Mathematics

Single Correct Medium Published on 17th 09, 2020
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Q1 Single Correct Medium
If $$\displaystyle \frac{1}{(1-2\mathrm{x})(1+3\mathrm{x})}$$ $$=\displaystyle \frac{\mathrm{A}}{1-2\mathrm{x}}+\frac{\mathrm{B}}{1+3\mathrm{x}}$$ then $$2\mathrm{B}=$$
  • A. A
  • B. 2A
  • C. -3A
  • D. 3A

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
$$ \int_{\pi /4}^{\pi /2} Cotx.dx_{=}$$
  • A. 2 log 2
  • B. $$\displaystyle \frac{\pi}{2}$$ log2
  • C. $$\log 2$$
  • D. $$\log\sqrt{2}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Medium
Evaluate : $$\displaystyle \int \sec x\tan x\sqrt{\sec ^{2}x+1}dx.$$
  • A. $$\displaystyle \frac{1}{2}t\sqrt{t^{2}+1}-\frac{1}{2}\log \left [ t+\sqrt{t^{2}+1} \right ].$$ where $$t=\sec x$$
  • B. $$\displaystyle t\sqrt{t^{2}+1}+\log \left [ t+\sqrt{t^{2}+1} \right ].$$ where $$t=\sec x$$
  • C. $$\displaystyle \frac{1}{2}t\sqrt{t^{2}+1}+\frac{1}{2}\log \left [ t-\sqrt{t^{2}+1} \right ].$$ where $$t=\sec x$$
  • D. $$\displaystyle \frac{1}{2}t\sqrt{t^{2}+1}+\frac{1}{2}\log \left [ t+\sqrt{t^{2}+1} \right ].$$ where $$t=\sec x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Medium
Evaluate: $$\displaystyle \int{(x-1)} dx$$
  • A. $$\dfrac{x^2}{2} -2x+C$$
  • B. $$\dfrac{x^2}{2} -1+C$$
  • C. $$\dfrac{x^2}{2} -2+C$$
  • D. $$\dfrac{x^2}{2} -x+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Single Correct Medium
$$ 4 \displaystyle \int \dfrac{\sqrt{a^6 + x^8}}{x} dx$$ is equal to ______________________.
  • A. $$a^6 ln\vert \dfrac {\sqrt{a^6 + x^8} - a^3} {\sqrt {a^6 + x^8} + a^3}\vert + c$$
  • B. $$\sqrt{a^6 + x^8} + \dfrac {a^3}{2} ln \vert \dfrac {\sqrt{a^6 + x^8} - a^3} {\sqrt {a^6 + x^8} + a^3}\vert + c$$
  • C. $$a^6 ln \vert \dfrac {\sqrt{a^6 + x^8} + a^3} {\sqrt {a^6 + x^8} - a^3}\vert + c$$
  • D. $$\sqrt{a^6 + x^8} + \dfrac{a^3}{2} ln \vert \dfrac {\sqrt{a^6 + x^8} + a^3} {\sqrt {a^6 + x^8} - a^3}\vert + c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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