This Article consist of most important ” Surds and Indices Questions and Answers ” that are mostly asked in all competitive exams. We collected these questions from the students who appeared in exams. Now try to solve these questions.

## Surds and Indices Questions and Answers

**Question : 1** If 3^(x – y) = 27 and 3^(x + y) = 243, then x is equal to:

A. 0

B. 2

C. 4

D. 6

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

3^x – y = 27 = 3^3 x – y = 3 ….(i)

3^x + y = 243 = 3^5 x + y = 5 ….(ii)

On solving (i) and (ii), we get x = 4.

**Question : 2 ** If 5^a = 3125, then the value of 5^(a – 3) is:

A. 25

B. 125

C. 625

D. 1625

**Show Answer**

**Correct Answer : ** **A**

**Explanation : **

5^a = 3125 5^a = 55

a = 5.

5^(a – 3) = 5^(5 – 3) = 5^2 = 25

**Question : 3** Given that 10^(0.48) = x, 10^(0.70) = y and x^z = y^2, then the value of z is close to:

A. 1.45

B. 1.88

C. 2.9

D. 3.7

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

x^z = y^2 10^(0.48z) = 10^(2 x 0.70) = 10^1.40

0.48z = 1.40

z = 140/48 = 35/12 = 2.9 (approx.)

**Question : 4 ** If(a/b)^x-1 = (b/a)^x-3, then the value of x is:

A. 1/2

B. 1

C. 2

D. 7/2

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

(a/b)^x-1 = (b/a)^x-3

(a/b)^x-1 = (a/b)^-(x-3)

x – 1 = 3 – x

2x = 4

x = 2.

**Question : 5** (17)^3.5 x (17)^? = 178

A. 2.29

B. 2.75

C. 4.25

D. 4.5

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

Let (17)^3.5 x (17)^x = 178.

Then, (17)^3.5 + x = 178.

3.5 + x = 8

x = (8 – 3.5)

x = 4.5