jee-main

Papers (169)
2025
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2024
session1_01feb_shift1 4 session1_01feb_shift2 22 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 30 session1_29jan_shift2 23 session1_30jan_shift1 17 session1_30jan_shift2 30 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 4 session2_04apr_shift2 30 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 22 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 30 session2_09apr_shift1 5 session2_09apr_shift2 30
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_29jun_shift1

20 maths questions

Q1 Vectors Introduction & 2D Angle or Cosine Between Vectors View
Two vectors $\vec { A }$ and $\vec { B }$ have equal magnitudes. If magnitude of $\vec { A } + \vec { B }$ is equal to two times the magnitude of $\vec { A } - \vec { B }$, then the angle between $\vec { A }$ and $\vec { B }$ will be
(1) $\cos ^ { - 1 } \left( \frac { 3 } { 5 } \right)$
(2) $\cos ^ { - 1 } \left( \frac { 1 } { 3 } \right)$
(3) $\sin ^ { - 1 } \left( \frac { 1 } { 3 } \right)$
(4) $\sin ^ { - 1 } \left( \frac { 3 } { 5 } \right)$
Q3 Constant acceleration (SUVAT) Two bodies meeting or catching up View
Two balls $A$ and $B$ are placed at the top of 180 m tall tower. Ball $A$ is released from the top at $t = 0 \mathrm {~s}$. Ball $B$ is thrown vertically down with an initial velocity $u$ at $t = 2 \mathrm {~s}$. After a certain time, both balls meet 100 m above the ground. Find the value of $u$ in $\mathrm { m } \mathrm { s } ^ { - 1 }$. [use $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$]
(1) 10
(2) 15
(3) 20
(4) 30
Q4 Impulse and momentum (advanced) View
A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of $1 \mathrm {~kg} \mathrm {~s} ^ { - 1 }$ and at a speed of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Then, the initial acceleration of the block, in $\mathrm { m } \mathrm { s } ^ { - 2 }$, will be
(1) 3
(2) 6
(3) 5
(4) 4
Q5 Work done and energy Work-energy theorem: finding speed or kinetic energy from net work View
A particle of mass 500 g is moving in a straight line with velocity $v = \mathrm { b } x ^ { \frac { 5 } { 2 } }$. The work done by the net force during its displacement from $x = 0$ to $x = 4 \mathrm {~m}$ is (Take $\mathrm { b } = 0.25 \mathrm {~m} ^ { \frac { - 3 } { 2 } } \mathrm {~s} ^ { - 1 }$).
(1) 2 J
(2) 4 J
(3) 8 J
(4) 16 J
Q6 Momentum and Collisions Explosion or Breakup – Fragment Velocities or Energies View
A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1 : 1 : 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. The velocity of the third piece will be
(1) $35 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
Q23 Simple Harmonic Motion View
A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air Jet when it is at 5 cm from its mean position. The new amplitude of vibration is $\sqrt { x } \mathrm {~cm}$. The value of $x$ is $\_\_\_\_$ .
Q61 Complex Numbers Arithmetic Powers of i or Complex Number Integer Powers View
Let $\alpha$ and $\beta$ be the roots of the equation $x ^ { 2 } + ( 2 i - 1 ) = 0$. Then, the value of $\left| \alpha ^ { 8 } + \beta ^ { 8 } \right|$ is equal to
(1) 50
(2) 250
(3) 1250
(4) 1550
Q62 Sequences and series, recurrence and convergence Summation of sequence terms View
Let $\left\{ a _ { n } \right\} _ { n = 0 } ^ { \infty }$ be a sequence such that $a _ { 0 } = a _ { 1 } = 0$ and $a _ { n + 2 } = 2 a _ { n + 1 } - a _ { n } + 1$ for all $n \geq 0$. Then, $\sum _ { n = 2 } ^ { \infty } \frac { a _ { n } } { 7 ^ { n } }$ is equal to
(1) $\frac { 6 } { 343 }$
(2) $\frac { 7 } { 216 }$
(3) $\frac { 8 } { 343 }$
(4) $\frac { 49 } { 216 }$
Q63 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
If the constant term in the expansion of $\left( 3 x ^ { 3 } - 2 x ^ { 2 } + \frac { 5 } { x ^ { 5 } } \right) ^ { 10 }$ is $2 ^ { k } \cdot l$, where $l$ is an odd integer, then the value of $k$ is equal to
(1) 6
(2) 7
(3) 8
(4) 9
Q64 Straight Lines & Coordinate Geometry Slope and Angle Between Lines View
The distance between the two points $A$ and $A ^ { \prime }$ which lie on $y = 2$ such that both the line segments $A B$ and $A ^ { \prime } B$ (where $B$ is the point $( 2,3 )$ ) subtend angle $\frac { \pi } { 4 }$ at the origin, is equal to
(1) 10
(2) $\frac { 48 } { 5 }$
(3) $\frac { 52 } { 5 }$
(4) 3
Q65 Circles Area and Geometric Measurement Involving Circles View
Let the tangent to the circle $C _ { 1 } : x ^ { 2 } + y ^ { 2 } = 2$ at the point $M ( - 1,1 )$ intersect the circle $C _ { 2 }$ : $( x - 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$, at two distinct points $A$ and $B$. If the tangents to $C _ { 2 }$ at the points $A$ and $B$ intersect at $N$, then the area of the triangle $A N B$ is equal to
(1) $\frac { 1 } { 2 }$
(2) $\frac { 2 } { 3 }$
(3) $\frac { 1 } { 6 }$
(4) $\frac { 5 } { 3 }$
Q66 Conic sections Focal Chord and Parabola Segment Relations View
Let $P Q$ be a focal chord of the parabola $y ^ { 2 } = 4 x$ such that it subtends an angle of $\frac { \pi } { 2 }$ at the point $( 3,0 )$. Let the line segment $P Q$ be also a focal chord of the ellipse $E : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 , a ^ { 2 } > b ^ { 2 }$. If $e$ is the eccentricity of the ellipse $E$, then the value of $\frac { 1 } { e ^ { 2 } }$ is equal to
(1) $1 + \sqrt { 2 }$
(2) $3 + 2 \sqrt { 2 }$
(3) $1 + 2 \sqrt { 3 }$
(4) $4 + 5 \sqrt { 3 }$
Q68 Measures of Location and Spread View
Let the mean and the variance of 5 observations $x _ { 1 } , x _ { 2 } , x _ { 3 } , x _ { 4 } , x _ { 5 }$ be $\frac { 24 } { 5 }$ and $\frac { 194 } { 25 }$ respectively. If the mean and variance of the first 4 observation are $\frac { 7 } { 2 }$ and $a$ respectively, then ( $4 a + x _ { 5 }$ ) is equal to
(1) 13
(2) 15
(3) 17
(4) 18
Q69 Proof True/False Justification View
Let a set $A = A _ { 1 } \cup A _ { 2 } \cup \ldots \cup A _ { k }$, where $A _ { i } \cap A _ { j } = \phi$ for $i \neq j ; 1 \leq i , j \leq k$. Define the relation $R$ from $A$ to $A$ by $R = \left\{ ( x , y ) : y \in A _ { i } \right.$ if and only if $\left. x \in A _ { i } , 1 \leq i \leq k \right\}$. Then, $R$ is:
(1) reflexive, symmetric but not transitive
(2) reflexive, transitive but not symmetric
(3) reflexive but not symmetric and transitive
(4) an equivalence relation
Q70 Probability Definitions Finite Equally-Likely Probability Computation View
The probability that a randomly chosen $2 \times 2$ matrix with all the entries from the set of first 10 primes, is singular, is equal to
(1) $\frac { 133 } { 10 ^ { 4 } }$
(2) $\frac { 19 } { 10 ^ { 3 } }$
(3) $\frac { 18 } { 10 ^ { 3 } }$
(4) $\frac { 271 } { 10 ^ { 4 } }$
Q71 Matrices Matrix Power Computation and Application View
Let $A = \left[ a _ { i j } \right]$ be a square matrix of order 3 such that $a _ { i j } = 2 ^ { j - i }$, for all $i , j = 1,2,3$. Then, the matrix $A ^ { 2 } + A ^ { 3 } + \ldots + A ^ { 10 }$ is equal to
(1) $\left( \frac { 3 ^ { 10 } - 1 } { 2 } \right) A$
(2) $\left( \frac { 3 ^ { 10 } + 1 } { 2 } \right) A$
(3) $\left( \frac { 3 ^ { 10 } + 3 } { 2 } \right) A$
(4) $\left( \frac { 3 ^ { 10 } - 3 } { 2 } \right) A$
Q72 Matrices Linear System and Inverse Existence View
If the system of linear equations $2 x + y - z = 7$ $x - 3 y + 2 z = 1$ $x + 4 y + \delta z = k$, where $\delta , k \in R$ has infinitely many solutions, then $\delta + k$ is equal to
(1) $- 3$
(2) 3
(3) 6
(4) 9
Q73 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
The domain of the function $\cos ^ { - 1 } \left( \frac { 2 \sin ^ { - 1 } \left( \frac { 1 } { 4 x ^ { 2 } - 1 } \right) } { \pi } \right)$ is
(1) $\left( - \infty , - \frac { 1 } { \sqrt { 2 } } \right] \cup \left[ \frac { 1 } { \sqrt { 2 } } , \infty \right) \cup \{ 0 \}$
(2) $\left( - \infty , - \frac { 1 } { \sqrt { 2 } } \right] \cup \left[ \frac { 1 } { \sqrt { 2 } } , \infty \right)$
(3) $\left( - \infty , - \frac { 1 } { \sqrt { 2 } } \right) \cup \left( \frac { 1 } { 2 } , \infty \right) \cup \{ 0 \}$
(4) $R - \left\{ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right\}$
Q74 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View
Let $f : R \rightarrow R$ be a function defined by : $f ( x ) = \left\{ \begin{array} { c c } \max _ { t \leq x } \left\{ t ^ { 3 } - 3 t \right\} ; & x \leq 2 \\ x ^ { 2 } + 2 x - 6 ; & 2 < x < 3 \\ { [ x - 3 ] + 9 ; } & 3 \leq x \leq 5 \\ 2 x + 1 ; & x > 5 \end{array} \right.$ Where $[ t ]$ is the greatest integer less than or equal to $t$. Let $m$ be the number of points where $f$ is not differentiable and $I = \int _ { - 2 } ^ { 2 } f ( x ) d x$. Then the ordered pair ( $m , I$ ) is equal to
(1) $\left( 3 , \frac { 27 } { 4 } \right)$
(2) $\left( 3 , \frac { 23 } { 4 } \right)$
(3) $\left( 4 , \frac { 27 } { 4 } \right)$
(4) $\left( 4 , \frac { 23 } { 4 } \right)$
Q75 Stationary points and optimisation Geometric or applied optimisation problem View
A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is equal to (if the full question text was truncated, this is the standard formulation of this problem).