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
2025 session2_08apr_shift2

35 maths questions

Q2 Constant acceleration (SUVAT) Braking and stopping distance View
Q2. Two cars are travelling towards each other at speed of $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of $2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. The distance between them when they come to rest is :
(1) 200 m
(2) 100 m
(3) 50 m
(4) 25 m
Q3 Forces, equilibrium and resultants View
Q3. A 1 kg mass is suspended from the ceiling by a rope of length 4 m . A horizontal force ' $F ^ { \prime }$ ' is applied at the mid point of the rope so that the rope makes an angle of $45 ^ { \circ }$ with respect to the vertical axis as shown in figure. The [Figure] magnitude of $F$ is : (Assume that the system is in equilibrium and $g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ )
(1) 10 N
(2) $\frac { 10 } { \sqrt { 2 } } \mathrm {~N}$
(3) 1 N
(4) $\frac { 1 } { 10 \times \sqrt { 2 } } \mathrm {~N}$
Q4 Work done and energy Work done by gravity in specific scenarios View
Q4. A satellite of $10 ^ { 3 } \mathrm {~kg}$ mass is revolving in circular orbit of radius $2 R$. If $\frac { 10 ^ { 4 } R } { 6 } J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 } , R =$ radius of earth)
(1) $2.5 R$
(2) $3 R$
(3) $4 R$
(4) $6 R$
Q21 Vectors Introduction & 2D Angle or Cosine Between Vectors View
Q21. The resultant of two vectors $\vec { A }$ and $\vec { B }$ is perpendicular to $\vec { A }$ and its magnitude is half that of $\vec { B }$. The angle between vectors $\vec { A }$ and $\vec { B }$ is $\_\_\_\_$ ○.
Q22 Work done and energy Work done by constant or variable force via integration View
Q22. A force $\left( 3 x ^ { 2 } + 2 x - 5 \right) \mathrm { N }$ displaces a body from $x = 2 \mathrm {~m}$ to $x = 4 \mathrm {~m}$. Work done by this force is $\_\_\_\_$ J.
Q23 Motion on a slope View
Q23. A circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane, if takes $t \mathrm {~s}$. When it rolls down the plane then it takes $\left( \frac { \alpha } { 2 } \right) ^ { 1 / 2 } t \mathrm {~s}$, where $\alpha$ is $\_\_\_\_$
Q61 Sequences and series, recurrence and convergence Direct term computation from recurrence View
Q61. Let $\alpha , \beta ; \alpha > \beta$, be the roots of the equation $x ^ { 2 } - \sqrt { 2 } x - \sqrt { 3 } = 0$. Let $\mathrm { P } _ { n } = \alpha ^ { n } - \beta ^ { n } , n \in \mathrm {~N}$. Then $( 11 \sqrt { 3 } - 10 \sqrt { 2 } ) \mathrm { P } _ { 10 } + ( 11 \sqrt { 2 } + 10 ) \mathrm { P } _ { 11 } - 11 \mathrm { P } _ { 12 }$ is equal to
(1) $10 \sqrt { 3 } \mathrm { P } _ { 9 }$
(2) $11 \sqrt { 3 } P _ { 9 }$
(3) $10 \sqrt { 2 } \mathrm { P } _ { 9 }$
(4) $11 \sqrt { 2 } \mathrm { P } _ { 9 }$
Q62 Complex Numbers Argand & Loci Distance and Region Optimization on Loci View
Q62. Let $z$ be a complex number such that the real part of $\frac { z - 2 i } { z + 2 i }$ is zero. Then, the maximum value of $| z - ( 6 + 8 i ) |$ is equal to
(1) 12
(2) 10
(3) 8
(4) $\infty$
Q63 Geometric Sequences and Series Sum of an Infinite Geometric Series (Direct Computation) View
Q63. Let $a , a r , a r ^ { 2 } , \quad$ be an infinite G.P. If $\sum _ { n = 0 } ^ { \infty } a r ^ { n } = 57$ and $\sum _ { n = 0 } ^ { \infty } a ^ { 3 } r ^ { 3 n } = 9747$, then $a + 18 r$ is equal to
(1) 46
(2) 38
(3) 31
(4) 27
Q64 Generalised Binomial Theorem View
Q64. The sum of the coefficient of $x ^ { 2 / 3 }$ and $x ^ { - 2 / 5 }$ in the binomial expansion of $\left( x ^ { 2 / 3 } + \frac { 1 } { 2 } x ^ { - 2 / 5 } \right) ^ { 9 }$ is
(1) $21 / 4$
(2) $63 / 16$
(3) $19 / 4$
(4) $69 / 16$
Q65 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
Q65. Two vertices of a triangle ABC are $\mathrm { A } ( 3 , - 1 )$ and $\mathrm { B } ( - 2,3 )$, and its orthocentre is $\mathrm { P } ( 1,1 )$. If the coordinates of the point C are $( \alpha , \beta )$ and the centre of the of the circle circumscribing the triangle PAB is $( \mathrm { h } , \mathrm { k } )$, then the value of $( \alpha + \beta ) + 2 ( \mathrm {~h} + \mathrm { k } )$ equals
(1) 5
(2) 81
(3) 15
(4) 51
Q66 Conic sections Equation Determination from Geometric Conditions View
Q66. Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E : \frac { ( x - 1 ) ^ { 2 } } { 100 } + \frac { ( y - 1 ) ^ { 2 } } { 75 } = 1$ and the eccentricity of the hyperbola $H$ be the reciprocal of the eccentricity of the ellipse $E$. If the length of the transverse axis of $H$ is $\alpha$ and the length of its conjugate axis is $\beta$, then $3 \alpha ^ { 2 } + 2 \beta ^ { 2 }$ is equal to
(1) 237
(2) 242
(3) 205
(4) 225
Q67 Integration by Substitution Substitution to Evaluate Limit of an Integral Expression View
Q67. $\lim _ { x \rightarrow \frac { \pi } { 2 } } \left( \frac { \int _ { x ^ { 3 } } ^ { ( \pi / 2 ) ^ { 3 } } \left( \sin \left( 2 t ^ { 1 / 3 } \right) + \cos \left( t ^ { 1 / 3 } \right) \right) d t } { \left( x - \frac { \pi } { 2 } \right) ^ { 2 } } \right)$ is equal to
(1) $\frac { 5 \pi ^ { 2 } } { 9 }$
(2) $\frac { 9 \pi ^ { 2 } } { 8 }$
(3) $\frac { 11 \pi ^ { 2 } } { 10 }$
(4) $\frac { 3 \pi ^ { 2 } } { 2 }$
Q68 Exponential Functions Limit Evaluation View
Q68. $\lim _ { x \rightarrow 0 } \frac { e - ( 1 + 2 x ) ^ { \frac { 1 } { 2 x } } } { x }$ is equal to
(1) 0
(2) $\frac { - 2 } { e }$
(3) e
(4) $e - e ^ { 2 }$
Q69. If the variance of the frequency distribution
$x$$c$$2 c$$3 c$$4 c$$5 c$$6 c$
$f$211111

is 160 , then the value of $c \in N$ is
(1) 7
(2) 8
(3) 5
(4) 6
Q70 Measures of Location and Spread View
Q70. Let $B = \left[ \begin{array} { l l } 1 & 3 \\ 1 & 5 \end{array} \right]$ and $A$ be a $2 \times 2$ matrix such that $A B ^ { - 1 } = A ^ { - 1 }$. If $B C B ^ { - 1 } = A$ and $C ^ { 4 } + \alpha C ^ { 2 } + \beta I = O$, then $2 \beta - \alpha$ is equal to
(1) 16
(2) 2
(3) 8
(4) 10
Q71 Matrices Determinant and Rank Computation View
Q71. The integral $\int _ { 1 / 4 } ^ { 3 / 4 } \cos \left( 2 \cot ^ { - 1 } \sqrt { \frac { 1 - x } { 1 + x } } \right) d x$ is equal to
(1) $1 / 2$
(2) $- 1 / 2$
(3) $- 1 / 4$
(4) $1 / 4$
Q72 Curve Sketching Range and Image Set Determination View
Q72. Let the range of the function $f ( x ) = \frac { 1 } { 2 + \sin 3 x + \cos 3 x } , x \in \mathbb { R }$ be $[ a , b ]$. If $\alpha$ and $\beta$ are respectively the A.M. and the G.M. of $a$ and $b$, then $\frac { \alpha } { \beta }$ is equal to
(1) $\pi$
(2) $\sqrt { \pi }$
(3) 2
(4) $\sqrt { 2 }$
Q73 Differentiating Transcendental Functions Higher-order or nth derivative computation View
Q73. If $\log _ { e } y = 3 \sin ^ { - 1 } x$, then $\left( 1 - x ^ { 2 } \right) y ^ { \prime \prime } - x y ^ { \prime }$ at $x = \frac { 1 } { 2 }$ is equal to
(1) $3 e ^ { \pi / 6 }$
(2) $9 e ^ { \pi / 2 }$
(3) $3 e ^ { \pi / 2 }$
(4) $9 e ^ { \pi / 6 }$
Q74 Second order differential equations Second-order ODE with initial or boundary value conditions View
Q74. Let $\int _ { 0 } ^ { x } \sqrt { 1 - \left( y ^ { \prime } ( t ) \right) ^ { 2 } } d t = \int _ { 0 } ^ { x } y ( t ) d t , 0 \leq x \leq 3 , y \geq 0 , y ( 0 ) = 0$. Then at $x = 2 , y ^ { \prime \prime } + y + 1$ is equal to
(1) 1
(2) 2
(3) $\sqrt { 2 }$
(4) $1 / 2$
Q75 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
Q75. The value of the integral $\int _ { - 1 } ^ { 2 } \log _ { e } \left( x + \sqrt { x ^ { 2 } + 1 } \right) d x$ is
(1) $\sqrt { 5 } - \sqrt { 2 } + \log _ { e } \left( \frac { 7 + 4 \sqrt { 5 } } { 1 + \sqrt { 2 } } \right)$
(2) $\sqrt { 5 } - \sqrt { 2 } + \log _ { e } \left( \frac { 9 + 4 \sqrt { 5 } } { 1 + \sqrt { 2 } } \right)$
(3) $\sqrt { 2 } - \sqrt { 5 } + \log _ { e } \left( \frac { 7 + 4 \sqrt { 5 } } { 1 + \sqrt { 2 } } \right)$
(4) $\sqrt { 2 } - \sqrt { 5 } + \log _ { e } \left( \frac { 9 + 4 \sqrt { 5 } } { 1 + \sqrt { 2 } } \right)$
Q76 Areas by integration View
Q76. The area (in square units) of the region enclosed by the ellipse $x ^ { 2 } + 3 y ^ { 2 } = 18$ in the first quadrant below the line $y = x$ is
(1) $\sqrt { 3 } \pi - \frac { 3 } { 4 }$
(2) $\sqrt { 3 } \pi + 1$
(3) $\sqrt { 3 } \pi$
(4) $\sqrt { 3 } \pi + \frac { 3 } { 4 }$
Q77 Vectors 3D & Lines Vector Algebra and Triple Product Computation View
Q77. Between the following two statements: Statement I : Let $\vec { a } = \hat { i } + 2 \hat { j } - 3 \hat { k }$ and $\vec { b } = 2 \hat { i } + \hat { j } - \hat { k }$. Then the vector $\vec { r }$ satisfying $\vec { a } \times \vec { r } = \vec { a } \times \vec { b }$ and $\vec { a } \cdot \vec { r } = 0$ is of magnitude $\sqrt { 10 }$. Statement II : In a triangle $A B C , \cos 2 A + \cos 2 B + \cos 2 C \geq - \frac { 3 } { 2 }$.
(1) Statement I is incorrect but Statement II is correct.
(2) Both Statement I and Statement II are correct.
(3) Statement I is correct but Statement II is incorrect.
(4) Both Statement I and Statement II are incorrect.
Q78 Vectors 3D & Lines Vector Algebra and Triple Product Computation View
Q78. Let $\vec { a } = 2 \hat { i } + \alpha \hat { j } + \hat { k } , \vec { b } = - \hat { i } + \hat { k } , \vec { c } = \beta \hat { j } - \hat { k }$, where $\alpha$ and $\beta$ are integers and $\alpha \beta = - 6$. Let the values of the ordered pair ( $\alpha , \beta$ ), for which the area of the parallelogram of diagonals $\vec { a } + \vec { b }$ and $\vec { b } + \vec { c }$ is $\frac { \sqrt { 21 } } { 2 }$, be ( $\alpha _ { 1 } , \beta _ { 1 }$ ) and $\left( \alpha _ { 2 } , \beta _ { 2 } \right)$. Then $\alpha _ { 1 } ^ { 2 } + \beta _ { 1 } ^ { 2 } - \alpha _ { 2 } \beta _ { 2 }$ is equal to
(1) 19
(2) 17
(3) 24
(4) 21
Q79 Vectors 3D & Lines Distance from a Point to a Line (Show/Compute) View
Q79. Consider the line $L$ passing through the points $( 1,2,3 )$ and $( 2,3,5 )$. The distance of the point $\left( \frac { 11 } { 3 } , \frac { 11 } { 3 } , \frac { 19 } { 3 } \right)$ from the line L along the line $\frac { 3 x - 11 } { 2 } = \frac { 3 y - 11 } { 1 } = \frac { 3 z - 19 } { 2 }$ is equal to
(1) 6
(2) 5
(3) 4
(4) 3
Q80 Probability Definitions Finite Equally-Likely Probability Computation View
Q80. If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i ^ { \text {th } }$ roll than the number obtained in the $( i - 1 ) ^ { \text {th } }$ roll, $i = 2,3$, is equal to
(1) $3 / 54$
(2) $2 / 54$
(3) $1 / 54$
(4) $5 / 54$
Q81 Permutations & Arrangements Forming Numbers with Digit Constraints View
Q81. The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is $\_\_\_\_$
Q82 Partial Fractions View
Q82. If $\left( \frac { 1 } { \alpha + 1 } + \frac { 1 } { \alpha + 2 } + \ldots \ldots + \frac { 1 } { \alpha + 1012 } \right) - \left( \frac { 1 } { 2 \cdot 1 } + \frac { 1 } { 4 \cdot 3 } + \frac { 1 } { 6 \cdot 5 } + \ldots . + \frac { 1 } { 2024 \cdot 2023 } \right) = \frac { 1 } { 2024 }$, then $\alpha$ is equal to $\_\_\_\_$
Q83 Circles Circle-Related Locus Problems View
Q83. Let $A , B$ and $C$ be three points on the parabola $y ^ { 2 } = 6 x$ and let the line segment $A B$ meet the line $L$ through $C$ parallel to the $x$-axis at the point $D$. Let $M$ and $N$ respectively be the feet of the perpendiculars from $A$ and $B$ on $L$. Then $\left( \frac { A M \cdot B N } { C D } \right) ^ { 2 }$ is equal to $\_\_\_\_$
Q84 Circles Intersection of Circles or Circle with Conic View
Q84. Consider the circle $C : x ^ { 2 } + y ^ { 2 } = 4$ and the parabola $P : y ^ { 2 } = 8 x$. If the set of all values of $\alpha$, for which three chords of the circle $C$ on three distinct lines passing through the point $( \alpha , 0 )$ are bisected by the parabola $P$ is the interval $( p , q )$, then $( 2 q - p ) ^ { 2 }$ is equal to $\_\_\_\_$
Q85 Matrices Linear System and Inverse Existence View
Q85. Consider the matrices : $A = \left[ \begin{array} { c c } 2 & - 5 \\ 3 & m \end{array} \right] , B = \left[ \begin{array} { l } 20 \\ m \end{array} \right]$ and $X = \left[ \begin{array} { l } x \\ y \end{array} \right]$. Let the set of all $m$, for which the system of equations $A X = B$ has a negative solution (i.e., $x < 0$ and $y < 0$ ), be the interval ( $a , b$ ). Then $8 \int _ { a } ^ { b } | A | d m$ is equal to $\_\_\_\_$
Q86 Standard trigonometric equations Inverse trigonometric equation View
Q86. Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $2 \sin ^ { - 1 } x + 3 \cos ^ { - 1 } x = \frac { 2 \pi } { 5 }$, is $\_\_\_\_$
Q87 Permutations & Arrangements Counting Functions with Constraints View
Q87. Let $A = \{ ( x , y ) : 2 x + 3 y = 23 , x , y \in \mathbb { N } \}$ and $B = \{ x : ( x , y ) \in A \}$. Then the number of one-one functions from $A$ to $B$ is equal to $\_\_\_\_$
Q88 First order differential equations (integrating factor) View
Q88. For a differentiable function $f : \mathbb { R } \rightarrow \mathbb { R }$, suppose $f ^ { \prime } ( x ) = 3 f ( x ) + \alpha$, where $\alpha \in \mathbb { R } , f ( 0 ) = 1$ and $\lim _ { x \rightarrow - \infty } f ( x ) = 7$. Then $9 f \left( - \log _ { \mathrm { e } } 3 \right)$ is equal to $\_\_\_\_$
Q89 Stationary points and optimisation Determine parameters from given extremum conditions View
Q89. Let the set of all values of $p$, for which $f ( x ) = \left( p ^ { 2 } - 6 p + 8 \right) \left( \sin ^ { 2 } 2 x - \cos ^ { 2 } 2 x \right) + 2 ( 2 - p ) x + 7$ does not have any critical point, be the interval $( a , b )$. Then $16 a b$ is equal to $\_\_\_\_$
Q90 Vectors 3D & Lines Distance from a Point to a Line (Show/Compute) View
Q90. The square of the distance of the image of the point $( 6,1,5 )$ in the line $\frac { x - 1 } { 3 } = \frac { y } { 2 } = \frac { z - 2 } { 4 }$, from the origin is
ANSWER KEYS

\begin{tabular}{|l|l|l|l|} \hline 1. (1) & 2. (2) & 3. (1) & 4. (4) \hline 9. (1) & 10. (1) & 11. (1) & 12. (2) \hline 17. (4) & 18. (1) & 19. (2) & 20. (2) \hline 25. (22) & 26. (16) & 27. (2500) & 28. (28) \hline 33. (1) & 34. (2) & 35. (2) & 36. (4) \hline 41. (4) & 42. (1) & 43. (1) & 44. (3) \hline