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Q.

Assertion (A) : If  y(x)=π216x2cosx.cosθ1+sin2θdθ,  then at  x=π,  dydx=π
Reason (R) :    ddxa(x)b(x)f(t)dt=f(b(x))dbdxf(a(x))dadx

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a

Both A and R are individually true but R is not the correct explanation of A

b

A is false but R is true

c

A is true but R is false

d

Both A and R are individually true and R is the correct explanation of A

answer is D.

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Detailed Solution

y=cosxπ216x2cosθ1+sin2θdθ   dydx=sinxπ216x2cosθ1+sin2θdθ+cosxddxπ216x2cosθ1+sin2θdθ      =sinxπ216x2cosθ1+sin2θdθ+cos2x1+sin2x.2x  At  x=π,dydx=2π

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