jee-main

Papers (191)
2026
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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
2022 session2_26jul_shift2

23 maths questions

Q1 Projectiles Ratio of Projectile Quantities for Different Launch Parameters View
Two projectiles are thrown with same initial velocity making an angle of $45^{\circ}$ and $30^{\circ}$ with the horizontal respectively. The ratio of their respective ranges will be
(1) $1 : \sqrt { 2 }$
(2) $\sqrt { 2 } : 1$
(3) $2 : \sqrt { 3 }$
(4) $\sqrt { 3 } : 2$
Q2 Pulley systems View
Two masses $M _ { 1 }$ and $M _ { 2 }$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M _ { 2 }$ is twice that of $M _ { 1 }$, the acceleration of the system is $a _ { 1 }$. When the mass $M _ { 2 }$ is thrice that of $M _ { 1 }$, the acceleration of the system is $a _ { 2 }$. The ratio $\frac { a _ { 1 } } { a _ { 2 } }$ will be
(1) $\frac { 1 } { 3 }$
(2) $\frac { 2 } { 3 }$
(3) $\frac { 3 } { 2 }$
(4) $\frac { 1 } { 2 }$
Q3 Impulse and momentum (advanced) View
A ball of mass 0.15 kg hits the wall with its initial speed of $12 \mathrm{~m~s}^{-1}$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of ball with the wall.
(1) 0.018 s
(2) 0.036 s
(3) 0.009 s
(4) 0.072 s
Q4 Momentum and Collisions Velocity of Centre of Mass View
A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be
(1) $1 : 1$
(2) $2 : 1$
(3) $1 : 4$
(4) $4 : 1$
Q21 Vectors Introduction & 2D Dot Product Computation View
If $\vec { A } = 2 \hat { \mathrm { i } } + 3 \hat { \mathrm { j } } - \hat { \mathrm { k } }$ m and $\vec { B } = \hat { \mathrm { i } } + 2 \hat { \mathrm { j } } + 2 \hat { \mathrm { k } }$ m. The magnitude of component of vector $\vec { A }$ along vector $\vec { B }$ will be $\_\_\_\_$ m.
Q24 Simple Harmonic Motion View
As per given figures, two springs of spring constants $K$ and $2K$ are connected to mass $m$. If the period of oscillation in figure (a) is 3 s, then the period of oscillation in figure (b) will be $\sqrt { x }$ s. The value of $x$ is $\_\_\_\_$.
Q61 Solving quadratics and applications Optimization or extremal value of an expression via completing the square View
The minimum value of the sum of the squares of the roots of $x ^ { 2 } + 3 - a x = 2 a - 1$ is
(1) 6
(2) 4
(3) 5
(4) 8
Q62 Complex Numbers Arithmetic Intersection of Loci and Simultaneous Geometric Conditions View
If $z = x + i y$ satisfies $|z - 2| = 0$ and $|z - i| - |z + 5i| = 0$, then
(1) $x + 2 y - 4 = 0$
(2) $x ^ { 2 } + y - 4 = 0$
(3) $x + 2 y + 4 = 0$
(4) $x ^ { 2 } - y + 3 = 0$
Q63 Binomial Theorem (positive integer n) Evaluate a Summation Involving Binomial Coefficients View
$\sum _ { i , j = 0 , i \neq j } ^ { n } { } ^ { n } C _ { i } { } ^ { n } C _ { j }$ is equal to
(1) $2 ^ { 2 n } - { } ^ { 2 n } C _ { n }$
(2) $2 ^ { 2 n - 1 } - { } ^ { 2 n - 1 } C _ { n - 1 }$
(3) $2 ^ { 2 n } - \frac { 1 } { 2 } { } ^ { 2 n } C _ { n }$
(4) $2 ^ { n - 1 } + { } ^ { 2 n - 1 } C _ { n }$
Q64 Circles Circle Equation Derivation View
Let the abscissae of the two points $P$ and $Q$ on a circle be the roots of $x ^ { 2 } - 4 x - 6 = 0$ and the ordinates of $P$ and $Q$ be the roots of $y ^ { 2 } + 2 y - 7 = 0$. If $PQ$ is a diameter of the circle $x ^ { 2 } + y ^ { 2 } + 2 a x + 2 b y + c = 0$, then the value of $a + b - c$ is
(1) 12
(2) 13
(3) 14
(4) 16
Q65 Curve Sketching Tangent Lines and Tangent Lengths View
The equation of a common tangent to the parabolas $y = x ^ { 2 }$ and $y = -(x - 2) ^ { 2 }$ is
(1) $y = 4 x - 2$
(2) $y = 4 x - 1$
(3) $y = 4 x + 1$
(4) $y = 4 x + 2$
Q66 Conic sections Tangent and Normal Line Problems View
The acute angle between the pair of tangents drawn to the ellipse $2 x ^ { 2 } + 3 y ^ { 2 } = 5$ from the point $(1, 3)$ is
(1) $\tan ^ { - 1 } \frac { 16 } { 7 \sqrt { 5 } }$
(2) $\tan ^ { - 1 } \frac { 24 } { 7 \sqrt { 5 } }$
(3) $\tan ^ { - 1 } \frac { 32 } { 7 \sqrt { 5 } }$
(4) $\tan ^ { - 1 } \frac { 3 + 8 \sqrt { 5 } } { 35 }$
Q67 Conic sections Equation Determination from Geometric Conditions View
If the line $x - 1 = 0$, is a directrix of the hyperbola $k x ^ { 2 } - y ^ { 2 } = 6$, then the hyperbola passes through the point
(1) $\left( - 2 \sqrt { 5 } , 6 \right)$
(2) $\left( - \sqrt { 5 } , 3 \right)$
(3) $\left( \sqrt { 5 } , - 2 \right)$
(4) $\left( 2 \sqrt { 5 } , 3 \sqrt { 6 } \right)$
Q68 Laws of Logarithms Convergence proof and limit determination View
Let $\beta = \lim _ { x \rightarrow 0 } \frac { \alpha x - \left( e ^ { 3 x } - 1 \right) } { \alpha x \left( e ^ { 3 x } - 1 \right) }$ for some $\alpha \in \mathbb { R }$. Then the value of $\alpha + \beta$ is:
(1) $\frac { 14 } { 5 }$
(2) $\frac { 3 } { 2 }$
(3) $\frac { 5 } { 2 }$
(4) $\frac { 1 } { 2 }$
Q70 3x3 Matrices Matrix Algebra and Product Properties View
Let $A = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}$ and $B = \begin{pmatrix} 9 ^ { 2 } & - 10 ^ { 2 } & 11 ^ { 2 } \\ 12 ^ { 2 } & 13 ^ { 2 } & - 14 ^ { 2 } \\ - 15 ^ { 2 } & 16 ^ { 2 } & 17 ^ { 2 } \end{pmatrix}$, then the value of $A ^ { \prime } B A$ is:
(1) 1224
(2) 1042
(3) 540
(4) 539
Q71 Trig Proofs Multi-Step Composite Problem Using Identities View
If $0 < x < \frac { 1 } { \sqrt { 2 } }$ and $\frac { \sin ^ { - 1 } x } { \alpha } = \frac { \cos ^ { - 1 } x } { \beta }$, then a value of $\sin \frac { 2 \pi \alpha } { \alpha + \beta }$ is
(1) $4 \sqrt { 1 - x ^ { 2 } } \left( 1 - 2 x ^ { 2 } \right)$
(2) $4 x \sqrt { 1 - x ^ { 2 } } \left( 1 - 2 x ^ { 2 } \right)$
(3) $2 x \sqrt { 1 - x ^ { 2 } } \left( 1 - 4 x ^ { 2 } \right)$
(4) $4 \sqrt { 1 - x ^ { 2 } } \left( 1 - 4 x ^ { 2 } \right)$
Q72 Differentiating Transcendental Functions Evaluate derivative at a point or find tangent slope View
The value of $\log _ { e } 2 \cdot \frac { \mathrm { d } } { \mathrm { d } x } \log _ { \cos x } \operatorname { cosec } x$ at $x = \frac { \pi } { 4 }$ is
(1) $- 2 \sqrt { 2 }$
(2) $2 \sqrt { 2 }$
(3) $-4$
(4) $4$
Q73 Stationary points and optimisation Optimization on a Circle View
Let $P$ and $Q$ be any points on the curves $( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 1$ and $y = x ^ { 2 }$, respectively. The distance between $P$ and $Q$ is minimum for some value of the abscissa of $P$ in the interval
(1) $\left( 0 , \frac { 1 } { 4 } \right)$
(2) $\left( \frac { 1 } { 2 } , \frac { 3 } { 4 } \right)$
(3) $\left( \frac { 1 } { 4 } , \frac { 1 } { 2 } \right)$
(4) $\left( \frac { 3 } { 4 } , 1 \right)$
Q74 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions View
If the maximum value of $a$, for which the function $f _ { a } ( x ) = \tan ^ { - 1 } 2 x - 3 a x + 7$ is non-decreasing in $\left[ - \frac { \pi } { 6 } , \frac { \pi } { 6 } \right]$, is $\bar { a }$, then $f _ { \bar { a } } \left( \frac { \pi } { 8 } \right)$ is equal to
(1) $8 - \frac { 9 \pi } { 49 + \pi ^ { 2 } }$
(2) $8 - \frac { 4 \pi } { 94 + \pi ^ { 2 } }$
(3) $8 \frac { 1 + \pi ^ { 2 } } { 9 + \pi ^ { 2 } }$
(4) $8 - \frac { \pi } { 4 }$
Q75 Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition View
The integral $\int \frac{ \left(1 - \frac { 1 } { \sqrt { 3 } }\right) \cos x - \sin x } { 1 + \frac { 2 } { \sqrt { 3 } } \sin 2 x } d x$ is equal to
(1) $\frac { 1 } { 2 } \log _ { e } \left| \frac { \tan \left( \frac { x } { 2 } + \frac { \pi } { 12} \right) } { \tan\left( \frac { x } { 2 } + \frac { \pi } { 6 } \right) } \right| + C$
(2) $\log _ { e } \left| \frac { \tan \left( \frac { x } { 2 } + \frac { \pi } { 6 } \right) } { \tan\left( \frac { x } { 2 } + \frac { \pi } { 3 } \right) } \right| + C$
(3) $\frac { 1 } { 2 } \log _ { e } \left| \frac { \tan \left( \frac { x } { 2 } + \frac { \pi } { 6 } \right) } { \tan\left( \frac { x } { 2 } + \frac { \pi } { 3 } \right) } \right| + C$
(4) $\frac { 1 } { 2 } \log _ { e } \left| \frac { \tan \left( \frac { x } { 2 } - \frac { \pi } { 12 } \right) } { \tan \left( \frac { x } { 2 } - \frac { \pi } { 6 } \right) } \right| + C$
Q76 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View
$\int _ { 0 } ^ { 20 \pi } ( | \sin x | + | \cos x | ) ^ { 2 } \, d x$ is equal to:
(1) $10 \pi + 4$
(2) $10 \pi + 2$
(3) $20 \pi - 2$
(4) $20 \pi + 2$
Q77 Areas Between Curves Area Involving Piecewise or Composite Functions View
The area bounded by the curves $y = | x ^ { 2 } - 1 |$ and $y = 1$ is
(1) $\frac { 2 } { 3 } ( \sqrt { 2 } + 1 )$
(2) $\frac { 4 } { 3 } ( \sqrt { 2 } - 1 )$
(3) $2 ( \sqrt { 2 } - 1 )$
(4) $\frac { 8 } { 3 } ( \sqrt { 2 } - 1 )$
Q78 First order differential equations (integrating factor) View
Let the solution curve $y = f(x)$ of the differential equation $\frac { d y } { d x } + \frac { x y } { x ^ { 2 } - 1 } = \frac { x ^ { 4 } + 2 x } { \sqrt { 1 - x ^ { 2 } } }$, $x \in ( - 1, 1 )$ pass through the origin. Then $\int _ { - \frac { \sqrt { 3 } } { 2 } } ^ { \frac { \sqrt { 3 } } { 2 } } f(x) \, d x$ is equal to