ExamSIDE
Questions
ExamSIDE.Com
Mathematics
Algebra
Complex Numbers
Quadratic Equation and Inequalities
Permutations and Combinations
Mathematical Induction and Binomial Theorem
Sequences and Series
Matrices and Determinants
Vector Algebra and 3D Geometry
Probability
Statistics
Mathematical Reasoning
Sets and Relations
Trigonometry
Trigonometric Functions & Equations
Properties of Triangle
Inverse Trigonometric Functions
Coordinate Geometry
Straight Lines and Pair of Straight Lines
Circle
Conic Sections
Calculus
Functions
Limits, Continuity and Differentiability
Differentiation
Application of Derivatives
Indefinite Integrals
Definite Integrals and Applications of Integrals
Differential Equations
Joint Entrance Examination
JEE Main
Chemistry
Physics
Mathematics
JEE Advanced
Physics
Chemistry
Mathematics
WB JEE
Physics
Chemistry
Mathematics
Graduate Aptitude Test in Engineering
GATE CSE
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
GATE ECE
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Communications
Electromagnetics
General Aptitude
Engineering Mathematics
GATE EE
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits
Electrical and Electronics Measurement
GATE ME
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Turbo Machinery
Heat Transfer
Thermodynamics
Production Engineering
Industrial Engineering
General Aptitude
GATE CE
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Hydrology
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude
GATE PI
Fluid Mechanics
Metrology
Theory of Machines
Engineering Mathematics
Heat Transfer
Machine Tools and Machining
Industrial Engineering
Engineering Mechanics
Strength of Materials
Thermodynamics
Machine Design
Casting
Joining of Materials
Metal Forming
GATE IN
Engineering Mathematics
Medical
NEET
Biology
Chemistry
Physics
NEW
New Website Launch
Experience the best way to solve previous year questions with
mock tests
(very detailed analysis),
bookmark your favourite questions
,
practice
etc...
VISIT NOW
JEE Main
Trigonometric Functions & Equations
Mathematics
Previous Years Questions
START HERE
MCQ (Single Correct Answer)
More
The number of elements in the set $$S=\left\{x \in \mathbb{R}: 2 \cos \left(\frac{x^{2}+x}{6}\right)=4^{x}+4^{-x}\right\...
JEE Main 2022 (Online) 29th July Evening Shift
GO TO QUESTION
Let $$S=\left\{\theta \in\left(0, \frac{\pi}{2}\right): \sum\limits_{m=1}^{9} \sec \left(\theta+(m-1) \frac{\pi}{6}\righ...
JEE Main 2022 (Online) 27th July Evening Shift
GO TO QUESTION
Let $$S=\left\{\theta \in[0,2 \pi]: 8^{2 \sin ^{2} \theta}+8^{2 \cos ^{2} \theta}=16\right\} .$$ Then $$n(s) + \sum\limi...
JEE Main 2022 (Online) 26th July Morning Shift
GO TO QUESTION
$$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\f...
JEE Main 2022 (Online) 25th July Evening Shift
GO TO QUESTION
The number of solutions of $$|\cos x|=\sin x$$, such that $$-4 \pi \leq x \leq 4 \pi$$ is :
JEE Main 2022 (Online) 25th July Morning Shift
GO TO QUESTION
Let $$S = \left\{ {\theta \in [ - \pi ,\pi ] - \left\{ { \pm \,\,{\pi \over 2}} \right\}:\sin \theta \tan \theta + \t...
JEE Main 2022 (Online) 24th June Morning Shift
GO TO QUESTION
The number of solutions of the equation $$\cos \left( {x + {\pi \over 3}} \right)\cos \left( {{\pi \over 3} - x} \righ...
JEE Main 2022 (Online) 24th June Evening Shift
GO TO QUESTION
The value of 2sin (12$$^\circ$$) $$-$$ sin (72$$^\circ$$) is :
JEE Main 2022 (Online) 25th June Evening Shift
GO TO QUESTION
$$16\sin (20^\circ )\sin (40^\circ )\sin (80^\circ )$$ is equal to :
JEE Main 2022 (Online) 26th June Evening Shift
GO TO QUESTION
The value of $$\cos \left( {{{2\pi } \over 7}} \right) + \cos \left( {{{4\pi } \over 7}} \right) + \cos \left( {{{6\pi }...
JEE Main 2022 (Online) 27th June Morning Shift
GO TO QUESTION
$$\alpha = \sin 36^\circ $$ is a root of which of the following equation?
JEE Main 2022 (Online) 27th June Evening Shift
GO TO QUESTION
Let for some real numbers $$\alpha$$ and $$\beta$$, $$a = \alpha - i\beta $$. If the system of equations $$4ix + (1 + i...
JEE Main 2022 (Online) 27th June Evening Shift
GO TO QUESTION
If cot$$\alpha$$ = 1 and sec$$\beta$$ = $$ - {5 \over 3}$$, where $$\pi ...
JEE Main 2022 (Online) 28th June Evening Shift
GO TO QUESTION
If n is the number of solutions of the equation $$2\cos x\left( {4\sin \left( {{\pi \over 4} + x} \right)\sin \left( {{...
JEE Main 2021 (Online) 1st September Evening Shift
GO TO QUESTION
The number of solutions of the equation $${32^{{{\tan }^2}x}} + {32^{{{\sec }^2}x}} = 81,\,0 \le x \le {\pi \over 4}$$ ...
JEE Main 2021 (Online) 31st August Evening Shift
GO TO QUESTION
The distance of the point (1, $$-$$2, 3) from the plane x $$-$$ y + z = 5 measured parallel to a line, whose direction r...
JEE Main 2021 (Online) 27th August Morning Shift
GO TO QUESTION
The value of $$2\sin \left( {{\pi \over 8}} \right)\sin \left( {{{2\pi } \over 8}} \right)\sin \left( {{{3\pi } \over 8...
JEE Main 2021 (Online) 26th August Evening Shift
GO TO QUESTION
The sum of solutions of the equation $${{\cos x} \over {1 + \sin x}} = \left| {\tan 2x} \right|$$, $$x \in \left( { - {\...
JEE Main 2021 (Online) 26th August Morning Shift
GO TO QUESTION
If $$\sin \theta + \cos \theta = {1 \over 2}$$, then 16(sin(2$$\theta$$) + cos(4$$\theta$$) + sin(6$$\theta$$)) is equ...
JEE Main 2021 (Online) 27th July Morning Shift
GO TO QUESTION
The value of $$\cot {\pi \over {24}}$$ is :
JEE Main 2021 (Online) 25th July Evening Shift
GO TO QUESTION
If $$\tan \left( {{\pi \over 9}} \right),x,\tan \left( {{{7\pi } \over {18}}} \right)$$ are in arithmetic progression a...
JEE Main 2021 (Online) 27th July Evening Shift
GO TO QUESTION
The sum of all values of x in [0, 2$$\pi$$], for which sin x + sin 2x + sin 3x + sin 4x = 0, is equal to :
JEE Main 2021 (Online) 25th July Morning Shift
GO TO QUESTION
If 15sin4$$\alpha$$ + 10cos4$$\alpha$$ = 6, for some $$\alpha$$$$\in$$R, then the value of 27sec6$$\alpha$$ + 8cosec6$$\...
JEE Main 2021 (Online) 18th March Evening Shift
GO TO QUESTION
The number of solutions of the equation x + 2tanx = $${\pi \over 2}$$ in the interval [0, 2$$\pi$$] is :
JEE Main 2021 (Online) 17th March Evening Shift
GO TO QUESTION
If for x $$\in$$ $$\left( {0,{\pi \over 2}} \right)$$, log10sinx + log10cosx = $$-$$1 and log10(sinx + cosx) = $${1 \ov...
JEE Main 2021 (Online) 16th March Morning Shift
GO TO QUESTION
The number of roots of the equation, (81)sin2x + (81)cos2x = 30 in the interval [ 0, $$\pi$$ ] is equal to :...
JEE Main 2021 (Online) 16th March Morning Shift
GO TO QUESTION
If 0 < x, y < $$\pi$$ and cosx + cosy $$-$$ cos(x + y) = $${3 \over 2}$$, then sinx + cosy is equal to :
JEE Main 2021 (Online) 25th February Evening Shift
GO TO QUESTION
All possible values of $$\theta$$ $$\in$$ [0, 2$$\pi$$] for which sin 2$$\theta$$ + tan 2$$\theta$$ > 0 lie in :
JEE Main 2021 (Online) 25th February Morning Slot
GO TO QUESTION
If $${e^{\left( {{{\cos }^2}x + {{\cos }^4}x + {{\cos }^6}x + ...\infty } \right){{\log }_e}2}}$$ satisfies the equation...
JEE Main 2021 (Online) 24th February Morning Slot
GO TO QUESTION
If L = sin2$$\left( {{\pi \over {16}}} \right)$$ - sin2$$\left( {{\pi \over {8}}} \right)$$ and M = cos2$$\left( {{\pi...
JEE Main 2020 (Online) 5th September Evening Slot
GO TO QUESTION
If the equation cos4 $$\theta $$ + sin4 $$\theta $$ + $$\lambda $$ = 0 has real solutions for $$\theta $$, then $$\lambd...
JEE Main 2020 (Online) 2nd September Evening Slot
GO TO QUESTION
If $$x = \sum\limits_{n = 0}^\infty {{{\left( { - 1} \right)}^n}{{\tan }^{2n}}\theta } $$ and $$y = \sum\limits_{n = 0...
JEE Main 2020 (Online) 9th January Evening Slot
GO TO QUESTION
The value of $${\cos ^3}\left( {{\pi \over 8}} \right)$$$${\cos}\left( {{3\pi \over 8}} \right)$$+$${\sin ^3}\left( {{...
JEE Main 2020 (Online) 9th January Morning Slot
GO TO QUESTION
Let S be the set of all $$\alpha $$ $$ \in $$ R such that the equation, cos2x + $$\alpha $$sinx = 2$$\alpha $$– 7 has a ...
JEE Main 2019 (Online) 12th April Evening Slot
GO TO QUESTION
If [x] denotes the greatest integer $$ \le $$ x, then the system of linear equations [sin $$\theta $$]x + [–cos$$\theta ...
JEE Main 2019 (Online) 12th April Evening Slot
GO TO QUESTION
The equation y = sinx sin (x + 2) – sin2 (x + 1) represents a straight line lying in :
JEE Main 2019 (Online) 12th April Morning Slot
GO TO QUESTION
The number of solutions of the equation 1 + sin4 x = cos23x, $$x \in \left[ { - {{5\pi } \over 2},{{5\pi } \over 2}} ...
JEE Main 2019 (Online) 12th April Morning Slot
GO TO QUESTION
The value of sin 10º sin30º sin50º sin70º is :-
JEE Main 2019 (Online) 9th April Evening Slot
GO TO QUESTION
Let S = {$$\theta $$ $$ \in $$ [–2$$\pi $$, 2$$\pi $$] : 2cos2$$\theta $$ + 3sin$$\theta $$ = 0}. Then the sum of the el...
JEE Main 2019 (Online) 9th April Morning Slot
GO TO QUESTION
The value of cos210° – cos10°cos50° + cos250° is
JEE Main 2019 (Online) 9th April Morning Slot
GO TO QUESTION
If cos($$\alpha $$ + $$\beta $$) = 3/5 ,sin ( $$\alpha $$ - $$\beta $$) = 5/13 and 0 < $$\alpha , \beta$$ < $$\pi ...
JEE Main 2019 (Online) 8th April Morning Slot
GO TO QUESTION
The maximum value of 3cos$$\theta $$ + 5sin $$\left( {\theta - {\pi \over 6}} \right)$$ for any real value of $$\thet...
JEE Main 2019 (Online) 12th January Morning Slot
GO TO QUESTION
The value of $$\cos {\pi \over {{2^2}}}.\cos {\pi \over {{2^3}}}\,.....\cos {\pi \over {{2^{10}}}}.\sin {\pi \over {...
JEE Main 2019 (Online) 10th January Evening Slot
GO TO QUESTION
The sum of all values of $$\theta $$ $$ \in $$$$\left( {0,{\pi \over 2}} \right)$$ satisfying sin2 2$$\theta $$ + cos4 ...
JEE Main 2019 (Online) 10th January Morning Slot
GO TO QUESTION
If 0 $$ \le $$ x < $${\pi \over 2}$$, then the number of values of x for which sin x $$-$$ sin 2x +...
JEE Main 2019 (Online) 9th January Evening Slot
GO TO QUESTION
For any $$\theta \in \left( {{\pi \over 4},{\pi \over 2}} \right)$$, the expression $$3{(\cos \theta - \sin \theta...
JEE Main 2019 (Online) 9th January Morning Slot
GO TO QUESTION
The number of solutions of sin3x = cos 2x, in the interval $$\left( {{\pi \over 2},\pi } \right)$$ is :
JEE Main 2018 (Online) 15th April Evening Slot
GO TO QUESTION
PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of...
JEE Main 2018 (Offline)
GO TO QUESTION
If sum of all the solutions of the equation $$8\cos x.\left( {\cos \left( {{\pi \over 6} + x} \right).\cos \left( {{\pi...
JEE Main 2018 (Offline)
GO TO QUESTION
Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground ...
JEE Main 2017 (Offline)
GO TO QUESTION
If $$5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9$$, then the value of $$\cos 4x$$ is
JEE Main 2017 (Offline)
GO TO QUESTION
Let f(x) = sin4x + cos4 x. Then f is an increasing function in the interval :
JEE Main 2016 (Online) 10th April Morning Slot
GO TO QUESTION
If m and M are the minimum and the maximum values of 4 + $${1 \over 2}$$ sin2 2x $$-$$ 2cos4 x, x $$ \in $$ R, the...
JEE Main 2016 (Online) 9th April Morning Slot
GO TO QUESTION
The number of x $$ \in $$ [0, 2$$\pi $$ ] for which $$\left| {\sqrt {2{{\sin }^4}x + 18{{\cos }^2}x} - \sqrt {...
JEE Main 2016 (Online) 9th April Morning Slot
GO TO QUESTION
If $$0 \le x < 2\pi $$, then the number of real values of $$x$$, which satisfy the equation $$\,\cos x + \cos 2x + \c...
JEE Main 2016 (Offline)
GO TO QUESTION
Let $$fk\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$$ where $$x \in R$$ and $$k \ge \,.$$...
JEE Main 2014 (Offline)
GO TO QUESTION
$$ABCD$$ is a trapezium such that $$AB$$ and $$CD$$ are parallel and $$BC \bot CD.$$ If $$\angle ADB = \theta ,\,BC = p$...
JEE Main 2013 (Offline)
GO TO QUESTION
The expression $${{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}$$ can be written...
JEE Main 2013 (Offline)
GO TO QUESTION
In a $$\Delta PQR,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} $$ If $$3{\mkern 1mu} \sin {\mkern 1mu} P + 4{\mkern 1mu} \cos...
AIEEE 2012
GO TO QUESTION
If $$A = {\sin ^2}x + {\cos ^4}x,$$ then for all real $$x$$:
AIEEE 2011
GO TO QUESTION
Let $$\cos \left( {\alpha + \beta } \right) = {4 \over 5}$$ and $$\sin \,\,\,\left( {\alpha - \beta } \right) = {5 \ov...
AIEEE 2010
GO TO QUESTION
Let A and B denote the statements A: $$\cos \alpha + \cos \beta + \cos \gamma = 0$$ B: $$\sin \alpha + \sin \beta ...
AIEEE 2009
GO TO QUESTION
If $$0 < x < \pi $$ and $$\cos x + \sin x = {1 \over 2},$$ then $$\tan x$$ is
AIEEE 2006
GO TO QUESTION
The number of values of $$x$$ in the interval $$\left[ {0,3\pi } \right]\,$$ satisfying the equation $$2{\sin ^2}x + 5\...
AIEEE 2006
GO TO QUESTION
A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis. If the angle $$\beta \,$$, which it m...
AIEEE 2004
GO TO QUESTION
Let $$\alpha ,\,\beta $$ be such that $$\pi < \alpha - \beta < 3\pi $$. If $$sin{\mkern 1mu} \alpha + \sin \be...
AIEEE 2004
GO TO QUESTION
If $$u = \sqrt {{a^2}{{\cos }^2}\theta + {b^2}{{\sin }^2}\theta } + \sqrt {{a^2}{{\sin }^2}\theta + {b^2}{{\cos }^2}...
AIEEE 2004
GO TO QUESTION
Which one is not periodic
AIEEE 2002
GO TO QUESTION
The number of solution of $$\tan \,x + \sec \,x = 2\cos \,x$$ in $$\left[ {0,\,2\,\pi } \right]$$ is
AIEEE 2002
GO TO QUESTION
The period of $${\sin ^2}\theta $$ is
AIEEE 2002
GO TO QUESTION
Numerical
More
Let $$S=\left\{\theta \in(0,2 \pi): 7 \cos ^{2} \theta-3 \sin ^{2} \theta-2 \cos ^{2} 2 \theta=2\right\}$$. Then, the su...
JEE Main 2022 (Online) 29th July Morning Shift
GO TO QUESTION
Let $$S=\left[-\pi, \frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}$$....
JEE Main 2022 (Online) 28th July Evening Shift
GO TO QUESTION
If the sum of solutions of the system of equations $$2 \sin ^{2} \theta-\cos 2 \theta=0$$ and $$2 \cos ^{2} \theta+3 \si...
JEE Main 2022 (Online) 26th July Evening Shift
GO TO QUESTION
Let $${S_1} = \{ x \in [0,12\pi ]:{\sin ^5}x + {\cos ^5}x = 1\} $$ and $${S_2} = \{ x \in [0,8\pi ]:{\sin ^7}x + {\cos ^...
JEE Main 2022 (Online) 30th June Morning Shift
GO TO QUESTION
The number of values of x in the interval $$\left( {{\pi \over 4},{{7\pi } \over 4}} \right)$$ for which $$14\cos e{c^2...
JEE Main 2022 (Online) 25th June Morning Shift
GO TO QUESTION
If $${\sin ^2}(10^\circ )\sin (20^\circ )\sin (40^\circ )\sin (50^\circ )\sin (70^\circ ) = \alpha - {1 \over {16}}\sin...
JEE Main 2022 (Online) 26th June Morning Shift
GO TO QUESTION
The number of solutions of the equation $$\sin x = {\cos ^2}x$$ in the interval (0, 10) is _________.
JEE Main 2022 (Online) 29th June Evening Shift
GO TO QUESTION
The number of solutions of the equation $$2\theta - {\cos ^2}\theta + \sqrt 2 = 0$$ in R is equal to ___________....
JEE Main 2022 (Online) 29th June Morning Shift
GO TO QUESTION
The number of elements in the set $$S = \{ \theta \in [ - 4\pi ,4\pi ]:3{\cos ^2}2\theta + 6\cos 2\theta - 10{\cos ^2...
JEE Main 2022 (Online) 29th June Morning Shift
GO TO QUESTION
Let S = {1, 2, 3, 4, 5, 6, 9}. Then the number of elements in the set T = {A $$ \subseteq $$ S : A $$\ne$$ $$\phi$$ and ...
JEE Main 2021 (Online) 27th August Evening Shift
GO TO QUESTION
Let z1 and z2 be two complex numbers such that $$\arg ({z_1} - {z_2}) = {\pi \over 4}$$ and z1, z2 satisfy the equation...
JEE Main 2021 (Online) 27th August Evening Shift
GO TO QUESTION
The probability distribution of random variable X is given by : .tg {border-collapse:collapse;border-spacing:0;} .tg td...
JEE Main 2021 (Online) 27th August Evening Shift
GO TO QUESTION
Let S be the sum of all solutions (in radians) of the equation $${\sin ^4}\theta + {\cos ^4}\theta - \sin \theta \cos ...
JEE Main 2021 (Online) 27th August Evening Shift
GO TO QUESTION
The number of solutions of the equation $$|\cot x| = \cot x + {1 \over {\sin x}}$$ in the interval [ 0, 2$$\pi$$ ] is...
JEE Main 2021 (Online) 18th March Morning Shift
GO TO QUESTION
The number of integral values of 'k' for which the equation $$3\sin x + 4\cos x = k + 1$$ has a solution, k$$\in$$R is _...
JEE Main 2021 (Online) 26th February Morning Shift
GO TO QUESTION
If $$\sqrt 3 ({\cos ^2}x) = (\sqrt 3 - 1)\cos x + 1$$, the number of solutions of the given equation when $$x \in \left...
JEE Main 2021 (Online) 26th February Morning Shift
GO TO QUESTION
If $${{\sqrt 2 \sin \alpha } \over {\sqrt {1 + \cos 2\alpha } }} = {1 \over 7}$$ and $$\sqrt {{{1 - \cos 2\beta } \over ...
JEE Main 2020 (Online) 8th January Evening Slot
GO TO QUESTION
Joint Entrance Examination
JEE Main
JEE Advanced
WB JEE
Graduate Aptitude Test in Engineering
GATE CSE
GATE ECE
GATE EE
GATE ME
GATE CE
GATE PI
GATE IN
Medical
NEET
CBSE
Class 12