# Surds and indices Questions and Answers updated daily – Aptitude

Surds and indices Questions: Solved 10 Surds and indices Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

## Surds and indices Questions

1. If 5^(a + b) = 5 x 25 x 125, find the value of (a + b)^2 ?

Correct Ans:36
Explanation:
Given 5^(a+b) = 5^1 x 5^2 x 5^3 => 5^(a+b) = 5^(1+2+3) => 5^(a + b) = 5^6 (a+b) = 6 => ( a + b )^2 = 36
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2. Evaluate 1000^7 / 10^14 = ?

Correct Ans:10 7
Explanation:
1000^7 / 10^14 = (10^3)^7 x 10^–14 = 10^(21 – 14) = 10^7
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3. If a = 1 / ( 3 – 2 ?2 ) then find 1/a =?

Correct Ans:3 + 2?2
Explanation:
Multiplying with conjugate we get a = (3 + 2?2)/1 = 3 + 2 ?2
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4. If a and b are positive integers such that a^b = 121 then (a-1)^(b + 1) = ?

Correct Ans:1000
Explanation:
a^b = 121 => a^b=11^2=> a = 11 and b =2 so (11-1)^(2+1) = 10^3 = 1000
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5. (256)^0.16 x (256)^0.09 = ?

Correct Ans:4
Explanation:
(256)0.16 x (256)0.09 = (256)0.25 = 2561/4 = (44)1/4 = 4
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6. (0.04) ^(–1.5) = ?

Correct Ans:125
Explanation:
(0.04)^–1.5 = (1/25)^ –1.5= 25^1.5 = 25^3/2 = (25)3/2 = 25xsqrt(25) = 25 x 5 = 125
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7. 3^( x – y )=27 and 3^( x + y )=243, then x is equal to

Correct Ans:4
Explanation:
3^( x – y) = 27 => 3 (x – y) = 3^3 => x – y = 3 3^( x + y) = 243 => 3^(x + y) = 3^5 => x + y = 5 Adding these two equations, we get 2x = 8 => x = 4
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8. If 5^a = 3125, then the value of 5^(a-3) = ?

Correct Ans:25
Explanation:
5a = 3125 => 5a = 55 => a=5 and 5a-3 = 55-3 = 52 = 25
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9. (16)3.5 x (16)? = 2564

Correct Ans:4.5
Explanation:
(16)^3.5 x 16^x = 2564 => 16^( x + 3.5) = (16^2)4 = 16^8 => x+ 3.5 = 8 => x = 4.5
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10. If (a/b)^(x-1)=(b/a)^(x-3) then the value of x is:

Correct Ans:2
Explanation:
(a/b)x-1 = (b/a)x-3 => (a/b)x-1 = (a/b)3-x => x-1 = 3-x => 2x = 4 => x=2
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