## Pre Boards

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## Sample Papers

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# 21.A geometric representation, showing the relationship between a whole and its part, ispie chart pictograph bar graph histogram

A.

pie chart

22.

In a park, 784 plants are arranged, so that number of plants in a row is same as the number of rows. The number of plants in each row is

• 28

• 38

• 48

• 18

A.

28

Required number of plants in each row

=$\sqrt{784}$

=$\sqrt{\overline{2×2}×\overline{2×2}×\overline{7×7}}$

$2×2×7$

$28$

23.

If ${\left(\frac{5}{7}\right)}^{4}×{\left(\frac{5}{7}\right)}^{-3}={\left(\frac{5}{7}\right)}^{5x-2}$ ,then x is equal to

• $\frac{2}{5}$

• $\frac{3}{5}$

• $\frac{4}{5}$

• $\frac{1}{5}$

B.

$\frac{3}{5}$

Given, ${\left(\frac{5}{7}\right)}^{4}$$×$${\left(\frac{5}{7}\right)}^{-3}$=${\left(\frac{5}{7}\right)}^{5x-2}$

$⇒$    ${\left(\frac{5}{7}\right)}^{4-3}$${\left(\frac{5}{7}\right)}^{5x-2}$

on comparing we get,

$1=5x-2$

$⇒$$5x=3$

$⇒$$x=\frac{3}{5}$

24.

Which one of the following 3D shapes does not have a vertex?

• Prism

• Cone

• Sphere

• Pyramid

C.

Sphere

25.

The numerical expression $\frac{3}{7}+\frac{\left(-7\right)}{8}=\frac{25}{56}$ shows that

• rational numbers are closed under subtraction

• rational numbers are closed under multiplication

• rational numbers are closed under division

• rational numbers are closed under addition

D.

rational numbers are closed under addition

26.

A coin is tossed 10 times and the outcomes are observed as
H, T, H, T, T, H, H, T, H, H
(H is Head; T is Tail)
What is the probability of getting Head?

• $\frac{4}{5}$

• $\frac{2}{5}$

• $\frac{1}{5}$

• $\frac{3}{5}$

D.

$\frac{3}{5}$

Given, outcomes are
H, T, H, T, T, H, H, T, H, H
Number of favorable outcomes, n(E)= 6
Total number of possible outcomes, n(S) = 10

Therefore, Required probability=$\frac{n\left(E\right)}{n\left(S\right)}=\frac{6}{10}=\frac{3}{5}$

27.

Let a, b, c be three rational numbers, where a=$\frac{3}{5}$, b= $\frac{2}{3}$ and c =$\frac{-5}{6}$, which one of the following is true?

• $a÷\left(b+c\right)=b÷\left(a+c\right)$

• $a-\left(b-c\right)=c-\left(a-b\right)$

• $a×\left(b+c\right)=b×\left(a+c\right)$

B.

Consider, a+(b+c) = c+(a+b)

$⇒$$\frac{3}{5}+\left(\frac{2}{3}-\frac{5}{6}\right)=\frac{-5}{6}+\left(\frac{3}{5}+\frac{2}{3}\right)$

$⇒$$\frac{3}{5}+\left(\frac{4-5}{6}\right)=\frac{-5}{6}+\left(\frac{9+10}{15}\right)$

$⇒$$\frac{3}{6}-\frac{1}{6}=\frac{-5}{6}+\frac{19}{15}$

$⇒$$\frac{18-5}{30}=\frac{-25+38}{30}$

$⇒$$13=13$

28.

If q is the square of a natural number p, then p is

• the square root of q

• equal to q

• greater than q

• the square of q

A.

the square root of q

If p2 = q, then p = $\sqrt{q}$

29.

The value of $\sqrt{91+\sqrt{70+\sqrt{121}}}$ is

• 10

• 11

• 12

• 9

A.

10

Given, $\sqrt{91+\sqrt{70+\sqrt{121}}}$

$\sqrt{91+\sqrt{70+11}}$

=$\sqrt{91+\sqrt{81}}$

=$\sqrt{91+9}$

=$\sqrt{91+9}$

=$\sqrt{100}$

$10$

30.

Given below is a data set of temperatures (in oC)
-6,-8,-2,3, 2, 0,5, 4, 8.

What is the range of the data?

• 16 oC

• 18 oC

• 10 oC

• 0 oC

A.

16 oC

Rangle = maximum value - minimum value

8-(-8)=8+8=16