jee-main

Papers (169)
2025
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2024
session1_01feb_shift1 4 session1_01feb_shift2 22 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 30 session1_29jan_shift2 23 session1_30jan_shift1 17 session1_30jan_shift2 30 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 4 session2_04apr_shift2 30 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 22 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 30 session2_09apr_shift1 5 session2_09apr_shift2 30
2023
session1_01feb_shift1 24 session1_01feb_shift2 3 session1_24jan_shift1 13 session1_24jan_shift2 12 session1_25jan_shift1 28 session1_25jan_shift2 27 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 2 session1_30jan_shift2 29 session1_31jan_shift1 28 session1_31jan_shift2 17 session2_06apr_shift1 5 session2_06apr_shift2 17 session2_08apr_shift1 29 session2_08apr_shift2 14 session2_10apr_shift1 29 session2_10apr_shift2 15 session2_11apr_shift1 5 session2_11apr_shift2 4 session2_12apr_shift1 26 session2_13apr_shift1 25 session2_13apr_shift2 20 session2_15apr_shift1 20
2022
session1_24jun_shift1 20 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 17 session1_26jun_shift1 26 session1_26jun_shift2 23 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 5 session2_25jul_shift1 29 session2_25jul_shift2 22 session2_26jul_shift1 29 session2_26jul_shift2 24 session2_27jul_shift1 26 session2_27jul_shift2 29 session2_28jul_shift1 12 session2_28jul_shift2 29 session2_29jul_shift1 18 session2_29jul_shift2 17
2021
session1_24feb_shift1 10 session1_24feb_shift2 7 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 17 session2_16mar_shift1 29 session2_16mar_shift2 15 session2_17mar_shift1 20 session2_17mar_shift2 24 session2_18mar_shift1 12 session2_18mar_shift2 11 session3_20jul_shift1 30 session3_20jul_shift2 29 session3_22jul_shift1 7 session3_25jul_shift1 2 session3_25jul_shift2 15 session3_27jul_shift1 3 session3_27jul_shift2 4 session4_01sep_shift2 11 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 28 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 26 session1_07jan_shift2 17 session1_08jan_shift1 5 session1_08jan_shift2 12 session1_09jan_shift1 22 session1_09jan_shift2 18 session2_02sep_shift1 19 session2_02sep_shift2 17 session2_03sep_shift1 21 session2_03sep_shift2 9 session2_04sep_shift1 10 session2_04sep_shift2 24 session2_05sep_shift1 23 session2_05sep_shift2 27 session2_06sep_shift1 13 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 30 session1_10jan_shift2 12 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 20 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 3 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 29 15apr 28 15apr_shift1 28 15apr_shift2 2 16apr 15
2017
02apr 28 08apr 29 09apr 30
2016
03apr 30 09apr 30 10apr 28
2015
04apr 29 10apr 30
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 14 22apr 5 23apr 14 25apr 13
2012
07may 18 12may 22 19may 13 26may 17 offline 30
2011
jee-main_2011.pdf 13
2010
jee-main_2010.pdf 1
2009
jee-main_2009.pdf 1
2008
jee-main_2008.pdf 1
2007
jee-main_2007.pdf 38
2005
jee-main_2005.pdf 19
2004
jee-main_2004.pdf 11
2003
jee-main_2003.pdf 9
2002
jee-main_2002.pdf 8
2019 session1_10jan_shift2

12 maths questions

Q2 Forces, equilibrium and resultants View
Two vectors $\vec { A }$ and $\vec { B }$ have equal magnitudes. The magnitude of $( \vec { A } + \vec { B } )$ is ' $n$ ' times the magnitude of $( \vec { A } - \vec { B } )$. The angle between $\vec { A }$ and $\vec { B }$ is:
(1) $\cos ^ { - 1 } \left[ \frac { n ^ { 2 } - 1 } { n ^ { 2 } + 1 } \right]$
(2) $\sin ^ { - 1 } \left[ \frac { n - 1 } { n + 1 } \right]$
(3) $\cos ^ { - 1 } \left[ \frac { n - 1 } { n + 1 } \right]$
(4) $\sin ^ { - 1 } \left[ \frac { n ^ { 2 } - 1 } { n ^ { 2 } + 1 } \right]$
Q3 Forces, equilibrium and resultants View
Two forces $P$ and $Q$, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\theta$ is:
(1) $120 ^ { \circ }$
(2) $60 ^ { \circ }$
(3) $30 ^ { \circ }$
(4) $90 ^ { \circ }$
Q4 Travel graphs View
A particle starts from the origin at time $t = 0$ and moves along the positive $x$-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time $t = 5s$?
(1) $10 m$
(2) $9 m$
(3) $6 m$
(4) $3 m$
Q5 Work done and energy Work-energy theorem: finding speed or kinetic energy from net work View
A particle which is experiencing a force, given by $\vec { F } = 3 \hat { \mathrm { i } } - 12 \hat { \mathrm { j } }$, undergoes a displacement of $\vec { d } = 4 \hat { \mathrm { i } }$. If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement?
(1) 9 J.
(2) 15 J.
(3) 12 J.
(4) 10 J.
Q13 Simple Harmonic Motion View
A particle executes simple harmonic motion with an amplitude of $5 cm$. When the particle is at $4 cm$ from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is:
(1) $\frac { 8 \pi } { 3 }$
(2) $\frac { 3 } { 8 } \pi$
(3) $\frac { 4 \pi } { 3 }$
(4) $\frac { 7 } { 3 } \pi$
Q14 Simple Harmonic Motion View
A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega$. If the radius of the bottle is 2.5 cm then $\omega$ is close to: (density of water $= 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$)
(1) $5.00 \mathrm { rad } \mathrm { sec } ^ { - 1 }$
(2) $2.50 \mathrm { rad } \mathrm { sec } ^ { - 1 }$
(3) $7.9 \mathrm { rad } \mathrm { sec } ^ { - 1 }$
(4) $3.75 \mathrm { rad } \mathrm { sec } ^ { - 1 }$
Q61 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
The value of $\lambda$ such that sum of the squares of the roots of the quadratic equation, $x ^ { 2 } + ( 3 - \lambda ) x + 2 = \lambda$ has the least value is:
(1) 2
(2) $\frac { 4 } { 9 }$
(3) $\frac { 15 } { 8 }$
(4) 1
Q62 Complex Numbers Arithmetic Trigonometric/Polar Form and De Moivre's Theorem View
Let $z = \left( \frac { \sqrt { 3 } } { 2 } + \frac { i } { 2 } \right) ^ { 5 } + \left( \frac { \sqrt { 3 } } { 2 } - \frac { i } { 2 } \right) ^ { 5 }$. If $R ( z )$ and $I ( z )$ respectively denote the real and imaginary parts of $z$, then
(1) $I ( z ) = 0$
(2) $R ( z ) < 0$ and $I ( z ) > 0$
(3) $R ( z ) > 0$ and $I ( z ) > 0$
(4) $R ( z ) = - 3$
Q63 Combinations & Selection Combinatorial Identity or Bijection Proof View
If $\sum _ { r = 0 } ^ { 25 } \left\{ \left( { } ^ { 50 } C _ { r } \right) \left( { } ^ { 50 - r } C _ { 25 - r } \right) \right\} = K \left( { } ^ { 50 } C _ { 25 } \right)$, then $K$ is equal to
(1) $2 ^ { 25 }$
(2) $2 ^ { 25 } - 1$
(3) $2 ^ { 24 }$
(4) $( 25 ) ^ { 2 }$
Q64 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
The positive value of $\lambda$ for which the co-efficient of $x ^ { 2 }$ in the expansion $x ^ { 2 } \left( \sqrt { x } + \frac { \lambda } { x ^ { 2 } } \right) ^ { 10 }$ is 720, is
(1) $\sqrt { 5 }$
(2) 3
(3) 4
(4) $2 \sqrt { 2 }$
Q65 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
The value of $\cos \frac { \pi } { 2 ^ { 2 } } \cdot \cos \frac { \pi } { 2 ^ { 3 } } \cdot \ldots \cdot \cos \frac { \pi } { 2 ^ { 10 } } \cdot \sin \frac { \pi } { 2 ^ { 10 } }$ is:
(1) $\frac { 1 } { 1024 }$
(2) $\frac { 1 } { 512 }$
(3) $\frac { 1 } { 2 }$
(4) $\frac { 1 } { 256 }$
Q66 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
Two vertices of a triangle are $( 0,2 )$ and $( 4,3 )$. If its orthocenter is at the origin, then its third vertex lies in which quadrant?