Mathematics · 2013
JEE Main · 9 April 2013, Shift 1 · Q69
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…
Statement $\displaystyle 1$ : The equation $\displaystyle x \log x=2-x$ is satisfied by at least one value of $\displaystyle x$ lying between $\displaystyle 1$ and 2.Statement $\displaystyle 2$ : The function $\displaystyle f(x)=x \log x$ is an increasing function in [$\displaystyle 1$, $\displaystyle 2$] and $\displaystyle \mathrm{g}(x)=2-x$ is a decreasing function in [$\displaystyle 1$, $\displaystyle 2$] and the graphs represented by these functions intersect at a point in [$\displaystyle 1$, $\displaystyle 2$]
Official answer
(1)
Statement-$\displaystyle 1$ is true, Statement-$\displaystyle 2$ is true; Statement-$\displaystyle 2$ is a correct explanation for Statement-1.
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JEE Main 2013 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.