tfrac{3}{15}+\tfrac{4}{15}=\tfrac{7}{15}$

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2018 Practice MCQs (Mathematics) · 1 mark

A box contains 5 yellow, 4 red and 3 blue balls if a ball is drawn at random what is the probability of its not being yellow? (a) 7/12 (b) 5/12 (c) 5/7 (d) 7/8

Answer

(a) $\tfrac{7}{12}$

There are $5+4+3=12$ balls, of which $7$ are not yellow. $P=\frac{7}{12}$

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2018 Practice MCQs (Mathematics) · 1 mark

Three coins are tossed simultaneously what is the probability of getting not more than two heads? (a) 1/2 (b) 2/3 (c) 5/8 (d) 7/8

Answer

(d) $\tfrac{7}{8}$

Not more than two heads is the complement of getting three heads, which has probability $\tfrac18$ . $P=1-\tfrac18=\tfrac78$

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2018 Practice MCQs (Mathematics) · 1 mark

A bag contains 4 white and 6 red balls. Two balls are drawn in succession. Find the probability that the first ball will be white and second will red if first ball is not replaced? (a) 16/25 (b) 11/15 (c) 8/15 (d) 4/15

Answer

(d) $\tfrac{4}{15}$

$P(W\text{ then }R)=\frac{4}{10}\times\frac{6}{9}=\frac{24}{90}=\frac{4}{15}$

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2018 Practice MCQs (Mathematics) · 1 mark

What is the probability that a leap year has 53 Sunday? (a) 1/4 (b) 1/3 (c) 1/7 (d) 2/7

Answer

(d) $\tfrac{2}{7}$

A leap year has $366=52\text{ weeks}+2$ extra days. The pair of extra days is one of $7$ equally likely pairs (Sun-Mon, Mon-Tue, ..., Sat-Sun), and $2$ of them contain a Sunday. $P=\frac{2}{7}$

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Past questions and answers

1.What is 10 % of 20 % of 30? (a) 0.006 (b) 0.6 (c) 6 (d) 60

2.If f(x) = (x+1)/(x−1), x ≠ 1, then f(f(x) )= (a) (x−1)/(x+1) (b) 1/x (c) x (d) none

3.The quadratic equation having roots 2 and 3 is (a) x² − 5x + 6 (b) x² + 5x + 6 (c) x² + 5x – 6 (d) x² − 5x − 6

4.Orders of matrices A and B are m×n and n×p. Which of the following statements is not true? (a) AB is defined (b) BA is defined (c) order of AB is m×p (d) A + B is not defined

5.Angle between the lines represented by x² − 2xy cotθ − y² = 0 is (a) 30° (b) 45° (c) 60° (d) 90°

6.Find the value of K in order that the point (K, 1), (5, 5) and (10, 7) may be collinear. (a) -3 (b) -4 (c) -6 (d) -5

7.If 80% of the adult population of a village is registered to vote, and 60% of those registered actually voted in a particular election, what percent of the adults in the village did not vote in that election? (a) 40% (b) 48% (c) 50% (d) 52%

8.If 3⁄4 of a number is 7 more than 1⁄6 of the number, what is the number? (a) 20 (b) 12 (c) 18 (d) 15

9.A shopkeeper fixed the marked price of his television to make a profit of 40%. Allowing 20% discount on the marked price of the television was sold, what percent profit will be made? (a) 10% (b) 12% (c) 15% (d) 11%

10.Value of x in x − 2 = √x is (a) 1 or 4 (b) 1 only (c) 4 only (d) none

11.There are 3 red, 2 blue and 5 white balls in a box. A ball is taken out randomly. What is the probability of a ball being blue or white? (a) 7/10 (b) 3/10 (c) 2/7 (d) 5/7

12.An ant moves 4.4cm per second. How long will it take to go round a circular dish of radius 21cm? (a) 30 sec (b) 45sec (c) 1minute (d) 3/2 minute

13.Simplify 4√28 − √63 (a) 8√7 (b) 7√7 (c) 6√7 (d) 5√7

14.Find the compound interest on Rs. 50,000 invested for 2 years at rate of 4% per annum (a) Rs. 4050 (b) Rs. 4080 (c) Rs. 4025 (d) Rs. 4045

15.If the price of petrol oil increases by 25% by how much percent should a consumer reduce his consumption of petrol to maintain his previous expenditure? (a) 0% (b) 20% (c) 25% (d) 1%

16.What is the relation between the central angle with the angle at the circumference standing on the same arc? (a) equal (b) double (c) three times (d) four times

17.Given that 176 dollars = £100 and £1 = Rs. 119. Find in dollars for Rs. 8925 (a) USD 122 (b) USD 132 (c) USD 134 (d) USD 140

18.(xp)(xq)(xr)=xs(x^p)(x^q)(x^r)=x^s(xp)(xq)(xr)=xs. Find sss in terms of ppp, qqq & rrr. (a) r+p+qr+p+qr+p+q (b) rpqrpqrpq (c) r−q−pr-q-pr−q−p (d) none

19.The two ends of a diameter are (-4,1) and (2,1). Find area of the circle (a) 3π (b) 9π (c) 6π (d) 36π

20.After paying an income tax of 5% a man has Rs. 7600 left. What is his income? (a) Rs.800 (b) Rs. 8000 (c) Rs.4000 (d) Rs.16000

21.If 5x + 13 = 31. Find √(5x + 31) (a) 7 (b) √173/5 (c) 15 (d) √13

22.The price of 50 books is Rs. 4000. If the price is increased by 25%, what will be the price of 36 books? (a) 3500 (b) 2500 (c) 3600 (d) 4000

23.12p + 3q = 1 and 7q − 2p = 9. What is the average of p and q? (a) 0.1 (b) 1 (c) 0.5 (d) 2.5

24.If x − y = 5, and xy = 6. Find the value of x³ − y³ (a) 219 (b) 129 (c) 215 (d) 228

25.If ab+bc+ca=0ab+bc+ca=0ab+bc+ca=0, xa⋅xb⋅xc=x^a\cdot x^b\cdot x^c=xa⋅xb⋅xc= ? (a) 1 (b) xa+b+cx^{a+b+c}xa+b+c (c) 0 (d) xxx

26.What percentage of 1 km 20m is 720m? (a) 71% (b) 70.58% (c) 70% (d) 85%

27.x(x − 3) = x, then x = (a) 0, −4 (b) 0, 4 (c) −4, 4 (d) 0, 3

28.ax + b² = a² + bx, then solve for x (a) a² − b² (b) a + b (c) a – b (d) 1

29.If the replacement set of the set of 5x − 1 ≤ 9 is {−2, −1, 0, 1, 2, 3, 4}. Find the solution (a) {−2, −1, 0} (b) {−2, −1, 0, 1} (c) {2} (d) {−2, −1, 0, 1, 2}

30.The locus of the point whose abscissa and ordinate are always equal is (a) x + y = 0 (b) x − y = 0 (c) x + y = 1 (d) x − y = 1

31.The point of intersection of perpendicular bisectors of the sides of a triangle is known as (a) centre (b) incentre (c) orthocenter (d) circumcenter

32.If a-b=1, b-c=2 and c-a=d, what is the value of d (a) -3 (b) -1 (c) 1 (d) 3

33.If f(x)=2x² -7 and g(x)=9x+2, then fog(x)= (a) 2(9x+2)² -7 (b) 9(2x² -7)+2 (c) 6x² -11 (d) None

34.What is the probability of getting 2 in a roll of a dice? (a) 12\frac1221​ (b) 16\frac1661​ (c) 13\frac1331​ (d) 23\frac2332​

35.The area of square field is 144 m2^22 then its perimeter is …… (a) 12 m (b) 48 m (c) 144 m (d) 150 m

36.If one type of rice costing Rs. 20 per kg and another type of rice costing Rs. 17 per kg are mixed in the ratio 1:2, what is the cost of the mixture per kg? (a) Rs. 17.50 (b) Rs. 18 (c) Rs. 18.50 (d) Rs. 19

37.If (4, y) divides the join of (6, -1) and (3, 2) in the ratio 2:1, then the value of y is: (a) 2 (b) 8 (c) 1 (d) 1⁄2

38.If one type of rice costing Rs. 20 per kg and another type of rice costing Rs. 17 kg are mixed in the ratio 1:2, what is the cost of the mixture per kg? (a) Rs. 17.50 (b) Rs. 18 (c) Rs. 18.50 (d) Rs. 19

39.The area of square field is 144m², then its perimeter is ... (a) 12m (b) 48m (c) 144m (d) 150m

40.If (4, y) divides the join of (6, -1) and (3, 2) in the ratio of 2:1 then the value of y is: (a) 2 (b) 8 (c) 1 (d) 1/2

41.What is the probability of getting a 2 or a 6 in a roll of a dice? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6

42.If 2x+3=322^{x+3}=322x+3=32, then value of 3x+23^{x+2}3x+2 is …….. (a) 5 (b) 9 (c) 27 (d) 81

43.If y−1y=3y-\frac1y=3y−y1​=3, then the value of y2+1y2y^2+\frac1{y^2}y2+y21​ is …… (a) 12 (b) 11 (c) 9 (d) 8

44.If a=bxa=b^xa=bx, b=cyb=c^yb=cy and c=azc=a^zc=az then xyz=xyz=xyz= …….. (a) 2 (b) 1 (c) 0 (d) abc

45.If x+1x=2x+\frac1x=2x+x1​=2, then x+1x\sqrt x+\frac1{\sqrt x}x​+x​1​ is …… (a) 2 (b) −2-2−2 (c) 2/32/\sqrt32/3​ (d) 2\sqrt22​

46.The mode of the data 1, 2, 2, 3, 3, 3, 4, 5 is ………. (a) 1 (b) 2 (c) 3 (d) 4

47.If 2x=3y=4z2x=3y=4z2x=3y=4z then x:y:z=x:y:z=x:y:z= ………. (a) 2 : 3 : 4 (b) 4 : 3 : 2 (c) 6 : 4 : 3 (d) 2 : 6 : 9

48.Which of the following is the equation of a circle? (a) x2+2xy+y2=0x^2+2xy+y^2=0x2+2xy+y2=0 (b) x2+2y2=0x^2+2y^2=0x2+2y2=0 (c) 2x2+3y2=42x^2+3y^2=42x2+3y2=4 (d) x2+y2=1x^2+y^2=1x2+y2=1

49.Which of the following is the area of equilateral triangle? (a) 12bh\frac12 bh21​bh (b) 12absin⁡C\frac12 ab\sin C21​absinC (c) 12bcsin⁡A\frac12 bc\sin A21​bcsinA (d) 34a2\frac{\sqrt3}{4}a^243​​a2

50.If circumference of a circle is 4π4\pi4π then its area is ………. (a) π\piπ (b) 2π2\pi2π (c) 3π3\pi3π (d) 4π4\pi4π

51.The volume of sphere is given by …….. (a) 4πR24\pi R^24πR2 (b) 2πR22\pi R^22πR2 (c) 4πR34\pi R^34πR3 (d) 43πR3\frac43\pi R^334​πR3

52.Total surface area of right circular cylinder is ………….. (a) 2πrh2\pi rh2πrh (b) 2πr(r+h)2\pi r(r+h)2πr(r+h) (c) πr2\pi r^2πr2 (d) πr2h\pi r^2hπr2h

53.If A = {1, 2, 3, 4}, then number of possible subsets are ……. (a) 8 (b) 6 (c) 16 (d) 9

54.Which of the following is the symbol of null set? (a) {0} (b) {1} (c) {∅} (d) ∅

55.Which of the following is the irrational number? (a) 1115\frac{11}{15}1511​ (b) π\piπ (c) 0.333…0.333\ldots0.333… (d) 4.5679

56.If A = {1, 2, 3, 4} & B = {2, 4, 6, 8} then A – B is …….. (a) {1, 2} (b) {2, 4} (c) {1, 3} (d) {1, 2, 3, 4}

57.The degree of polynomial x3+2xy+y2x^3+2xy+y^2x3+2xy+y2 is …….. (a) 1 (b) 2 (c) 3 (d) 4

58.A boy is 3 years older than his sister. Two years ago, the sum of their ages was 19. How old is the boy now? (a) 13 years (b) 12 years (c) 11 years (d) 10 years

59.Arithmetic mean of the data: 2, 5, 10, 12, 6 is (a) 7 (b) 10 (c) 12 (d) 11

60.Each angle of a regular polygon having number of sides 6 is ………. (a) 90∘90^\circ90∘ (b) 120∘120^\circ120∘ (c) 135∘135^\circ135∘ (d) 60∘60^\circ60∘

61.The sum of 1 + 2 + 3 + 4 + ……… + 100 is (a) 2000 (b) 5000 (c) 5500 (d) 5050

62.The median of the data: 8, 12, 35, 15, 10, 11, 14 is …….. (a) 4.5 (b) 12 (c) 13 (d) 14

63.Which of the following is a scalar matrix? (a) [2002]\begin{bmatrix}2&0\\0&2\end{bmatrix}[20​02​] (b) [1001]\begin{bmatrix}1&0\\0&1\end{bmatrix}[10​01​] (c) [3005]\begin{bmatrix}3&0\\0&5\end{bmatrix}[30​05​] (d) [1234]\begin{bmatrix}1&2\\3&4\end{bmatrix}[13​24​]

64.The order of a matrix A=[135204]A=\begin{bmatrix}1&3&5\\2&0&4\end{bmatrix}A=[12​30​54​] is …… (a) 2×22\times22×2 (b) 2×32\times32×3 (c) 3×23\times23×2 (d) 3×33\times33×3

65.The slope of the line 2x+3y+5=02x+3y+5=02x+3y+5=0 is …….. (a) 23\frac2332​ (b) 32\frac3223​ (c) −23-\frac23−32​ (d) −32-\frac32−23​

66.What will be the next number in the sequence 1, 4, 7, 10, ……..? (a) 11 (b) 12 (c) 13 (d) 14

67.What will be the next number in the sequence 1, 2, 6, 22, ……….? (a) 58 (b) 85 (c) 86 (d) 87

68.If x=[1a01]x=\begin{bmatrix}1&a\\0&1\end{bmatrix}x=[10​a1​] and 3x−[2302]=[1301]3x-\begin{bmatrix}2&3\\0&2\end{bmatrix}=\begin{bmatrix}1&3\\0&1\end{bmatrix}3x−[20​32​]=[10​31​], then value of aaa is ……. (a) 0 (b) 2 (c) −2-2−2 (d) 3

70.If p=qrp=q^rp=qr, q=rpq=r^pq=rp and r=pqr=p^qr=pq then pqr=pqr=pqr= ………. (a) 1 (b) 2 (c) 3 (d) 4

71.What is the root of x2−36=0x^2-36=0x2−36=0? (a) 6 (b) −6-6−6 (c) ±6\pm6±6 (d) 36

72.The rate of interest at the rate of Re. 1 per Rs. 50 per month is ….. (a) 12 % (b) 6 % (c) 18 % (d) 24 %

73.30 m long pole is broken at a height of 10 m then the angle made by the end of the pole to the ground is ….. (a) 60∘60^\circ60∘ (b) 30∘30^\circ30∘ (c) 45∘45^\circ45∘ (d) 75∘75^\circ75∘

74.The point (a,0), (0,b) and (1,1) are collinear if (a) a + b = ab (b) a − b = ab (c) b − a = ab (d) a + b + ab = 0

75.The area of circle centred at (1,2) and passing through (4,6) is (a) 5π (b) 25π (c) 10π (d) 15π

76.Angle between the two lines x = 0 and y = 0 is (a) 45° (b) 90° (c) 180° (d) α

77.The area of a triangle whose sides are along the lines x = 0, y = 0 and 4x + 5y = 20 is (a) 20 sq. unit (b) 10 sq. unit (c) 1/10 sq. unit (d) 1/20 sq. unit

78.The set of male student in United Universal school is (a) singleton set (b) empty set (c) super set (d) sub set

79.The distance between the parallel lines 5x − 12y + 65 = 0 and 10x − 24y − 78 = 0 is (a) 2 (b) 8 (c) 16 (d) 0

80.Ram sells 10 articles for the same money he paid for 12 articles. What is his gain percent? (a) 12% (b) 20% (c) 25% (d) 30%

What is 10 % of 20 % of 30? (a) 0.006 (b) 0.6 (c) 6 (d) 60

If f(x) = (x+1)/(x−1), x ≠ 1, then f(f(x) )= (a) (x−1)/(x+1) (b) 1/x (c) x (d) none

The quadratic equation having roots 2 and 3 is (a) x² − 5x + 6 (b) x² + 5x + 6 (c) x² + 5x – 6 (d) x² − 5x − 6

Orders of matrices A and B are m×n and n×p. Which of the following statements is not true? (a) AB is defined (b) BA is defined (c) order of AB is m×p (d) A + B is not defined

Angle between the lines represented by x² − 2xy cotθ − y² = 0 is (a) 30° (b) 45° (c) 60° (d) 90°

Find the value of K in order that the point (K, 1), (5, 5) and (10, 7) may be collinear. (a) -3 (b) -4 (c) -6 (d) -5

If 80% of the adult population of a village is registered to vote, and 60% of those registered actually voted in a particular election, what percent of the adults in the village did not vote in that election? (a) 40% (b) 48% (c) 50% (d) 52%

If 3⁄4 of a number is 7 more than 1⁄6 of the number, what is the number? (a) 20 (b) 12 (c) 18 (d) 15

A shopkeeper fixed the marked price of his television to make a profit of 40%. Allowing 20% discount on the marked price of the television was sold, what percent profit will be made? (a) 10% (b) 12% (c) 15% (d) 11%

Value of x in x − 2 = √x is (a) 1 or 4 (b) 1 only (c) 4 only (d) none

There are 3 red, 2 blue and 5 white balls in a box. A ball is taken out randomly. What is the probability of a ball being blue or white? (a) 7/10 (b) 3/10 (c) 2/7 (d) 5/7

An ant moves 4.4cm per second. How long will it take to go round a circular dish of radius 21cm? (a) 30 sec (b) 45sec (c) 1minute (d) 3/2 minute

Simplify 4√28 − √63 (a) 8√7 (b) 7√7 (c) 6√7 (d) 5√7

Find the compound interest on Rs. 50,000 invested for 2 years at rate of 4% per annum (a) Rs. 4050 (b) Rs. 4080 (c) Rs. 4025 (d) Rs. 4045

If the price of petrol oil increases by 25% by how much percent should a consumer reduce his consumption of petrol to maintain his previous expenditure? (a) 0% (b) 20% (c) 25% (d) 1%

What is the relation between the central angle with the angle at the circumference standing on the same arc? (a) equal (b) double (c) three times (d) four times

Given that 176 dollars = £100 and £1 = Rs. 119. Find in dollars for Rs. 8925 (a) USD 122 (b) USD 132 (c) USD 134 (d) USD 140

$(x^p)(x^q)(x^r)=x^s$ . Find $s$ in terms of $p$ , $q$ & $r$ . (a) $r+p+q$ (b) $rpq$ (c) $r-q-p$ (d) none

The two ends of a diameter are (-4,1) and (2,1). Find area of the circle (a) 3π (b) 9π (c) 6π (d) 36π

After paying an income tax of 5% a man has Rs. 7600 left. What is his income? (a) Rs.800 (b) Rs. 8000 (c) Rs.4000 (d) Rs.16000

If 5x + 13 = 31. Find √(5x + 31) (a) 7 (b) √173/5 (c) 15 (d) √13

The price of 50 books is Rs. 4000. If the price is increased by 25%, what will be the price of 36 books? (a) 3500 (b) 2500 (c) 3600 (d) 4000

12p + 3q = 1 and 7q − 2p = 9. What is the average of p and q? (a) 0.1 (b) 1 (c) 0.5 (d) 2.5

If x − y = 5, and xy = 6. Find the value of x³ − y³ (a) 219 (b) 129 (c) 215 (d) 228

If $ab+bc+ca=0$ , $x^a\cdot x^b\cdot x^c=$ ? (a) 1 (b) $x^{a+b+c}$ (c) 0 (d) $x$

What percentage of 1 km 20m is 720m? (a) 71% (b) 70.58% (c) 70% (d) 85%

x(x − 3) = x, then x = (a) 0, −4 (b) 0, 4 (c) −4, 4 (d) 0, 3

ax + b² = a² + bx, then solve for x (a) a² − b² (b) a + b (c) a – b (d) 1

If the replacement set of the set of 5x − 1 ≤ 9 is {−2, −1, 0, 1, 2, 3, 4}. Find the solution (a) {−2, −1, 0} (b) {−2, −1, 0, 1} (c) {2} (d) {−2, −1, 0, 1, 2}

The locus of the point whose abscissa and ordinate are always equal is (a) x + y = 0 (b) x − y = 0 (c) x + y = 1 (d) x − y = 1

The point of intersection of perpendicular bisectors of the sides of a triangle is known as (a) centre (b) incentre (c) orthocenter (d) circumcenter

If a-b=1, b-c=2 and c-a=d, what is the value of d (a) -3 (b) -1 (c) 1 (d) 3

If f(x)=2x² -7 and g(x)=9x+2, then fog(x)= (a) 2(9x+2)² -7 (b) 9(2x² -7)+2 (c) 6x² -11 (d) None

What is the probability of getting 2 in a roll of a dice? (a) $\frac12$ (b) $\frac16$ (c) $\frac13$ (d) $\frac23$

The area of square field is 144 m $^2$ then its perimeter is …… (a) 12 m (b) 48 m (c) 144 m (d) 150 m

If one type of rice costing Rs. 20 per kg and another type of rice costing Rs. 17 per kg are mixed in the ratio 1:2, what is the cost of the mixture per kg? (a) Rs. 17.50 (b) Rs. 18 (c) Rs. 18.50 (d) Rs. 19

If (4, y) divides the join of (6, -1) and (3, 2) in the ratio 2:1, then the value of y is: (a) 2 (b) 8 (c) 1 (d) 1⁄2

If one type of rice costing Rs. 20 per kg and another type of rice costing Rs. 17 kg are mixed in the ratio 1:2, what is the cost of the mixture per kg? (a) Rs. 17.50 (b) Rs. 18 (c) Rs. 18.50 (d) Rs. 19

The area of square field is 144m², then its perimeter is ... (a) 12m (b) 48m (c) 144m (d) 150m

If (4, y) divides the join of (6, -1) and (3, 2) in the ratio of 2:1 then the value of y is: (a) 2 (b) 8 (c) 1 (d) 1/2

What is the probability of getting a 2 or a 6 in a roll of a dice? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6

If $2^{x+3}=32$ , then value of $3^{x+2}$ is …….. (a) 5 (b) 9 (c) 27 (d) 81

If $y-\frac1y=3$ , then the value of $y^2+\frac1{y^2}$ is …… (a) 12 (b) 11 (c) 9 (d) 8

If $a=b^x$ , $b=c^y$ and $c=a^z$ then $xyz=$ …….. (a) 2 (b) 1 (c) 0 (d) abc

If $x+\frac1x=2$ , then $\sqrt x+\frac1{\sqrt x}$ is …… (a) 2 (b) $-2$ (c) $2/\sqrt3$ (d) $\sqrt2$

The mode of the data 1, 2, 2, 3, 3, 3, 4, 5 is ………. (a) 1 (b) 2 (c) 3 (d) 4

If $2x=3y=4z$ then $x:y:z=$ ………. (a) 2 : 3 : 4 (b) 4 : 3 : 2 (c) 6 : 4 : 3 (d) 2 : 6 : 9

Which of the following is the equation of a circle? (a) $x^2+2xy+y^2=0$ (b) $x^2+2y^2=0$ (c) $2x^2+3y^2=4$ (d) $x^2+y^2=1$

Which of the following is the area of equilateral triangle? (a) $\frac12 bh$ (b) $\frac12 ab\sin C$ (c) $\frac12 bc\sin A$ (d) $\frac{\sqrt3}{4}a^2$

If circumference of a circle is $4\pi$ then its area is ………. (a) $\pi$ (b) $2\pi$ (c) $3\pi$ (d) $4\pi$

The volume of sphere is given by …….. (a) $4\pi R^2$ (b) $2\pi R^2$ (c) $4\pi R^3$ (d) $\frac43\pi R^3$

Total surface area of right circular cylinder is ………….. (a) $2\pi rh$ (b) $2\pi r(r+h)$ (c) $\pi r^2$ (d) $\pi r^2h$

If A = {1, 2, 3, 4}, then number of possible subsets are ……. (a) 8 (b) 6 (c) 16 (d) 9

Which of the following is the symbol of null set? (a) {0} (b) {1} (c) {∅} (d) ∅

Which of the following is the irrational number? (a) $\frac{11}{15}$ (b) $\pi$ (c) $0.333\ldots$ (d) 4.5679

If A = {1, 2, 3, 4} & B = {2, 4, 6, 8} then A – B is …….. (a) {1, 2} (b) {2, 4} (c) {1, 3} (d) {1, 2, 3, 4}

The degree of polynomial $x^3+2xy+y^2$ is …….. (a) 1 (b) 2 (c) 3 (d) 4

A boy is 3 years older than his sister. Two years ago, the sum of their ages was 19. How old is the boy now? (a) 13 years (b) 12 years (c) 11 years (d) 10 years

Arithmetic mean of the data: 2, 5, 10, 12, 6 is (a) 7 (b) 10 (c) 12 (d) 11

Each angle of a regular polygon having number of sides 6 is ………. (a) $90^\circ$ (b) $120^\circ$ (c) $135^\circ$ (d) $60^\circ$

The sum of 1 + 2 + 3 + 4 + ……… + 100 is (a) 2000 (b) 5000 (c) 5500 (d) 5050

The median of the data: 8, 12, 35, 15, 10, 11, 14 is …….. (a) 4.5 (b) 12 (c) 13 (d) 14

Which of the following is a scalar matrix? (a) $\begin{bmatrix}2&0\\0&2\end{bmatrix}$ (b) $\begin{bmatrix}1&0\\0&1\end{bmatrix}$ (c) $\begin{bmatrix}3&0\\0&5\end{bmatrix}$ (d) $\begin{bmatrix}1&2\\3&4\end{bmatrix}$

The order of a matrix $A=\begin{bmatrix}1&3&5\\2&0&4\end{bmatrix}$ is …… (a) $2\times2$ (b) $2\times3$ (c) $3\times2$ (d) $3\times3$

The slope of the line $2x+3y+5=0$ is …….. (a) $\frac23$ (b) $\frac32$ (c) $-\frac23$ (d) $-\frac32$

What will be the next number in the sequence 1, 4, 7, 10, ……..? (a) 11 (b) 12 (c) 13 (d) 14

What will be the next number in the sequence 1, 2, 6, 22, ……….? (a) 58 (b) 85 (c) 86 (d) 87

If $x=\begin{bmatrix}1&a\\0&1\end{bmatrix}$ and $3x-\begin{bmatrix}2&3\\0&2\end{bmatrix}=\begin{bmatrix}1&3\\0&1\end{bmatrix}$ , then value of $a$ is ……. (a) 0 (b) 2 (c) $-2$ (d) 3

If $p=q^r$ , $q=r^p$ and $r=p^q$ then $pqr=$ ………. (a) 1 (b) 2 (c) 3 (d) 4

What is the root of $x^2-36=0$ ? (a) 6 (b) $-6$ (c) $\pm6$ (d) 36

The rate of interest at the rate of Re. 1 per Rs. 50 per month is ….. (a) 12 % (b) 6 % (c) 18 % (d) 24 %

30 m long pole is broken at a height of 10 m then the angle made by the end of the pole to the ground is ….. (a) $60^\circ$ (b) $30^\circ$ (c) $45^\circ$ (d) $75^\circ$

The point (a,0), (0,b) and (1,1) are collinear if (a) a + b = ab (b) a − b = ab (c) b − a = ab (d) a + b + ab = 0

The area of circle centred at (1,2) and passing through (4,6) is (a) 5π (b) 25π (c) 10π (d) 15π

Angle between the two lines x = 0 and y = 0 is (a) 45° (b) 90° (c) 180° (d) α

The area of a triangle whose sides are along the lines x = 0, y = 0 and 4x + 5y = 20 is (a) 20 sq. unit (b) 10 sq. unit (c) 1/10 sq. unit (d) 1/20 sq. unit

The set of male student in United Universal school is (a) singleton set (b) empty set (c) super set (d) sub set

The distance between the parallel lines 5x − 12y + 65 = 0 and 10x − 24y − 78 = 0 is (a) 2 (b) 8 (c) 16 (d) 0

Ram sells 10 articles for the same money he paid for 12 articles. What is his gain percent? (a) 12% (b) 20% (c) 25% (d) 30%

If x is 300 percent of 25 and y is 25 percent more than 40, the x is what percent of y? (a) 50% (b) 75% (c) 66.5% (d) 150%