jee-main

Papers (169)
2025
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2024
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2023
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2022
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2021
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2020
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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
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2015
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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
2012 offline

30 maths questions

Q2 Projectiles Maximum Range or Maximum Height from Given Constraints View
A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be
(1) $20\sqrt{2}$ m
(2) 10 m
(3) $10\sqrt{2}$ m
(4) 20 m
Q61 Vectors 3D & Lines MCQ: Relationship Between Two Lines View
If the lines $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $\frac{x-3}{1} = \frac{y-k}{2} = \frac{z}{1}$ intersect, then $k$ is equal to
(1) $\frac{2}{9}$
(2) $\frac{9}{2}$
(3) 0
(4) $-1$
Q62 Vectors: Cross Product & Distances View
If $\vec{a} = \frac{1}{\sqrt{10}}(3\hat{i}+\hat{k})$ and $\vec{b} = \frac{1}{7}(2\hat{i}+3\hat{j}-6\hat{k})$, then the value of $(2\vec{a}-\vec{b})\cdot[(\vec{a}\times\vec{b})\times(\vec{a}+2\vec{b})]$ is
(1) $-5$
(2) $-3$
(3) 5
(4) 3
Q63 Differential equations Applied Modeling with Differential Equations View
The population $p(t)$ at time $t$ of a certain mouse species satisfies the differential equation $\frac{dp(t)}{dt} = 0.5\,p(t) - 450$. If $p(0) = 850$, then the time at which the population becomes zero is
(1) $\ln 18$
(2) $\ln 9$
(3) $\frac{1}{2}\ln 18$
(4) $2\ln 18$
Q64 Vectors Introduction & 2D Perpendicularity or Parallel Condition View
Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\vec{c} = \hat{a} + 2\hat{b}$ and $\vec{d} = 5\hat{a} - 4\hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is
(1) $\frac{\pi}{6}$
(2) $\frac{\pi}{2}$
(3) $\frac{\pi}{3}$
(4) $\frac{\pi}{4}$
Q65 Complex Numbers Argand & Loci Algebraic Conditions for Geometric Properties (Real, Imaginary, Collinear) View
If $z \neq 1$ and $\frac{z^{2}}{z-1}$ is real, then the point represented by the complex number $z$ lies
(1) either on the real axis or on a circle passing through the origin
(2) on a circle with centre at the origin
(3) either on the real axis or on a circle not passing through the origin
(4) on the imaginary axis
Q66 Binomial Theorem (positive integer n) Integer Part or Limit Involving Conjugate Surd Binomial Expansions View
If $n$ is a positive integer, then $(\sqrt{3}+1)^{2n} - (\sqrt{3}-1)^{2n}$ is
(1) an irrational number
(2) an odd positive integer
(3) an even positive integer
(4) a rational number other than positive integers
Q67 Sine and Cosine Rules Determine an angle or side from a trigonometric identity/equation View
In a $\triangle PQR$, if $3\sin P + 4\cos Q = 6$ and $4\sin Q + 3\cos P = 1$, then the angle $R$ is equal to
(1) $\frac{5\pi}{6}$
(2) $\frac{\pi}{6}$
(3) $\frac{\pi}{4}$
(4) $\frac{3\pi}{4}$
Q68 Conic sections Equation Determination from Geometric Conditions View
An ellipse is drawn by taking a diameter of the circle $(x-1)^{2}+y^{2}=1$ as its semi-minor axis and a diameter of the circle $x^{2}+(y-2)^{2}=4$ as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is
(1) $4x^{2}+y^{2}=4$
(2) $x^{2}+4y^{2}=8$
(3) $4x^{2}+y^{2}=8$
(4) $x^{2}+4y^{2}=16$
Q69 Straight Lines & Coordinate Geometry Area Computation in Coordinate Geometry View
A line is drawn through the point $(1,2)$ to meet the coordinate axes at $P$ and $Q$ such that it forms a triangle of area $\frac{9}{2}$ sq. units with the coordinate axes. The equation of the line $PQ$ is
(1) $x+2y=5$
(2) $3x+y=5$
(3) $x+2y=4$
(4) $2x+y=4$
Q70 Circles Circle Equation Derivation View
The equation of the circle passing through the point $(1,0)$ and $(0,1)$ and having the smallest radius is
(1) $x^{2}+y^{2}-2x-2y+1=0$
(2) $x^{2}+y^{2}+2x+2y-7=0$
(3) $x^{2}+y^{2}-x-y=0$
(4) $x^{2}+y^{2}+x+y-2=0$
Q71 Sine and Cosine Rules Multi-step composite figure problem View
ABCD is a trapezium such that AB and CD are parallel and $BC \perp CD$. If $\angle ADB = \theta$, $BC = p$ and $CD = q$, then $AB$ is equal to
(1) $\frac{(p^{2}+q^{2})\sin\theta}{p\cos\theta+q\sin\theta}$
(2) $\frac{p^{2}+q^{2}\cos\theta}{p\cos\theta+q\sin\theta}$
(3) $\frac{p^{2}+q^{2}}{p^{2}\cos\theta+q^{2}\sin\theta}$
(4) $\frac{(p^{2}+q^{2})\sin\theta}{(p\cos\theta+q\sin\theta)^{2}}$
Q73 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View
If the integral $\displaystyle\int_{0}^{10} \frac{\lfloor x \rfloor e^{x}}{e^{\lfloor x \rfloor}} dx = \alpha(e-1)$, then $\alpha$ is equal to (where $\lfloor x \rfloor$ denotes the greatest integer function)
(1) $\frac{1}{e-1}$
(2) $\frac{10}{e-1}$
(3) $\frac{e}{e-1}$
(4) $\frac{e^{10}-1}{e-1}$
Q74 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
If $100$ times the $100^{\text{th}}$ term of an AP with non-zero common difference equals the $50$ times its $50^{\text{th}}$ term, then the $150^{\text{th}}$ term of this AP is
(1) $-150$
(2) 150 times its $50^{\text{th}}$ term
(3) 150
(4) zero
Q75 Composite & Inverse Functions Recover a Function from a Composition or Functional Equation View
If $g(x) = x^{2} + x - 2$ and $\frac{1}{2}\,g\circ f(x) = 2x^{2} - 5x + 2$, then $f(x)$ is equal to
(1) $2x-3$
(2) $2x+3$
(3) $2x^{2}+3x+1$
(4) $2x^{2}-3x-1$
Q76 Measures of Location and Spread View
Let $x_{1}, x_{2}, \ldots, x_{n}$ be $n$ observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^{2}$ be their variance. Statement 1: Variance of $2x_{1}, 2x_{2}, \ldots, 2x_{n}$ is $4\sigma^{2}$. Statement 2: Arithmetic mean of $2x_{1}, 2x_{2}, \ldots, 2x_{n}$ is $4\bar{x}$.
(1) Statement 1 is false, Statement 2 is true
(2) Statement 1 is true, Statement 2 is false
(3) Statement 1 is true, Statement 2 is the correct explanation for Statement 1
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1
Q77 Matrices Determinant and Rank Computation View
Let $P$ and $Q$ be $3 \times 3$ matrices with $P \neq Q$. If $P^{3} = Q^{3}$ and $P^{2}Q = Q^{2}P$, then the determinant of $(P^{2}+Q^{2})$ is equal to
(1) $-2$
(2) 1
(3) 0
(4) $-1$
Q78 Circles Circle Equation Derivation View
The length of the diameter of the circle which touches the $x$-axis at the point $(1,0)$ and passes through the point $(2,3)$ is
(1) $\frac{10}{3}$
(2) $\frac{3}{5}$
(3) $\frac{6}{5}$
(4) $\frac{5}{3}$
Q79 Areas Between Curves Area Involving Conic Sections or Circles View
The area bounded between the parabolas $x^{2} = \frac{y}{4}$ and $x^{2} = 9y$, and the straight line $y = 2$ is
(1) $20\sqrt{2}$
(2) $\frac{10\sqrt{2}}{3}$
(3) $\frac{20\sqrt{2}}{3}$
(4) $10\sqrt{2}$
Q80 Stationary points and optimisation Determine parameters from given extremum conditions View
Let $a, b \in \mathbb{R}$ be such that the function $f$ given by $f(x) = \ln|x| + bx^{2} + ax$, $x \neq 0$ has extreme values at $x = -1$ and $x = 2$. Statement 1: $f$ has local maximum at $x = -1$ and at $x = 2$. Statement 2: $a = \frac{1}{2}$ and $b = \frac{-1}{4}$.
(1) Statement 1 is false, Statement 2 is true
(2) Statement 1 is true, Statement 2 is false
(3) Statement 1 is true, Statement 2 is the correct explanation for Statement 1
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1
Q81 Connected Rates of Change Volume/Height Related Rates for Containers and Solids View
A spherical balloon is filled with 4500$\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is
(1) $\frac{9}{7}$
(2) $\frac{7}{9}$
(3) $\frac{2}{9}$
(4) $\frac{9}{2}$
Q82 Vectors 3D & Lines Vector Algebra and Triple Product Computation View
Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{b} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{c} = \hat{i} - \hat{j} - \hat{k}$ be three vectors. A vector $\vec{v}$ in the plane of $\vec{a}$ and $\vec{b}$, whose projection on $\vec{c}$ is $\frac{1}{\sqrt{3}}$, is
(1) $\hat{i} - 3\hat{j} + 3\hat{k}$
(2) $-3\hat{i} - 3\hat{j} - \hat{k}$
(3) $3\hat{i} - \hat{j} + 3\hat{k}$
(4) $\hat{i} + 3\hat{j} - 3\hat{k}$
Q83 Vectors 3D & Lines MCQ: Relationship Between Two Lines View
If the lines $\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}$ and $\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}$ are coplanar, then $k$ can be
(1) $-1$ or $-3$
(2) $-1$ or $3$
(3) $1$ or $-1$
(4) $0$ or $-3$
Q84 Integration by Parts Indefinite Integration by Parts View
If $\displaystyle\int f(x)\,dx = \psi(x)$, then $\displaystyle\int x^{5}f(x^{3})\,dx$ is equal to
(1) $\frac{1}{3}x^{3}\psi(x^{3}) - 3\displaystyle\int x^{3}\psi(x^{3})\,dx + C$
(2) $\frac{1}{3}\left[x^{3}\psi(x^{3}) - \displaystyle\int x^{2}\psi(x^{3})\,dx\right] + C$
(3) $\frac{1}{3}x^{3}\psi(x^{3}) - \displaystyle\int x^{2}\psi(x^{3})\,dx + C$
(4) $\frac{1}{3}\left[x^{3}\psi(x^{3}) - \displaystyle\int x^{3}\psi(x^{3})\,dx\right] + C$
Q85 Matrices Linear System and Inverse Existence View
Let $A = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{pmatrix}$. If $u_{1}$ and $u_{2}$ are column matrices such that $Au_{1} = \begin{pmatrix}1\\0\\0\end{pmatrix}$ and $Au_{2} = \begin{pmatrix}0\\1\\0\end{pmatrix}$, then $u_{1}+u_{2}$ is equal to
(1) $\begin{pmatrix}-1\\1\\0\end{pmatrix}$
(2) $\begin{pmatrix}-1\\1\\-1\end{pmatrix}$
(3) $\begin{pmatrix}-1\\-1\\0\end{pmatrix}$
(4) $\begin{pmatrix}1\\-1\\-1\end{pmatrix}$
Q86 Matrices Linear System and Inverse Existence View
The number of values of $k$ for which the linear equations $4x+ky+2z=0$, $kx+4y+z=0$, $2x+2y+z=0$ possess a non-zero solution is
(1) 2
(2) 1
(3) zero
(4) 3
Q87 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
The sum of first 20 terms of the sequence $0.7, 0.77, 0.777, \ldots$ is
(1) $\frac{7}{81}(179-10^{-20})$
(2) $\frac{7}{9}(99-10^{-20})$
(3) $\frac{7}{81}(179+10^{-20})$
(4) $\frac{7}{9}(99+10^{-20})$
Q88 Complex Numbers Argand & Loci Powers and Roots of Unity with Geometric Consequences View
If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg\left(\frac{1+z}{1+\bar{z}}\right)$ equals
(1) $-\theta$
(2) $\frac{\pi}{2}-\theta$
(3) $\theta$
(4) $\pi-\theta$
Q89 Permutations & Arrangements Forming Numbers with Digit Constraints View
The number of 3-digit numbers, with distinct digits, that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ and divisible by 3 is
(1) 80
(2) 120
(3) 40
(4) 108
Q90 Arithmetic Sequences and Series Properties of AP Terms under Transformation View
If $x, y, z$ are in AP and $\tan^{-1}x$, $\tan^{-1}y$ and $\tan^{-1}z$ are also in AP, then
(1) $x = y = z$
(2) $2x = 3y = 6z$
(3) $6x = 3y = 2z$
(4) $6x = 4y = 3z$