Trigonometry · JEE Main previous year questions

2022 34 questions

1. Q252022 · 26 Jun 2022 · Shift 1· Numerical answer

   If ${\sin }^2(10^{\circ })\sin (20^{\circ })\sin (40^{\circ })\sin (50^{\circ })\sin (70^{\circ })=\alpha -\frac{1}{16}\sin (10^{\circ })$, then $16+{\alpha }^{-1}$ is equal to ____.

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   Answer: 80

2. Q132022 · 26 Jun 2022 · Shift 2

   $16\sin (20^{\circ })\sin (40^{\circ })\sin (80^{\circ })$ is equal to :

   1. A.$\sqrt{3}$
   2. B.$2\sqrt{3}$
   3. C.3
   4. D.$4\sqrt{3}$
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   Answer: B

3. Q142022 · 26 Jun 2022 · Shift 2

   If the inverse trigonometric functions take principal values then ${\cos }^{-1}\left(\frac{3}{10}\cos \left({\tan }^{-1}\left(\frac{4}{3}\right)\right)+\frac{2}{5}\sin \left({\tan }^{-1}\left(\frac{4}{3}\right)\right)\right)$ is equal to :

   1. A.0
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{\pi }{3}$
   4. D.$\frac{\pi }{6}$
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   Answer: C

4. Q272022 · 25 Jun 2022 · Shift 1· Numerical answer

   The number of values of x in the interval $\left(\frac{\pi }{4},\frac{7\pi }{4}\right)$ for which $14{\mathrm{cosec}}^{2}x-2{\sin }^{2}x=21-4{\cos }^{2}x$ holds, is $\underline{}$.

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   Answer: 4

5. Q112022 · 25 Jun 2022 · Shift 2

   The value of $2\sin (12^{\circ })-\sin (72^{\circ })$ is :

   1. A.$\frac{\sqrt{5}(1-\sqrt{3})}{4}$
   2. B.$\frac{1-\sqrt{5}}{8}$
   3. C.$\frac{\sqrt{3}(1-\sqrt{5})}{2}$
   4. D.$\frac{\sqrt{3}(1-\sqrt{5})}{4}$
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   Answer: D

6. Q132022 · 25 Jun 2022 · Shift 2

   The value of ${\tan }^{-1}\left(\frac{\cos \left(\frac{15\pi }{4}\right)-1}{\sin \left(\frac{\pi }{4}\right)}\right)$ is equal to :

   1. A.$-\frac{\pi }{4}$
   2. B.$-\frac{\pi }{8}$
   3. C.$-\frac{5\pi }{12}$
   4. D.$-\frac{4\pi }{9}$
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   Answer: B

7. Q182022 · 25 Jun 2022 · Shift 2

   If the angle made by the tangent at the point $(x_0,y_0)$ on the curve $x=12(t+\sin t\cos t)$, $y=12(1+\sin t{)}^2$, $0<t<\frac{\pi }{2}$, with the positive x-axis is $\frac{\pi }{3}$, then $y_0$ is equal to:

   1. A.$6\left(3+2\sqrt{2}\right)$
   2. B.$3\left(7+4\sqrt{3}\right)$
   3. C.$27$
   4. D.$48$
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   Answer: C

8. Q142022 · 24 Jun 2022 · Shift 2

   If $y={\tan }^{-1}\left(\sec x^3-\tan x^3\right)$, $\frac{\pi }{2}<x^3<\frac{3\pi }{2}$, then

   1. A.$x{y}^{\prime \prime }+2y^{\prime }=0$
   2. B.$x^2{y}^{\prime \prime }-6y+\frac{3\pi }{2}=0$
   3. C.$x^2{y}^{\prime \prime }-6y+3\pi =0$
   4. D.$x{y}^{\prime \prime }-4y^{\prime }=0$
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   Answer: B

9. Q172022 · 24 Jun 2022 · Shift 2

   The number of solutions of the equation $\cos \left(x+\frac{\pi }{3}\right)\cos \left(\frac{\pi }{3}-x\right)=\frac{1}{4}{\cos }^{2}2x$, $x\in [-3\pi ,3\pi ]$ is :

   1. A.8
   2. B.5
   3. C.6
   4. D.7
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   Answer: D