2012-II-31 – Solving Master

Ans: B
Let

2^{p} a^{q} b^{r} c^{s}

be the third expression.

$\begin{aligned} 1st expression = & 2 & \times & a^{2} & \times & b^{4} & \times & c \\ 2nd expression = & 2^{2} & \times & a^{4} & \times & b^{2} & \times & c^{6} \\ 3rd expression = & 2^{p} & \times & a^{q} & \times & b^{r} & \times & c^{s} \\ H.C.F. = & 2^{0} & \times & a & \times & b^{2} & \times & c^{0} \\ L.C.M. = & 2^{2} & \times & a^{4} & \times & b^{5} & \times & c^{6} \end{aligned}$

Therefore, $p = 0$ , $q = 1$ , $r = 5$ and $s = 0$ . i.e. the third expression is $a b^{5}$ .

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