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Question

If x=2costcos2t,y=2sintsin2t, then the value of d2ydx2 |t=π/2 is

A
32
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B
52
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C
52
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D
32
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Solution

The correct option is D 32
dydx=dydt×dtdx=2cost2cos2t2sint+2sin2t
ddt(dydx)dtdx=d2ydx2
d2ydx2=ddt(costcos2tsin2tsint)(12sint+2sin2t)
d2ydx2 |t=π/2=(sint+2sin2t)(sin2tsint)(costcos2t)(2cos2tcost)[sin2tsint]2(2sin2t2sint)
=(1)(1)(1)(2)(1)2(2)
=32

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