# Surds and Indices Quiz Set 010

### Question 1

If \$2^x = 16\$, then what is the value of \$2^{x - 1}\$?

A

8.

B

9.

C

7.

D

10.

Soln.
Ans: a

We can write the given expression as \$2^x = 2^4\$. The bases are same so powers should be same. Comparing we get x = 4. So x - 1 = 3, we get \$2^3 = 8\$.

### Question 2

If \$2^3.4 = p, and 2^2.6 = q\$ and \$p^m = q^3\$ then what is the value of m?

A

2.29.

B

2.53.

C

2.43.

D

2.83.

Soln.
Ans: a

Substituting in \$p^m = q^3\$, we get \$2^{3.4m} = 2^{2.6 × 3}\$. Bases are same so powers should be same. Hence, \$3.4m = {2.6 × 3}\$, which gives m = 2.29.

### Question 3

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 4

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 5

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.