jee-main

Papers (191)
2026
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2025
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2024
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2023
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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
2020 session2_04sep_shift2

27 maths questions

Q3 Advanced work-energy problems View
A small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $m k v ^ { 2 }$ where $v$ is it speed. The maximum height attained by the ball is:
(1) $\frac { 1 } { 2 k } \tan ^ { - 1 } \frac { k u ^ { 2 } } { g }$
(2) $\frac { 1 } { k } \ln \left( 1 + \frac { k u ^ { 2 } } { 2 g } \right)$
(3) $\frac { 1 } { k } \tan ^ { - 1 } \frac { k u ^ { 2 } } { 2 g }$
(4) $\frac { 1 } { 2 k } \ln \left( 1 + \frac { k u ^ { 2 } } { g } \right)$
Q4 Work done and energy Work done by constant or variable force via integration View
A person pushes a box on a rough horizontal platform surface. He applies a force of $200$ N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?
(1) 3280 J
(2) 2780 J
(3) 5690 J
(4) 5250 J
Q5 Moments View
Consider two uniform discs of the same thickness and different radii $R _ { 1 } = R$ and $R _ { 2 } = \alpha R$ made of the same material. If the ratio of their moments of inertia $I _ { 1 }$ and $I _ { 2 }$, respectively, about their axes is $I _ { 1 } : I _ { 2 } = 1 : 16$ then the value of $\alpha$ is:
(1) $2 \sqrt { 2 }$
(2) $\sqrt { 2 }$
(3) 2
(4) 4
Q6 Moments View
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and $\mathrm { O } ^ { \prime }$ (corner point) is:
(1) $2/3$
(2) $1/4$
(3) $1/8$
(4) $1/2$
Q21 Travel graphs View
The speed verses time graph for a particle is shown in the figure. The distance travelled (in $m$) by the particle during the time interval $\mathrm { t } = 0$ to $\mathrm { t } = 5$ s will be $\_\_\_\_$
Q51 Roots of polynomials Finding roots or coefficients of a quadratic using Vieta's relations View
Let $\lambda \neq 0$ be in $R$. If $\alpha$ and $\beta$ are the roots of the equation, $x ^ { 2 } - x + 2 \lambda = 0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3 x ^ { 2 } - 10 x + 27 \lambda = 0$, then $\frac { \beta \gamma } { \lambda }$ is equal to:
(1) 27
(2) 18
(3) 9
(4) 36
Q52 Complex Numbers Arithmetic Roots of Unity and Cyclotomic Expressions View
If $a$ and $b$ are real numbers such that $( 2 + \alpha ) ^ { 4 } = a + b \alpha$, where $\alpha = \frac { - 1 + i \sqrt { 3 } } { 2 }$, then $a + b$ is equal to:
(1) 9
(2) 24
(3) 33
(4) 57
Q53 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
Let $a _ { 1 } , a _ { 2 } , \ldots , a _ { n }$ be a given A.P. whose common difference is an integer and $S _ { n } = a _ { 1 } + a _ { 2 } + \ldots + a _ { n }$. If $a _ { 1 } = 1 , a _ { n } = 300$ and $15 \leq n \leq 50$, then the ordered pair $\left( \mathrm { S } _ { n - 4 } , a _ { n - 4 } \right)$ is equal to:
(1) $( 2490,249 )$
(2) $( 2480,249 )$
(3) $( 2480,248 )$
(4) $( 2490,248 )$
Q54 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
If for some positive integer $n$, the coefficients of three consecutive terms in the binomial expansion of $( 1 + x ) ^ { n + 5 }$ are in the ratio $5 : 10 : 14$, then the largest coefficient in the expansion is:
(1) 462
(2) 330
(3) 792
(4) 252
Q55 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
If the perpendicular bisector of the line segment joining the points $P ( 1,4 )$ and $Q ( k , 3 )$ has $y$-intercept equal to $-4$, then a value of $k$ is:
(1) $-2$
(2) $-4$
(3) $\sqrt { 14 }$
(4) $\sqrt { 15 }$
Q56 Circles Circle Equation Derivation View
The circle passing through the intersection of the circles, $x ^ { 2 } + y ^ { 2 } - 6 x = 0$ and $x ^ { 2 } + y ^ { 2 } - 4 y = 0$ having its centre on the line, $2 x - 3 y + 12 = 0$, also passes through the point:
(1) $( - 1,3 )$
(2) $( - 3,6 )$
(3) $( - 3,1 )$
(4) $( 1 , - 3 )$
Q57 Tangents, normals and gradients Tangent and Normal Line Problems View
Let $x = 4$ be a directrix to an ellipse whose centre is at the origin and its eccentricity is $\frac { 1 } { 2 }$. If $P ( 1 , \beta ) , \beta > 0$ is a point on this ellipse, then the equation of the normal to it at $P$ is
(1) $4 x - 3 y = 2$
(2) $8 x - 2 y = 5$
(3) $7 x - 4 y = 1$
(4) $4 x - 2 y = 1$
Q59 Sine and Cosine Rules Heights and distances / angle of elevation problem View
The angle of elevation of a cloud $C$ from a point $P$, $200$ m above a still lake is $30 ^ { \circ }$. If the angle of depression of the image of $C$ in the lake from the point $P$ is $60 ^ { \circ }$, then $PC$ (in m) is equal to
(1) 100
(2) $200 \sqrt { 3 }$
(3) 400
(4) $400 \sqrt { 3 }$
Q60 Combinations & Selection Subset Counting with Set-Theoretic Conditions View
Let $\cup _ { i = 1 } ^ { 50 } X _ { i } = \cup _ { i = 1 } ^ { n } Y _ { i } = T$, where each $X _ { i }$ contains 10 elements and each $Y _ { i }$ contains 5 elements. If each element of the set $T$ is an element of exactly 20 of sets $X _ { i }$'s and exactly 6 of sets $Y _ { i }$'s then $n$ is equal to:
(1) 15
(2) 50
(3) 45
(4) 30
Q61 Simultaneous equations Linear System and Inverse Existence View
If the system of equations $x + y + z = 2$ $2 x + 4 y - z = 6$ $3 x + 2 y + \lambda z = \mu$ has infinitely many solutions, then:
(1) $\lambda + 2 \mu = 14$
(2) $2 \lambda - \mu = 5$
(3) $\lambda - 2 \mu = - 5$
(4) $2 \lambda + \mu = 14$
Q62 Matrices Determinant and Rank Computation View
Suppose the vectors $x _ { 1 } , x _ { 2 }$ and $x _ { 3 }$ are the solutions of the system of linear equations, $A x = b$ when the vector $b$ on the right side is equal to $b _ { 1 } , b _ { 2 }$ and $b _ { 3 }$ respectively. If $x _ { 1 } = \left[ \begin{array} { l } 1 \\ 1 \\ 1 \end{array} \right] , x _ { 2 } = \left[ \begin{array} { l } 0 \\ 2 \\ 1 \end{array} \right] , x _ { 3 } = \left[ \begin{array} { l } 0 \\ 0 \\ 1 \end{array} \right] ; b _ { 1 } = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right] , b _ { 2 } = \left[ \begin{array} { l } 0 \\ 2 \\ 0 \end{array} \right] , b _ { 3 } = \left[ \begin{array} { l } 0 \\ 0 \\ 2 \end{array} \right]$, then the determinant of $A$ is equal to
(1) 4
(2) 2
(3) $\frac { 1 } { 2 }$
(4) $\frac { 3 } { 2 }$
Q63 Exponential Functions Find absolute extrema on a closed interval or domain View
The minimum value of $2 ^ { \sin x } + 2 ^ { \cos x }$ is:
(1) $2 ^ { - 1 + \frac { 1 } { \sqrt { 2 } } }$
(2) $2 ^ { - 1 + \sqrt { 2 } }$
(3) $2 ^ { 1 - \sqrt { 2 } }$
(4) $2 ^ { 1 - \frac { 1 } { \sqrt { 2 } } }$
Q64 Composite & Inverse Functions Finding parameter values from differentiability or equation constraints View
The function $f ( x ) = \left\{ \begin{array} { l l } \frac { \pi } { 4 } + \tan ^ { - 1 } x , & | x | \leq 1 \\ \frac { 1 } { 2 } ( | x | - 1 ) , & | x | > 1 \end{array} \right.$ is:
(1) continuous on $R - \{ 1 \}$ and differentiable on $R - \{ - 1,1 \}$.
(2) both continuous and differentiable on $R - \{ 1 \}$
(3) continuous on $R - \{ - 1 \}$ and differentiable on $R - \{ - 1,1 \}$
(4) both continuous and differentiable on $R - \{ - 1 \}$
Q65 Differential equations Properties of differentiable functions (abstract/theoretical) View
Let $f : ( 0 , \infty ) \rightarrow ( 0 , \infty )$ be a differentiable function such that $f ( 1 ) = e$ and $\lim _ { t \rightarrow x } \frac { t ^ { 2 } f ^ { 2 } ( x ) - x ^ { 2 } f ^ { 2 } ( t ) } { t - x } = 0$. If $f ( x ) = 1$, then $x$ is equal to:
(1) $\frac { 1 } { e }$
(2) $2 e$
(3) $\frac { 1 } { 2 e }$
(4) $e$
Q66 Stationary points and optimisation Geometric or applied optimisation problem View
The area (in sq. units) of the largest rectangle $ABCD$ whose vertices $A$ and $B$ lie on the $x$-axis and vertices $C$ and $D$ lie on the parabola, $y = x ^ { 2 } - 1$ below the $x$-axis, is:
(1) $\frac { 2 } { 3 \sqrt { 3 } }$
(2) $\frac { 1 } { 3 \sqrt { 3 } }$
(3) $\frac { 4 } { 3 }$
(4) $\frac { 4 } { 3 \sqrt { 3 } }$
Q67 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
The integral $\int _ { \frac { \pi } { 6 } } ^ { \frac { \pi } { 3 } } \tan ^ { 3 } x \cdot \sin ^ { 2 } 3 x \left( 2 \sec ^ { 2 } x \cdot \sin ^ { 2 } 3 x + 3 \tan x \cdot \sin 6 x \right) d x$ is equal to:
(1) $\frac { 7 } { 18 }$
(2) $- \frac { 1 } { 9 }$
(3) $- \frac { 1 } { 18 }$
(4) $\frac { 9 } { 2 }$
Q68 First order differential equations (integrating factor) Solving Separable DEs with Initial Conditions View
The solution of the differential equation $\frac { d y } { d x } - \frac { y + 3 x } { \log _ { e } ( y + 3 x ) } + 3 = 0$ is (where $C$ is a constant of integration)
(1) $x - \frac { 1 } { 2 } \left( \log _ { e } ( y + 3 x ) \right) ^ { 2 } = C$
(2) $x - \log _ { e } ( y + 3 x ) = C$
(3) $y + 3 x - \frac { 1 } { 2 } \left( \log _ { e } x \right) ^ { 2 } = C$
(4) $x - 2 \log _ { e } ( y + 3 x ) = C$
Q69 Vectors 3D & Lines Distance Computation (Point-to-Plane or Line-to-Line) View
The distance of the point $( 1 , - 2,3 )$ from the plane $x - y + z = 5$ measured parallel to the line $\frac { x } { 2 } = \frac { y } { 3 } = \frac { z } { - 6 }$ is:
(1) $\frac { 7 } { 5 }$
(2) 1
(3) $\frac { 1 } { 7 }$
(4) 7
Q70 Probability Definitions Recurrence Relations and Sequences Involving Probabilities View
In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and total of scores on the two dice, in each throw is noted. $A$ wins the game if he throws a total of 6 before $B$ throws a total of 7 and $B$ wins the game if he throws a total of 7 before $A$ throws a total of six. The game stops as soon as either of the players wins. The probability of $A$ winning the game is:
(1) $\frac { 5 } { 31 }$
(2) $\frac { 31 } { 61 }$
(3) $\frac { 5 } { 6 }$
(4) $\frac { 30 } { 61 }$
Q71 Combinations & Selection Selection with Group/Category Constraints View
A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is $\_\_\_\_$
Q72 Circles Optimization on a Circle View
Let $PQ$ be a diameter of the circle $x ^ { 2 } + y ^ { 2 } = 9$. If $\alpha$ and $\beta$ are the lengths of the perpendiculars from $P$ and $Q$ on the straight line, $x + y = 2$ respectively, then the maximum value of $\alpha \beta$ is $\_\_\_\_$
Q73 Measures of Location and Spread View
If the variance of the following frequency distribution:
Class:$10 - 20$$20 - 30$$30 - 40$
Frequency:2$x$2

is 50, then $x$ is equal to $\_\_\_\_$