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 session2_25jul_shift2

22 maths questions

Q2 Projectiles Finding Angle of Projection from Given Conditions View
A ball is projected from the ground with a speed $15 \mathrm{~m}\mathrm{~s}^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then $\tan\theta$ will be equal to
(1) $\frac{1}{4}$
(2) $\frac{1}{2}$
(3) 2
(4) 4
Q21 Connected Rates of Change Parametric or Curve-Based Particle Motion Rates View
A particle is moving in a straight line such that its velocity is increasing at $5 \mathrm{~m}\mathrm{~s}^{-1}$ per meter. The acceleration of the particle is $\_\_\_\_$ $\mathrm{m}\mathrm{~s}^{-2}$ at a point where its velocity is $20 \mathrm{~m}\mathrm{~s}^{-1}$.
Q22 Centre of Mass 1 View
Three identical spheres each of mass $M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $\sqrt{x}$ m. The value of $x$ is
Q61 Complex Numbers Argand & Loci Distance and Region Optimization on Loci View
For $z \in \mathbb{C}$ if the minimum value of $(|z - 3\sqrt{2}| + |z - p\sqrt{2}i|)$ is $5\sqrt{2}$, then a value of $p$ is $\_\_\_\_$.
(1) 3
(2) $\frac{7}{2}$
(3) 4
(4) $\frac{9}{2}$
Q62 Sequences and Series Evaluation of a Finite or Infinite Sum View
The sum $\sum_{n=1}^{21} \frac{3}{(4n-1)(4n+3)}$ is equal to
(1) $\frac{7}{87}$
(2) $\frac{7}{29}$
(3) $\frac{14}{87}$
(4) $\frac{21}{29}$
Q63 Number Theory Modular Arithmetic Computation View
The remainder when $(11)^{1011} + (1011)^{11}$ is divided by 9 is $\_\_\_\_$.
(1) 1
(2) 8
(3) 6
(4) 4
Q64 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
The value of $2\sin\frac{\pi}{22}\sin\frac{3\pi}{22}\sin\frac{5\pi}{22}\sin\frac{7\pi}{22}\sin\frac{9\pi}{22}$ is equal to:
(1) $\frac{1}{16}$
(2) $\frac{5}{16}$
(3) $\frac{7}{16}$
(4) $\frac{3}{16}$
Q65 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation View
Let the point $P(\alpha, \beta)$ be at a unit distance from each of the two lines $L_1: 3x - 4y + 12 = 0$, and $L_2: 8x + 6y + 11 = 0$. If $P$ lies below $L_1$ and above $L_2$, then $100(\alpha + \beta)$ is equal to
(1) $-14$
(2) 42
(3) $-22$
(4) 14
Q66 Circles Area and Geometric Measurement Involving Circles View
The tangents at the points $A(1,3)$ and $B(1,-1)$ on the parabola $y^2 - 2x - 2y = 1$ meet at the point $P$. Then the area (in unit$^2$) of the triangle $PAB$ is:
(1) 4
(2) 6
(3) 7
(4) 8
Q67 Conic sections Eccentricity or Asymptote Computation View
If the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ meets the line $\frac{x}{7} + \frac{y}{2\sqrt{6}} = 1$ on the $x$-axis and the line $\frac{x}{7} - \frac{y}{2\sqrt{6}} = 1$ on the $y$-axis, then the eccentricity of the ellipse is
(1) $\frac{5}{7}$
(2) $\frac{2\sqrt{6}}{7}$
(3) $\frac{3}{7}$
(4) $\frac{2\sqrt{5}}{7}$
Q68 Conic sections Eccentricity or Asymptote Computation View
Let the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{7} = 1$ and the hyperbola $\frac{x^2}{144} - \frac{y^2}{\alpha} = \frac{1}{25}$ coincide. Then the length of the latus rectum of the hyperbola is:
(1) $\frac{32}{9}$
(2) $\frac{18}{5}$
(3) $\frac{27}{4}$
(4) $\frac{27}{10}$
Q69 Chain Rule Limit Evaluation Involving Composition or Substitution View
$\lim_{x \rightarrow \frac{\pi}{4}} \frac{8\sqrt{2} - (\cos x + \sin x)^7}{\sqrt{2} - \sqrt{2}\sin 2x}$ is equal to
(1) 14
(2) 7
(3) $14\sqrt{2}$
(4) $7\sqrt{2}$
Q70 Proof True/False Justification View
Consider the following statements: $P$: Ramu is intelligent. $Q$: Ramu is rich. $R$: Ramu is not honest. The negation of the statement ``Ramu is intelligent and honest if and only if Ramu is not rich'' can be expressed as:
(1) $((P \wedge (\sim R)) \wedge Q) \wedge ((\sim Q) \wedge ((\sim P) \vee R))$
(2) $((P \wedge R) \wedge Q) \vee ((\sim Q) \wedge ((\sim P) \vee (\sim R)))$
(3) $((P \wedge R) \wedge Q) \wedge ((\sim Q) \wedge ((\sim P) \vee (\sim R)))$
(4) $((P \wedge (\sim R)) \wedge Q) \vee ((\sim Q) \wedge ((\sim P) \wedge R))$
Q71 Measures of Location and Spread View
If the mean deviation about median for the number $3, 5, 7, 2k, 12, 16, 21, 24$ arranged in the ascending order, is 6 then the median is
(1) 11.5
(2) 10.5
(3) 12
(4) 11
Q72 Matrices Linear System and Inverse Existence View
The number of real values of $\lambda$, such that the system of linear equations $2x - 3y + 5z = 9$ $x + 3y - z = -18$ $3x - y + (\lambda^2 - |\lambda|)z = 16$ has no solutions, is
(1) 0
(2) 1
(3) 2
(4) 4
Q73 Combinations & Selection Counting Functions or Mappings with Constraints View
The number of bijective functions $f:\{1,3,5,7,\cdots,99\} \rightarrow \{2,4,6,8,\cdots,100\}$ if $f(3) > f(5) > f(7) \cdots > f(99)$ is
(1) ${}^{50}C_1$
(2) ${}^{50}C_2$
(3) $\frac{50!}{2}$
(4) ${}^{50}C_3 \times 3!$
Q74 Indefinite & Definite Integrals Definite Integral as a Limit of Riemann Sums View
$\lim_{n \rightarrow \infty} \frac{1}{2^n} \left( \frac{1}{\sqrt{1 - \frac{1}{2^n}}} + \frac{1}{\sqrt{1 - \frac{2}{2^n}}} + \frac{1}{\sqrt{1 - \frac{3}{2^n}}} + \ldots + \frac{1}{\sqrt{1 - \frac{2^n - 1}{2^n}}} \right)$ is equal to
(1) $\frac{1}{2}$
(2) 1
(3) 2
(4) $-2$
Q75 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View
Let $[t]$ denote the greatest integer less than or equal to $t$. Then the value of the integral $\int_{-3}^{101} \left([\sin(\pi x)] + e^{[\cos(2\pi x)]}\right) dx$ is equal to
(1) $\frac{52(1-e)}{e}$
(2) $\frac{52}{e}$
(3) $\frac{52(2+e)}{e}$
(4) $\frac{104}{e}$
Q76 Differential equations Solving Separable DEs with Initial Conditions View
Let a smooth curve $y = f(x)$ be such that the slope of the tangent at any point $(x, y)$ on it is directly proportional to $\left(\frac{-y}{x}\right)$. If the curve passes through the points $(1, 2)$ and $(8, 1)$, then $\left|y\left(\frac{1}{8}\right)\right|$ is equal to
(1) $2\log_e 2$
(2) 4
(3) 1
(4) $4\log_e 2$
Q77 Vectors Introduction & 2D Angle or Cosine Between Vectors View
Let $\vec{a} = \hat{i} - \hat{j} + 2\hat{k}$ and let $\vec{b}$ be a vector such that $\vec{a} \times \vec{b} = 2\hat{i} - \hat{k}$ and $\vec{a} \cdot \vec{b} = 3$. Then the projection of $\vec{b}$ on the vector $\vec{a} - \vec{b}$ is:
(1) $\frac{2}{\sqrt{21}}$
(2) $2\sqrt{\frac{3}{7}}$
(3) $\frac{2}{3}\sqrt{\frac{7}{3}}$
(4) $\frac{2}{3}$
Q78 Vectors 3D & Lines Normal Vector and Plane Equation View
A plane $E$ is perpendicular to the two planes $2x - 2y + z = 0$ and $x - y + 2z = 4$, and passes through the point $P(1, -1, 1)$. If the distance of the plane $E$ from the point $Q(a, a, 2)$ is $3\sqrt{2}$, then $(PQ)^2$ is equal to
(1) 9
(2) 12
(3) 21
(4) 33
Q79 Vectors 3D & Lines Shortest Distance Between Two Lines View
The shortest distance between the lines $\frac{x+7}{-6} = \frac{y-6}{7} = z$ and $\frac{7-x}{2} = y-2 = z-6$ is
(1) $2\sqrt{29}$
(2) 1
(3) $\sqrt{\frac{37}{2}}$
(4) (truncated)