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Question

Assertion :The number of solutions of the pair of equations 2sin2θcos2θ= 2cos2θ3sinθ=0 in the interval [0, 2π] is two. Reason: If 2cos2θ3sinθ=0, then θ can not lie in III or IV quadrant.

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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Given system of equations
2sin2θcos2θ=0
2cos2θ3sinθ=0
Now, 2sin2θcos2θ=0
4sin2θ1=0
sinθ=±12
θ=π6, 5π6 , 7π6 , 11π6
Now, 2cos2θ3sinθ=0
2sin2θ+3sinθ2=0
sinθ=12,2(not possible)
So sinθ=12
θ=π6 ,5π6
Here, θ lies in first or second quadrant
Hence, statement 2 is correct
So, the number of common solutions is 2.
Hence, statement 1 is correct. Hence, reason is the correct explanation for assertion.

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