Competitive Exams : Quantitative Aptitude - Simplification (Set 6) | Concept of Maths

Question 1

Find the value of the expression:
$$ \frac{\sqrt{42 + \sqrt{42 + \sqrt{42 + \dots \infty}}}}{\sqrt{20 - \sqrt{20 - \sqrt{20 - \dots \infty}}}} $$

Accepted Answer

B) 1.75

Answer

A) 1.5

Answer

C) 2.0

Answer

D) 1.25

Question 2

Simplify the following:
$$ \frac{0.064 + 0.027}{0.16 - 0.12 + 0.09} $$

Accepted Answer

C) 0.7

Answer

A) 0.1

Answer

B) 0.4

Answer

D) 0.9

Question 3

If $x = 1 + \frac{1}{2 + \frac{1}{3 + \frac{1}{4}}}$, then find the value of $x$.

Accepted Answer

A) $\frac{43}{30}$

Answer

B) $\frac{30}{43}$

Answer

C) $\frac{13}{30}$

Answer

D) $\frac{43}{13}$

Question 4

Find the value of $k$ if $2^{k-1} imes 4^{2k+1} = 8^{k+3}$.

Accepted Answer

D) 4

Answer

A) 2

Answer

B) 3

Answer

C) 5

Question 5

Simplify: $$ \sqrt{11 + 2\sqrt{30}} - \frac{1}{\sqrt{11 + 2\sqrt{30}}} $$

Accepted Answer

C) $\frac{10}{\sqrt{6} + \sqrt{5}}$

Answer

A) $2\sqrt{5}$

Answer

B) $2\sqrt{6}$

Answer

D) $\frac{10}{\sqrt{11}}$

Question 6

What is the unit digit of the expression:
$7^{105} + 3^{58} imes 2^{41}$?

Accepted Answer

B) 5

Answer

A) 3

Answer

C) 7

Answer

D) 1

Question 7

Simplify: $$ \frac{(x^a/x^b)^{a+b} \cdot (x^b/x^c)^{b+c} \cdot (x^c/x^a)^{c+a}}{1} $$

Accepted Answer

A) 1

Answer

B) $x^{a+b+c}$

Answer

C) $x^{abc}$

Answer

D) 0

Question 8

Find the value of $x$ if:
$$ \sqrt[3]{x} = \sqrt[3]{4} + \sqrt[3]{16} + 1 $$
Then $x$ is equivalent to: (Hint: use $a^3 - b^3$ identity on $\sqrt[3]{4}-1$)

Accepted Answer

C) Not solvable directly - let's re-evaluate: Solve $\frac{3}{\sqrt[3]{4}-1}$

Answer

A) 3

Answer

B) 27

Answer

D) 64

Question 9

Simplify: $$ 999\frac{1}{7} + 999\frac{2}{7} + 999\frac{3}{7} + 999\frac{4}{7} + 999\frac{5}{7} + 999\frac{6}{7} $$

Accepted Answer

B) 5997

Answer

A) 5994

Answer

C) 5999

Answer

D) 6000

Question 10

Solve for $x$: $$ 0.\overline{37} + 8.\overline{5} + 1.\overline{23} $$

Accepted Answer

D) $10.\overline{16}$

Answer

A) $10.\overline{15}$

Answer

B) 10.15

Answer

C) $10.\overline{14}$