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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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Q 24. The greatest four digit number which is also a perfect square is
9701
9801
9901
None of these