Quantitative Aptitude: Simplification Quiz Set 4 | Concept of Maths

Question 1

Simplify the following nested radical expression:
$$\sqrt{30 - 12\sqrt{6}}$$

Accepted Answer

C) $3\sqrt{2} - 2\sqrt{3}$

Answer

A) $3\sqrt{2} + 2\sqrt{3}$

Answer

B) $2\sqrt{6} - 3$

Answer

D) $5\sqrt{6} - 12$

Question 2

Find the value of:
$$\frac{(2.3)^3 + (1.7)^3 + (5)^3 - 3 imes 2.3 imes 1.7 imes 5}{(2.3)^2 + (1.7)^2 + 5^2 - (2.3 imes 1.7) - (1.7 imes 5) - (5 imes 2.3)}$$

Accepted Answer

A) 9.0

Answer

B) 10.0

Answer

C) 4.0

Answer

D) 5.7

Question 3

Solve the continued fraction:
$$x = 1 + \frac{1}{2 + \frac{1}{1 + \frac{1}{4}}}$$

Accepted Answer

B) $\frac{19}{14}$

Answer

A) $\frac{13}{9}$

Answer

C) $\frac{17}{12}$

Answer

D) $\frac{21}{16}$

Question 4

If $x + \frac{1}{x} = 4$, then find the value of $x^4 + \frac{1}{x^4}$.

Accepted Answer

D) 194

Answer

A) 196

Answer

B) 192

Answer

C) 254

Question 5

Evaluate the expression:
$$ \frac{2^{n+4} - 2 \cdot 2^n}{2 \cdot 2^{n+3}} + 2^{-3} $$

Accepted Answer

C) 1/2

Answer

A) $2^n$

Answer

B) 1

Answer

D) 7/8

Question 6

If $x = \sqrt{7 + 4\sqrt{3}}$, find the value of $x + \frac{1}{x}$.

Accepted Answer

A) 4

Answer

B) $2\sqrt{7}$

Answer

C) $4\sqrt{3}$

Answer

D) 2

Question 7

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

B) 0.55

Answer

A) 0.5

Answer

C) 0.65

Answer

D) 0.45

Question 8

If $5^{x+3} = 25^{3x-4}$, then find the value of $x$.

Accepted Answer

D) 2.2

Answer

A) 1.5

Answer

B) 2.4

Answer

C) 3.2

Question 9

Find the square root of $x$ if:
$$ x = \frac{(0.03)^2 + (0.21)^2 + (0.065)^2}{(0.003)^2 + (0.021)^2 + (0.0065)^2} $$

Accepted Answer

A) 10

Answer

B) 100

Answer

C) 1

Answer

D) 0.1

Question 10

Simplify: $3 imes 0.3 imes 0.03 imes 0.003 imes 30$.

Accepted Answer

B) 0.00243

Answer

A) 0.000243

Answer

C) 0.0243

Answer

D) 0.243