Integral Calculus & Area · JEE Main previous year questions

2019 29 questions

1. Q72019 · 11 Jan 2019 · Shift 2

   If $$\left|\begin{array}{ccc}a-b-c& 2a& 2a\\ 2b& b-c-a& 2b\\ 2c& 2c& c-a-b\end{array}\right|=(a+b+c)(x+a+b+c{)}^2,x\ne 0,$$ then x is equal to :

   1. A.$-2(a+b+c)$
   2. B.$2(a+b+c)$
   3. C.abc
   4. D.$-(a+b+c)$
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   Answer: A

2. Q102019 · 11 Jan 2019 · Shift 2

   If $\int \frac{x+1}{\sqrt{2x-1}}dx=f(x)\sqrt{2x-1}+C$, where C is a constant of integration, then $f(x)$ is equal to :

   1. A.$\frac{2}{3}(x-4)$
   2. B.$\frac{1}{3}(x+4)$
   3. C.$\frac{1}{3}(x+1)$
   4. D.$\frac{2}{3}(x+2)$
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   Answer: B

3. Q132019 · 11 Jan 2019 · Shift 2

   The integral ${\int }_{\pi /6}^{\pi /4}\frac{dx}{\sin 2x({\tan }^{5}x+{\cot }^{5}x)}$ equals :

   1. A.$\frac{\pi }{40}$
   2. B.$\frac{1}{20}{\tan }^{-1}\left(\frac{1}{9\sqrt{3}}\right)$
   3. C.$\frac{1}{10}\left(\frac{\pi }{4}-{\tan }^{-1}\left(\frac{1}{9\sqrt{3}}\right)\right)$
   4. D.$\frac{1}{5}\left(\frac{\pi }{4}-{\tan }^{-1}\left(\frac{1}{3\sqrt{3}}\right)\right)$
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   Answer: C

4. Q42019 · 9 Jan 2019 · Shift 1

   For $x^2\ne n\pi +1$, $n\in \mathbb{N}$ (the set of natural numbers), the integral $$\int x\sqrt{\frac{2\sin (x^2-1)-\sin 2(x^2-1)}{2\sin (x^2-1)+\sin 2(x^2-1)}}dx$$ is equal to : (where c is a constant of integration)

   1. A.${\log }_e\left|\frac{1}{2}{\sec }^2(x^2-1)\right|+c$
   2. B.$\frac{1}{2}{\log }_e\left|\sec (x^2-1)\right|+c$
   3. C.$\frac{1}{2}{\log }_e\left|{\sec }^2\left(\frac{x^2-1}{2}\right)\right|+c$
   4. D.${\log }_e\left|\sec \left(\frac{x^2-1}{2}\right)\right|+c$
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   Answer: C, D