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.
eSaral helps the students in clearing and understanding each topic in a better way. eSaral is providing complete chapter-wise notes of Class 11th and 12th both for all subjects.
Besides this, eSaral also offers NCERT Solutions, Previous year questions for JEE Main and Advance, Practice questions, Test Series for JEE Main, JEE Advanced and NEET, Important questions of Physics, Chemistry, Math, and Biology and many more.
Download eSaral app for free study material and video tutorials.
Q. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is –
(1) At least 750 but less than 1000
(2) At least 1000
(3) Less than 500
(4) At least 500 but less than 750
[AIEEE 2009]
Ans. (2)
The no. of ways to select 4 novels $\& 1$ dictionary from 6 different novels $\& 3$ different dictionary are $6 \mathrm{C}_{4} \times^{3} \mathrm{C}_{1}$
and to arrange these things in shelf so that dictionary is always in middle $-\mathrm{D}--\mathrm{are} 4 !$
Required No. of ways $^{6} \mathrm{C}_{4} \times^{3} \mathrm{C}_{1} \times 4 !=1080$
Q. There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is -
(1) 3 (2) 36 (3) 66 (4) 108
[AIEEE-2010]
Ans. (4)
Urn $\mathrm{A} \rightarrow 3$ Red balls
Urn $\mathrm{B} \rightarrow 9$ Blue balls
So the number of ways $=$ selection of 2 balls from urn $\mathrm{A} \& \mathrm{B}$ each.
$=^{3} \mathrm{C}_{2} \cdot^{9} \mathrm{C}_{2}=108$
Q. Statement - 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is $^{9} \mathrm{C}_{3}$
Statement - 2 : The number of ways of choosing any 3 places from 9 different places is $^{9} \mathrm{C}_{3}$
(1) Statement-1 is true, Statement-2 is false.
(2) Statement-1 is false, Statement-2 is true
(3) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement- 1
(4) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement- 1
[AIEEE-2011]
Ans. (3)
$\mathrm{B}_{1}+\mathrm{B}_{2}+\mathrm{B}_{3}+\mathrm{B}_{4}=10$
$\mathrm{St}-1: \mathrm{B}_{1} \geq 1, \mathrm{B}_{2} \geq 1, \mathrm{B}_{3} \geq 1, \mathrm{B}_{4} \geq 1$
so no. of negative integers solution of equation
$\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\mathrm{x}_{4}=10-4=6$
$6+4-1 \mathrm{C}_{4-1}=9 \mathrm{C}_{3}$
$\mathrm{St}-2:$ selction of 3 places from out of
9 places $=^{9} \mathrm{C}_{3}$
Both statements are true and correct explaination
Q. There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then :
(1) $\mathrm{N}>190$
(2) $\mathrm{N} \leq 100$
(3) $100<\mathrm{N} \leq 140$
(4) $140<\mathrm{N} \leq 190$
[AIEEE-2011]
Ans. (2)
$\begin{aligned} \mathrm{N}=10 \mathrm{C}_{3}-^{6} \mathrm{C}_{3} &=\frac{10 \times 9 \times 8}{3 \times 2 \times 1}-\frac{6 \times 5 \times 4}{3 \times 2 \times 1} \\ &=120-20=100 \end{aligned}$
$\mathrm{N} \leq 100$
Q. Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is –
(1) 879 (2) 880 (3) 629 (4) 630
[AIEEE-2012]
Ans. (1)
$\mathrm{W}^{10}, \mathrm{G}^{9}, \mathrm{B}^{7}$
selection of one or more balls
$=(10+1)(9+1)(7+1)-1$
$=11 \times 10 \times 8-1=879$
Q. Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is
(1) 256 (2) 220 (3) 219 (4) 211
[JEE (Main)-2013]
Ans. (3)
$\mathrm{n}(\mathrm{A})=2, \mathrm{n}(\mathrm{B})=4, \mathrm{n}(\mathrm{A} \times \mathrm{B})=\mathrm{n}(\mathrm{A}) \cdot \mathrm{n}(\mathrm{B})=8$
Now subsets having 3 or more elements.
$\mathrm{S} \mathrm{C}_{3}+^{8} \mathrm{C}_{4}+\ldots .+^{8} \mathrm{C}_{8}=2^{8}-^{8} \mathrm{C}_{0}-^{8} \mathrm{C}_{1}-^{8} \mathrm{C}_{2}=256-37=219$
Q. Let $\mathrm{T}_{\mathrm{n}}$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $\mathrm{T}_{\mathrm{n}+1} \mathrm{T}_{\mathrm{n}}=10,$ then the value of $\mathrm{n}$ is :
(1) 7 (2) 5 (3) 10 (4) 8
[JEE (Main)-2013]
Ans. (2)
$\mathrm{T}_{\mathrm{n}}=\mathrm{n} \mathrm{C}_{3} \Rightarrow \mathrm{n}+1 \mathrm{C}_{3}-^{\mathrm{n}} \mathrm{C}_{3}=10$
$(\mathrm{n}+1) \mathrm{n}(\mathrm{n}-1)-\mathrm{n}(\mathrm{n}-1)(\mathrm{n}-2)=60$
$\mathrm{n}(\mathrm{n}-1)=20$
$\mathrm{n}=5$
Q. The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0) is :
(1) 820 (2) 780 (3) 901 (4) 861
[JEE (Main)-2015]
Ans. (2)

Q. Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is :
(1) 275 (2) 510 (3) 219 (4) 256
[JEE (Main)-2015]
Ans. (3)
$\mathrm{n}(\mathrm{A})=4, \mathrm{n}(\mathrm{B})=2$
$\mathrm{n}(\mathrm{A} \times \mathrm{B})=8$
Number of subsets having atleast 3 elements
$=2^{8}-\left(1+^{8} \mathrm{C}_{1}+^{8} \mathrm{C}_{2}\right)=219$
Q. The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8 without repetition, is :
(1) 120 (2) 72 (3) 216 (4) 192
[JEE (Main)-2015]
Ans. (4)
Number of 4 digit numbers greater than 6000 is $\frac{3}{2} \times 4 \times 3 \times 2=72$
Number of 5 digit numbers greater than 6000 is $5 !=120$
So total number of numbers $=72+120=192$
Q. If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:
[JEE (Main)-2016]
Ans. (1)
Total number of words which can be formed using all the letters of the word 'SMALL'
$=\frac{5 !}{2 !}=60$
Now, $60^{\text {th }}$ word is $\rightarrow$ SMLLA
59th word is $\rightarrow$ SMALL
58th word is $\rightarrow$ SMALL
Q. A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :
(1) 484 (2) 485 (3) 468 (4) 469
[JEE (Main)-2017]
Ans. (2)

Q. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is-
(1) less than 500
(2) at least 500 but less than 750
(3) at least 750 but less than 1000
(4) at least 1000
[JEE (Main)-2018]
Ans. (4)
$\begin{aligned} \text { Number of ways } &=\left(\begin{array}{c}{6} \\ {4}\end{array}\right)\left(\begin{array}{l}{3} \\ {1}\end{array}\right) 4 ! \\ &=15 \times 3 \times 24 \\ &=1080 \end{aligned}$
Comments
Manoswini panda - Feb. 16, 2021, 5:02 p.m.
Sorry it is given actually my phone is not. Working properly
Manoswini panda - Feb. 16, 2021, 4:39 p.m.
No answer is coming why?😨😠
Bala - Dec. 30, 2020, 10:56 p.m.
Easy ra
Abhijeet Kumar - Dec. 21, 2020, 10:35 a.m.
Nice, but need more questions to practice!!!!
kk - Dec. 18, 2020, 8:39 p.m.
good website
IIT JEE Aspirant 2022 - Dec. 17, 2020, 2:09 p.m.
Nice website
aryan - Dec. 10, 2020, 5:18 p.m.
where are 2019 and 2020
asdf - Dec. 10, 2020, 5:18 p.m.
where are 2019 and 2020
Sidhartha - Dec. 5, 2020, 9:59 p.m.
ThankU!!! My work made simpler now😀
Khushi - Dec. 3, 2020, 5:43 p.m.
Thank you so much !!!!
Rhittik Kumar Barman - Oct. 13, 2020, 7:53 p.m.
Thank you so much for giving questions
Manoj - Sept. 3, 2020, 7:19 p.m.
Please give solution in a easy way
Srigowthami - Aug. 27, 2020, 2:23 p.m.
Thanks...
Kd - Aug. 19, 2020, 10:54 a.m.
Tq
Jyothi - Aug. 10, 2020, 2:38 p.m.
It's really very helpful.
himanshi sharma - June 27, 2020, 3:46 p.m.
please make these practice worksheets printable. this is a humble request... the content is too good but the only problem is they are not printable. if they can be downloaded it would be a great help
Esther Evangeline - May 28, 2020, 6:45 p.m.
Really helpful
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
Free Study Material