Power, Indices and Surds MCQ Question with Answer

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


Q21. The value of x for which 42x -22x = 12 holds, is:

(a) 2

(b) 3

(c) 1

(d) -1

(e) None of these

Answer: (c)

Solution: $4^{2x}-2^{2x}=12$

$\Rightarrow 2^{4x}-2^{2x}=12, Let\,\,2^{2x\,\,}=a$

$\therefore a^2-a-12=0$

$\Rightarrow \left( a-4 \right) \left( a+3 \right) =0$

$\therefore a=\,\,4 or\,\,a=-3; if\,\,a=-3 then\,\,it\,\,complex\,\,number$

$\therefore a=4$

$\Rightarrow 2^{2x}=2^2$

$\Rightarrow x=1$

Q22. If 9x – 10.3x + 9 = 0 then x is equal to:

(a) 2 or 0

(b) 1 or 3

(c) 1 or 9

(d) 1 or -2

(e) None of these

Answer: (a)

Solution: $9^x-10.3^x+9=0$

$\Rightarrow 3^{2x}-10.3^x+9=0, Let\,\,3^x=a$

$\Rightarrow a^2-10a+9=0$

$\Rightarrow \left( a-9 \right) \left( a-1 \right) =0$

$\therefore a=9 or\,\,a=1$

$\Rightarrow 3^x=3^2\,\,or\,\,3^x=3^0$

$\Rightarrow x=2 or\,\,0$

Q23. The value of $\sqrt[3]{x^{12}}+\sqrt{x^6}$is:

(a) x7

(b) x6

(c) x8

(d) x10

(e) None of these

Answer: (e)

Solution: $\sqrt[3]{x^{12}}+\sqrt{x^6}=x^{\frac{12}{3}}+x^{\frac{6}{2}}=\,\,x^4+x^3$



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