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JEE Advanced 2020 Paper 1

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Question : 43

Total: 54

Let the function f:R→R be defined by f(x)=x3−x2+(x−1)‌sin‌x and let g:R→R be an arbitrary function. Let fg:R→R be the product function defined by (f,g)(x)=f(x)g(x). Then which of the following statements is/are TRUE?

[JEE Adv 2020 P1]

If g is continuous at x=1, then fg is differentiable at x=1
If fg is differentiable at x=1, then g is continuous at x=1
If g is differentiable at x=1, then fg is differentiable at x=1
If fg is differentiable at x=1, then g is differentiable at x=1

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