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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]
Ans. (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]
Ans. (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]
Ans. (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]
Ans. (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]
Ans. (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]
Ans. (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]
Ans. (1)
