Mathematics

Single Correct Medium Published on 17th 09, 2020
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Realted Questions

Q1 Single Correct Medium
The solution for x of the equation $$\displaystyle \int_{\sqrt{2}}^{x}\frac{dt}{t\sqrt{t^{2}-1}}=\frac{\pi }{2}$$ is
  • A. $$\displaystyle \frac{\sqrt{3}}{2}$$
  • B. $$2$$
  • C. $$\pi $$
  • D. $$-\sqrt{2}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
Using integral $$\int _{ 0 }^{ \pi /2 }{ \ln { \left( \sin { x }  \right)  }  } dx=\int _{ 0 }^{ \pi /2 }{ \ln { \left( \sec { x }  \right)  }  } dx=-\cfrac { \pi  }{ 2 } \ln { 2 } $$
Evaluate $$\int _{ -\pi /4 }^{ \pi /4 }{ \ln { \left( \cfrac { \sin { x } +\cos { x }  }{ \cos { x } -\sin { x }  }  \right)  } dx= } $$
  • A. $$\pi \ln{2}$$
  • B. $$\cfrac{\pi \ln{2}}{2}$$
  • C. $$-\pi \ln{2}$$
  • D. $$0$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Hard
Primitive of $$\displaystyle \dfrac{3x^4-1}{(x^4+x+1)^2}$$ w.r.t  $$x$$ is
  • A. $$\displaystyle \dfrac{x}{(x^4+x+1)}+c$$
  • B. $$\displaystyle \dfrac{x+1}{(x^4+x+1)}+c$$
  • C. $$-\displaystyle \dfrac{x+1}{(x^4+x+1)}+c$$
  • D. $$-\displaystyle \dfrac{x}{(x^4+x+1)}+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Hard
The value of $$\displaystyle \int_{-\pi /2}^{\pi /2}\log \left ( \frac{2-\sin \theta }{2+\sin \theta } \right )d\theta$$is
  • A. $$1$$
  • B. $$2$$
  • C. None of these
  • D. $$0$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Passage Medium
Consider two differentiable functions $$f(x), g(x)$$ satisfying $$\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$$ & $$\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$$. where $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

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