JEE Advanced Problem 1

Calculus Level 5

Statement 1 :f(x)=0x1+t2dt\displaystyle f(x) = \int_0^x \sqrt{ 1 +t^{2}} dt is an odd function and g(x)=f(x)g(x) = f ' (x) is an even function

Statement 2 : For a differentiable function f(x) if f(x) f ' (x) is an even function then f(x) f(x) is an odd function

1 ) Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement 1.

2) Statement 1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement 1.

3) Statement 1 is true , statement 2 is false

4) Statement 1 is false , statement 2 is correct

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