jee-main

Papers (169)
2025
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2024
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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_12jan_shift1

10 maths questions

Q2 Constant acceleration (SUVAT) Relative velocity and observed length/time View
A passenger train of length $60 m$ travels at a speed of $80 \mathrm {~km} / \mathrm { hr }$. Another freight train of length $120 m$ travels at a speed of $30 \mathrm {~km} / \mathrm { hr }$. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is:
(1) $\frac { 5 } { 2 }$
(2) $\frac { 3 } { 2 }$
(3) $\frac { 11 } { 5 }$
(4) $\frac { 25 } { 11 }$
Q3 Momentum and Collisions Elastic Collision – Velocity or Mass Determination View
A simple pendulum, made of a string of length $l$ and a bob of mass $m$, is released from a small angle $\theta _ { 0 }$. It strikes a block of mass $M$, kept on horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle $\theta _ { 1 }$. Then $M$ is given by:
(1) $m \left( \frac { \theta _ { 0 } - \theta _ { 1 } } { \theta _ { 0 } + \theta _ { 1 } } \right)$
(2) $m \left( \frac { \theta _ { 0 } + \theta _ { 1 } } { \theta _ { 0 } - \theta _ { 1 } } \right)$
(3) $\frac { m } { 2 } \left( \frac { \theta _ { 0 } + \theta _ { 1 } } { \theta _ { 0 } - \theta _ { 1 } } \right)$
(4) $\frac { m } { 2 } \left( \frac { \theta _ { 0 } - \theta _ { 1 } } { \theta _ { 0 } + \theta _ { 1 } } \right)$
Q4 Centre of Mass 1 View
The position vector of the center of mass $\overrightarrow { \mathrm { r } } _ { \mathrm { cm } }$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:
(1) $\overrightarrow { \mathrm { r } } _ { \mathrm { cm } } = \frac { 13 } { 8 } \mathrm {~L} \hat { \mathrm { x } } + \frac { 5 } { 8 } \mathrm {~L} \hat { \mathrm { y } }$
(2) $\vec { r } _ { \mathrm { cm } } = \frac { 5 } { 8 } \mathrm {~L} \hat { \mathrm { x } } + \frac { 13 } { 8 } \mathrm {~L} \hat { \mathrm { y } }$
(3) $\overrightarrow { \mathrm { r } } _ { \mathrm { cm } } = \frac { 3 } { 8 } \mathrm {~L} \hat { \mathrm { x } } + \frac { 11 } { 8 } \mathrm {~L} \hat { \mathrm { y } }$
(4) $\overrightarrow { \mathrm { r } } _ { \mathrm { cm } } = \frac { 11 } { 8 } \mathrm {~L} \hat { \mathrm { x } } + \frac { 3 } { 8 } \mathrm {~L} \hat { \mathrm { y } }$
Q11 Simple Harmonic Motion View
Two light identical springs of spring constant $k$ are attached horizontally at the two ends of a uniform horizontal rod $AB$ of length $l$ and mass $m$. The rod is pivoted at its center '$O$' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is:
(1) $\frac { 1 } { 2 \pi } \sqrt { \frac { 3 k } { m } }$
(2) $\frac { 1 } { 2 \pi } \sqrt { \frac { k } { m } }$
(3) $\frac { 1 } { 2 \pi } \sqrt { \frac { 6 \mathrm { k } } { m } }$
(4) $\frac { 1 } { 2 \pi } \sqrt { \frac { 2 k } { m } }$
Q61 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
If $\lambda$ be the ratio of the roots of the quadratic equation in $x , 3 m ^ { 2 } x ^ { 2 } + m ( m - 4 ) x + 2 = 0$, then the least value of $m$ for which $\lambda + \frac { 1 } { \lambda } = 1$, is :
(1) $2 - \sqrt { 3 }$
(2) $- 2 + \sqrt { } \overline { 2 }$
(3) $4 - 2 \sqrt { 3 }$
(4) $4 - 3 \sqrt { 2 }$
Q62 Complex Numbers Argand & Loci Algebraic Conditions for Geometric Properties (Real, Imaginary, Collinear) View
If $\frac { z - \alpha } { z + \alpha } ( \alpha \in R )$ is a purely imaginary number and $| z | = 2$, then a value of $\alpha$ is :
(1) 1
(2) $\frac { 1 } { 2 }$
(3) $\sqrt { 2 }$
(4) 2
Q63 Combinations & Selection Subset Counting with Set-Theoretic Conditions View
Let $S = \{ 1,2,3 , \ldots , 100 \}$, then number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even is :
(1) $2 ^ { 100 } - 1$
(2) $2 ^ { 50 } + 1$
(3) $2 ^ { 50 } \left( 2 ^ { 50 } - 1 \right)$
(4) $2 ^ { 50 } - 1$
Q64 Combinations & Selection Basic Combination Computation View
Consider three boxes, each containing 10 balls labelled $1,2 , \ldots , 10$. Suppose one ball is randomly drawn from each of the boxes. Denote by $n _ { i }$, the label of the ball drawn from the $i ^ { \text {th } }$ box, $( i = 1,2,3 )$. Then, the number of ways in which the balls can be chosen such that $n _ { 1 } < n _ { 2 } < n _ { 3 }$ is:
(1) 240
(2) 82
(3) 120
(4) 164
Q65 Sequences and Series Evaluation of a Finite or Infinite Sum View
Let $S _ { k } = \frac { 1 + 2 + 3 + \ldots + k } { k }$. If $S _ { 1 } ^ { 2 } + S _ { 2 } ^ { 2 } + \ldots + S _ { 10 } ^ { 2 } = \frac { 5 } { 12 } A$, then $A$ is equal to :
(1) 301
(2) 303
(3) 156
(4) 283
Q66 Geometric Sequences and Series Arithmetic-Geometric Sequence Interplay View
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the G.P. is: