The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Given system of equations
2sin2θ−cos2θ=0
2cos2θ−3sinθ=0
Now, 2sin2θ−cos2θ=0
⇒4sin2θ−1=0
⇒sinθ=±12
⇒θ=π6, 5π6 , 7π6 , 11π6
Now, 2cos2θ−3sinθ=0
⇒2sin2θ+3sinθ−2=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.