Question

$\text{List I}$ has four entries and $\text{List II}$ has five entries. Each entry of $\text{List I}$ is to be correctly matched with one or more than one entries of $\text{List II}.$

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{Let}f:A\to B\text{be a function defined by}& \text{(P)}& -1\\ & f\left(x\right)=\log (x^2-7|x|+12)\text{. If}C=Z-A& & \\ & \text{is a set, then an element in}C\text{is}& & \\ \text{(B)}& \text{A solution of the inequation}& \text{(Q)}& 0\\ & \left|\frac{2}{x-4}\right|>1\text{is}& & \\ \text{(C)}& \text{If}f\left(x\right)=\log \left(\frac{1-|x|}{|x-2|}\right),\text{then an}& \text{(R)}& 1\\ & \text{integer which is not in the domain}& & \\ & \text{of}f\text{, is}& & \\ \text{(D)}& \text{An element in the domain of the}& \text{(S)}& 2\\ & \text{function}f\left(x\right)=\frac{e^{x-4x^2}}{\sqrt{4x-x^2}}\text{is}& & \\ & & \text{(T)}& 3\end{array}$

Which of the following is the only INCORRECT combination?

• A. $\text{(C)}\to \text{(P), (Q), (R), (S), (T)}$
• B. $\text{(C)}\to \text{(P), (R), (S), (T)}$
• C. $\text{(D)}\to \text{(R), (S)}$
• D. $\text{(D)}\to \text{(R), (S), (T)}$

Answer 1

The correct option is A $\text{(C)}\to \text{(P), (Q), (R), (S), (T)}$

$\left(C\right)$
For $f$ to be defined,
$\frac{1-|x|}{|x-2|}>0$
$\Rightarrow |x|-1<0$ and $x\ne 2$
$\Rightarrow x\in (-1,1)$
$\therefore$ Integers not in the domain of $f$ is $Z-\left\{0\right\}.$
$\text{(C)}\to \text{(P), (R), (S), (T)}$

$\left(D\right)$
For $f$ to be defined,
$4x-x^2>0$
$\Rightarrow x(x-4)<0$
$\Rightarrow x\in (0,4)$
$\text{(D)}\to \text{(R), (S), (T)}$