NCERT Exemplar MCQ

Chapter 7 Class 12 Integrals
Serial order wise

## (D) 1

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### Transcript

Question 6 If π₯= β«1_0^π¦βγ ππ‘/β(1 + 9π‘^2 )γ and (π^2 π¦)/(ππ₯^2 )=ππ¦, then π is equal to 3 (B) 6 (C) 9 (D) 1 Since π₯= β«1_0^π¦βγ ππ‘/β(1 + 9π‘^2 )γ Changing variable from t to y π₯= β«1_0^π¦βγ ππ¦/β(1 + 9π¦^2 )γ It means x is a function of y So, we can write ππ/ππ=π/β(π + ππ^π ) And, ππ/ππ±=β(1 + 9π¦^2 ) Differentiating again w.r.t x (π^π π)/(ππ±^π )=π/(πβ(1 + 9π¦^2 )) Γπ(ππ^π )/ππ (d^2 π¦)/(dx^2 )=1/(2β(1 + 9π¦^2 )) Γ 9 Γ 2π¦ Γππ/ππ Putting value of ππ¦/ππ₯ (π^π π)/(ππ±^π )=π/(πβ(1 + 9π¦^2 )) Γ π Γ ππ Γβ(1 + 9π¦^2 ) (π^π π)/(ππ±^π )=ππ Thus, a = 9 So, the correct answer is (c)

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.