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
2021 session2_17mar_shift1

20 maths questions

Q1 Constant acceleration (SUVAT) Acceleration then deceleration (two-phase motion) View
A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is t seconds, the total distance travelled is:
(1) $\frac { 4 \alpha \beta } { ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
(2) $\frac { 2 \alpha \beta } { ( \alpha + \beta ) } t ^ { 2 }$
(3) $\frac { \alpha \beta } { 2 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
(4) $\frac { \alpha \beta } { 4 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
Q3 Work done and energy Work-energy theorem: finding speed or kinetic energy from net work View
A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The ball gets deflected by an obstacle on the way. After deflection it moves with $5\%$ of its initial kinetic energy. What is the speed of the ball now?
(1) $19.0 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $4.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $14.41 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $1.00 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
Q4 Moments View
A triangular plate is shown. A force $\vec { F } = 4 \hat { \mathrm { i } } - 3 \hat { \mathrm { j } }$ is applied at point $P$. The torque at point $P$ with respect to point $O$ and $Q$ are:
(1) $- 15 - 20 \sqrt { 3 } , 15 - 20 \sqrt { 3 }$
(2) $15 + 20 \sqrt { 3 } , 15 - 20 \sqrt { 3 }$
(3) $15 - 20 \sqrt { 3 } , 15 + 20 \sqrt { 3 }$
(4) $- 15 + 20 \sqrt { 3 } , 15 + 20 \sqrt { 3 }$
Q5 Circular Motion 1 Conical Pendulum / Horizontal Circle on String View
A mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass $M$ moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity $\omega$. The angular momentum of $M$ about point $A$ is $L _ { A }$ which lies in the positive $z$ direction and the angular momentum of $M$ about $B$ is $L _ { B }$. The correct statement for this system is:
(1) $L _ { A }$ and $L _ { B }$ are both constant in magnitude and direction
(2) $L _ { B }$ is constant in direction with varying magnitude
(3) $L _ { B }$ is constant, both in magnitude and direction
(4) $L _ { A }$ is constant, both in magnitude and direction
Q61 Sequences and series, recurrence and convergence Convergence proof and limit determination View
The value of $4 + \frac { 1 } { 5 + \frac { 1 } { 4 + \frac { 1 } { 5 + \frac { 1 } { 4 + \ldots . . \infty } } } }$ is:
(1) $2 + \frac { 2 } { 5 } \sqrt { 30 }$
(2) $2 + \frac { 4 } { \sqrt { 5 } } \sqrt { 30 }$
(3) $4 + \frac { 4 } { \sqrt { 5 } } \sqrt { 30 }$
(4) $5 + \frac { 2 } { 5 } \sqrt { 30 }$
Q62 Complex Numbers Arithmetic Geometric Interpretation and Triangle/Shape Properties View
The area of the triangle with vertices $P ( z ) , Q ( i z )$ and $R ( z + i z )$ is
(1) 1
(2) $\frac { 1 } { 2 } | z | ^ { 2 }$
(3) $\frac { 1 } { 2 }$
(4) $\frac { 1 } { 2 } | z + i z | ^ { 2 }$
Q63 Combinations & Selection Selection with Group/Category Constraints View
Team '$A$' consists of 7 boys and $n$ girls and Team '$B$' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $n$ is equal to:
(1) 5
(2) 2
(3) 4
(4) 6
Q64 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
If the fourth term in the expansion of $\left( x + x ^ { \log _ { 2 } x } \right) ^ { 7 }$ is 4480, then the value of $x$ where $x \in N$ is equal to:
(1) 2
(2) 4
(3) 3
(4) 1
Q65 Circles Inscribed/Circumscribed Circle Computations View
In a triangle $PQR$, the co-ordinates of the points $P$ and $Q$ are $(-2, 4)$ and $(4, -2)$ respectively. If the equation of the perpendicular bisector of $PR$ is $2x - y + 2 = 0$, then the centre of the circumcircle of the $\triangle PQR$ is:
(1) $(-1, 0)$
(2) $(-2, -2)$
(3) $(0, 2)$
(4) $(1, 4)$
Q66 Circles Circle Equation Derivation View
The line $2x - y + 1 = 0$ is a tangent to the circle at the point $(2, 5)$ and the centre of the circle lies on $x - 2y = 4$. Then, the radius of the circle is:
(1) $3\sqrt{5}$
(2) $5\sqrt{3}$
(3) $5\sqrt{4}$
(4) $4\sqrt{5}$
Q67 Circles Intersection of Circles or Circle with Conic View
Choose the incorrect statement about the two circles whose equations are given below: $x ^ { 2 } + y ^ { 2 } - 10 x - 10 y + 41 = 0$ and $x ^ { 2 } + y ^ { 2 } - 16 x - 10 y + 80 = 0$
(1) Distance between two centres is the average of radii of both the circles.
(2) Both circles' centres lie inside region of one another.
(3) Both circles pass through the centre of each other.
(4) Circles have two intersection points.
Q68 Applied differentiation Limit evaluation involving derivatives or asymptotic analysis View
The value of $\lim _ { x \rightarrow 0 ^ { + } } \frac { \cos ^ { - 1 } \left( x - [ x ] ^ { 2 } \right) \cdot \sin ^ { - 1 } \left( x - [ x ] ^ { 2 } \right) } { x - x ^ { 3 } }$, where $[ x ]$ denotes the greatest integer $\leq x$ is:
(1) $\pi$
(2) 0
(3) $\frac { \pi } { 4 }$
(4) $\frac { \pi } { 2 }$
Q69 Proof True/False Justification View
If the Boolean expression $( p \Rightarrow q ) \Leftrightarrow \left( q ^ { * } ( \sim p ) \right)$ is a tautology, then the Boolean expression $p ^ { * } ( \sim q )$ is equivalent to:
(1) $q \Rightarrow p$
(2) $\sim q \Rightarrow p$
(3) $p \Rightarrow \sim q$
(4) $p \Rightarrow q$
Q71 Matrices Determinant and Rank Computation View
If $A = \left[ \begin{array} { c c } 0 & \sin \alpha \\ \sin \alpha & 0 \end{array} \right]$ and $\operatorname { det } \left( A ^ { 2 } - \frac { 1 } { 2 } \mathrm { I } \right) = 0$, then a possible value of $\alpha$ is
(1) $\frac { \pi } { 2 }$
(2) $\frac { \pi } { 3 }$
(3) $\frac { \pi } { 4 }$
(4) $\frac { \pi } { 6 }$
Q72 Matrices Linear System and Inverse Existence View
The system of equations $kx + y + z = 1$, $x + ky + z = k$ and $x + y + zk = k^2$ has no solution if $k$ is equal to:
(1) 0
(2) 1
(3) $-1$
(4) $-2$
Q73 Sequences and Series Evaluation of a Finite or Infinite Sum View
If $\cot ^ { - 1 } ( \alpha ) = \cot ^ { - 1 } 2 + \cot ^ { - 1 } 8 + \cot ^ { - 1 } 18 + \cot ^ { - 1 } 32 + \ldots$ upto 100 terms, then $\alpha$ is:
(1) 1.01
(2) 1.00
(3) 1.02
(4) 1.03
Q74 Reciprocal Trig & Identities View
The sum of possible values of $x$ for $\tan ^ { - 1 } ( x + 1 ) + \cot ^ { - 1 } \left( \frac { 1 } { x - 1 } \right) = \tan ^ { - 1 } \left( \frac { 8 } { 31 } \right)$ is:
(1) $- \frac { 32 } { 4 }$
(2) $- \frac { 31 } { 4 }$
(3) $- \frac { 30 } { 4 }$
(4) $- \frac { 33 } { 4 }$
Q75 Laws of Logarithms Solve a Logarithmic Equation View
The inverse of $y = 5 ^ { \log x }$ is:
(1) $x = 5 ^ { \log y }$
(2) $x = y ^ { \log 5 }$
(3) $y = x ^ { \frac { 1 } { \log 5 } }$
(4) $x = 5 ^ { \frac { 1 } { \log y } }$
Q76 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View
Which of the following statement is correct for the function $g ( \alpha )$ for $\alpha \in R$ such that $g ( \alpha ) = \int _ { \frac { \pi } { 6 } } ^ { \frac { \pi } { 3 } } \frac { \sin ^ { \alpha } x } { \cos ^ { \alpha } x + \sin ^ { \alpha } x } d x$
(1) $g ( \alpha )$ is a strictly increasing function
(2) $g ( \alpha )$ has an inflection point at $\alpha = - \frac { 1 } { 2 }$
(3) $g ( \alpha )$ is a strictly decreasing function
(4) $g ( \alpha )$ is an even function
Q77 Differential equations Solving Separable DEs with Initial Conditions View
Which of the following is true for $y ( x )$ that satisfies the differential equation $\frac { d y } { d x } = x y - 1 + x - y ; y ( 0 ) = 0$
(1) $y ( 1 ) = \mathrm { e } ^ { - \frac { 1 } { 2 } } - 1$
(2) $y ( 1 ) = e ^ { \frac { 1 } { 2 } } - e ^ { - \frac { 1 } { 2 } }$
(3) $y ( 1 ) = 1$
(4) $y ( 1 ) = e^{\frac{1}{2}} - 1$