Compound Angle – JEE Main Previous Year Question with Solutions

JEE Main Previous Year Question of Math with Solutions are available at eSaral. Practicing JEE Main Previous Year Papers Questions of mathematics will help the JEE aspirants in realizing the question pattern as well as help in analyzing weak & strong areas.

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Previous Years AIEEE/JEE Mains Questions

Q. Let $\cos (\alpha+\beta)=\frac{4}{5}$ and $\operatorname{let} \sin (\alpha-\beta)=\frac{5}{13},$ where $0 \leq \alpha, \beta \leq \frac{\pi}{4} .$ Then $\tan 2 \alpha=$

(1) $\frac{25}{16}$

(2) $\frac{56}{33}$

(3) $\frac{19}{12}$

(3) $\frac{19}{12}$

[AIEEE-2010]

Sol. (2)


Q. If $\mathrm{A}=\sin ^{2} \mathrm{x}+\cos ^{4} \mathrm{x},$ then for all real $\mathrm{x}:-$

(1) $1 \leq \mathrm{A} \leq 2$

(2) $\frac{3}{4} \leq \mathrm{A} \leq \frac{13}{16}$

(3) $\frac{3}{4} \leq \mathrm{A} \leq 1$

(4) $\frac{13}{16} \leq \mathrm{A} \leq 1$

[AIEEE-2011]

Sol. (3)


Q. In a $\Delta \mathrm{PQR},$ if $3 \sin \mathrm{P}+4 \cos \mathrm{Q}=6$ and $4 \sin \mathrm{Q}+3 \cos \mathrm{P}=1,$ then the angle $\mathrm{R}$ is equal to:

(1) $\frac{3 \pi}{4}$

(2) $\frac{5 \pi}{6}$

(3) $\frac{\pi}{6}$

(4) $\frac{\pi}{4}$

[AIEEE-2012]

Sol. (3)


Q. The expression $\frac{\tan \mathrm{A}}{1-\cot \mathrm{A}}+\frac{\cot \mathrm{A}}{1-\tan \mathrm{A}}$ can be written as

(1) sinA cosA + 1

(2) secA cosecA + 1

(3) tanA + cotA

(4) secA + cosecA

[JEE-MAIN 2013]

Sol. (2)


Q. $\mathrm{ABCD}$ is a trapezium such that $\mathrm{AB}$ and $\mathrm{CD}$ are parallel and $\mathrm{BC} \perp \mathrm{CD} .$ If $\angle \mathrm{ADB}=\theta, \mathrm{BC}$

$=\mathrm{p}$ and $\mathrm{CD}=\mathrm{q},$ then $\mathrm{AB}$ is equal to

(1) $\frac{\left(\mathrm{p}^{2}+\mathrm{q}^{2}\right) \sin \theta}{\mathrm{p} \cos \theta+\mathrm{q} \sin \theta}$

(2) $\frac{\mathrm{p}^{2}+\mathrm{q}^{2} \cos \theta}{\mathrm{p} \cos \theta+\mathrm{q} \sin \theta}$

(3) $\frac{\mathrm{p}^{2}+\mathrm{q}^{2}}{\mathrm{p}^{2} \cos \theta+\mathrm{q}^{2} \sin \theta}$

(4) $\frac{\left(p^{2}+q^{2}\right) \sin \theta}{(p \cos \theta+q \sin \theta)^{2}}$

[JEE-MAIN 2013]

Sol. (1)


Q. Let $\mathrm{f}_{\mathrm{K}}(\mathrm{x})=\frac{1}{\mathrm{k}}\left(\sin ^{\mathrm{k}} \mathrm{x}+\cos ^{\mathrm{k}} \mathrm{x}\right)$ where $\mathrm{x} \in \mathrm{R}$ and $\mathrm{k} \geq 1 .$ Then $\mathrm{f}_{4}(\mathrm{x})-\mathrm{f}_{6}(\mathrm{x})$ equals :

(1) $\frac{1}{6}$

(2) $\frac{1}{3}$

(3) $\frac{1}{4}$

(4) $\frac{1}{12}$

[JEE-MAIN 2014]

Sol. (4)


Q. If $5\left(\tan ^{2} x-\cos ^{2} x\right)=2 \cos 2 x+9,$ then the value of $\cos 4 x$ is :-

$(1)-\frac{7}{9}$

$(2)-\frac{3}{5}$

(3) $\frac{1}{3}$

(4) $\frac{2}{9}$

[JEE-MAIN 2017]

Sol. (1)


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Comments
  • July 3, 2020 at 9:06 am

    Nice questions
    Make some more difficult
    Nice..

  • June 20, 2020 at 4:18 pm

    You can have aa better explanation ….

  • May 22, 2020 at 7:38 am

    Chill bro

  • April 7, 2020 at 12:56 pm

    nice perfomance from you i loved your work we students who are preparing for furture exams must need it a lot thank you so much

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    March 23, 2020 at 12:40 pm

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