# Surds and Indices Quiz Set 001

### Question 1

If \$p^q = 25\$, then what could be \$(p - 1)^(q + 1)\$?

A

64.

B

65.

C

63.

D

66.

Soln.
Ans: a

By inspection we can see that p = 5, q= 2. So \$(5 - 1)^(2 + 1)\$ will be \$4^3\$, i.e., 64.

### Question 2

What is x if \$6^x = 36\$?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

We can write the given expression as \$6^x = 6^2\$. The bases are same so powers should be same. Comparing we get x = 2.

### Question 3

If \$34^0.21 = p, and 34^0.22 = q\$ and \$p^m = q^4\$ then what is the value of m?

A

4.19.

B

4.43.

C

4.33.

D

4.73.

Soln.
Ans: a

Substituting in \$p^m = q^4\$, we get \$34^{0.21m} = 34^{0.22 × 4}\$. Bases are same so powers should be same. Hence, \$0.21m = {0.22 × 4}\$, which gives m = 4.19.

### Question 4

If \$p^q = 512\$, then what could be \$(p - 1)^(q + 1)\$?

A

2401.

B

2402.

C

2400.

D

2403.

Soln.
Ans: a

By inspection we can see that p = 8, q= 3. So \$(8 - 1)^(3 + 1)\$ will be \$7^4\$, i.e., 2401.

### Question 5

What is the value of x if \$(25)^1.5 × 5^9\$ ÷ \$625^3\$ = \$5^x\$?

A

0.

B

2.

C

4.

D

6.

Soln.
Ans: a

Simplifying, we get \$(5^2)^1.5 × 5^9\$ ÷ \$(5 ^ 4)^3\$ = \$5^x\$, which simplifies to \$5^3 × 5^9\$ ÷ \$5^12\$ = \$5^x.\$ Equating the powers x = 3 + 9 - 12 = 0. 