Surds and Indices Aptitude Questions and Answers | MCQ Problems

Surds and Indices Aptitude Questions and Answers | MCQ Problems: So, not able to clear the Surds and Indices in Aptitude Section? Well, want to practice more and more. Then this article, which contains the Surds and Indices Quiz is the answer for all your searches. Therefore, all those aspirants who want to get the real concept of this Topic can check this post to find out better information. You can prepare with the given Surds & Indices Aptitude Questions and Answers by taking a mock test below.

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Surds and Indices Quiz

Quiz Name	Surds and Indices
Category	Aptitude
Number of Questions	20
Time	30 Minutes
Exam Type	MCQ (Multiple Choice Questions)

Surds and Indices Online Test – Practice Now

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1. Value of (256)¹⁶x (256)^0.09 is

a. 64

b. 4

c. 8

d. 16

Answer: B

Explanation:

(256)^0.16 x (256)^0.09

(256)^0.16+0.09 = (256)^0.25 = (256)^1/4

= (4⁴)^1/4 = 4^{4 x 1/4} = 4

2. The value of x^1/2. Y^-1.z^2/3 , when x = 9, y = 3, and z = 8 is

a. 18

b. 12

c. 6

d. 4

Answer: D

Explanation:

x^1/2. Y^-1 .z^2/3

Putting the value of x, y, z from the question in the above equation

9^1/2. 3^-1. 8^2/3

3 .3^-1.2

3. 3^-1.2²= 3⁰.2²= 4

3. If m and n are whole numbers such that, mⁿ = 121, then the value of (m-1)ⁿ⁺¹ is

a. 1

b. 10

c. 121

d. 1000

Answer: D

Explanation:

If mⁿ = 121

mⁿ = 11²

n = 2;

m = 11; then

(m-1) ⁿ⁺¹ = (11- 1) ²⁺¹ = 10³ = 1000

4.  If 2^x-1+2^x+1=320, then x is equal to

a. 6

b. 8

c. 5

d. 7

Answer: D

Explanation:

By equating the powers
x-6=1
x = 1+6 = 7

5. If x = √196 + √200, then x/2 + 2/x is?

A. 14
B. 7
C. 2√50
D. √50

Answer: Option C

Explanation:

x = 14 + 10√2

x/2 = 7 + 5√2

2/x = (7 – 5√2) / (7 + 5√2)(7 – 5√2) = 5√2 – 7

x/2 + 2/x = 10√2 = 2√50

6. If x = √8 – √7, y = √6 – √5 and z = √10 – 3, which of the following is true?

A. x < z < y
B. z < x < y
C. x < y < z
D. z < y < x

Answer: Option B

Explanation:

x = √8 – √7 = 1/(√8 + √7) and y = √6 – √5 = 1/(√6 + √5) and z = √10 – 3 = 1/(√10 + 3)

As (√8 + √7) > (√6 + √5), (√8 – √7) < (√6 – √5)

As (√10 + 3) > (√8 + √7) > (√6 + √5)

z < x < y.

7. If x = √3 – √2, then find (x – 1/x)²

A. 2
B. 4
C. 2√2
D. 9

Answer: Option E

Explanation:

• x = √3 – √2
• 1/x = 1/√3 – √2 = (√3 + √2) / (√3 – √2)(√3 + √2)
• = √3 + √2
• (x – 1/x)²= [(√3 – √2) – (√3 + √2)]²
• = (-2√2)²= 8

8. If x = √11 + √20, y = √15 + √17 and z = √14 + √18, then which of the following holds true?

A. x < y < z

B. y < z < x

C. y < x < z

D. x < z < y

Answer: Option D

Explanation:

• By squaring and simplifying,
• x²= 31 + 2√220
• y²= 32 + 2√255
• z²= 32 + 2√252
• x²< z² < y² => x < z < y.

9. [(√7 + √5) / ( (√7 – √5)] + [(√7 – √5) / (√7 + √5)] = ?

A. 6

B. 12

C. 14

D. 18

Answer: Option B

Explanation:

[(√7 + √5) / ( (√7 – √5)] + [(√7 – √5) / (√7 + √5)]

= [(√7 + √5)² + (√7 – √5)²] / (√7 + √5)(√7 – √5)

[(√7 + √5)² + (√7 – √5)²] / 2 = 12

10. If y³ = 0.008, y⁵ = ?

A. 0.00032

B. 0.0032

C. 0.032

D. 0.000032

Answer: Option A

Explanation: 

• y⁵= (0.2)⁵ = 0.00032.

11. Solve for m if 3(√3)^m+4 = (√3)^2m+7

A. 0

B. -1

C. 2

D. 3

Answer: Option B

12. Identify the greatest numbers: 4⁵⁰, 2¹⁰⁰, 16²⁵

A. 4⁵⁰

B. 2¹⁰⁰

C. 16²⁵

D. All are equal

Answer: Option D

Explanation:

• 4⁵⁰= (2²)⁵⁰ = 2¹⁰⁰ => 16²⁵ = (2⁴)²⁵ = 2¹⁰⁰
• Hence, 4⁵⁰, 2¹⁰⁰and 164²⁵ are all equal.

13. Which of the following is the greatest?

A. 4^1/4

B. 3^7/10

C. 5^1/2

D. 6^1/5

Answer: Option C

Explanation:

• 5 > 4 and 1/2 > 1/4
• 5^1/2> 4^1/4
• 4^1/4cannot be the greatest. Hence 3^1/4 also cannot be the greatest.
• 3^7/10= (3⁷)^1/10 = (2187)^1/10
• 5^1/2= 5^5/10 = (5⁵)^1/10 = (3125)^1/10
• 6^1/5= 6^2/10 = (6²)^1/10 = (36)^1/10
• As (3125)^1/10> (2187)^1/10 > (36)^1/10 , 5^1/2 is the greatest.

14. (3^a+1 9^a+2 27^a) / (3^a-1 9^a 27^a+1) = ?

A. 3

B. 9

C. 27

D. 1

Answer: Option C

Explanation:

• (3^a+19^a+2 27^a) / (3^a-1 9^a 27^a+1) = [3^a+1 3^2(a+2) (3³)^a] / [3^a-1 (3²)^a (3³)^a+1] = 3^6a+5 / 3^6a+2 = 3³ = 27.

15. (27^2/3 * 9^1/2 * 81^1/4)^-1/4 = ?

A. 3

B. 9

C. 1/3

D. 1/9

Answer: Option C

Explanation:

• (27^2/3* 9^1/2 * 81^1/4)^-1/4 = [(3³)^2/3 * (3²)^1/2 * (3⁴)^1/4]^-1/4
• = (3²* 3 * 3)^-1/4 = (3⁴)^-1/4 = 1/3.

16. (3^-3 * 9^5/2) / (27^2/3 * 3^-4) = ?

A. 3

B. 9

C. 81

D. 21

Answer: Option C

Explanation:

• (3^-3* 9^5/2) / (27^2/3 * 3^-4) = [3^-3 * (3²)^5/2] / [(3³)^2/3 * 3^-4]
• = (3^-3* 3⁵) / (3² * 3^-4) = (3^-3+5)/(3^2-4) = 3²/3^-2 = 3² * 3² = 81.

17. (9^-7 / 27^-3)^4/5 = ?

A. 3^-1

B. 3^-2

C. 3^-3

D. 3^-4

Answer: Option D

Explanation:

• (9^-7/ 27^-3)^4/5 = [(3²)^-7 / (3³)^-3]^4/5
• = (3^-143⁹)^4/5 = 3^-4 .

18. (17¹⁴ * 17¹⁶) / 17^-8 = ?

A. 17²⁸

B. 17²⁴

C. 17²⁶

D. 17²²

Answer: Option D

Explanation:

• ? = 17^14+16-8= 17²²

19. (27²/4^-3)^-5/6 = ?

A. 1/1296

B. 1/46656

C. 1/7256

D. 1/7776

Answer: Option D

Explanation:

• (27²/4^-3)^-5/6= [(3³)²/(2²)^-3]^-5/6
• = (3⁶* 2⁶)^-5/6
• = (6⁶)^-5/6= 1/6⁵ = 1/ 7776.

20. (8x⁹ / 27y^-6)^-2/3 = ?

A. 9/4 x^-6 y^-4

B. 9/4 x^-4 y^-6

C. 9/4 x^-6 y⁴

D. 9/4 x^-4 y⁶

Answer: Option A

Explanation:

• (8x⁹/ 27y^-6)^-2/3 = (8x⁹y⁶ / 27)^-2/3 = [(2/3 x³ y²)³]^-2/3
• = 9/4 x^-6y^-4.

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Surds and Indices Aptitude Formulae

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Surds and Indices MCQ Problems | Online Quiz

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Surds and Indices Quiz Questions in Aptitude

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