Practice MCQ Questions and Answer on Surds and Indices

11.

$$\frac{{{2^{n + 4}} - 2 \times {2^n}}}{{2 \times {2^{\left( {n + 3} \right)}}}} + {2^{ - 3}}$$     is equal to = ?

  • (A) 2(n+1)
  • (B) $$\left( {\frac{9}{8} - {2^n}} \right)$$
  • (C) $$\left( { - {2^{n + 1}} + \frac{1}{8}} \right)$$
  • (D) 1

12.

The simplified form of $$\frac{2}{{\sqrt 7 + \sqrt 5 }} + $$   $$\frac{7}{{\sqrt {12} - \sqrt 5 }} - $$   $$\frac{5}{{\sqrt {12} - \sqrt 7 }}$$   is = ?

  • (A) 5
  • (B) 2
  • (C) 1
  • (D) 0

13.

Given that $$\sqrt 5 $$ = 2.236 and $$\sqrt 3 $$ = 1.732, then the value of $$\frac{1}{{\sqrt 5 + \sqrt 3 }}{\text{ is = ?}}$$

  • (A) 0.564
  • (B) 0.504
  • (C) 0.252
  • (D) 0.202

14.

The value of $$\frac{{{2^{n - 1}} - {2^n}}}{{{2^{n + 4}} + {2^{n + 1}}}}{\text{is = ?}}$$

  • (A) $$ - \frac{1}{{36}}$$
  • (B) $$\frac{2}{3}$$
  • (C) $$\frac{1}{{13}}$$
  • (D) $$\frac{5}{{13}}$$

15.

(3x - 2y) : (2x + 3y) = 5 : 6, then one of the value of $${\left( {\frac{{\root 3 \of x + \root 3 \of y }}{{\root 3 \of x - \root 3 \of y }}} \right)^2}{\text{ is = ?}}$$

  • (A) $$\frac{1}{{25}}$$
  • (B) 5
  • (C) $$\frac{1}{5}$$
  • (D) 25

16.

$${\left( {\frac{{{x^b}}}{{{x^c}}}} \right)^{\left( {b + c - a} \right)}}.$$   $${\left( {\frac{{{x^c}}}{{{x^a}}}} \right)^{\left( {c + a - b} \right)}}.$$   $${\left( {\frac{{{x^a}}}{{{x^b}}}} \right)^{\left( {a + b - c} \right)}} = ?$$

  • (A) xabc
  • (B) 1
  • (C) xab+bc+ca
  • (D) xa+b+c

17.

Which of the following statements(s) is/are true? $$\eqalign{ & {\text{I}}.\frac{3}{{71}} \frac{5}{{91}} \frac{7}{{99}} \cr & {\text{II}}.\frac{{11}}{{135}} > \frac{{12}}{{157}} > \frac{{13}}{{181}} \cr} $$

  • (A) Only I
  • (B) Only II
  • (C) Both I and II
  • (D) Neither l nor II

18.

What are the values of x and y that satisfy the equation, $${{\text{2}}^{0.7x}}{\text{.}}{{\text{3}}^{ - 1.25y}}{\text{ = }}\frac{{8\sqrt 6 }}{{27}}{\text{ ?}}$$

  • (A) x = 2.5, y = 6
  • (B) x = 3, y = 5
  • (C) x = 3, y = 4
  • (D) x = 5, y = 2

19.

Simplify : $$\left( {\frac{{\frac{3}{{2 + \sqrt 3 }} - \frac{2}{{2 - \sqrt 3 }}}}{{2 - 5\sqrt 3 }}} \right) = ?$$

  • (A) $$\frac{1}{2} - 5\sqrt 3 $$
  • (B) 2 - $$5\sqrt 3 $$
  • (C) 1
  • (D) 0

20.

If 5√3 + $$\sqrt {75} $$ = 17.32, then the value of 14√3 + $$\sqrt {108} $$  is.

  • (A) 32.46
  • (B) 35.64
  • (C) 34.64
  • (D) 33.86