Power, Indices and Surds: Quantitative Aptitude MCQ Question with Answer
Q21. The value of x for which 4^{2x} -2^{2x} = 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 9^{x} – 10.3^{x} + 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) x^{7}
(b) x^{6}
(c) x^{8}
(d) x^{10}
(e) None of these
Answer: (e) Solution: $\sqrt[3]{x^{12}}+\sqrt{x^6}=x^{\frac{12}{3}}+x^{\frac{6}{2}}=\,\,x^4+x^3$ |