Competitive Exams : Quantitative Aptitude - Simplification (Set 10) | Concept of Maths

Question 1

Simplify the following nested radical expression: $$\sqrt{10 + \sqrt{24} + \sqrt{40} + \sqrt{60}}$$

Accepted Answer

A) $\sqrt{2} + \sqrt{3} + \sqrt{5}$

Answer

B) $\sqrt{2} + \sqrt{3} - \sqrt{5}$

Answer

C) $\sqrt{5} + \sqrt{2} + 1$

Answer

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

Question 2

Evaluate the expression: $$\frac{(0.13 - 0.21)^3 + (0.21 - 0.34)^3 + (0.34 - 0.13)^3}{3(0.13 - 0.21)(0.21 - 0.34)(0.34 - 0.13)}$$

Accepted Answer

B) 1

Answer

A) 0

Answer

C) 3

Answer

D) -1

Question 3

Find the value of $x$ in the following continued fraction: $$x = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{2}}}}$$

Accepted Answer

C) $\rac{13}{8}$

Answer

A) $\rac{8}{5}$

Answer

B) $\rac{11}{7}$

Answer

D) $\rac{21}{13}$

Question 4

If $3^{x-y} = 27$ and $3^{x+y} = 243$, then find the value of $x$.

Accepted Answer

A) 4

Answer

B) 2

Answer

C) 1

Answer

D) 8

Question 5

Simplify: $$5\frac{1}{3} \div 1\frac{1}{9} imes \frac{1}{4} \left( 10 + \frac{3}{1 - \frac{1}{5}} ight)$$

Accepted Answer

D) 16.5

Answer

A) 12.5

Answer

B) 14.25

Answer

C) 15

Question 6

Find the sum: $0.\overline{63} + 0.\overline{37} + 0.\overline{80}$

Accepted Answer

B) $1.\overline{81}$

Answer

A) $1.\overline{79}$

Answer

C) 1.80

Answer

D) $1.\overline{80}$

Question 7

If $\sqrt{1 + \frac{x}{144}} = \frac{13}{12}$, find the value of $x$.

Accepted Answer

C) 25

Answer

A) 1

Answer

B) 13

Answer

D) 169

Question 8

Which of the following is larger: $\sqrt[3]{4}$ or $\sqrt[4]{6}$?

Accepted Answer

A) $\sqrt[3]{4}$

Answer

B) $\sqrt[4]{6}$

Answer

C) They are equal

Answer

D) Cannot be compared

Question 9

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

Accepted Answer

B) 0.55

Answer

A) 0.5

Answer

C) 0.62

Answer

D) 0.45

Question 10

Simplify: $999\frac{998}{999} imes 999$

Accepted Answer

C) 998999

Answer

A) 998001

Answer

B) 998998

Answer

D) 999999