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
2022 session1_26jun_shift2

23 maths questions

Q21 Constant acceleration (SUVAT) Two bodies meeting or catching up View
A ball is projected vertically upward with an initial velocity of $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at $t = 0 \mathrm {~s}$. At $t = 2 \mathrm {~s}$, another ball is projected vertically upward with same velocity. At $t =$ $\_\_\_\_$ s, second ball will meet the first ball $\left( \mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 } \right)$.
Q22 Newton's laws and connected particles Atwood machine and pulley systems View
A system of 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $7 ^ { \text {th} }$ and $8 ^ { \text {th} }$ ball is $\_\_\_\_$ N when $6 ^ { \text {th} }$ ball just leaves the table.
Q23 Impulse and momentum (advanced) View
A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The impulse imparted to the ball is $\_\_\_\_$ Ns.
Q61 Sequences and Series Evaluation of a Finite or Infinite Sum View
If $A = \sum _ { n = 1 } ^ { \infty } \frac { 1 } { \left( 3 + ( - 1 ) ^ { n } \right) ^ { n } }$ and $B = \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { \left( 3 + ( - 1 ) ^ { n } \right) ^ { n } }$, then $\frac { A } { B }$ is equal to
(1) $\frac { 11 } { 9 }$
(2) 1
(3) $- \frac { 11 } { 9 }$
(4) $- \frac { 11 } { 3 }$
Q62 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
$16 \sin \left( 20 ^ { \circ } \right) \sin \left( 40 ^ { \circ } \right) \sin \left( 80 ^ { \circ } \right)$ is equal to
(1) $\sqrt { 3 }$
(2) $2 \sqrt { 3 }$
(3) 3
(4) $4 \sqrt { 3 }$
Q63 Conic sections Tangent and Normal Line Problems View
If $m$ is the slope of a common tangent to the curves $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ and $x ^ { 2 } + y ^ { 2 } = 12$, then $12 \mathrm {~m} ^ { 2 }$ is equal to
(1) 6
(2) 9
(3) 10
(4) 12
Q64 Conic sections Locus and Trajectory Derivation View
The locus of the mid-point of the line segment joining the point $( 4,3 )$ and the points on the ellipse $x ^ { 2 } + 2 y ^ { 2 } = 4$ is an ellipse with eccentricity
(1) $\frac { \sqrt { 3 } } { 2 }$
(2) $\frac { 1 } { 2 \sqrt { 2 } }$
(3) $\frac { 1 } { \sqrt { 2 } }$
(4) $\frac { 1 } { 2 }$
Q65 Conic sections Tangent and Normal Line Problems View
The normal to the hyperbola $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { 9 } = 1$ at the point $( 8,3 \sqrt { 3 } )$ on it passes through the point
(1) $( 15 , - 2 \sqrt { 3 } )$
(2) $( 9,2 \sqrt { 3 } )$
(3) $( - 1,9 \sqrt { 3 } )$
(4) $( - 1,6 \sqrt { 3 } )$
Q66 Chain Rule Limit Evaluation Involving Composition or Substitution View
$\lim _ { x \rightarrow 0 } \frac { \cos ( \sin x ) - \cos x } { x ^ { 4 } }$ is equal to
(1) $\frac { 1 } { 3 }$
(2) $\frac { 1 } { 6 }$
(3) $\frac { 1 } { 4 }$
(4) $\frac { 1 } { 12 }$
Q68 Measures of Location and Spread View
Let the mean of 50 observations is 15 and the standard deviation is 2. However, one observation was wrongly recorded. The sum of the correct and incorrect observations is 70. If the mean of the correct set of observations is 16, then the variance of the correct set is equal to
(1) 10
(2) 36
(3) 43
(4) 60
Q69 Matrices Linear System and Inverse Existence View
If the system of equations $\alpha x + y + z = 5 , x + 2 y + 3 z = 4 , x + 3 y + 5 z = \beta$ has infinitely many solutions, then the ordered pair $( \alpha , \beta )$ is equal to
(1) $( 1 , - 3 )$
(2) $( - 1,3 )$
(3) $( 1,3 )$
(4) $( - 1 , - 3 )$
Q70 Reciprocal Trig & Identities View
If the inverse trigonometric functions take principal values, then $\cos ^ { - 1 } \left( \frac { 3 } { 10 } \cos \left( \tan ^ { - 1 } \left( \frac { 4 } { 3 } \right) \right) + \frac { 2 } { 5 } \sin \left( \tan ^ { - 1 } \left( \frac { 4 } { 3 } \right) \right) \right)$ is equal to
(1) 0
(2) $\frac { \pi } { 4 }$
(3) $\frac { \pi } { 3 }$
(4) $\frac { \pi } { 6 }$
Q71 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification View
Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be defined as $f ( x ) = x - 1$ and $g : R \rightarrow \{ 1 , - 1 \} \rightarrow \mathbb { R }$ be defined as $g ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 1 }$. Then the function $f o g$ is:
(1) One-one but not onto
(2) onto but not one-one
(3) Both one-one and onto
(4) Neither one-one nor onto
Q72 Applied differentiation MCQ on derivative and graph interpretation View
Let $f ( x ) = \min \{ 1,1 + x \sin x \} , 0 \leq x \leq 2 \pi$. If $m$ is the number of points, where $f$ is not differentiable and $n$ is the number of points, where $f$ is not continuous, then the ordered pair $( m , n )$ is equal to
(1) $( 2,0 )$
(2) $( 1,0 )$
(3) $( 1,1 )$
(4) $( 2,1 )$
Q73 Stationary points and optimisation Geometric or applied optimisation problem View
Consider a cuboid of sides $2 x , 4 x$ and $5 x$ and a closed hemisphere of radius $r$. If the sum of their surface areas is constant $k$, then the ratio $x : r$, for which the sum of their volumes is maximum, is
(1) $2 : 5$
(2) $19 : 45$
(3) $3 : 8$
(4) $19 : 15$
Q74 Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition View
If $\int \frac { 1 } { x } \sqrt { \frac { 1 - x } { 1 + x } } d x = g ( x ) + c , g ( 1 ) = 0$, then $g \left( \frac { 1 } { 2 } \right)$ is equal to
(1) $\log _ { e } \left( \frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 } \right) + \frac { \pi } { 3 }$
(2) $\log _ { \mathrm { e } } \left( \frac { \sqrt { 3 } + 1 } { \sqrt { 3 } - 1 } \right) + \frac { \pi } { 3 }$
(3) $\log _ { \mathrm { e } } \left( \frac { \sqrt { 3 } + 1 } { \sqrt { 3 } - 1 } \right) - \frac { \pi } { 3 }$
(4) $\frac { 1 } { 3 } \log _ { e } \left( \frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 } \right) - \frac { \pi } { 6 }$
Q75 Areas Between Curves Area Involving Conic Sections or Circles View
The area of the region bounded by $y ^ { 2 } = 8 x$ and $y ^ { 2 } = 16 ( 3 - x )$ is equal to
(1) $\frac { 32 } { 3 }$
(2) $\frac { 40 } { 3 }$
(3) 16
(4) 9
Q76 Differential equations First-Order Linear DE: General Solution View
If $y = y ( x )$ is the solution of the differential equation $x \frac { d y } { d x } + 2 y = x e ^ { x } , y ( 1 ) = 0$ then the local maximum value of the function $z ( x ) = x ^ { 2 } y ( x ) - e ^ { x } , x \in R$ is
(1) $1 - e$
(2) 0
(3) $\frac { 1 } { 2 }$
(4) $\frac { 4 } { e } - e$
Q77 Differential equations First-Order Linear DE: General Solution View
If $\frac { d y } { d x } + e ^ { x } \left( x ^ { 2 } - 2 \right) y = \left( x ^ { 2 } - 2 x \right) \left( x ^ { 2 } - 2 \right) e ^ { 2 x }$ and $y ( 0 ) = 0$, then the value of $y ( 2 )$ is
(1) $-1$
(2) 1
(3) 0
(4) $e$
Q78 Vectors Introduction & 2D Expressing a Vector as a Linear Combination View
Let $\vec { a } = \hat { i } + \hat { j } + 2 \widehat { k } , \vec { b } = 2 \hat { i } - 3 \hat { j } + \widehat { k }$ and $\vec { c } = \hat { i } - \hat { j } + \widehat { k }$ be the three given vectors. Let $\vec { v }$ be a vector in the plane of $\vec { a }$ and $\vec { b }$ whose projection on $\vec { c }$ is $\frac { 2 } { \sqrt { 3 } }$. If $\vec { v } \cdot \hat { j } = 7$, then $\vec { v } \cdot ( \hat { i } + \hat { k } )$ is equal to
(1) 6
(2) 7
(3) 8
(4) 9
Q79 Vectors 3D & Lines Plane Rotation About a Line View
If the plane $2 x + y - 5 z = 0$ is rotated about its line of intersection with the plane $3 x - y + 4 z - 7 = 0$ by an angle of $\frac { \pi } { 2 }$, then the plane after the rotation passes through the point
(1) $( 2 , - 2,0 )$
(2) $( - 2,2,0 )$
(3) $( 1,0,2 )$
(4) $( - 1,0 , - 2 )$
Q80 Vectors 3D & Lines MCQ: Relationship Between Two Lines View
If the lines $\vec { r } = ( \hat { i } - \hat { j } + \widehat { k } ) + \lambda ( 3 \hat { j } - \widehat { k } )$ and $\vec { r } = ( \alpha \hat { i } - \hat { j } ) + \mu ( 2 \hat { i } - 3 \widehat { k } )$ are co-planar, then the distance of the plane containing these two lines from the point $( \alpha , 0,0 )$ is
(1) $\frac { 2 } { 9 }$
(2) $\frac { 2 } { 11 }$
(3) $\frac { 4 } { 11 }$
(4) 2
Q81 Arithmetic Sequences and Series Arithmetic-Geometric Hybrid Problem View
If $p$ and $q$ are real numbers such that $p + q = 3 , p ^ { 4 } + q ^ { 4 } = 369$, then the value of $\left( \frac { 1 } { p } + \frac { 1 } { q } \right) ^ { - 2 }$ is equal to (if the full expression were available).