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Q.

Statement-1: π/6π/3dx1+tanx=π6

Statement-2: abf(x) dx=abf(a+bx) dx

Which of above statements are true

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a

Statement-1 is false, Statement-2 is true

b

Statement-1 is true, Statement-2 is false

c

Statement-1 is true, Statement-2 is true, Statemetn-2 is correct explanation for Statement-1

d

Statement-1 is true, Statement-2 is true, Statemetn-2 is not correct explanation for Statement-1

answer is B.

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Detailed Solution

Step1:

π/6π/3dx1+tanx=π6

Step2:

abf(x)dx=abf(a+bx)dx

Statement 2 is true since it is a property

NowI=π/6π/3dx1+tanx

=π/6π/3dx1+tanπ6+π3x

=π/6π/3dx1+cotx=π/6π/3tanxtanx+1dx

I+I=π/6π/311+tanx+tanxtanx+1dx

2I=π/6π/31+tanx1+tanxdx

=(x)π/6π/3=π3π6=π6I=π12

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