Compound Angle – JEE Advanced Previous Year Questions with Solutions

JEE Advanced Previous Year Questions of Math with Solutions are available at eSaral. Practicing JEE Advanced 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 JEE Advance Questions

One or more than one is/are correct : [Q.1(a) & (b)]

Q. If $\frac{\sin ^{4} x}{2}+\frac{\cos ^{4} x}{3}=\frac{1}{5},$ then

(A) $\tan ^{2} x=\frac{2}{3}$

(B) $\frac{\sin ^{8} x}{8}+\frac{\cos ^{8} x}{27}=\frac{1}{125}$

(C) $\tan ^{2} \mathrm{x}=\frac{1}{3}$

(D) $\frac{\sin ^{8} x}{8}+\frac{\cos ^{8} x}{27}=\frac{2}{125}$

[JEE 2009, 4 + 4]

Sol. (A,B)

(a) $\frac{\tan ^{4} x}{2}+\frac{1}{3}=\frac{\sec ^{4} x}{5}$

put $\tan ^{2} \mathrm{x}=\mathrm{t}$

on solving we get $t=2 / 3$

$\Rightarrow \sin ^{2} x=\frac{2}{5} \quad \Rightarrow \quad \cos ^{2} x=\frac{3}{5}$

Q. For $0<\theta<\frac{\pi}{2},$ the solution(s) of $\sum_{m=1}^{6} \csc \left(\theta+\frac{(m-1) \pi}{4}\right) \csc \left(\theta+\frac{m \pi}{4}\right)=4 \sqrt{2}$ is (are)

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

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

(C) $\frac{\pi}{12}$

(D) $\frac{5 \pi}{12}$

[JEE 2009, 4 + 4]

Sol. (C,D)

Q. The maximum value of the expression $\frac{1}{\sin ^{2} \theta+3 \sin \theta \cos \theta+5 \cos ^{2} \theta}$ is

[JEE 2010,3+3]

Sol. 2

Q. Two parallel chords of a circle of radius 2 are at a distance $\sqrt{3}+1$ apart. If the chords subtend at the center, angles of $\frac{\pi}{k}$ and $\frac{2 \pi}{k}$ where $\mathrm{k}>0$, Glue of $[\mathrm{k}]$ is –

[JEE 2010,3+3]

Sol. k=3

Q. Let $\mathrm{P}=\{\theta: \sin \theta-\cos \theta=\sqrt{2} \cos \theta\}$ and $\mathrm{Q}=\{\theta: \sin \theta+\cos \theta=\sqrt{2} \sin \theta\}$ be two sets. Then

[JEE 2011,3]

Sol. (D)

Q. The value of $\sum_{\mathrm{k}=1}^{13} \frac{1}{\sin \left(\frac{\pi}{4}+\frac{(\mathrm{k}-1) \pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{\mathrm{k} \pi}{6}\right)}$ is equal to

(A) $3-\sqrt{3}$

(B) $2(3-\sqrt{3})$

(C) $2(\sqrt{3}-1)$

(D) $2(2+\sqrt{3})$

Sol. (C)

Q. Let $\alpha$ and $\beta$ be nonzero real numbers such that $2(\cos \beta-\cos \alpha)+\cos \alpha \cos \beta=1$. Then which of the following is/are true ?

(A) $\tan \left(\frac{\alpha}{2}\right)-\sqrt{3} \tan \left(\frac{\beta}{2}\right)=0$

(B) $\sqrt{3} \tan \left(\frac{\alpha}{2}\right)-\tan \left(\frac{\beta}{2}\right)=0$

(C) $\tan \left(\frac{\alpha}{2}\right)+\sqrt{3} \tan \left(\frac{\beta}{2}\right)=0$

(D) $\sqrt{3} \tan \left(\frac{\alpha}{2}\right)+\tan \left(\frac{\beta}{2}\right)=0$