Practice MCQ Questions and Answer on Surds and Indices
11.
$$\frac{{{2^{n + 4}} - 2 \times {2^n}}}{{2 \times {2^{\left( {n + 3} \right)}}}} + {2^{ - 3}}$$ ÃÂÃÂ ÃÂÃÂ 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 $$\frac{2}{{\sqrt 7 + \sqrt 5 }} + $$ ÃÂÃÂ $$\frac{7}{{\sqrt {12} - \sqrt 5 }} - $$ ÃÂÃÂ $$\frac{5}{{\sqrt {12} - \sqrt 7 }}$$ ÃÂÃÂ 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.
$${\left( {\frac{{{x^b}}}{{{x^c}}}} \right)^{\left( {b + c - a} \right)}}.$$ ÃÂÃÂ $${\left( {\frac{{{x^c}}}{{{x^a}}}} \right)^{\left( {c + a - b} \right)}}.$$ ÃÂÃÂ $${\left( {\frac{{{x^a}}}{{{x^b}}}} \right)^{\left( {a + b - c} \right)}} = ?$$
- (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 5ÃÂÃÂÃÂâÃÂÃÂÃÂÃÂ3 + $$\sqrt {75} $$ = 17.32, then the value of 14ÃÂÃÂÃÂâÃÂÃÂÃÂÃÂ3 + $$\sqrt {108} $$ ÃÂÃÂÃÂàis.
- (A) 32.46
- (B) 35.64
- (C) 34.64
- (D) 33.86