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–1 is True, Statement–2 is False

Statement–1 is True, Statement–2 is True; Statement–2 is a correct explanation for Statement–1

Statement –1 is False, Statement–2 is True

Statement–1 is True, Statement–2 is True; Statement–2 NOT a correct explanation for Statement-1.

answer is A.

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Detailed Solution

$f (x) = x \log x, f (1) = 0, f (2) = 4; g (x) = 2 - x, g (1) = 1, g (2) = 0$

$\log 10 > \log 4 \Rightarrow 1 > \log 4$

Thus statement 1 and 2 both are true and statement 2 is a correct explanaton of statement 1.

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