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Question

Assertion :If f(x)=x1lntdt1+t+t2(x>0) then f(x)=f(1x) Reason: If f(x)=x1lntdtt+1, then f(x)+f(1x)=12(lnx)2

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 incorrect but Reason is correct
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D
Both Assertion and Reason are incorrect
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Solution

The correct option is C Assertion is incorrect but Reason is correct
f(1x)=1x1logt1+t+t2dt
Substitute t=1zdt=1z2dz
f(1x)=x1log1z1+1z+1z2(dzz2)
=x1logzdzz2+z+1=x1logtdt1+t+t2=f(x)

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