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
2020 session2_05sep_shift2

27 maths questions

Q21 Power and driving force View
A body of mass 2 kg is driven by an engine delivering a constant power of $1\,\mathrm{J\,s^{-1}}$. The body starts from rest and moves in a straight line. After 9 s, the body has moved a distance (in m) ...
Q22 Impulse and momentum (advanced) View
A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of mass 0.1 kg moving in a straight line with velocity $80\,\mathrm{m\,s^{-1}}$ hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in $\mathrm{rad\,s^{-1}}$) of the rod immediately after the collision will be $\_\_\_\_$
Q51 Solving quadratics and applications Evaluating an algebraic expression given a constraint View
If $\alpha$ and $\beta$ are the roots of the equation, $7x^2 - 3x - 2 = 0$, then the value of $\frac{\alpha}{1-\alpha^2} + \frac{\beta}{1-\beta^2}$ is equal to:
(1) $\frac{27}{32}$
(2) $\frac{1}{24}$
(3) $\frac{3}{8}$
(4) $\frac{27}{16}$
Q52 Complex Numbers Arithmetic Trigonometric/Polar Form and De Moivre's Theorem View
The value of $\left(\frac{-1+i\sqrt{3}}{1-i}\right)^{30}$ is:
(1) $6^5$
(2) $2^{15}\mathrm{i}$
(3) $-2^{15}$
(4) $-2^{15}\mathrm{i}$
Q53 Combinations & Selection Selection with Group/Category Constraints View
There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:
(1) 3000
(2) 1500
(3) 2255
(4) 2250
Q54 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is:
(1) $\frac{1}{26}\left(3^{49}-1\right)$
(2) $\frac{1}{26}\left(3^{50}-1\right)$
(3) $\frac{2}{13}\left(3^{50}-1\right)$
(4) $\frac{1}{13}\left(3^{50}-1\right)$
Q55 Laws of Logarithms Solve a Logarithmic Equation View
If the sum of the first 20 terms of the series $\log_{(7^{1/2})}x + \log_{(7^{1/3})}x + \log_{(7^{1/4})}x + \ldots$ is 460, then $x$ is equal to:
(1) $7^2$
(2) $7^{1/2}$
(3) $e^2$
(4) $7^{46/21}$
Q56 Addition & Double Angle Formulae Half-Angle Formula Evaluation View
If $L = \sin^2\left(\frac{\pi}{16}\right) - \sin^2\left(\frac{\pi}{8}\right)$ and $M = \cos^2\left(\frac{\pi}{16}\right) - \sin^2\left(\frac{\pi}{8}\right)$
(1) $L = -\frac{1}{2\sqrt{2}} + \frac{1}{2}\cos\frac{\pi}{8}$
(2) $L = \frac{1}{4\sqrt{2}} - \frac{1}{4}\cos\frac{\pi}{8}$
(3) $M = \frac{1}{4\sqrt{2}} + \frac{1}{4}\cos\frac{\pi}{8}$
(4) $M = \frac{1}{2\sqrt{2}} + \frac{1}{2}\cos\frac{\pi}{8}$
Q57 Circles Chord Length and Chord Properties View
If the length of the chord of the circle, $x^2 + y^2 = r^2$ $(r > 0)$ along the line, $y - 2x = 3$ is $r$, then $r^2$ is equal to:
(1) $\frac{9}{5}$
(2) 12
(3) $\frac{24}{5}$
(4) $\frac{12}{5}$
Q58 Conic sections Circle-Conic Interaction with Tangency or Intersection View
If the line $y = mx + c$ is a common tangent to the hyperbola $\frac{x^2}{100} - \frac{y^2}{64} = 1$ and the circle $x^2 + y^2 = 36$, then which one of the following is true?
(1) $c^2 = 369$
(2) $5m = 4$
(3) $4c^2 = 369$
(4) $8m + 5 = 0$
Q59 Differentiation from First Principles View
$\lim_{x\rightarrow 0} \frac{x\left(e^{\left(\sqrt{1+x^2+x^4}-1\right)/x}-1\right)}{\sqrt{1+x^2+x^4}-1}$
(1) is equal to $\sqrt{e}$
(2) is equal to 1
(3) is equal to 0
(4) does not exist
Q60 Proof True/False Justification View
The statement $(p \rightarrow (q \rightarrow p)) \rightarrow (p \rightarrow (p \vee q))$ is:
(1) equivalent to $(p \wedge q) \vee (\sim q)$
(2) a contradiction
(3) equivalent to $(p \vee q) \wedge (\sim p)$
(4) a tautology
Q61 Measures of Location and Spread View
If the mean and the standard deviation of the data $3, 5, 7, a, b$ are 5 and 2 respectively, then $a$ and $b$ are the roots of the equation:
(1) $x^2 - 10x + 18 = 0$
(2) $2x^2 - 20x + 19 = 0$
(3) $x^2 - 10x + 19 = 0$
(4) $x^2 - 20x + 18 = 0$
Q62 Matrices Linear System and Inverse Existence View
If the system of linear equations $$x + y + 3z = 0$$ $$x + 3y + k^2z = 0$$ $$3x + y + 3z = 0$$ has a non-zero solution $(x, y, z)$ for some $k \in \mathrm{R}$, then $x + \left(\frac{y}{z}\right)$ is equal to:
(1) $-3$
(2) $9$
(3) $3$
(4) $-9$
Q63 3x3 Matrices Direct Determinant Computation View
If $a + x = b + y = c + z + 1$, where $a, b, c, x, y, z$ are non-zero distinct real numbers, then $\left|\begin{array}{lll} x & a+y & x+a \\ y & b+y & y+b \\ z & c+y & z+c \end{array}\right|$ is equal to:
(1) $y(b-a)$
(2) $y(a-b)$
(3) $0$
(4) $y(a-c)$
Q64 Differentiating Transcendental Functions Evaluate derivative at a point or find tangent slope View
The derivative of $\tan^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ with respect to $\tan^{-1}\left(\frac{2x\sqrt{1-x^2}}{1-2x^2}\right)$ at $x = \frac{1}{2}$ is:
(1) $\frac{2\sqrt{3}}{5}$
(2) $\frac{\sqrt{3}}{12}$
(3) $\frac{2\sqrt{3}}{3}$
(4) $\frac{\sqrt{3}}{10}$
Q65 Stationary points and optimisation Find critical points and classify extrema of a given function View
If $x = 1$ is a critical point of the function $f(x) = (3x^2 + ax - 2 - a)e^x$, then
(1) $x = 1$ and $x = -\frac{2}{3}$ are local minima of $f$
(2) $x = 1$ and $x = -\frac{2}{3}$ is a local maxima of $f$
(3) $x = 1$ is a local maxima and $x = -\frac{2}{3}$ is a local minima of $f$
(4) $x = 1$ is a local minima and $x = -\frac{2}{3}$ are local maxima of $f$
Q66 Implicit equations and differentiation Compute slope at a point via implicit differentiation (single-step) View
Which of the following points lies on the tangent to the curve $x^4 e^y + 2\sqrt{y+1} = 3$ at the point $(1, 0)$?
(1) $(2, 2)$
(2) $(2, 6)$
(3) $(-2, 6)$
(4) $(-2, 4)$
Q67 Standard Integrals and Reverse Chain Rule Reverse Chain Rule Antiderivative (MCQ) View
If $\int \frac{\cos\theta}{5 + 7\sin\theta - 2\cos^2\theta}\,d\theta = A\log_e|B(\theta)| + C$, where $C$ is a constant of integration, then $\frac{B(\theta)}{A}$ can be:
(1) $\frac{2\sin\theta+1}{\sin\theta+3}$
(2) $\frac{2\sin\theta+1}{5(\sin\theta+3)}$
(3) $\frac{5(\sin\theta+3)}{2\sin\theta+1}$
(4) $\frac{5(2\sin\theta+1)}{\sin\theta+3}$
Q68 Areas Between Curves Area Involving Piecewise or Composite Functions View
The area (in sq. units) of the region $A = \{(x,y) : (x-1)[x] \leq y \leq 2\sqrt{x},\, 0 \leq x \leq 2\}$, where $[t]$ denotes the greatest integer function, is:
(1) $\frac{8}{3}\sqrt{2} - \frac{1}{2}$
(2) $\frac{4}{3}\sqrt{2} + 1$
(3) $\frac{8}{3}\sqrt{2} - 1$
(4) $\frac{4}{3}\sqrt{2} - \frac{1}{2}$
Q69 First order differential equations (integrating factor) View
Let $y = y(x)$ be the solution of the differential equation $\cos x\frac{dy}{dx} + 2y\sin x = \sin 2x$, $x \in \left(0, \frac{\pi}{2}\right)$. If $y(\pi/3) = 0$, then $y(\pi/4)$ is equal to:
(1) $2 - \sqrt{2}$
(2) $2 + \sqrt{2}$
(3) $\sqrt{2} - 2$
(4) $\frac{1}{\sqrt{2}} - 1$
Q70 Vectors: Lines & Planes Coplanarity and Relative Position of Planes View
If for some $\alpha \in \mathrm{R}$, the lines $L_1: \frac{x+1}{2} = \frac{y-2}{-1} = \frac{z-1}{1}$ and $L_2: \frac{x+2}{\alpha} = \frac{y+1}{5-\alpha} = \frac{z+1}{1}$ are coplanar, then the line $L_2$ passes through the point:
(1) $(10, 2, 2)$
(2) $(2, -10, -2)$
(3) $(10, -2, -2)$
(4) $(-2, 10, 2)$
Q71 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
The coefficient of $x^4$ in the expansion of $\left(1 + x + x^2 + x^3\right)^6$ in powers of $x$, is
Q72 Composite & Inverse Functions Counting Functions with Composition or Mapping Constraints View
Let $A = \{a, b, c\}$ and $B = \{1, 2, 3, 4\}$. Then the number of elements in the set $C = \{f: A \rightarrow B \mid 2 \in f(A)$ and $f$ is not one-one$\}$ is ...
Q73 Tangents, normals and gradients Determine unknown parameters from tangent conditions View
If the lines $x + y = a$ and $x - y = b$ touch the curve $y = x^2 - 3x + 2$ at the points where the curve intersects the $x$-axis, then $\frac{a}{b}$ is equal to ...
Q74 Vectors Introduction & 2D Magnitude of Vector Expression View
Let the vectors $\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{c}}$ be such that $|\overrightarrow{\mathrm{a}}| = 2$, $|\overrightarrow{\mathrm{b}}| = 4$ and $|\overrightarrow{\mathrm{c}}| = 4$. If the projection of $\overrightarrow{\mathrm{b}}$ on $\overrightarrow{\mathrm{a}}$ is equal to the projection of $\overrightarrow{\mathrm{c}}$ on $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ is perpendicular to $\overrightarrow{\mathrm{c}}$, then the value of $|\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} - \overrightarrow{\mathrm{c}}|$ is ...
Q75 Binomial Distribution Find Minimum n for a Probability Threshold View
In a bombing attack, there is $50\%$ chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that the probability of the target being destroyed is at least $0.99$, is ...