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Question

Assertion :f(x)=|x|.sinx is differentiable at x=0. Reason: If f(x) is not differentiable and g(x) is differentiable at x=a, then f(x).g(x) will be differentiable at x=a

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is C Assertion is correct but Reason is incorrect
Assertion
f(x)=|x|sinx
f(x)=|x|xsinx+|x|cosx
|x| and sinx are continuous, f(x) is also continuous
f(0)=0
f(0+)=0
f(0)=f(0+)=0
f(x) is differentiable at x=0
Reason
if f(x) is not differentiable and g(x) is differentiable at
x=a Then f(x).g(x) is may (or) may not be differentiable at x=a
Reason is not correct.

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