Number System Ques 14
Question
$\left(x^{2 a}\right)^{b}=\sqrt{x^{\frac{4 b}{c}}}$ and $\frac{x^{4 b}}{x^{3 a}}$ $=x^{3(a-b)} \cdot x^{b}, a, b$ and $c$ being natural numbers.
(1) $a \neq b \neq c$
(2) $a=b \lt c$
(3) $a \lt b=c$
(4) $a=b=c$
(5) None of these
(IBPS Bank PO/MT CWE (Main) 18.11.2016)
Show Answer
Answer: (4)
Solution: (4)
$\left(x^{2 a}\right)^{b}=(x)^{\frac{4 b}{2 c}}$
$\Rightarrow 2 ab=\frac{2 b}{c} $
$\Rightarrow a c=1$
$a=c=1[\because$ Both $a$ and $c$ are natural numbers]
$\frac{x^{4 b}}{x^{3 a}}=x^{3(a-b)} \cdot x^{b}$
$\Rightarrow x^{4 b-3 a}=x^{3 a-2 b}$
$\Rightarrow 4 b-3 a=3 a-2 b$
$\Rightarrow 6 b=6 a$
$\Rightarrow a=b$
From (i) and (ii) we have,
$a=b=c$
BETA
