Question

Statement-1 : The equation $xlogx=2-x$ is satisfied by at least one value of $x$ lying between $1$ and $2$.
Statement-2 : The function $f(x)=xlogx$ is an increasing function in $[1,2]$ and $g(x)=2-x$ is a decreasing function in $[1,2]$ and the graphs represented by these functions intersect at a point in $[1,2]$

• A. Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
• B. Statement-1 is true; Statement-2 is true; Statement-2 is not correct explanation for Statement-1.
• C. Statement-1 is false, Statement-2 is true.
• D. Statement-1 is true, Statement-2 is false.

Answer 1

Answer: (A)

$f\left(x\right)=xlogx,f\left(1\right)=0,f\left(2\right)=4$
$g\left(x\right)=2-x,g\left(1\right)=1,g\left(2\right)=0$
$log10>log4\Rightarrow 1>log4$
Thus statement -1 and 2 both are true and statement-2 is a correct explanation of statement 1.