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Q.

If x=acos3θsin2θ,y=asin3θcos2θ and x2+y2p(xy)q(p,q,∈N) is independent of θ,  then

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a

4p = 5q

b

4q = 5p

c

p + q = 9

d

pq = 20

answer is A.

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Detailed Solution

x2+y2p(xy)q=asin2⁡θcos2⁡θ2pa2sin5⁡θcos5⁡θq=a2p(sin⁡θcos⁡θ)4pa2q(sin⁡θcos⁡θ)5qwhich is independent of θ if 4p=5q.
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If x=acos3θsin2θ,y=asin3θcos2θ and x2+y2p(xy)q(p,q,∈N) is independent of θ,  then