Quantitative Aptitude: Simplification Quiz Set 8 | Concept of Maths

Question 1

Let $a = \sqrt{13 + \sqrt{13 + \sqrt{13 + \dots \infty}}}$ and $b = \sqrt{13 - \sqrt{13 - \sqrt{13 - \dots \infty}}}$. What is the value of $a - b$?

Accepted Answer

A) 1

Answer

B) 13

Answer

C) 0

Answer

D) $\sqrt{13}$

Question 2

Simplify the following expression:
$$ \frac{0.051 imes 0.051 imes 0.051 + 0.041 imes 0.041 imes 0.041}{0.051 imes 0.051 - 0.051 imes 0.041 + 0.041 imes 0.041} $$

Accepted Answer

B) 0.092

Answer

A) 0.01

Answer

C) 0.002

Answer

D) 0.1

Question 3

Find the sum of the series:
$$ \frac{1}{3 imes 5} + \frac{1}{5 imes 7} + \frac{1}{7 imes 9} + \dots + \frac{1}{19 imes 21} $$

Accepted Answer

A) $1/7$

Answer

B) $2/21$

Answer

C) $3/7$

Answer

D) $5/21$

Question 4

Evaluate:
$$ \frac{1}{\sqrt{1} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \dots + \frac{1}{\sqrt{99} + \sqrt{100}} $$

Accepted Answer

C) 9

Answer

A) 10

Answer

B) 11

Answer

D) 8

Question 5

If $2^a = 3^b = 6^{-c}$, then what is the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$?

Accepted Answer

B) 0

Answer

A) 1

Answer

C) -1

Answer

D) 2

Question 6

Find the value of:
$$ \frac{1}{2!} + \frac{2}{3!} + \frac{3}{4!} + \frac{4}{5!} $$

Accepted Answer

B) $119/120$

Answer

A) $1/120$

Answer

C) $23/24$

Answer

D) 1

Question 7

Simplify:
$$ 1 + \frac{1}{2 + \frac{1}{1 + \frac{1}{3}}} $$

Accepted Answer

A) $15/11$

Answer

B) $11/15$

Answer

C) $7/11$

Answer

D) $13/11$

Question 8

If $a = 997, b = 998$ and $c = 999$, find the value of $a^3 + b^3 + c^3 - 3abc$.

Accepted Answer

A) 8982

Answer

B) 2994

Answer

C) 4491

Answer

D) 8991

Question 9

Simplify: $(256)^{0.16} imes (16)^{0.18}$

Accepted Answer

C) 4

Answer

A) 2

Answer

B) 16

Answer

D) 8

Question 10

Evaluate the value of the nested radical:
$$ \sqrt{1 + 2024 \sqrt{1 + 2025 \sqrt{1 + 2026 imes 2028}}} $$

Accepted Answer

B) 2025

Answer

A) 2024

Answer

C) 2026

Answer

D) 1