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# Power, Indices and Surds MCQ Question with Answer

## Power, Indices and Surds: Quantitative Aptitude MCQ Question with Answer

Q11. If I6 × 8n+2 = 2m, then m is equal to :

(a) n + 8

(b) 2n + 8

(c) 3n + 2

(d) 3n + 10

(e) None of these

 Answer: (d)Solution: $16\times 8^{n+2}=2^m$$\Rightarrow 2^4\times 2^{3n+6}=2^m$$\Rightarrow 2^{4+3n+6}=2^m$$\Rightarrow 3n+10 =m Q12. The value of\sqrt[3]{512}=2^x, then x is equal to: (a) 5 (b) 4 (c) (d) 3 (e) None of these  Answer: (d)Solution: \sqrt[3]{512}=2^x$$\Rightarrow \sqrt[3]{2^9}=2^x$$\Rightarrow 2^{\frac{9}{3}}=2^x$$\Rightarrow x=3$

Q13. The value of x satisfying $\sqrt{4+\sqrt{x}}=4$is:

(a) 125

(b) 144

(c) 120

(d)

(e) None of these

 Answer: (b)Solution: $\sqrt{4+\sqrt{x}}=4$$\Rightarrow 4+\sqrt{x}=16$$\Rightarrow \sqrt{x}=12$$\Rightarrow x=144 Q14. If5^{x+3}\,\,=\,\,\left( 25 \right) ^{3x-4}, then the value of x is: (a) \frac{5}{11} (b) \frac{11}{5} (c) \frac{11}{3} (d) \frac{13}{5} (e) None of these  Answer: (b)Solution: 5^{x+3}\,\,=\,\,\left( 25 \right) ^{3x-4}$$\Rightarrow 5^{x+3}\,\,=\,\,5^{\begin{array}{c} 6x-8\\ \end{array}}$$\Rightarrow 6x-8 =\,\,x+3$$\Rightarrow 5x\,\,=\,\,11$$\Rightarrow x=\frac{11}{5} Q15. If 34x-2 = 729, then the value of x is: (a) 1 (b) 1.5 (c) 2 (d) 3 (e) None of these  Answer: (c)Solution: 3^{4x-2}\,\,=\,\,729$$\Rightarrow 3^{4x-2}=3^6$$\Rightarrow 4x-2=6$$\Rightarrow x=2$

Q16. If $2^{2x-1}\,\,=\,\,\frac{1}{8^{x-3}}$ then n the value of x is:

(a) 3

(b) 2

(c) 0

(d) -2

(e) None of these

 Answer: (b)Solution: $2^{2x-1}\,\,=\,\,\frac{1}{8^{x-3}}$$\Rightarrow 2^{2x-1}\,\,=\,\,2^{-3\left( x-3 \right)}$$\Rightarrow 2x-1=-3x+9$$\Rightarrow 5x=10$$\Rightarrow x=2$

Q17. If, $\left( \frac{a}{b} \right) ^{x-1}\,\,=\,\,\left( \frac{b}{a} \right) ^{x-3}$ then n the value of x is:

(a) 1

(b) 4

(c) 2

(d) 3

(e) None of these

 Answer: (c)Solution: $\left( \frac{a}{b} \right) ^{x-1}\,\,=\,\,\left( \frac{b}{a} \right) ^{x-3}$$\Rightarrow \left( \frac{a}{b} \right) ^{x-1}=\,\,\frac{b^{x-3}}{a^{x-3}}$$\Rightarrow \left( \frac{a}{b} \right) ^{x-1}=\frac{a^{-\left( x-3 \right)}}{b^{-\left( x-3 \right)}}=\left( \frac{a}{b} \right) ^{-\left( x-3 \right)}$$\Rightarrow x-1=-x+3$$\Rightarrow x=2$

Q18. If$2^x\times 8^{\frac{1}{5}}=2^{\frac{1}{5}}\,\,$, then x is equal to:

(a) $\frac{1}{5}$

(b) $-\frac{1}{5}$

(c) $\frac{2}{5}$

(d) $-\frac{2}{5}$

(e) None of these

 Answer: (d)Solution: $2^x\times 8^{\frac{1}{5}}=2^{\frac{1}{5}}\,\,$$2^x\times 2^{\frac{3}{5}}\,\,=2^{\frac{1}{5}}\,\,$$\Rightarrow 2^{x+\frac{3}{5}}\,\,=2^{\frac{1}{5}}\,\,$$\Rightarrow x+\frac{3}{5}=\frac{1}{5}$$\Rightarrow x=\,\,-\frac{2}{5}$

Q19. If 2x – 2x-1 = 4 , then The value of x3 is:

(a) 27

(b) 4

(c) 1

(d) 256

(e) None of these

 Answer: (a)Solution: $2^x-2^{x-1}=4$$\Rightarrow 2^x-\frac{2^x}{2}=4$$\Rightarrow \frac{2.2^x-2^x}{2}=4$$\Rightarrow 2^x\left( 2-1 \right) =8$$\Rightarrow 2^x=2^3$$\Rightarrow x=3$$\Rightarrow x^3=27$

Q20. The value of x for which 2x+4 – 2x-1 = 31, is:

(a) 0

(b) -2

(c) 2

(d) 1

(e) None of these

 Answer: (d)Solution: $2^{x+4}-2^{x-1}=31$$\Rightarrow 16\times 2^x-\frac{2^x}{2}=31$$\Rightarrow 2^x\left( 16-\frac{1}{2} \right) =31$$\Rightarrow 2^x\times \frac{31}{2}=31$$\Rightarrow 2^x=2^1$$x=1$

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