Ans: A
$\begin{array}{lllllllllll}
3x^4y^2z & = & & & 3 & \times & x^4 & \times & y^2 & \times & z \\
4xy^5z & = & 2^2 & \times & & & x & \times & y^5 & \times & z \\
6x^2y^3 & = & 2 & \times & 3 & \times & x^2 & \times & y^3 & & \\ \hline
\text{H.C.F.} & = & & & & & x & \times & y^2
\end{array}$
$\begin{array}{lllllllllll}
3x^4y^2z & = & & & 3 & \times & x^4 & \times & y^2 & \times & z \\
4xy^5z & = & 2^2 & \times & & & x & \times & y^5 & \times & z \\
6x^2y^3 & = & 2 & \times & 3 & \times & x^2 & \times & y^3 & & \\ \hline
\text{H.C.F.} & = & & & & & x & \times & y^2
\end{array}$
Therefore, the required H.C.F. is $xy^2$.
