ExamSIDE
Questions
ExamSIDE.Com
Complex Numbers
Numerical
MCQ (Single Correct Answer)
Quadratic Equation and Inequalities
Numerical
MCQ (Single Correct Answer)
Permutations and Combinations
Numerical
MCQ (Single Correct Answer)
Mathematical Induction and Binomial Theorem
Numerical
MCQ (Single Correct Answer)
Sequences and Series
Numerical
MCQ (Single Correct Answer)
Matrices and Determinants
Numerical
MCQ (Single Correct Answer)
Vector Algebra and 3D Geometry
Numerical
MCQ (Single Correct Answer)
Probability
Numerical
MCQ (Single Correct Answer)
Statistics
Numerical
MCQ (Single Correct Answer)
Mathematical Reasoning
MCQ (Single Correct Answer)
Trigonometric Functions & Equations
Numerical
MCQ (Single Correct Answer)
Properties of Triangle
Numerical
MCQ (Single Correct Answer)
Inverse Trigonometric Functions
MCQ (Single Correct Answer)
Straight Lines and Pair of Straight Lines
Numerical
MCQ (Single Correct Answer)
Circle
Numerical
MCQ (Single Correct Answer)
Conic Sections
Numerical
MCQ (Single Correct Answer)
Functions
Numerical
MCQ (Single Correct Answer)
Limits, Continuity and Differentiability
Numerical
MCQ (Single Correct Answer)
Differentiation
Numerical
MCQ (Single Correct Answer)
Application of Derivatives
Numerical
MCQ (Single Correct Answer)
Indefinite Integrals
Numerical
MCQ (Single Correct Answer)
Definite Integrals and Applications of Integrals
Numerical
MCQ (Single Correct Answer)
MCQ (Multiple Correct Answer)
Differential Equations
Numerical
MCQ (Single Correct Answer)
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
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
GATE ECE
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
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
Machine Design
Strength of Materials
Heat Transfer
Production Engineering
Industrial Engineering
Turbo Machinery
Theory of Machines
Engineering Mathematics
Fluid Mechanics
Thermodynamics
General Aptitude
GATE CE
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Hydrology
Transportation Engineering
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
GATE PI
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Heat Transfer
Thermodynamics
Casting
Joining of Materials
Metal Forming
Machine Tools and Machining
Metrology
Industrial Engineering
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
Previous
Next
1
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
The probability distribution of random variable X is given by :
X
1
2
3
4
5
P(X)
K
2K
2K
3K
K
Let p = P(1 < X < 4 | X < 3). If 5p = $$\lambda$$K, then $$\lambda$$ equal to ___________.
Your Input
________
⬅
1
2
3
4
5
6
7
8
9
•
0
−
CHECK ANSWER
Answer
Correct Answer is
30
Explanation
$$\sum {P(X) = 1 \Rightarrow k + 2k + 3} k + k = 1$$
$$ \Rightarrow k = {1 \over 9}$$
Now, $$p = P\left( {{{kx < 4} \over {X < 3}}} \right) = {{P(X = 2)} \over {P(X < 3)}} = {{{{2k} \over {9k}}} \over {{k \over {9k}} + {{2k} \over {9k}}}} = {2 \over 3}$$
$$ \Rightarrow p = {2 \over 3}$$
Now, $$5p = \lambda k$$
$$ \Rightarrow (5)\left( {{2 \over 3}} \right) = \lambda (1/9)$$
$$ \Rightarrow \lambda = 30$$
2
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
Let S be the sum of all solutions (in radians) of the equation $${\sin ^4}\theta + {\cos ^4}\theta - \sin \theta \cos \theta = 0$$ in [0, 4$$\pi$$]. Then $${{8S} \over \pi }$$ is equal to ____________.
Your Input
________
⬅
1
2
3
4
5
6
7
8
9
•
0
−
CHECK ANSWER
Answer
Correct Answer is
56
Explanation
Given equation
$${\sin ^4}\theta + {\cos ^4}\theta - \sin \theta \cos \theta = 0$$
$$ \Rightarrow 1 - {\sin ^2}\theta {\cos ^2}\theta - \sin \theta \cos \theta = 0$$
$$ \Rightarrow 2 - {(\sin 2\theta )^2} - \sin 2\theta = 0$$
$$ \Rightarrow {(\sin 2\theta )^2} + (\sin 2\theta ) - 2 = 0$$
$$ \Rightarrow (\sin 2\theta + 2)(\sin 2\theta - 1) = 0$$
$$ \Rightarrow \sin 2\theta = 1$$ or $$\sin 2\theta = - 2$$ (Not Possible)
$$ \Rightarrow 2\theta = {\pi \over 2},{{5\pi } \over 2},{{9\pi } \over 2},{{13\pi } \over 2}$$
$$ \Rightarrow \theta = {\pi \over 4},{{5\pi } \over 4},{{9\pi } \over 4},{{13\pi } \over 4}$$
$$ \Rightarrow S = {\pi \over 4} + {{5\pi } \over 4} + {{9\pi } \over 4} + {{13\pi } \over 4} = 7\pi $$
$$ \Rightarrow {{8S} \over \pi } = {{8 \times 7\pi } \over \pi } = 56.00$$
3
JEE Main 2021 (Online) 18th March Morning Shift
Numerical
The number of solutions of the equation
$$|\cot x| = \cot x + {1 \over {\sin x}}$$ in the interval [ 0, 2$$\pi$$ ] is
Your Input
________
⬅
1
2
3
4
5
6
7
8
9
•
0
−
CHECK ANSWER
Answer
Correct Answer is
1
Explanation
Case I : When cot x > 0, $$x \in \left[ {0,{\pi \over 2}} \right] \cup \left[ {\pi ,{{3\pi } \over 2}} \right]$$
$$\cot x = \cot x + {1 \over {\sin x}} \Rightarrow $$ not possible
Case II : When cot x < 0, $$x \in \left[ {{\pi \over 2},\pi } \right] \cup \left[ {{{3\pi } \over 2},2\pi } \right]$$
$$ - \cot x = \cot x + {1 \over {\sin x}}$$
$$ \Rightarrow {{ - 2\cos x} \over {\sin x}} = {1 \over {\sin x}}$$
$$ \Rightarrow \cos x = {{ - 1} \over 2}$$
$$ \Rightarrow x = {{2\pi } \over 3},{{4\pi } \over 3}$$(Rejected)
One solution.
4
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
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 ___________.
Your Input
________
⬅
1
2
3
4
5
6
7
8
9
•
0
−
CHECK ANSWER
Answer
Correct Answer is
11
Explanation
We know,
$$ - \sqrt {{a^2} + {b^2}} \le a\cos x + b\sin x \le \sqrt {{a^2} + {b^2}} $$
$$ \therefore $$ $$ - \sqrt {{3^2} + {4^2}} \le 3\cos x + 4\sin x \le \sqrt {{3^2} + {4^2}} $$
$$ - 5 \le k + 1 \le 5$$
$$ - 6 \le k \le 4$$
$$ \therefore $$ Set of integers = $$ - 6, - 5, - 4, - 3, - 2, - 1,0,1,2,3,4$$ = Total 11 intergers.
Previous
Next
Questions Asked from Trigonometric Functions & Equations
On those following papers in Numerical
Number in Brackets after Paper Indicates No. of Questions
JEE Main 2021 (Online) 27th August Evening Shift (4)
JEE Main 2021 (Online) 18th March Morning Shift (1)
JEE Main 2021 (Online) 26th February Morning Shift (2)
JEE Main 2020 (Online) 8th January Evening Slot (1)
Chapters Map
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
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
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