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 session1_25jun_shift2

17 maths questions

Q22 Circular Motion 1 Flat Curve with Friction (Unbanked Road) View
A curve in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be $30 \mathrm{~m~s}^{-1}$ without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be $\_\_\_\_$ $\mathrm{m~s}^{-1}$.
Q61 Inequalities Set Operations Using Inequality-Defined Sets View
Let $A = \{x \in R : |x + 1| < 2\}$ and $B = \{x \in R : |x - 1| \geq 2\}$. Then which one of the following statements is NOT true?
(1) $A - B = (-1,1)$
(2) $B - A = R - (-3,1)$
(3) $A \cap B = (-3,-1]$
(4) $A \cup B = R - [1,3)$
Q62 Solving quadratics and applications Finding roots or coefficients of a quadratic using Vieta's relations View
Let $a, b \in R$ be such that the equation $ax^2 - 2bx + 15 = 0$ has repeated root $\alpha$ and if $\alpha$ and $\beta$ are the roots of the equation $x^2 - 2bx + 21 = 0$, then $\alpha^2 + \beta^2$ is equal to:
(1) 37
(2) 58
(3) 68
(4) 92
Q63 Complex Numbers Argand & Loci Locus Identification from Modulus/Argument Equation View
Let $z_1$ and $z_2$ be two complex numbers such that $\bar{z}_1 = i\bar{z}_2$ and $\arg\frac{z_1}{\bar{z}_2} = \pi$, then the argument of $z_1$ is
(1) $\arg z_2 = \frac{\pi}{4}$
(2) $\arg z_2 = -\frac{3\pi}{4}$
(3) $\arg z_1 = \frac{\pi}{4}$
(4) $\arg z_1 = -\frac{3\pi}{4}$
Q64 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
The sum $1 + 2 \cdot 3 + 3 \cdot 3^2 + \ldots + 10 \cdot 3^9$ is equal to
(1) $\frac{2 \cdot 3^{12} + 10}{4}$
(2) $\frac{19 \cdot 3^{10} + 1}{4}$
(3) $5 \cdot 3^{10} - 2$
(4) $\frac{9 \cdot 3^{10} + 1}{2}$
Q65 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions View
The coefficient of $x^{101}$ in the expression $(5 + x)^{500} + x(5 + x)^{499} + x^2(5 + x)^{498} + \ldots + x^{500}$, $x > 0$ is
(1) ${}^{501}C_{101} \times 5^{399}$
(2) ${}^{501}C_{101} \times 5^{400}$
(3) ${}^{501}C_{100} \times 5^{400}$
(4) ${}^{500}C_{101} \times 5^{399}$
Q66 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
The value of $2\sin 12^\circ - \sin 72^\circ$ is
(1) $\frac{\sqrt{5}(1 - \sqrt{3})}{4}$
(2) $\frac{1 - \sqrt{5}}{8}$
(3) $\frac{\sqrt{3}(1 - \sqrt{5})}{2}$
(4) $\frac{\sqrt{3}(1 - \sqrt{5})}{4}$
Q67 Circles Circle-Related Locus Problems View
A circle touches both the $y$-axis and the line $x + y = 0$. Then the locus of its center is
(1) $y = \sqrt{2}x$
(2) $x = \sqrt{2}y$
(3) $y^2 - x^2 = 2xy$
(4) $x^2 - y^2 = 2xy$
Q68 Circles Chord Length and Chord Properties View
The line $y = x + 1$ meets the ellipse $\frac{x^2}{4} + \frac{y^2}{2} = 1$ at two points $P$ and $Q$. If $r$ is the radius of the circle with $PQ$ as diameter then $3r^2$ is equal to
(1) 20
(2) 12
(3) 11
(4) 8
Q69 Chain Rule Limit Evaluation Involving Composition or Substitution View
$\lim_{x \to \frac{\pi}{2}} \tan^2 x \left[(2\sin^2 x + 3\sin x + 4)^{\frac{1}{2}} - (\sin^2 x + 6\sin x + 2)^{\frac{1}{2}}\right]$ is equal to
(1) $\frac{1}{12}$
(2) $-\frac{1}{18}$
(3) $-\frac{1}{12}$
(4) $\frac{1}{6}$
Q70 Proof Proof of Equivalence or Logical Relationship Between Conditions View
The negation of the Boolean expression $(\sim q \wedge p) \Rightarrow (\sim p \vee q)$ is logically equivalent to
(1) $p \Rightarrow q$
(2) $q \Rightarrow p$
(3) $\sim p \Rightarrow q$
(4) $\sim q \Rightarrow p$
Q71 Matrices Linear System and Inverse Existence View
The system of equations $-kx + 3y - 14z = 25$ $-15x + 4y - kz = 3$ $-4x + y + 3z = 4$ is consistent for all $k$ in the set
(1) $R$
(2) $R - \{-11, 13\}$
(3) $R - \{-13\}$
(4) $R - \{-11, 11\}$
Q72 Reciprocal Trig & Identities View
The value of $\tan^{-1}\left(\frac{\cos\frac{15\pi}{4} - 1}{\sin\frac{\pi}{4}}\right)$ is equal to
(1) $-\frac{\pi}{4}$
(2) $-\frac{\pi}{8}$
(3) $-\frac{5\pi}{12}$
(4) $-\frac{4\pi}{9}$
Q73 Connected Rates of Change Volume/Height Related Rates for Containers and Solids View
Water is being filled at the rate of $1 \mathrm{~cm}^3 \mathrm{sec}^{-1}$ in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in $\mathrm{cm}^2 \mathrm{sec}^{-1}$) at which the wet conical surface area of the vessel increases is
(1) 5
(2) $\frac{\sqrt{21}}{5}$
(3) $\frac{\sqrt{26}}{5}$
(4) $\frac{\sqrt{26}}{10}$
Q74 Tangents, normals and gradients Find tangent line with a specified slope or from an external point View
If the line $y = 4 + kx$, $k > 0$, is the tangent to the parabola $y = x - x^2$ at the point $P$ and $V$ is the vertex of the parabola, then the slope of the line through $P$ and $V$ is
(1) $\frac{3}{2}$
(2) $\frac{26}{9}$
(3) $\frac{5}{2}$
(4) $\frac{23}{6}$
Q75 Parametric differentiation View
If the angle made by the tangent at the point $(x_0, y_0)$ on the curve $x = 12(t + \sin t \cos t)$, $y = 12(1 + \sin t)^2$, $0 < t < \frac{\pi}{2}$, with the positive $x$-axis is $\frac{\pi}{3}$, then $y_0$ is equal to
(1) $63 + 2\sqrt{2}$
(2) $37 + 4\sqrt{3}$
(3) 27
(4) 48
Q76 Indefinite & Definite Integrals Integral Inequalities and Limit of Integral Sequences View
If $b_n = \int_0^{\frac{\pi}{2}} \frac{\cos^2 nx}{\sin x} dx$, $n \in \mathbb{N}$, then
(1) $b_3 - b_2, b_4 - b_3, b_5 - b_4$ are in an A.P. with common difference $-2$
(2) $\frac{1}{b_3 - b_2}, \frac{1}{b_4 - b_3}, \frac{1}{b_5 - b_4}$ are in an A.P. with common difference $2$
(3) $b_3 - b_2, b_4 - b_3, b_5 - b_4$ are in a G.P.
(4) $\frac{1}{b_3 - b_2}, \frac{1}{b_4 - b_3}, \frac{1}{b_5 - b_4}$ are in an A.P. with common difference $-2$