Quantitative Aptitude: Simplification Quiz (Hard) | Concept of Maths

Question 1

Find the value of the expression:
$$ \frac{(0.13)^3 + (0.21)^3 - (0.34)^3}{3 imes 0.13 imes 0.21 imes 0.34} $$

Accepted Answer

C) -1

Answer

A) 1

Answer

B) 0

Answer

D) 0.5

Question 2

If $x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ and $y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$, then find the value of $x^2 + xy + y^2$.

Accepted Answer

B) 63

Answer

A) 62

Answer

C) 65

Answer

D) 64

Question 3

Simplify: $$ \left( 1 - \frac{1}{2^2} \right) \left( 1 - \frac{1}{3^2} \right) \left( 1 - \frac{1}{4^2} \right) \dots \left( 1 - \frac{1}{10^2} \right) $$

Accepted Answer

A) 0.55

Answer

B) 0.45

Answer

C) 0.65

Answer

D) 0.75

Question 4

If $x = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{x}}}$, then find the positive value of $x$.

Accepted Answer

D) $\sqrt{3}$

Answer

A) $\sqrt{2}$

Answer

B) $\frac{1 + \sqrt{3}}{2}$

Answer

C) $\frac{\sqrt{5} - 1}{2}$

Question 5

Find the value of $x$ if: $$ \sqrt{x \sqrt{x \sqrt{x \dots \infty}}} = (0.125)^{-2/3} $$

Accepted Answer

C) 4

Answer

A) 2

Answer

B) 8

Answer

D) 16

Question 6

If $3^x = 4^y = 12^z$, then $z$ is equal to:

Accepted Answer

A) $\frac{xy}{x+y}$

Answer

B) $\frac{x+y}{xy}$

Answer

C) $x+y$

Answer

D) xy

Question 7

Simplify the following expression: $$ \frac{5^{n+2} - 6 \cdot 5^{n+1}}{13 \cdot 5^n - 2 \cdot 5^{n+1}} $$

Accepted Answer

B) -5/3

Answer

A) 5/3

Answer

C) 3/5

Answer

D) -3/5

Question 8

What is the value of $\sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + \sqrt{225}}}}}$?

Accepted Answer

D) 4

Answer

A) 8

Answer

B) 6

Answer

C) 2

Question 9

If $x + \frac{1}{x} = 3$, find the value of $x^5 + \frac{1}{x^5}$.

Accepted Answer

C) 123

Answer

A) 126

Answer

B) 110

Answer

D) 120

Question 10

Simplify: $0.4\overline{7} + 0.5\overline{8}$

Accepted Answer

B) $1.0\overline{6}$

Answer

A) $1.0\overline{5}$

Answer

C) 1.06

Answer

D) $1.1\overline{6}$