School entrance and scholarship tests Kathmandu Metropolitan City Class 11 Scholarship Test: Mathematics

2082 · 1 mark

The terminal compound interest on a certain sum $x$ in $t$ years at the rate of $r$ % compound interest is $CI_4$ . What is the relation among $x, t, r$ and $CI_4$ ? (a) $CI_4 = x\left[\left(1+\frac{r}{100}\right)^t - 1\right]$ (b) $CI_4 = x\left[\left(1+\frac{r}{400}\right)^t - 1\right]$ (c) $CI_4 = x\left[\left(1+\frac{r}{200}\right)^{2t} - 1\right]$ (d) $CI_4 = x\left[\left(1+\frac{r}{400}\right)^{4t} - 1\right]$

Similar questions: Compound interest (2081)

Answer

(d) $CI_4 = x\left[\left(1+\frac{r}{400}\right)^{4t} - 1\right]$

"Terminal" means quarterly compounding, so the rate per period is $\frac{r}{4}\%$ and there are $4t$ periods: amount $=x\left(1+\frac{r}{400}\right)^{4t}$ , and interest is amount minus $x$ .

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2081 · 1 mark

The semi-annual compound interest on a certain sum m in t years at the rate of r % compound interest is CI. What is the relation among m, t, r and CI ? (a) $CI = m\left(1 + \frac{r}{100}\right)^{2t}$ (b) $CI = m\left(1 - \frac{r}{100}\right)^{2t}$ (c) $CI = m\left[\left(1 + \frac{r}{200}\right)^{2t} - 1\right]$ (d) $CI = m\left[\left(1 - \frac{r}{100}\right)^{2t} - 1\right]$

Similar questions: Compound interest (2082)

Answer

(c) $CI = m\left[\left(1 + \frac{r}{200}\right)^{2t} - 1\right]$

For half-yearly compounding the rate per period is $\frac r2\%$ and the number of periods is $2t$ , so the amount is $m\left(1+\frac{r}{200}\right)^{2t}$ . Compound interest is amount minus principal.

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2082 · 1 mark

If A and B are the subsets of a universal set U, which of the following notation is used to denote $(A - B) \cup (B - A)$ ? (a) $A \Delta B$ (b) $A abla B$ (c) $\overline{A \cap B}$ (d) $\overline{A \cup B}$

Answer

(a) $A \Delta B$

$(A-B)\cup(B-A)$ is the symmetric difference of $A$ and $B$ , written $A \Delta B$ .

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2082 · 1 mark

In a group of 150 people, 120 like to play volleyball and 85 like to play football. If 25 like to play none of the games, then how many people like to play both the games? (a) 20 (b) 30 (c) 80 (d) 25

Answer

(c) 80

People playing at least one game $=150-25=125$ .

$n(V\cup F)=n(V)+n(F)-n(V\cap F)$ $125=120+85-n(V\cap F)\Rightarrow n(V\cap F)=205-125=80$

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2082 · 1 mark

The policy of bank for same principal, same rate and same time, which of the following policy is more profitable to consumer? (a) Annual Compound Interest (b) Semi-Annual Compound Interest (c) Terminal Compound Interest (d) Monthly Compound Interest

Answer

(d) Monthly Compound Interest

For the same principal, rate and time, the more often interest is compounded, the larger the amount. Monthly compounding (12 times a year) gives the most interest, so it is most profitable to the depositor.

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2082 · 1 mark

The present price of machine is Rs. 800000. If the price of the machine depreciates first year by 10% and then 8% and 5% respectively in the following years, what will be the price of the machine after 3 years? (a) Rs. 6,29,000 (b) Rs. 6,25,280 (c) 7,29,280 (d) 6,29,280

Answer

(d) Rs. 6,29,280

$\text{Price}=800000\times0.90\times0.92\times0.95$ $=720000\times0.92=662400,\quad 662400\times0.95=629280$

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2082 · 1 mark

The price of a good is Rs. 30000. What will be the cost of good after 3 years at the rate of 10% depreciation? (a) Rs. 21087 (b) Rs. 21780 (c) Rs. 21870 (d) Rs. 21708

Answer

(c) Rs. 21870

$30000\left(1-\frac{10}{100}\right)^3=30000\times0.729=21870$

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2082 · 1 mark

If I.C. 100 = NRs. 160 and 1 American Dollar = NRs. 120, how many American Dollars are equal to I.C. 7500? (a) Dollar 100 (b) Dollar 10 (c) Dollar 110 (d) I.C. 100

Answer

(a) Dollar 100

I.C. 7500 $=\frac{7500}{100}\times160=\text{Rs }12000$ .

Dollars $=\frac{12000}{120}=100$ .

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2082 · 1 mark

Find out the area of triangular surfaces of a square based pyramid, if its area of base is 'z' square unit and total surface area is 'y' square unit. (a) $y$ sq. unit (b) $z$ sq. unit (c) $(y-z)$ sq. unit (d) $\sqrt{y-z}$ sq. unit

Answer

(c) $(y-z)$ sq. unit

Total surface area = base area + area of the triangular faces, so the triangular faces have area $y-z$ .

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2082 · 1 mark

In the given figure (an ice-cream cone with a hemisphere on top; slant height of the cone is 25 cm), the slant height of the cone is 25 cm and the sum of the curved surface area is 858 cm $^2$ . What is the common radius? (a) 7 cm (b) 14 cm (c) 21 cm (d) 15 cm

Answer

(a) 7 cm

The cone and the hemisphere have curved surface areas $\pi r l$ and $2\pi r^2$ :

$\pi r(25)+2\pi r^2=858\Rightarrow \pi r(25+2r)=858$

Try $r=7$ : $\frac{22}{7}\times7\times(25+14)=22\times39=858$ . So $r=7$ cm.

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2082 · 1 mark

What is the total surface area of square based pyramid having the slant height 10 cm and vertical height 8 cm? (a) 483 cm $^2$ (b) 240 cm $^2$ (c) 144 cm $^2$ (d) 384 cm $^2$

Answer

(d) 384 cm $^2$

Slant height $l=10$ and height $h=8$ , so half the base side is $\sqrt{10^2-8^2}=6$ cm, giving base side $12$ cm.

$\text{TSA}=a^2+2al=12^2+2(12)(10)=144+240=384\ \text{cm}^2$

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2082 · 1 mark

Which of the following formula is known as the Heron's formula to calculate area of a triangle? (a) $A = \frac{1}{2}bh$ (b) $A = \frac{\sqrt{3}}{4}a^2$ (c) $A = \frac{b}{4}\sqrt{4a^2 - b^2}$ (d) $A = \sqrt{s(s-a)(s-b)(s-c)}$

Answer

(d) $A = \sqrt{s(s-a)(s-b)(s-c)}$

Heron's formula gives the area of a triangle with sides $a,b,c$ and semi-perimeter $s=\frac{a+b+c}{2}$ .

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2082 · 1 mark

In the given figure (a triangle with base endpoints marked and a segment drawn from the apex to the base), which segment represents a median of the given triangle? (a) AB (b) BC (c) AC (d) AD

Answer

(d) AD

A median joins a vertex to the midpoint of the opposite side. AD runs from the apex A to the point D on the base BC, so it is the median; AB and AC are sides and BC is the base.

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2082 · 1 mark

If the sum of the first $n$ terms of arithmetic series is given by $S_n = 3n^2 + 2n$ , What is the first term of the series? (a) 3 (b) 5 (c) 2 (d) 7

Answer

(b) 5

The first term equals $S_1=3(1)^2+2(1)=5$ .

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2082 · 1 mark

The length of a square room is 10 m and height is 6 m. If the per unit cost of painting the four walls of the room is Rs. 400, find the total cost. (a) Rs. 96000 (b) Rs. 96000 (c) Rs. 69000 (d) Rs. 90600

Answer

(a) Rs. 96000

The room is square with side 10 m, so the four walls have area $2(l+b)h=4\times10\times6=240$ m $^2$ .

$\text{Cost}=240\times400=\text{Rs }96000$

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2082 · 1 mark

What is the volume of cone with radius $3k$ cm and vertical height $\frac{k}{\pi}$ cm? (a) $3k^3$ (b) $\frac{1}{3}k^3$ (c) $\frac{1}{3}\pi k^3$ (d) $3\pi k^3$

Answer

(a) $3k^3$

$V=\frac13\pi r^2h=\frac13\pi(3k)^2\cdot\frac{k}{\pi}=\frac13\cdot9k^2\cdot k=3k^3$

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2082 · 1 mark

The present age of husband and wife is 25 years and 22 years. What will be the product of their ages after 3 years? (a) 418 (b) 700 (c) 550 (d) 53

Answer

(b) 700

After 3 years the ages are $25+3=28$ and $22+3=25$ , and $28\times25=700$ .

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2082 · 1 mark

What is sum of the roots of the quadratic equation: $x^2 - 2x - 15 = 0$ ? (a) 2 (b) 3 (c) 4 (d) 5

Answer

(a) 2

For $ax^2+bx+c=0$ the sum of roots is $-\frac{b}{a}=-\frac{-2}{1}=2$ . (Check: roots are $5$ and $-3$ , sum $2$ .)

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2082 · 1 mark

200 is obtained when subtracted 42 from the double of the square of a natural number, what is the natural number? (a) 7 (b) 9 (c) 11 (d) 13

Answer

(c) 11

$2x^2-42=200\Rightarrow x^2=121\Rightarrow x=11$

(natural number, so the negative root is rejected).

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2082 · 1 mark

If 3 is added to the numerator of a fraction, the value of the fraction becomes 1 and when 3 is added to the denominator of the fraction, the value of fraction becomes $\frac{1}{4}$ . What is the fraction? (a) $\frac{1}{3}$ (b) $\frac{2}{3}$ (c) $\frac{2}{5}$ (d) $\frac{3}{5}$

Answer

(c) $\frac{2}{5}$

Let the fraction be $\frac{n}{d}$ . Then $\frac{n+3}{d}=1\Rightarrow d=n+3$ , and $\frac{n}{d+3}=\frac14\Rightarrow 4n=d+3=n+6\Rightarrow n=2,\ d=5$ .

Check: $\frac{5}{5}=1$ and $\frac{2}{8}=\frac14$ .

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2082 · 1 mark

What is the value of m in " $4^m = 0.25$ "? (a) 0 (b) 1 (c) $-1$ (d) 5

Answer

(c) $-1$

$4^m=0.25=\frac14=4^{-1}\Rightarrow m=-1$

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2082 · 1 mark

If $p(x)$ and $q(x)$ are the two polynomial which have no common factors except 1. What is the L.C.M.? (a) $p(x)$ (b) $q(x)$ (c) 1 (d) $p(x) \times q(x)$

Answer

(d) $p(x) \times q(x)$

Since $p(x)$ and $q(x)$ have no common factor other than 1, their H.C.F. is 1. Using $\text{L.C.M.} \times \text{H.C.F.} = p(x)\times q(x)$ , the L.C.M. is $p(x)\times q(x)$ .

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2082 · 1 mark

In the given figure, ABCD is a parallelogram with AD parallel to BE (B, C, E on one line, with E beyond C), and the area of parallelogram ABCD is 100 sq. cm. What is the area of triangle ABE? (a) 50 sq. cm (b) 100 sq. cm (c) 200 sq. cm (d) 40 sq. cm

Answer

(a) 50 sq. cm

The triangle and the parallelogram stand on the same base and lie between the same parallel lines, so the triangle has half the area of the parallelogram:

$\frac12 \times 100 = 50 \text{ sq. cm}$

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2082 · 1 mark

Which of the following statements is true? (a) Rhombus is a square. (b) Parallelogram is a rectangle. (c) Rectangle is a parallelogram. (d) All squares are not Rectangle.

Answer

(c) Rectangle is a parallelogram.

A rectangle has both pairs of opposite sides parallel and equal, so it is a parallelogram. The other statements are false: a rhombus need not have right angles, a parallelogram need not have right angles, and every square is a rectangle.

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2082 · 1 mark

If $A + B = 90^\circ$ then A and B are: (a) Supplementary (b) Complementary (c) Adjacent (d) All of the above

Answer

(b) Complementary

Two angles whose sum is $90^\circ$ are complementary. A sum of $180^\circ$ would make them supplementary.

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2082 · 1 mark

In the given figure, ABCD is a square and EBCF a parallelogram. If AB = 4 cm, what is the area of parallelogram EBCF? (a) 32 cm $^2$ (b) 16 cm $^2$ (c) 20 cm $^2$ (d) 10 cm $^2$

Answer

(b) 16 cm $^2$

The square ABCD and the parallelogram EBCF have the same base BC and lie between the same parallels, so their areas are equal:

$4\times 4 = 16 \text{ cm}^2$

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2082 · 1 mark

In the given figure, O is the center of circle. If TAN is tangent then, what is the value of $\angle AON + \angle ONA$ ? (a) $45^\circ$ (b) $60^\circ$ (c) $90^\circ$ (d) $180^\circ$

Answer

(c) $90^\circ$

The radius OA is perpendicular to the tangent TAN at A, so $\angle OAN = 90^\circ$ . In triangle OAN the angle sum is $180^\circ$ , hence

$\angle AON + \angle ONA = 180^\circ - 90^\circ = 90^\circ$

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2082 · 1 mark

What is the value of x in given figure? (A square ABCD is inscribed in a circle with centre O; x is the angle between the diagonal AC and the side from A.) (a) $90^\circ$ (b) $45^\circ$ (c) $180^\circ$ (d) $60^\circ$

Answer

(b) $45^\circ$

The diagonal AC of a square bisects the right angle at A, so $x = \frac{90^\circ}{2} = 45^\circ$ .

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2082 · 1 mark

A fair dice is rolled. What is the probability of getting a number greater than 4? (a) $\frac{1}{6}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) $\frac{2}{3}$

Answer

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

Numbers greater than 4 on a die are 5 and 6, so there are 2 favourable outcomes out of 6:

$P = \frac{2}{6} = \frac13$

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2082 · 1 mark

In a continuous series, if $\sum fm = 120 + 8k$ and $\sum f = 15 + k$ , what is the value of mean? (a) 12 (b) 20 (c) 8 (d) 15

Answer

(c) 8

$\text{Mean} = \frac{\sum fm}{\sum f} = \frac{120+8k}{15+k} = \frac{8(15+k)}{15+k} = 8$

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2082 · 1 mark

What is the value of x in given figure? (Right-angled figure: A and B are 2 m apart vertically, with B and C at the bottom, AD = 18 m horizontal and DE perpendicular to AD at D, total height of E above the base 20 m; x is the angle at A between AD and AE.) (a) $45^\circ$ (b) $60^\circ$ (c) $90^\circ$ (d) $30^\circ$

Answer

(a) $45^\circ$

The height of E above A is $20-2 = 18$ m and the horizontal distance AD is 18 m, so

$\tan x = \frac{18}{18} = 1 \Rightarrow x = 45^\circ$

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2081 · 1 mark

What is the Volume of a Cylinder with radius K and vertical height Y ? (a) $\pi k^2 y$ (b) $\frac{1}{3}\pi k^2 y$ (c) $\frac{2}{3}\pi k^2 y$ (d) $\frac{1}{3}k\pi^2 y$

Answer

(a) $\pi k^2 y$

Volume of a cylinder = base area $\times$ height = $\pi r^2 h$ . With $r=k$ and $h=y$ this gives $\pi k^2 y$ . The factor $\frac13$ belongs to a cone.

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2081 · 1 mark

If 20, x, y, z, 40 are arithmetic sequence then what is the value of y ? (a) 25 (b) 60 (c) 35 (d) 30

Answer

(d) 30

$y$ is the middle (third) term of the five terms, so it is the mean of the first and last:

$y=\frac{20+40}{2}=30$

Check: the common difference is $(40-20)/4=5$ , giving 20, 25, 30, 35, 40.

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2081 · 1 mark

In $5 + 10 + 15 + \cdots$ which term is 65 ? (a) 10 (b) 11 (c) 12 (d) 13

Answer

(d) 13

Here $a=5$ , $d=5$ , so $t_n=5+(n-1)5=5n$ . Setting $5n=65$ gives $n=13$ .

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2081 · 1 mark

If 11 is subtracted from the square of a number the result is 38. Find the number. (a) $-7$ (b) 7 (c) $\pm 7$ (d) $-6$

Answer

(c) $\pm 7$

$x^2-11=38 \Rightarrow x^2=49 \Rightarrow x=\pm 7$

Both $7$ and $-7$ satisfy the condition, since $(-7)^2-11=38$ .

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2081 · 1 mark

The present ages of mother and daughter are 45 years and 15 years respectively. What will be the sum of their ages after 10 years? (a) 50 (b) 60 (c) 70 (d) 80

Answer

(d) 80

After 10 years, mother is $45+10=55$ and daughter is $15+10=25$ . Sum $=55+25=80$ years.

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2081 · 1 mark

Which one is a quadratic equation in which the values of y are 2 and $-1$ ? (a) $y^2 + y - 2 = 0$ (b) $y^2 - y + 2 = 0$ (c) $y^2 - y - 2 = 0$ (d) $2y^2 - y - 1 = 0$

Answer

(c) $y^2 - y - 2 = 0$

Roots $2$ and $-1$ : sum $=1$ , product $=-2$ . The equation is $y^2-(\text{sum})y+\text{product}=0$ , i.e. $y^2-y-2=0$ .

Check: $(y-2)(y+1)=y^2-y-2$ .

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2081 · 1 mark

What is the value of $\sqrt[3]{\sqrt{(729)^{-1}}}$ ? (a) $\frac{1}{3}$ (b) $\frac{1}{2}$ (c) 3 (d) 2

Answer

(a) $\frac{1}{3}$

$729^{-1}=3^{-6},\quad \sqrt{3^{-6}}=3^{-3},\quad \sqrt[3]{3^{-3}}=3^{-1}=\frac13$

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2081 · 1 mark

If $\left(\frac{1}{a^m}\right)^n = a^x$ , what is the value of x ? (a) $m$ (b) $n$ (c) $mn$ (d) $-mn$

Answer

(d) $-mn$

$\left(\frac{1}{a^m}\right)^n=(a^{-m})^n=a^{-mn}$

so $x=-mn$ .

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2081 · 1 mark

$f(x)$ and $p(x)$ are two polynomials. If there is no common factor to both the polynomials, what will be their lowest common factor (L.C.M.)? (a) $f(x)$ (b) $p(x)$ (c) $f(x) \times p(x)$ (d) 1

Answer

(c) $f(x)\times p(x)$

When two polynomials have no common factor (their H.C.F. is 1), their L.C.M. is the product: $\text{L.C.M.}=\dfrac{f(x)\,p(x)}{\text{H.C.F.}}=f(x)\,p(x)$ .

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2081 · 1 mark

Find the value of $x$ : $3^{x+1} \cdot 5^{x-2} = 27$ (a) 2 (b) 3 (c) 4 (d) 5

Answer

(a) 2

Try $x=2$ : $3^{3}\cdot 5^{0}=27\cdot 1=27$ , which matches.

Check others: $x=3$ gives $81\cdot5=405\neq27$ , and larger values are bigger still, so $x=2$ .

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2081 · 1 mark

In the given figure, the height of the pole including the lamp AF = 19.6 m and the height of the man CE = 1.6 m. If the angle of elevation is $45^\circ$ when a person looks at the top of the lamp, what is the distance between the person and the lamp post? (a) 1.6 m (b) 18 m (c) 19.6 m (d) 21.2 m

Answer

(b) 18 m

The eye level is at the man's height $1.6$ m, so the lamp top is $19.6-1.6=18$ m above the eye. With elevation $45^\circ$ :

$\tan 45^\circ=\frac{18}{d}\Rightarrow d=18\text{ m}$

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2081 · 1 mark

In the given figure, $\triangle RST$ and square PQRS are standing on the same base and between the same parallel lines SR and PT. If PS = 4 cm, what is the area of $\triangle RST$ ? (a) 4 cm $^2$ (b) 8 cm $^2$ (c) 16 cm $^2$ (d) 32 cm $^2$

Answer

(b) 8 cm $^2$

Square PQRS has side $4$ cm, and $\triangle RST$ has base $SR=4$ cm and height $4$ cm (the distance between the parallel lines).

$\text{Area}=\tfrac12\times 4\times 4=8\text{ cm}^2$

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2081 · 1 mark

In the given figure, the area of the $\triangle ABE$ is 108 cm $^2$ and AB = 18 cm. What is the height of the parallelogram ABCD ? (a) 9 cm (b) 6 cm (c) 12 cm (d) 18 cm

Answer

(c) 12 cm

$\triangle ABE$ and parallelogram ABCD stand on the same base AB between the same parallels, so they have the same height $h$ .

$\tfrac12\times 18\times h=108\Rightarrow 9h=108\Rightarrow h=12\text{ cm}$

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2081 · 1 mark

In the given figure (a circle through P, Q, R, S with a tangent at R), which angle is equal to the $\angle QRT$ ? (a) $\angle QRS$ (b) $\angle PQR$ (c) $\angle PSR$ (d) $\angle QPS$

Answer

(d) $\angle QPS$

PQRS is a cyclic quadrilateral, and $\angle QRT$ is an exterior angle at R (T on the extension of SR). An exterior angle of a cyclic quadrilateral equals the interior opposite angle, which is $\angle QPS$ .

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2081 · 1 mark

ABCD is a circle in the given figure where AB = BC. What is the value of $\angle ECD$ ? (a) $100^\circ$ (b) $70^\circ$ (c) $50^\circ$ (d) $80^\circ$

Answer

(d) $80^\circ$

Since AB = BC, the angles subtended by these equal chords in the circle are equal. The exterior angle $\angle ECD$ of the cyclic quadrilateral ABCD equals the interior opposite angle, which works out to $80^\circ$ .

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2081 · 1 mark

In a continuous series, mean $(\bar{x}) = 18 + 3m$ and $\sum fx = 126 + 21m$ , find the number of observations. (a) 6 (b) 7 (c) 8 (d) 9

Answer

(b) 7

Since $\bar{x}=\dfrac{\sum fx}{N}$ ,

$N=\frac{126+21m}{18+3m}=\frac{21(6+m)}{3(6+m)}=7$

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2081 · 1 mark

What is the measure of central tendency that divides the given data into two equal parts keeping the given data either ascending or descending order. (a) Mean (b) Mode (c) Quartile (d) Median

Answer

(d) Median

The median is the middle value of data arranged in order, dividing it into two equal parts.

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2081 · 1 mark

The first quartile is calculated by the formula ............ in a continuous data. (a) $Q_1 = L + \frac{\frac{N}{4} - cf}{f} \times i$ (b) $Q_1 = L + \frac{\frac{N}{2} - cf}{f} \times i$ (c) $Q_1 = L + \frac{\frac{3N}{4} - cf}{f} \times i$ (d) $Q_1 = L + \frac{\frac{N}{4} + cf}{f} \times i$

Answer

(a) $Q_1 = L + \dfrac{\frac{N}{4} - cf}{f} \times i$

The first quartile lies in the class containing the $\frac N4$ -th item; $L$ is its lower limit, $cf$ the cumulative frequency before it, $f$ its frequency and $i$ its class width.

Answer checked by Claude Sonnet · Oct 21, 2026

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2081 · 1 mark

If three children are born in a family, what is the probability that all three children are not daughters? (a) $\frac{1}{8}$ (b) $\frac{1}{6}$ (c) $\frac{3}{2}$ (d) $\frac{7}{8}$

Answer

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

Total outcomes $=2^3=8$ . The only outcome with all three daughters is 1. So

$P(\text{not all daughters})=1-\frac18=\frac78$

Answer checked by Claude Sonnet · Oct 21, 2026

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2081 · 1 mark

A and B are two mutually exclusive events with $P(A) = \frac{1}{4}$ and $P(B) = \frac{1}{2}$ . What is the value of $P(A \cup B)$ ? (a) $\frac{1}{2}$ (b) $\frac{1}{4}$ (c) $\frac{1}{8}$ (d) $\frac{3}{4}$

Answer

(d) $\frac{3}{4}$

For mutually exclusive events, $P(A\cup B)=P(A)+P(B)=\frac14+\frac12=\frac34$ .

Answer checked by Claude Sonnet · Oct 21, 2026

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2081 · 1 mark

If $n(A) = 80$ , $n(B) = 90$ then, What is the maximum value of $n(A \cap B)$ ? (a) 10 (b) 80 (c) 90 (d) 170

Answer

(b) 80

$n(A\cap B)\le \min\{n(A),n(B)\}=\min\{80,90\}=80$ . The maximum occurs when $A\subseteq B$ .

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2081 · 1 mark

If $n(U) = 1000$ , $n(A) = 500$ , $n(B) = 400$ , $n(A \cap B) = 300$ then What is the value of $n(\overline{A} \cap B)$ ? (a) 300 (b) 700 (c) 400 (d) 600

Answer

$n(\overline{A}\cap B)=n(B)-n(A\cap B)=400-300=100$

None of the listed options equals 100, so the question has no correct option as printed. (For reference: $n(A\cup B)=500+400-300=600$ .)

Answer checked by Claude Sonnet · Oct 21, 2026

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2081 · 1 mark

A sum of money amounts Rs. 14520 in 2 years and 15972 in 3 years at certain compound interest. What is the rate of compound interest? (a) 12 % (b) 10% (c) 15% (d) 11%

Answer

(b) 10%

The amount in the third year divided by the amount in the second year is $1+\frac{R}{100}$ :

$1+\frac{R}{100}=\frac{15972}{14520}=1.1\Rightarrow R=10\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2081 · 1 mark

If the cost is depreciated at the rate of 20% per annum, the cost of motorcycle is 175000. Find the price of the motorcycle after 3 years. (a) Rs. 102400 (b) Rs. 300000 (c) Rs. 89600 (d) Rs. 75000

Answer

(c) Rs. 89600

$V=175000\left(1-\frac{20}{100}\right)^3=175000\times(0.8)^3=175000\times0.512=\text{Rs. }89600$

Answer checked by Claude Sonnet · Oct 21, 2026

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2081 · 1 mark

If the population of a village becomes nine times in 2 years, find the population growth rate. (a) 100% (b) 200% (c) 300% (d) 900%

Answer

(b) 200%

$P\left(1+\frac{R}{100}\right)^2=9P\Rightarrow 1+\frac{R}{100}=3\Rightarrow R=200\%$

Answer checked by Claude Sonnet · Oct 21, 2026

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2081 · 1 mark

According to the exchange rate of a day, US $1 = Rs. 132. If the Nepali currency was devaluated by 2%, what is the new exchange rate? (a)$ 129.36 (b) $130 (c)$ 134 (d) $ 134.64

Answer

(d) Rs. 134.64

Devaluing the Nepali rupee by 2% makes a dollar cost 2% more rupees: $132\times1.02=\text{Rs. }134.64$ per US $1.

Answer checked by Claude Sonnet · Oct 21, 2026

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2081 · 1 mark

The base side and slant height of a square based pyramid is $2x$ cm and $y$ cm respectively. What is the real height of the pyramid? (a) $\sqrt{y^2 - 4x^2}$ (b) $\sqrt{y^2 + x^2}$ (c) $\sqrt{y^2 - x^2}$ (d) $\sqrt{y^2 + 4x^2}$

Similar questions: Pyramid volume (2081)

Answer

(c) $\sqrt{y^2 - x^2}$

The base side is $2x$ , so the distance from the centre of the base to the midpoint of a side is $x$ . In the right triangle formed by the height $h$ , this distance and the slant height $y$ : $h^2=y^2-x^2$ .

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2081 · 1 mark

The base side and slant height of a square based pyramid is 16 cm and 10 cm respectively. What is the volume of the pyramid? (a) 853.33 cm $^3$ (b) 512 cm $^3$ (c) 2560 cm $^3$ (d) 1536 cm $^3$

If area of the base of the cylinder is 154 cm $^2$ , Height is 15 cm. What is the total surface area of cylinder? (a) 968 cm $^2$ (b) 528 cm $^2$ (c) 308 cm $^2$ (d) 616 cm $^2$

Answer

(a) 968 cm $^2$

$\pi r^2=154\Rightarrow r^2=49\Rightarrow r=7$ cm.

$TSA=2\pi r(h+r)=2\times\frac{22}{7}\times7\times(15+7)=44\times22=968\text{ cm}^2$

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Past questions and answers

3.If A and B are the subsets of a universal set U, which of the following notation is used to denote (A−B)∪(B−A)(A - B) \cup (B - A)(A−B)∪(B−A)? (a) AΔBA \Delta BAΔB (b) AablaBA abla BAablaB (c) A∩B‾\overline{A \cap B}A∩B (d) A∪B‾\overline{A \cup B}A∪B

4.In a group of 150 people, 120 like to play volleyball and 85 like to play football. If 25 like to play none of the games, then how many people like to play both the games? (a) 20 (b) 30 (c) 80 (d) 25

5.The policy of bank for same principal, same rate and same time, which of the following policy is more profitable to consumer? (a) Annual Compound Interest (b) Semi-Annual Compound Interest (c) Terminal Compound Interest (d) Monthly Compound Interest

6.The present price of machine is Rs. 800000. If the price of the machine depreciates first year by 10% and then 8% and 5% respectively in the following years, what will be the price of the machine after 3 years? (a) Rs. 6,29,000 (b) Rs. 6,25,280 (c) 7,29,280 (d) 6,29,280

7.The price of a good is Rs. 30000. What will be the cost of good after 3 years at the rate of 10% depreciation? (a) Rs. 21087 (b) Rs. 21780 (c) Rs. 21870 (d) Rs. 21708

8.If I.C. 100 = NRs. 160 and 1 American Dollar = NRs. 120, how many American Dollars are equal to I.C. 7500? (a) Dollar 100 (b) Dollar 10 (c) Dollar 110 (d) I.C. 100

9.Find out the area of triangular surfaces of a square based pyramid, if its area of base is 'z' square unit and total surface area is 'y' square unit. (a) yyy sq. unit (b) zzz sq. unit (c) (y−z)(y-z)(y−z) sq. unit (d) y−z\sqrt{y-z}y−z​ sq. unit

10.In the given figure (an ice-cream cone with a hemisphere on top; slant height of the cone is 25 cm), the slant height of the cone is 25 cm and the sum of the curved surface area is 858 cm2^22. What is the common radius? (a) 7 cm (b) 14 cm (c) 21 cm (d) 15 cm

11.What is the total surface area of square based pyramid having the slant height 10 cm and vertical height 8 cm? (a) 483 cm2^22 (b) 240 cm2^22 (c) 144 cm2^22 (d) 384 cm2^22

13.In the given figure (a triangle with base endpoints marked and a segment drawn from the apex to the base), which segment represents a median of the given triangle? (a) AB (b) BC (c) AC (d) AD

14.If the sum of the first nnn terms of arithmetic series is given by Sn=3n2+2nS_n = 3n^2 + 2nSn​=3n2+2n, What is the first term of the series? (a) 3 (b) 5 (c) 2 (d) 7

15.The length of a square room is 10 m and height is 6 m. If the per unit cost of painting the four walls of the room is Rs. 400, find the total cost. (a) Rs. 96000 (b) Rs. 96000 (c) Rs. 69000 (d) Rs. 90600

16.What is the volume of cone with radius 3k3k3k cm and vertical height kπ\frac{k}{\pi}πk​ cm? (a) 3k33k^33k3 (b) 13k3\frac{1}{3}k^331​k3 (c) 13πk3\frac{1}{3}\pi k^331​πk3 (d) 3πk33\pi k^33πk3

17.The present age of husband and wife is 25 years and 22 years. What will be the product of their ages after 3 years? (a) 418 (b) 700 (c) 550 (d) 53

18.What is sum of the roots of the quadratic equation: x2−2x−15=0x^2 - 2x - 15 = 0x2−2x−15=0? (a) 2 (b) 3 (c) 4 (d) 5

19.200 is obtained when subtracted 42 from the double of the square of a natural number, what is the natural number? (a) 7 (b) 9 (c) 11 (d) 13

21.What is the value of m in "4m=0.254^m = 0.254m=0.25"? (a) 0 (b) 1 (c) −1-1−1 (d) 5

22.If p(x)p(x)p(x) and q(x)q(x)q(x) are the two polynomial which have no common factors except 1. What is the L.C.M.? (a) p(x)p(x)p(x) (b) q(x)q(x)q(x) (c) 1 (d) p(x)×q(x)p(x) \times q(x)p(x)×q(x)

23.In the given figure, ABCD is a parallelogram with AD parallel to BE (B, C, E on one line, with E beyond C), and the area of parallelogram ABCD is 100 sq. cm. What is the area of triangle ABE? (a) 50 sq. cm (b) 100 sq. cm (c) 200 sq. cm (d) 40 sq. cm

24.Which of the following statements is true? (a) Rhombus is a square. (b) Parallelogram is a rectangle. (c) Rectangle is a parallelogram. (d) All squares are not Rectangle.

25.If A+B=90∘A + B = 90^\circA+B=90∘ then A and B are: (a) Supplementary (b) Complementary (c) Adjacent (d) All of the above

26.In the given figure, ABCD is a square and EBCF a parallelogram. If AB = 4 cm, what is the area of parallelogram EBCF? (a) 32 cm2^22 (b) 16 cm2^22 (c) 20 cm2^22 (d) 10 cm2^22

27.In the given figure, O is the center of circle. If TAN is tangent then, what is the value of ∠AON+∠ONA\angle AON + \angle ONA∠AON+∠ONA? (a) 45∘45^\circ45∘ (b) 60∘60^\circ60∘ (c) 90∘90^\circ90∘ (d) 180∘180^\circ180∘

28.What is the value of x in given figure? (A square ABCD is inscribed in a circle with centre O; x is the angle between the diagonal AC and the side from A.) (a) 90∘90^\circ90∘ (b) 45∘45^\circ45∘ (c) 180∘180^\circ180∘ (d) 60∘60^\circ60∘

29.A fair dice is rolled. What is the probability of getting a number greater than 4? (a) 16\frac{1}{6}61​ (b) 13\frac{1}{3}31​ (c) 12\frac{1}{2}21​ (d) 23\frac{2}{3}32​

30.In a continuous series, if ∑fm=120+8k\sum fm = 120 + 8k∑fm=120+8k and ∑f=15+k\sum f = 15 + k∑f=15+k, what is the value of mean? (a) 12 (b) 20 (c) 8 (d) 15

32.What is the Volume of a Cylinder with radius K and vertical height Y ? (a) πk2y\pi k^2 yπk2y (b) 13πk2y\frac{1}{3}\pi k^2 y31​πk2y (c) 23πk2y\frac{2}{3}\pi k^2 y32​πk2y (d) 13kπ2y\frac{1}{3}k\pi^2 y31​kπ2y

33.If 20, x, y, z, 40 are arithmetic sequence then what is the value of y ? (a) 25 (b) 60 (c) 35 (d) 30

34.In 5+10+15+⋯5 + 10 + 15 + \cdots5+10+15+⋯ which term is 65 ? (a) 10 (b) 11 (c) 12 (d) 13

35.If 11 is subtracted from the square of a number the result is 38. Find the number. (a) −7-7−7 (b) 7 (c) ±7\pm 7±7 (d) −6-6−6

36.The present ages of mother and daughter are 45 years and 15 years respectively. What will be the sum of their ages after 10 years? (a) 50 (b) 60 (c) 70 (d) 80

37.Which one is a quadratic equation in which the values of y are 2 and −1-1−1? (a) y2+y−2=0y^2 + y - 2 = 0y2+y−2=0 (b) y2−y+2=0y^2 - y + 2 = 0y2−y+2=0 (c) y2−y−2=0y^2 - y - 2 = 0y2−y−2=0 (d) 2y2−y−1=02y^2 - y - 1 = 02y2−y−1=0

38.What is the value of (729)−13\sqrt[3]{\sqrt{(729)^{-1}}}3(729)−1​​ ? (a) 13\frac{1}{3}31​ (b) 12\frac{1}{2}21​ (c) 3 (d) 2

39.If (1am)n=ax\left(\frac{1}{a^m}\right)^n = a^x(am1​)n=ax, what is the value of x ? (a) mmm (b) nnn (c) mnmnmn (d) −mn-mn−mn

40.f(x)f(x)f(x) and p(x)p(x)p(x) are two polynomials. If there is no common factor to both the polynomials, what will be their lowest common factor (L.C.M.)? (a) f(x)f(x)f(x) (b) p(x)p(x)p(x) (c) f(x)×p(x)f(x) \times p(x)f(x)×p(x) (d) 1

41.Find the value of xxx: 3x+1⋅5x−2=273^{x+1} \cdot 5^{x-2} = 273x+1⋅5x−2=27 (a) 2 (b) 3 (c) 4 (d) 5

43.In the given figure, △RST\triangle RST△RST and square PQRS are standing on the same base and between the same parallel lines SR and PT. If PS = 4 cm, what is the area of △RST\triangle RST△RST ? (a) 4 cm2^22 (b) 8 cm2^22 (c) 16 cm2^22 (d) 32 cm2^22

44.In the given figure, the area of the △ABE\triangle ABE△ABE is 108 cm2^22 and AB = 18 cm. What is the height of the parallelogram ABCD ? (a) 9 cm (b) 6 cm (c) 12 cm (d) 18 cm

45.In the given figure (a circle through P, Q, R, S with a tangent at R), which angle is equal to the ∠QRT\angle QRT∠QRT ? (a) ∠QRS\angle QRS∠QRS (b) ∠PQR\angle PQR∠PQR (c) ∠PSR\angle PSR∠PSR (d) ∠QPS\angle QPS∠QPS

46.ABCD is a circle in the given figure where AB = BC. What is the value of ∠ECD\angle ECD∠ECD ? (a) 100∘100^\circ100∘ (b) 70∘70^\circ70∘ (c) 50∘50^\circ50∘ (d) 80∘80^\circ80∘

47.In a continuous series, mean (xˉ)=18+3m(\bar{x}) = 18 + 3m(xˉ)=18+3m and ∑fx=126+21m\sum fx = 126 + 21m∑fx=126+21m, find the number of observations. (a) 6 (b) 7 (c) 8 (d) 9

48.What is the measure of central tendency that divides the given data into two equal parts keeping the given data either ascending or descending order. (a) Mean (b) Mode (c) Quartile (d) Median

50.If three children are born in a family, what is the probability that all three children are not daughters? (a) 18\frac{1}{8}81​ (b) 16\frac{1}{6}61​ (c) 32\frac{3}{2}23​ (d) 78\frac{7}{8}87​

51.A and B are two mutually exclusive events with P(A)=14P(A) = \frac{1}{4}P(A)=41​ and P(B)=12P(B) = \frac{1}{2}P(B)=21​. What is the value of P(A∪B)P(A \cup B)P(A∪B) ? (a) 12\frac{1}{2}21​ (b) 14\frac{1}{4}41​ (c) 18\frac{1}{8}81​ (d) 34\frac{3}{4}43​

52.If n(A)=80n(A) = 80n(A)=80, n(B)=90n(B) = 90n(B)=90 then, What is the maximum value of n(A∩B)n(A \cap B)n(A∩B) ? (a) 10 (b) 80 (c) 90 (d) 170

53.If n(U)=1000n(U) = 1000n(U)=1000, n(A)=500n(A) = 500n(A)=500, n(B)=400n(B) = 400n(B)=400, n(A∩B)=300n(A \cap B) = 300n(A∩B)=300 then What is the value of n(A‾∩B)n(\overline{A} \cap B)n(A∩B) ? (a) 300 (b) 700 (c) 400 (d) 600

54.A sum of money amounts Rs. 14520 in 2 years and 15972 in 3 years at certain compound interest. What is the rate of compound interest? (a) 12 % (b) 10% (c) 15% (d) 11%

55.If the cost is depreciated at the rate of 20% per annum, the cost of motorcycle is 175000. Find the price of the motorcycle after 3 years. (a) Rs. 102400 (b) Rs. 300000 (c) Rs. 89600 (d) Rs. 75000

56.If the population of a village becomes nine times in 2 years, find the population growth rate. (a) 100% (b) 200% (c) 300% (d) 900%

57.According to the exchange rate of a day, US 1=Rs.132.IftheNepalicurrencywasdevaluatedby2(a)1 = Rs. 132. If the Nepali currency was devaluated by 2%, what is the new exchange rate? (a) 1=Rs.132.IftheNepalicurrencywasdevaluatedby2(a) 129.36 (b) 130(c)130 (c) 130(c) 134 (d) $ 134.64

58.The base side and slant height of a square based pyramid is 2x2x2x cm and yyy cm respectively. What is the real height of the pyramid? (a) y2−4x2\sqrt{y^2 - 4x^2}y2−4x2​ (b) y2+x2\sqrt{y^2 + x^2}y2+x2​ (c) y2−x2\sqrt{y^2 - x^2}y2−x2​ (d) y2+4x2\sqrt{y^2 + 4x^2}y2+4x2​

59.The base side and slant height of a square based pyramid is 16 cm and 10 cm respectively. What is the volume of the pyramid? (a) 853.33 cm3^33 (b) 512 cm3^33 (c) 2560 cm3^33 (d) 1536 cm3^33

60.If area of the base of the cylinder is 154 cm2^22, Height is 15 cm. What is the total surface area of cylinder? (a) 968 cm2^22 (b) 528 cm2^22 (c) 308 cm2^22 (d) 616 cm2^22

If A and B are the subsets of a universal set U, which of the following notation is used to denote $(A - B) \cup (B - A)$ ? (a) $A \Delta B$ (b) $A abla B$ (c) $\overline{A \cap B}$ (d) $\overline{A \cup B}$

In a group of 150 people, 120 like to play volleyball and 85 like to play football. If 25 like to play none of the games, then how many people like to play both the games? (a) 20 (b) 30 (c) 80 (d) 25

The policy of bank for same principal, same rate and same time, which of the following policy is more profitable to consumer? (a) Annual Compound Interest (b) Semi-Annual Compound Interest (c) Terminal Compound Interest (d) Monthly Compound Interest

The present price of machine is Rs. 800000. If the price of the machine depreciates first year by 10% and then 8% and 5% respectively in the following years, what will be the price of the machine after 3 years? (a) Rs. 6,29,000 (b) Rs. 6,25,280 (c) 7,29,280 (d) 6,29,280

The price of a good is Rs. 30000. What will be the cost of good after 3 years at the rate of 10% depreciation? (a) Rs. 21087 (b) Rs. 21780 (c) Rs. 21870 (d) Rs. 21708

If I.C. 100 = NRs. 160 and 1 American Dollar = NRs. 120, how many American Dollars are equal to I.C. 7500? (a) Dollar 100 (b) Dollar 10 (c) Dollar 110 (d) I.C. 100

Find out the area of triangular surfaces of a square based pyramid, if its area of base is 'z' square unit and total surface area is 'y' square unit. (a) $y$ sq. unit (b) $z$ sq. unit (c) $(y-z)$ sq. unit (d) $\sqrt{y-z}$ sq. unit

In the given figure (an ice-cream cone with a hemisphere on top; slant height of the cone is 25 cm), the slant height of the cone is 25 cm and the sum of the curved surface area is 858 cm $^2$ . What is the common radius? (a) 7 cm (b) 14 cm (c) 21 cm (d) 15 cm

What is the total surface area of square based pyramid having the slant height 10 cm and vertical height 8 cm? (a) 483 cm $^2$ (b) 240 cm $^2$ (c) 144 cm $^2$ (d) 384 cm $^2$

In the given figure (a triangle with base endpoints marked and a segment drawn from the apex to the base), which segment represents a median of the given triangle? (a) AB (b) BC (c) AC (d) AD

If the sum of the first $n$ terms of arithmetic series is given by $S_n = 3n^2 + 2n$ , What is the first term of the series? (a) 3 (b) 5 (c) 2 (d) 7

The length of a square room is 10 m and height is 6 m. If the per unit cost of painting the four walls of the room is Rs. 400, find the total cost. (a) Rs. 96000 (b) Rs. 96000 (c) Rs. 69000 (d) Rs. 90600

What is the volume of cone with radius $3k$ cm and vertical height $\frac{k}{\pi}$ cm? (a) $3k^3$ (b) $\frac{1}{3}k^3$ (c) $\frac{1}{3}\pi k^3$ (d) $3\pi k^3$

The present age of husband and wife is 25 years and 22 years. What will be the product of their ages after 3 years? (a) 418 (b) 700 (c) 550 (d) 53

What is sum of the roots of the quadratic equation: $x^2 - 2x - 15 = 0$ ? (a) 2 (b) 3 (c) 4 (d) 5

200 is obtained when subtracted 42 from the double of the square of a natural number, what is the natural number? (a) 7 (b) 9 (c) 11 (d) 13

What is the value of m in " $4^m = 0.25$ "? (a) 0 (b) 1 (c) $-1$ (d) 5

If $p(x)$ and $q(x)$ are the two polynomial which have no common factors except 1. What is the L.C.M.? (a) $p(x)$ (b) $q(x)$ (c) 1 (d) $p(x) \times q(x)$

In the given figure, ABCD is a parallelogram with AD parallel to BE (B, C, E on one line, with E beyond C), and the area of parallelogram ABCD is 100 sq. cm. What is the area of triangle ABE? (a) 50 sq. cm (b) 100 sq. cm (c) 200 sq. cm (d) 40 sq. cm

Which of the following statements is true? (a) Rhombus is a square. (b) Parallelogram is a rectangle. (c) Rectangle is a parallelogram. (d) All squares are not Rectangle.

If $A + B = 90^\circ$ then A and B are: (a) Supplementary (b) Complementary (c) Adjacent (d) All of the above

In the given figure, ABCD is a square and EBCF a parallelogram. If AB = 4 cm, what is the area of parallelogram EBCF? (a) 32 cm $^2$ (b) 16 cm $^2$ (c) 20 cm $^2$ (d) 10 cm $^2$

In the given figure, O is the center of circle. If TAN is tangent then, what is the value of $\angle AON + \angle ONA$ ? (a) $45^\circ$ (b) $60^\circ$ (c) $90^\circ$ (d) $180^\circ$

What is the value of x in given figure? (A square ABCD is inscribed in a circle with centre O; x is the angle between the diagonal AC and the side from A.) (a) $90^\circ$ (b) $45^\circ$ (c) $180^\circ$ (d) $60^\circ$

A fair dice is rolled. What is the probability of getting a number greater than 4? (a) $\frac{1}{6}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) $\frac{2}{3}$

In a continuous series, if $\sum fm = 120 + 8k$ and $\sum f = 15 + k$ , what is the value of mean? (a) 12 (b) 20 (c) 8 (d) 15

What is the Volume of a Cylinder with radius K and vertical height Y ? (a) $\pi k^2 y$ (b) $\frac{1}{3}\pi k^2 y$ (c) $\frac{2}{3}\pi k^2 y$ (d) $\frac{1}{3}k\pi^2 y$

If 20, x, y, z, 40 are arithmetic sequence then what is the value of y ? (a) 25 (b) 60 (c) 35 (d) 30

In $5 + 10 + 15 + \cdots$ which term is 65 ? (a) 10 (b) 11 (c) 12 (d) 13

If 11 is subtracted from the square of a number the result is 38. Find the number. (a) $-7$ (b) 7 (c) $\pm 7$ (d) $-6$

The present ages of mother and daughter are 45 years and 15 years respectively. What will be the sum of their ages after 10 years? (a) 50 (b) 60 (c) 70 (d) 80

Which one is a quadratic equation in which the values of y are 2 and $-1$ ? (a) $y^2 + y - 2 = 0$ (b) $y^2 - y + 2 = 0$ (c) $y^2 - y - 2 = 0$ (d) $2y^2 - y - 1 = 0$

What is the value of $\sqrt[3]{\sqrt{(729)^{-1}}}$ ? (a) $\frac{1}{3}$ (b) $\frac{1}{2}$ (c) 3 (d) 2

If $\left(\frac{1}{a^m}\right)^n = a^x$ , what is the value of x ? (a) $m$ (b) $n$ (c) $mn$ (d) $-mn$

$f(x)$ and $p(x)$ are two polynomials. If there is no common factor to both the polynomials, what will be their lowest common factor (L.C.M.)? (a) $f(x)$ (b) $p(x)$ (c) $f(x) \times p(x)$ (d) 1

Find the value of $x$ : $3^{x+1} \cdot 5^{x-2} = 27$ (a) 2 (b) 3 (c) 4 (d) 5

In the given figure, $\triangle RST$ and square PQRS are standing on the same base and between the same parallel lines SR and PT. If PS = 4 cm, what is the area of $\triangle RST$ ? (a) 4 cm $^2$ (b) 8 cm $^2$ (c) 16 cm $^2$ (d) 32 cm $^2$

In the given figure, the area of the $\triangle ABE$ is 108 cm $^2$ and AB = 18 cm. What is the height of the parallelogram ABCD ? (a) 9 cm (b) 6 cm (c) 12 cm (d) 18 cm

In the given figure (a circle through P, Q, R, S with a tangent at R), which angle is equal to the $\angle QRT$ ? (a) $\angle QRS$ (b) $\angle PQR$ (c) $\angle PSR$ (d) $\angle QPS$

ABCD is a circle in the given figure where AB = BC. What is the value of $\angle ECD$ ? (a) $100^\circ$ (b) $70^\circ$ (c) $50^\circ$ (d) $80^\circ$

In a continuous series, mean $(\bar{x}) = 18 + 3m$ and $\sum fx = 126 + 21m$ , find the number of observations. (a) 6 (b) 7 (c) 8 (d) 9

What is the measure of central tendency that divides the given data into two equal parts keeping the given data either ascending or descending order. (a) Mean (b) Mode (c) Quartile (d) Median

If three children are born in a family, what is the probability that all three children are not daughters? (a) $\frac{1}{8}$ (b) $\frac{1}{6}$ (c) $\frac{3}{2}$ (d) $\frac{7}{8}$

A and B are two mutually exclusive events with $P(A) = \frac{1}{4}$ and $P(B) = \frac{1}{2}$ . What is the value of $P(A \cup B)$ ? (a) $\frac{1}{2}$ (b) $\frac{1}{4}$ (c) $\frac{1}{8}$ (d) $\frac{3}{4}$

If $n(A) = 80$ , $n(B) = 90$ then, What is the maximum value of $n(A \cap B)$ ? (a) 10 (b) 80 (c) 90 (d) 170

If $n(U) = 1000$ , $n(A) = 500$ , $n(B) = 400$ , $n(A \cap B) = 300$ then What is the value of $n(\overline{A} \cap B)$ ? (a) 300 (b) 700 (c) 400 (d) 600

A sum of money amounts Rs. 14520 in 2 years and 15972 in 3 years at certain compound interest. What is the rate of compound interest? (a) 12 % (b) 10% (c) 15% (d) 11%

If the cost is depreciated at the rate of 20% per annum, the cost of motorcycle is 175000. Find the price of the motorcycle after 3 years. (a) Rs. 102400 (b) Rs. 300000 (c) Rs. 89600 (d) Rs. 75000

If the population of a village becomes nine times in 2 years, find the population growth rate. (a) 100% (b) 200% (c) 300% (d) 900%

According to the exchange rate of a day, US $1 = Rs. 132. If the Nepali currency was devaluated by 2%, what is the new exchange rate? (a)$ 129.36 (b) $130 (c)$ 134 (d) $ 134.64

The base side and slant height of a square based pyramid is $2x$ cm and $y$ cm respectively. What is the real height of the pyramid? (a) $\sqrt{y^2 - 4x^2}$ (b) $\sqrt{y^2 + x^2}$ (c) $\sqrt{y^2 - x^2}$ (d) $\sqrt{y^2 + 4x^2}$

The base side and slant height of a square based pyramid is 16 cm and 10 cm respectively. What is the volume of the pyramid? (a) 853.33 cm $^3$ (b) 512 cm $^3$ (c) 2560 cm $^3$ (d) 1536 cm $^3$

If area of the base of the cylinder is 154 cm $^2$ , Height is 15 cm. What is the total surface area of cylinder? (a) 968 cm $^2$ (b) 528 cm $^2$ (c) 308 cm $^2$ (d) 616 cm $^2$