Chemical Effects of Electric Current
Some Natural Phenomena
Force and Pressure
Pollution of Air and Water
Cell Structure and Functions
Crop Production and Management
Friction
Reproduction in Animals
Synthetic Fibres and Plastics
Coal and Petroleum
Combustion and Flame
Reaching the Age of Adolescence
Conservation and Flame
Light
Materials: Metals and Non-Metals
Microorganisms: Friend and Foe
Sound
Stars and the Solar System
Conservation of Plants and Animals

Algebraic Expressions and Identities
Data Handling
Direct and Inverse Proportions
Linear Equations in One Variable
Visualising Solid Shapes
Introduction to Graphs
Understanding Quadrilaterals
Factorisation
Cubes and Cube Roots
Comparing Quantities
Practical Geometry
Rational Numbers
Squares and Square Roots
Exponents and Powers
Mensuration
Playing with Numbers

Squares and Square Roots

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Q 1. The smallest number by which 136 must be multiplied so that it becomes a perfect square is

2

17

34

None of these

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Q 2. The product of the two numbers is 1936. If one number is 4 times the other, the numbers are

16, 121

22, 88

44, 44

None of these

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Q 3. The least square number exactly divisible by 4, 6, 10, 15 is

400

100

25

900

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Q 4. The value of {tex}\sqrt{388+\sqrt{127+\sqrt{289}}}{/tex} is

17

12

20

None of these

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Q 5. A gardener arranges plants in rows to form a square. He finds that in doing so 15 plants are left out. If the total number of plants is 3984, the number of plants in each row is

62

63

64

None of these

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Q 6. If a is a natural number then {tex}a^2+\frac{1}{a^2}{/tex} is always greater than or equal to

6

4

3

2

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Q 7. If {tex}\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b}{/tex}, then value of {tex}\frac{b}{a}{/tex}

0.016

{tex}\frac{125}{2}{/tex}

0.16

None of these

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Q 8. The hypotenuse of an isosceles right-angled triangular field has a length of {tex}30\sqrt{2}{/tex} m, then the length of other side is

{tex}30\sqrt{2}{/tex}

30 m

25 m

None of these

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Q 9. The sides of a triangle are denoted by x, y and z. Area of the triangle and semi perimeter of the triangle are denoted by P and q respectively. If P = {tex}\sqrt{q(q-x)(q-y)(q-z)}{/tex} and {tex}x+y-z=y+z-x=z+x-y=4{/tex}. Find P (in square units).

{tex}2\sqrt{3}{/tex}

{tex}3\sqrt{3}{/tex}

{tex}4\sqrt{3}{/tex}

{tex}6\sqrt{3}{/tex}

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Q 10. Find the square root of {tex}\frac{81b^2a^4}{36x^2y^6}{/tex}

{tex}\frac{3ba^2}{2xy^3}{/tex}

{tex}\frac{3b^2a}{2x^2y}{/tex}

{tex}\frac{3ba}{2x^3y}{/tex}

{tex}\frac{3ba}{2xy^2}{/tex}

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Q 11. Which of the following can be a perfect square?

A number ending in 3 or 7

A number ending with odd number of zeros

A number ending with even number of zeros

A number ending in 2.

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Q 12. Which of the following can be the square of a natural number 'n'?

sum of the squares of first n natural numbers

sum of the first n natural numbers

sum of first (n - 1) natural numbers

sum of first 'n' odd natural numbers

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Q 13. Which of the following is the number of non-perfect square numbers between the squares of the numbers n and n + 1?

n + 1

n

2n

2n + 1

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Q 14. Which of the following is the difference between the squares of two consecutive natural numbers is

sum of the two numbers

difference of the numbers

twice the sum of the two numbers

twice the sum of the two numbers

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Q 15. Which of the following is the number of a non-perfect square numbers between 17{tex}^2{/tex} and 18{tex}^2{/tex}?

613

35

34

70

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Q 16. Which of the following is the number of zeros in the square of 900?

3

4

5

2

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Q 17. If a number of n-digits is a perfect square and 'n' is an even number, then which of the following is the number of digits of its square root?

{tex}\frac{n-1}{2}{/tex}

{tex}\frac{n}{2}{/tex}

{tex}\frac{n+1}{2}{/tex}

{tex}2n{/tex}

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Q 18. If a number of n-digit is a perfect square and 'n' is an odd number then which of the following is the number of digits of its square root?

{tex}\frac{n-1}{2}{/tex}

{tex}\frac{n}{2}{/tex}

{tex}\frac{n+1}{2}{/tex}

{tex}2n{/tex}

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Q 19. Which of the following is a Pythagorean-triplet?

{tex}n, (n^2- 1){/tex} and {tex}(n^2 + 1){/tex}

{tex}(n-1), (n^2- 1){/tex} and {tex}(n^2 + 1){/tex}

{tex}(n + 1), (n^2- 1){/tex} and {tex}(n^2 + 1){/tex}

{tex}2n, (n^2- 1){/tex} and {tex}(n^2 + 1){/tex}

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Q 20. The greatest perfect square of a natural number smaller than {tex}(51)^2{/tex} is

50

2500

3600

2551

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Q 21. {tex}\sqrt{176+\sqrt{2401}}{/tex} is equal to

12

13

14

15

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Q 22. If {tex}\frac{1872}{\sqrt{x}}=234{/tex}, then x is equal to

8

64

256

4

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Q 23. If 140{tex}\sqrt{x}{/tex}+315=1015 , then x is equal to

15

225

5

25

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