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Question

Statement-I: The value of the integral π/3π/6dx1+tanx is equal to π6.
Statement-II: baf(x)d(x)=baf(a+bx)d(x).

A
Statement-I is true; Statement-II is true; Statement-II is a correct explanation for Statement-I.
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B
Statement-I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I.
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C
Statement-I is true; Statement-II is false.
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D
Statement-I is false; Statement-II is true.
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Solution

The correct option is D Statement-I is false; Statement-II is true.
I=π/3π/6dx1+tanx...(1)
=π/3π/6dx1+tan(π3+π6x)
=π/3π/6dx1+cotx
=π/3π/6tanx1+tanxdx...(2)
Adding (1) and (2)
2I=π/3π/61+tanx1+tanxdx
2I=π/3π/61dx
2I=π6
I=π12
Statement-I is not true and Statement-II is the property
So, Statement-II is always true

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