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Statement-1: The equation $x \log x=2-x$ is satisfied by at least one value of $x$ lying between 1 and 2.
Statement-2: The function $f(x)=x \log x$ 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 $[1,2]$
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Statement-2: The function $f(x)=x \log x$ 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 $[1,2]$
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The correct answer is:
Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
$f(x)=x \log x, f(1)=0, f(2)=4$
$g(x)=2-x, g(1)=1, g(2)=0$
$\log 10>\log 4 \Rightarrow 1>\log 4$
Thus statement $-1$ and 2 both are true and statement-2 is a correct explanation of statement 1 .
$g(x)=2-x, g(1)=1, g(2)=0$
$\log 10>\log 4 \Rightarrow 1>\log 4$
Thus statement $-1$ and 2 both are true and statement-2 is a correct explanation of statement 1 .
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