Surds and Indices Quiz Set 013

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Question 1

What is $6561^0.12 × 6561^0.13$?

 A

9.

 B

10.

 C

8.

 D

11.

Soln.
Ans: a

By inspection, we get $(3^8)^0.12 × (3^8)^0.13$, which equals $(3^8)^(0.12 + 0.13)$, which equals $(3^8)^0.25$, which equals $3^2$, or 9. Note: The trick in such type of questions is to keep an eye on the "bases".


Question 2

If $4^0.16 = p, and 4^0.34 = q$ and $p^m = q^4$ then what is the value of m?

 A

8.50.

 B

8.74.

 C

8.64.

 D

9.04.

Soln.
Ans: a

Substituting in $p^m = q^4$, we get $4^{0.16m} = 4^{0.34 × 4}$. Bases are same so powers should be same. Hence, $0.16m = {0.34 × 4}$, which gives m = 8.50.


Question 3

If $√65$ is approximately $8$, then what is $65^3.5$?

 A

2097152.

 B

2097153.

 C

2097151.

 D

2097154.

Soln.
Ans: a

Since $√x = x^{1/2}$, we can see that $65^3.5$ is same as $(√65)^7$ which gives $8^7$ = 2097152.


Question 4

What is the value of x if $(117649)^3.5 × 7^8$ ÷ $49^2.5$ = $7^x$?

 A

24.

 B

30.

 C

36.

 D

42.

Soln.
Ans: a

Simplifying, we get $(7^6)^3.5 × 7^8$ ÷ $(7 ^ 2)^2.5$ = $7^x$, which simplifies to $7^21 × 7^8$ ÷ $7^5$ = $7^x.$ Equating the powers x = 21 + 8 - 5 = 24.


Question 5

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.


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This Blog Post/Article "Surds and Indices Quiz Set 013" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-08-12.

Posted by Parveen(Hoven),
Aptitude Trainer


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