jee-main

Papers (169)
2025
session1_22jan_shift1 25 session1_22jan_shift2 25 session1_23jan_shift1 25 session1_23jan_shift2 25 session1_24jan_shift1 25 session1_24jan_shift2 25 session1_28jan_shift1 25 session1_28jan_shift2 25 session1_29jan_shift1 29 session1_29jan_shift2 25
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_29jul_shift2

17 maths questions

Q61 Complex Numbers Arithmetic Modulus Computation View
If $z \neq 0$ be a complex number such that $z - \frac{1}{z} = 2$, then the maximum value of $|z|$ is
(1) $\sqrt{2}$
(2) 1
(3) $\sqrt{2} - 1$
(4) $\sqrt{2} + 1$
Q62 Complex Numbers Argand & Loci Intersection of Loci and Simultaneous Geometric Conditions View
Let $S = \{z = x + iy : |z - 1 + i| \geq |z|, |z| < 2, |z + i| = |z - 1|\}$. Then the set of all values of $x$, for which $w = 2x + iy \in S$ for some $y \in \mathbb{R}$, is
(1) $\left(-\sqrt{2}, \frac{1}{2\sqrt{2}}\right)$
(2) $\left(-\frac{1}{\sqrt{2}}, \frac{1}{4}\right)$
(3) $\left(-\sqrt{2}, \frac{1}{2}\right)$
(4) $\left(-\frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}\right)$
Q63 Sequences and series, recurrence and convergence Closed-form expression derivation View
Let $\{a_n\}_{n=0}^{\infty}$ be a sequence such that $a_0 = a_1 = 0$ and $a_{n+2} = 3a_{n+1} - 2a_n + 1, \forall n \geq 0$. Then $a_{25}a_{23} - 2a_{25}a_{22} - 2a_{23}a_{24} + 4a_{22}a_{24}$ is equal to
(1) 483
(2) 528
(3) 575
(4) 624
Q66 Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane View
Let $m_1, m_2$ be the slopes of two adjacent sides of a square of side $a$ such that $a^2 + 11a + 3(m_1^2 + m_2^2) = 220$. If one vertex of the square is $(10\cos\alpha - \sin\alpha, 10\sin\alpha + \cos\alpha)$, where $\alpha \in \left(0, \frac{\pi}{2}\right)$ and the equation of one diagonal is $(\cos\alpha - \sin\alpha)x + (\sin\alpha + \cos\alpha)y = 10$, then $72(\sin^4\alpha + \cos^4\alpha) + a^2 - 3a + 13$ is equal to
(1) 119
(2) 128
(3) 145
(4) 155
Q67 Circles Inscribed/Circumscribed Circle Computations View
Let $A(\alpha, -2)$, $B(\alpha, 6)$ and $C\left(\frac{\alpha}{4}, -2\right)$ be vertices of a $\triangle ABC$. If $\left(5, \frac{\alpha}{4}\right)$ is the circumcentre of $\triangle ABC$, then which of the following is NOT correct about $\triangle ABC$
(1) area is 24
(2) perimeter is 25
(3) circumradius is 5
(4) inradius is 2
Q68 Proof Proof of Equivalence or Logical Relationship Between Conditions View
The statement $(p \Rightarrow (q \vee p)) \Rightarrow r$ is NOT equivalent to:
(1) $p \wedge \sim r \Rightarrow q$
(2) $\sim q \Rightarrow (\sim r \vee p)$
(3) $p \Rightarrow (q \vee r)$
(4) $p \wedge \sim q \Rightarrow r$
Q69 Matrices True/False or Multiple-Select Conceptual Reasoning View
Which of the following matrices can NOT be obtained from the matrix $\begin{pmatrix} -1 & 2 \\ 1 & -1 \end{pmatrix}$ by a single elementary row operation?
(1) $\begin{pmatrix} 0 & 1 \\ 1 & -1 \end{pmatrix}$
(2) $\begin{pmatrix} 1 & -1 \\ -1 & 2 \end{pmatrix}$
(3) $\begin{pmatrix} -1 & 2 \\ -2 & 7 \end{pmatrix}$
(4) $\begin{pmatrix} -1 & 2 \\ -1 & 3 \end{pmatrix}$
Q70 Matrices Linear System and Inverse Existence View
If the system of equations $x + y + z = 6$ $2x + 5y + \alpha z = \beta$ $x + 2y + 3z = 14$ has infinitely many solutions, then $\alpha + \beta$ is equal to
(1) 8
(2) 36
(3) 44
(4) 48
Q71 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
The domain of the function $f(x) = \sin^{-1}\left(\frac{x^2 - 3x + 2}{x^2 + 2x + 7}\right)$ is
(1) $[1, \infty)$
(2) $(-1, 2]$
(3) $[-1, \infty)$
(4) $(-\infty, 2]$
Q72 Laws of Logarithms Determine Parameters of a Logarithmic Function View
Let the function $f(x) = \begin{cases} \frac{\log_e(1 + 5x) - \log_e(1 + \alpha x)}{x} & \text{if } x \neq 0 \\ 10 & \text{if } x = 0 \end{cases}$ be continuous at $x = 0$. Then $\alpha$ is equal to
(1) 10
(2) $-10$
(3) 5
(4) $-5$
Q73 Integration by Parts Reduction Formula or Recurrence via Integration by Parts View
For $I(x) = \int \frac{\sec^2 x - 2022}{\sin^{2022} x} dx$, if $I\left(\frac{\pi}{4}\right) = 2^{1011}$, then
(1) $3^{1010} I\left(\frac{\pi}{3}\right) - I\left(\frac{\pi}{6}\right) = 0$
(2) $3^{1010} I\left(\frac{\pi}{6}\right) - I\left(\frac{\pi}{3}\right) = 0$
(3) $3^{1011} I\left(\frac{\pi}{3}\right) - I\left(\frac{\pi}{6}\right) = 0$
(4) $3^{1011} I\left(\frac{\pi}{6}\right) - I\left(\frac{\pi}{3}\right) = 0$
Q74 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View
If $[t]$ denotes the greatest integer $\leq t$, then the value of $\int_0^1 \left[2x - \left|3x^2 - 5x + 2\right| + 1\right] dx$ is
(1) $\frac{\sqrt{37} + \sqrt{13} - 4}{6}$
(2) $\frac{\sqrt{37} - \sqrt{13} - 4}{6}$
(3) $\frac{-\sqrt{37} - \sqrt{13} + 4}{6}$
(4) $\frac{-\sqrt{37} + \sqrt{13} + 4}{6}$
Q75 First order differential equations (integrating factor) View
If the solution curve of the differential equation $\frac{dy}{dx} = \frac{x + y - 2}{x - y}$ passes through the point $(2, 1)$ and $(k + 1, 2)$, $k > 0$, then
(1) $2\tan^{-1}\left(\frac{1}{k}\right) = \log_e(k^2 + 1)$
(2) $\tan^{-1}\left(\frac{1}{k}\right) = \log_e(k^2 + 1)$
(3) $2\tan^{-1}\left(\frac{1}{k+1}\right) = \log_e(k^2 + 2k + 2)$
(4) $2\tan^{-1}\left(\frac{1}{k}\right) = \log_e\frac{k^2 + 1}{k^2}$
Q76 First order differential equations (integrating factor) View
Let $y = y(x)$ be the solution curve of the differential equation $\frac{dy}{dx} + \frac{2x^2 + 11x + 13}{x^3 + 6x^2 + 11x + 6} y = \frac{x + 3}{x + 1}$, $x > -1$, which passes through the point $(0, 1)$. Then $y(1)$ is equal to
(1) $\frac{1}{2}$
(2) $\frac{3}{2}$
(3) $\frac{5}{2}$
(4) $\frac{7}{2}$
Q77 Vectors 3D & Lines Normal Vector and Plane Equation View
If $(2, 3, 9)$, $(5, 2, 1)$, $(1, \lambda, 8)$ and $(\lambda, 2, 3)$ are coplanar, then the product of all possible values of $\lambda$ is
(1) $\frac{21}{2}$
(2) $\frac{59}{8}$
(3) $\frac{57}{8}$
(4) $\frac{95}{8}$
Q78 Vectors Introduction & 2D Magnitude of Vector Expression View
Let $\vec{a}, \vec{b}, \vec{c}$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and $(\vec{a} \times \vec{b}) \cdot (\vec{b} \times \vec{c}) + (\vec{b} \times \vec{c}) \cdot (\vec{c} \times \vec{a}) + (\vec{c} \times \vec{a}) \cdot (\vec{a} \times \vec{b}) = 168$, then $|\vec{a} + \vec{b} + \vec{c}|$ is equal to
(1) 10
(2) 14
(3) 16
(4) 18
Q79 Vectors 3D & Lines Distance from a Point to a Line (Show/Compute) View
Let $Q$ be the foot of perpendicular drawn from the point $P(1, 2, 3)$ to the plane $x + 2y + z = 14$. If $R$ is a point on the plane such that $\angle PRQ = 60^\circ$, then the area of $\triangle PQR$ is equal to