Surds and Indices Quiz Set 001

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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.


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This Blog Post/Article "Surds and Indices Quiz Set 001" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-06-22.

Posted by Parveen(Hoven),
Aptitude Trainer


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