Mathematics

Single Correct Hard Published on 17th 09, 2020
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Q1 Single Correct Hard
Evaluate $$\displaystyle \int_{0}^{\pi /4}\frac{\cos x-\sin x}{10+\sin 2x}dx$$
  • A. $$\displaystyle \frac{1}{3}\left (\tan^{-1} \frac{\sqrt{2}}{3}+\tan^{-1} \frac{1}{3} \right )$$
  • B. $$\displaystyle \frac{1}{3}\left (\tan^{-1} \frac{\sqrt{1}}{3}-\cot^{-1} \frac{2}{3} \right )$$
  • C. $$\displaystyle \frac{1}{3}\left ( \tan^{-1} \frac{\sqrt{1}}{3}-\cot^{-1} \frac{1}{3} \right )$$
  • D. $$\displaystyle \frac{1}{3}\left ( \tan^{-1} \frac{\sqrt{2}}{3}-\tan^{-1} \frac{1}{3} \right )$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
Resolve into partial fraction $$\displaystyle \frac{7+x}{(1+x)(1+x^2)}$$
  • A. $$\displaystyle \frac{5}{1+x}+\frac{4-3x}{1+x^2}$$
  • B. $$\displaystyle \frac{3}{1+x}-\frac{4-3x}{1+x^2}$$
  • C. $$\displaystyle \frac{5}{1+x}-\frac{4-3x}{1+x^2}$$
  • D. $$\displaystyle \frac{3}{1+x}+\frac{4-3x}{1+x^2}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Hard
Find the value of $$\displaystyle\int _{ 0 }^{ 2\pi  }{ \sin ^{ 2 }{ x } \cdot \cos ^{ 4 }{ x } dx } $$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Medium

$$\displaystyle \int_{0}^{\pi}x.\sin^{3}xdx_{=}$$
  • A. $$\displaystyle \frac{\pi}{3}$$
  • B. $$\displaystyle \frac{\pi}{5}$$
  • C. $$\displaystyle \frac{2\pi}{5}$$
  • D. $$\displaystyle \frac{2\pi}{3}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Single Correct Medium
The value of $$\displaystyle\int\limits_{1}^{e^2}\dfrac{dx}{x}$$
  • A. $$1$$
  • B. $$-1$$
  • C. $$-2$$
  • D. $$2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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