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                Statement 1: The equation \[x\log x=2-x\] is satisfied by least one value of \[x\] lying between 1 and 2.                 Statement 2: The function \[f(x)\]= \[x\log x\] is an increasing function is \[[1,2]\] 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].                   JEE Main Online Paper (Held On 09 April 2013)

A)                 Statement -1 is true, Statement-2 is true. Statement -2 is 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.                

Correct Answer: A

Solution :

                Curve of \[g(x)=2-x\] and \[f(x)=x\log x\] from graph we observe that f(x) and g(x) are increasing and decreasing in the internal [1, 2] respectively at least one point in [1, 2] will be exist where the both curve intersect each other.