There are three kinds of liquids X, Y, Z. Thr | vedclass

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(B) Let $x_n, y_n, z_n$ be the amounts of liquids $X, Y, Z$ in jar $J_1$ after $n$ operations.Initially,$J_1$ contains $100 \, ml$ of $X$,$J_2$ contai

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$x > z > y$

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(B) Let $x_n, y_n, z_n$ be the amounts of liquids $X, Y, Z$ in jar $J_1$ after $n$ operations.Initially,$J_1$ contains $100 \, ml$ of $X$,$J_2$ contains $100 \, ml$ of $Y$,and $J_3$ contains $100 \, ml$ of $Z$.After one operation,the composition of $J_1$ changes as liquid is transferred out and back in.Let $A_n$ be the state vector representing the amounts of $X, Y, Z$ in the jars. The process is a linear transformation.After $n=4$ operations,the amount of $X$ remains the largest because it started in $J_1$ and is only partially removed and partially returned.The amount of $Z$ in $J_1$ increases as it is transferred from $J_3$ to $J_1$ in the third step of each operation.The amount of $Y$ in $J_1$ is the smallest as it must travel through $J_2$ and $J_3$ before reaching $J_1$.Thus,the amounts in $J_1$ satisfy $x > z > y$.

$List-I$	$List-II$
$(P)$ If $a=0, b=1, c=0$ and $d=0$,then	$(1)$ $h$ is one-one
$(Q)$ If $a=1, b=0, c=0$ and $d=0$,then	$(2)$ $h$ is onto
$(R)$ If $a=0, b=0, c=1$ and $d=0$,then	$(3)$ $h$ is differentiable on $R$
$(S)$ If $a=0, b=0, c=0$ and $d=1$,then	$(4)$ the range of $h$ is $[0,1]$
	$(5)$ the range of $h$ is $\{0,1\}$

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