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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].

1. Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
2. Statement-1 is true; Statement-2 is true; Statement-2 is not correct explanation for Statement-1.
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 is false.

Correct answer: Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Solution

Both statements are true because the increasing nature of f(x) and the decreasing nature of g(x) in the interval [1, 2] guarantees that they will intersect at least once, confirming that there is at least one solution to the equation in that range.

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