jee-main

Papers (191)
2026
session1_21jan_shift1 13 session1_21jan_shift2 9 session1_22jan_shift1 16 session1_22jan_shift2 10 session1_23jan_shift1 11 session1_23jan_shift2 7 session1_24jan_shift1 14 session1_24jan_shift2 10 session1_28jan_shift1 10 session1_28jan_shift2 9
2025
session1_22jan_shift1 25 session1_22jan_shift2 25 session1_23jan_shift1 25 session1_23jan_shift2 25 session1_24jan_shift1 25 session1_24jan_shift2 25 session1_28jan_shift1 25 session1_28jan_shift2 25 session1_29jan_shift1 29 session1_29jan_shift2 25 session2_02apr_shift1 31 session2_02apr_shift2 36 session2_03apr_shift1 35 session2_03apr_shift2 35 session2_04apr_shift1 37 session2_04apr_shift2 33 session2_07apr_shift1 32 session2_07apr_shift2 32 session2_08apr_shift1 36 session2_08apr_shift2 35
2024
session1_01feb_shift1 5 session1_01feb_shift2 21 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 28 session1_29jan_shift2 29 session1_30jan_shift1 20 session1_30jan_shift2 29 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 5 session2_04apr_shift2 28 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 21 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 29 session2_09apr_shift1 8 session2_09apr_shift2 30
2023
session1_01feb_shift1 28 session1_01feb_shift2 3 session1_24jan_shift1 11 session1_24jan_shift2 11 session1_25jan_shift1 29 session1_25jan_shift2 29 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 5 session1_30jan_shift2 27 session1_31jan_shift1 28 session1_31jan_shift2 15 session2_06apr_shift1 5 session2_06apr_shift2 16 session2_08apr_shift1 29 session2_08apr_shift2 13 session2_10apr_shift1 29 session2_10apr_shift2 16 session2_11apr_shift1 6 session2_11apr_shift2 8 session2_12apr_shift1 26 session2_13apr_shift1 24 session2_13apr_shift2 24 session2_15apr_shift1 19
2022
session1_24jun_shift1 19 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 14 session1_26jun_shift1 29 session1_26jun_shift2 24 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 4 session2_25jul_shift1 29 session2_25jul_shift2 20 session2_26jul_shift1 29 session2_26jul_shift2 23 session2_27jul_shift1 28 session2_27jul_shift2 29 session2_28jul_shift1 11 session2_28jul_shift2 29 session2_29jul_shift1 17 session2_29jul_shift2 18
2021
session1_24feb_shift1 9 session1_24feb_shift2 4 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 15 session2_16mar_shift1 29 session2_16mar_shift2 18 session2_17mar_shift1 21 session2_17mar_shift2 27 session2_18mar_shift1 18 session2_18mar_shift2 9 session3_20jul_shift1 29 session3_20jul_shift2 29 session3_22jul_shift1 9 session3_25jul_shift1 8 session3_25jul_shift2 14 session3_27jul_shift1 4 session3_27jul_shift2 7 session4_01sep_shift2 14 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 29 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 28 session1_07jan_shift2 20 session1_08jan_shift1 5 session1_08jan_shift2 11 session1_09jan_shift1 26 session1_09jan_shift2 16 session2_02sep_shift1 18 session2_02sep_shift2 16 session2_03sep_shift1 23 session2_03sep_shift2 8 session2_04sep_shift1 14 session2_04sep_shift2 27 session2_05sep_shift1 22 session2_05sep_shift2 29 session2_06sep_shift1 11 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 29 session1_10jan_shift2 14 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 29 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 5 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 30 15apr 28 15apr_shift1 28 15apr_shift2 6 16apr 19
2017
02apr 30 08apr 30 09apr 34
2016
03apr 28 09apr 29 10apr 30
2015
04apr 29 10apr 29 11apr 8
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 12 22apr 5 23apr 14 25apr 13
2012
07may 17 12may 21 19may 14 26may 17 offline 30
2011
jee-main_2011.pdf 18
2010
jee-main_2010.pdf 6
2009
jee-main_2009.pdf 2
2008
jee-main_2008.pdf 4
2007
jee-main_2007.pdf 38
2006
jee-main_2006.pdf 15
2005
jee-main_2005.pdf 25
2004
jee-main_2004.pdf 22
2003
jee-main_2003.pdf 8
2002
jee-main_2002.pdf 12
2021 session2_17mar_shift1

21 maths questions

Q1 Constant acceleration (SUVAT) Acceleration then deceleration (two-phase motion) View
A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is t seconds, the total distance travelled is:
(1) $\frac { 4 \alpha \beta } { ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
(2) $\frac { 2 \alpha \beta } { ( \alpha + \beta ) } t ^ { 2 }$
(3) $\frac { \alpha \beta } { 2 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
(4) $\frac { \alpha \beta } { 4 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
Q3 Work done and energy Work-energy theorem: finding speed or kinetic energy from net work View
A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The ball gets deflected by an obstacle on the way. After deflection it moves with $5\%$ of its initial kinetic energy. What is the speed of the ball now?
(1) $19.0 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $4.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $14.41 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $1.00 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
Q4 Moments View
A triangular plate is shown. A force $\vec { F } = 4 \hat { \mathrm { i } } - 3 \hat { \mathrm { j } }$ is applied at point $P$. The torque at point $P$ with respect to point $O$ and $Q$ are:
(1) $- 15 - 20 \sqrt { 3 } , 15 - 20 \sqrt { 3 }$
(2) $15 + 20 \sqrt { 3 } , 15 - 20 \sqrt { 3 }$
(3) $15 - 20 \sqrt { 3 } , 15 + 20 \sqrt { 3 }$
(4) $- 15 + 20 \sqrt { 3 } , 15 + 20 \sqrt { 3 }$
Q11 Simple Harmonic Motion View
For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?
(1) $x = 0$
(2) $x = \pm A$
(3) $x = \pm \frac { A } { \sqrt { 2 } }$
(4) $x = \frac { A } { 2 }$
Q21 Forces, equilibrium and resultants View
Two blocks ($m = 0.5 \mathrm {~kg}$ and $M = 4.5 \mathrm {~kg}$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac { 3 } { 7 }$. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is $N$. (Round off to the Nearest Integer) [Take $g$ as $9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$]
Q25 Simple Harmonic Motion View
Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is $\frac { T _ { b } } { T _ { a } } = \sqrt { x }$, where value of $x$ is $\_\_\_\_$. (Round off to the Nearest Integer)
Q61 Sequences and series, recurrence and convergence Convergence proof and limit determination View
The value of $4 + \frac { 1 } { 5 + \frac { 1 } { 4 + \frac { 1 } { 5 + \frac { 1 } { 4 + \ldots . . \infty } } } }$ is:
(1) $2 + \frac { 2 } { 5 } \sqrt { 30 }$
(2) $2 + \frac { 4 } { \sqrt { 5 } } \sqrt { 30 }$
(3) $4 + \frac { 4 } { \sqrt { 5 } } \sqrt { 30 }$
(4) $5 + \frac { 2 } { 5 } \sqrt { 30 }$
Q62 Complex Numbers Argand & Loci Geometric Interpretation and Triangle/Shape Properties View
The area of the triangle with vertices $P ( z ) , Q ( i z )$ and $R ( z + i z )$ is
(1) 1
(2) $\frac { 1 } { 2 } | z | ^ { 2 }$
(3) $\frac { 1 } { 2 }$
(4) $\frac { 1 } { 2 } | z + i z | ^ { 2 }$
Q63 Permutations & Arrangements Selection with Group/Category Constraints View
Team '$A$' consists of 7 boys and $n$ girls and Team '$B$' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $n$ is equal to:
(1) 5
(2) 2
(3) 4
(4) 6
Q64 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
If the fourth term in the expansion of $\left( x + x ^ { \log _ { 2 } x } \right) ^ { 7 }$ is 4480, then the value of $x$ where $x \in N$ is equal to:
(1) 2
(2) 4
(3) 3
(4) 1
Q65 Circles Inscribed/Circumscribed Circle Computations View
In a triangle $PQR$, the co-ordinates of the points $P$ and $Q$ are $(-2, 4)$ and $(4, -2)$ respectively. If the equation of the perpendicular bisector of $PR$ is $2x - y + 2 = 0$, then the centre of the circumcircle of the $\triangle PQR$ is:
(1) $(-1, 0)$
(2) $(-2, -2)$
(3) $(0, 2)$
(4) $(1, 4)$
Q66 Circles Circle Equation Derivation View
The line $2x - y + 1 = 0$ is a tangent to the circle at the point $(2, 5)$ and the centre of the circle lies on $x - 2y = 4$. Then, the radius of the circle is:
(1) $3\sqrt{5}$
(2) $5\sqrt{3}$
(3) $5\sqrt{4}$
(4) $4\sqrt{5}$
Q67 Circles Intersection of Circles or Circle with Conic View
Choose the incorrect statement about the two circles whose equations are given below: $x ^ { 2 } + y ^ { 2 } - 10 x - 10 y + 41 = 0$ and $x ^ { 2 } + y ^ { 2 } - 16 x - 10 y + 80 = 0$
(1) Distance between two centres is the average of radii of both the circles.
(2) Both circles' centres lie inside region of one another.
(3) Both circles pass through the centre of each other.
(4) Circles have two intersection points.
Q68 Chain Rule Limit evaluation involving derivatives or asymptotic analysis View
The value of $\lim _ { x \rightarrow 0 ^ { + } } \frac { \cos ^ { - 1 } \left( x - [ x ] ^ { 2 } \right) \cdot \sin ^ { - 1 } \left( x - [ x ] ^ { 2 } \right) } { x - x ^ { 3 } }$, where $[ x ]$ denotes the greatest integer $\leq x$ is:
(1) $\pi$
(2) 0
(3) $\frac { \pi } { 4 }$
(4) $\frac { \pi } { 2 }$
Q71 Matrices Determinant and Rank Computation View
If $A = \left[ \begin{array} { c c } 0 & \sin \alpha \\ \sin \alpha & 0 \end{array} \right]$ and $\operatorname { det } \left( A ^ { 2 } - \frac { 1 } { 2 } \mathrm { I } \right) = 0$, then a possible value of $\alpha$ is
(1) $\frac { \pi } { 2 }$
(2) $\frac { \pi } { 3 }$
(3) $\frac { \pi } { 4 }$
(4) $\frac { \pi } { 6 }$
Q72 Simultaneous equations Linear System and Inverse Existence View
The system of equations $kx + y + z = 1$, $x + ky + z = k$ and $x + y + zk = k^2$ has no solution if $k$ is equal to:
(1) 0
(2) 1
(3) $-1$
(4) $-2$
Q73 Sequences and Series Evaluation of a Finite or Infinite Sum View
If $\cot ^ { - 1 } ( \alpha ) = \cot ^ { - 1 } 2 + \cot ^ { - 1 } 8 + \cot ^ { - 1 } 18 + \cot ^ { - 1 } 32 + \ldots$ upto 100 terms, then $\alpha$ is:
(1) 1.01
(2) 1.00
(3) 1.02
(4) 1.03
Q74 Standard trigonometric equations Inverse trigonometric equation View
The sum of possible values of $x$ for $\tan ^ { - 1 } ( x + 1 ) + \cot ^ { - 1 } \left( \frac { 1 } { x - 1 } \right) = \tan ^ { - 1 } \left( \frac { 8 } { 31 } \right)$ is:
(1) $- \frac { 32 } { 4 }$
(2) $- \frac { 31 } { 4 }$
(3) $- \frac { 30 } { 4 }$
(4) $- \frac { 33 } { 4 }$
Q75 Laws of Logarithms Solve a Logarithmic Equation View
The inverse of $y = 5 ^ { \log x }$ is:
(1) $x = 5 ^ { \log y }$
(2) $x = y ^ { \log 5 }$
(3) $y = x ^ { \frac { 1 } { \log 5 } }$
(4) $x = 5 ^ { \frac { 1 } { \log y } }$
Q76 Integration by Substitution Integral Equation with Symmetry or Substitution View
Which of the following statement is correct for the function $g ( \alpha )$ for $\alpha \in R$ such that $g ( \alpha ) = \int _ { \frac { \pi } { 6 } } ^ { \frac { \pi } { 3 } } \frac { \sin ^ { \alpha } x } { \cos ^ { \alpha } x + \sin ^ { \alpha } x } d x$
(1) $g ( \alpha )$ is a strictly increasing function
(2) $g ( \alpha )$ has an inflection point at $\alpha = - \frac { 1 } { 2 }$
(3) $g ( \alpha )$ is a strictly decreasing function
(4) $g ( \alpha )$ is an even function
Q77 First order differential equations (integrating factor) Solving Separable DEs with Initial Conditions View
Which of the following is true for $y ( x )$ that satisfies the differential equation $\frac { d y } { d x } = x y - 1 + x - y ; y ( 0 ) = 0$
(1) $y ( 1 ) = \mathrm { e } ^ { - \frac { 1 } { 2 } } - 1$
(2) $y ( 1 ) = e ^ { \frac { 1 } { 2 } } - e ^ { - \frac { 1 } { 2 } }$
(3) $y ( 1 ) = 1$
(4) $y ( 1 ) = e^{\frac{1}{2}} - 1$