jee-main

Papers (191)
2026
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2025
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2024
session1_01feb_shift1 5 session1_01feb_shift2 21 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 28 session1_29jan_shift2 29 session1_30jan_shift1 20 session1_30jan_shift2 29 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 5 session2_04apr_shift2 28 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 21 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 29 session2_09apr_shift1 8 session2_09apr_shift2 30
2023
session1_01feb_shift1 28 session1_01feb_shift2 3 session1_24jan_shift1 11 session1_24jan_shift2 11 session1_25jan_shift1 29 session1_25jan_shift2 29 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 5 session1_30jan_shift2 27 session1_31jan_shift1 28 session1_31jan_shift2 15 session2_06apr_shift1 5 session2_06apr_shift2 16 session2_08apr_shift1 29 session2_08apr_shift2 13 session2_10apr_shift1 29 session2_10apr_shift2 16 session2_11apr_shift1 6 session2_11apr_shift2 8 session2_12apr_shift1 26 session2_13apr_shift1 24 session2_13apr_shift2 24 session2_15apr_shift1 19
2022
session1_24jun_shift1 19 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 14 session1_26jun_shift1 29 session1_26jun_shift2 24 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 4 session2_25jul_shift1 29 session2_25jul_shift2 20 session2_26jul_shift1 29 session2_26jul_shift2 23 session2_27jul_shift1 28 session2_27jul_shift2 29 session2_28jul_shift1 11 session2_28jul_shift2 29 session2_29jul_shift1 17 session2_29jul_shift2 18
2021
session1_24feb_shift1 9 session1_24feb_shift2 4 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 15 session2_16mar_shift1 29 session2_16mar_shift2 18 session2_17mar_shift1 21 session2_17mar_shift2 27 session2_18mar_shift1 18 session2_18mar_shift2 9 session3_20jul_shift1 29 session3_20jul_shift2 29 session3_22jul_shift1 9 session3_25jul_shift1 8 session3_25jul_shift2 14 session3_27jul_shift1 4 session3_27jul_shift2 7 session4_01sep_shift2 14 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 29 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 28 session1_07jan_shift2 20 session1_08jan_shift1 5 session1_08jan_shift2 11 session1_09jan_shift1 26 session1_09jan_shift2 16 session2_02sep_shift1 18 session2_02sep_shift2 16 session2_03sep_shift1 23 session2_03sep_shift2 8 session2_04sep_shift1 14 session2_04sep_shift2 27 session2_05sep_shift1 22 session2_05sep_shift2 29 session2_06sep_shift1 11 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 29 session1_10jan_shift2 14 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 29 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 5 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 30 15apr 28 15apr_shift1 28 15apr_shift2 6 16apr 19
2017
02apr 30 08apr 30 09apr 34
2016
03apr 28 09apr 29 10apr 30
2015
04apr 29 10apr 29 11apr 8
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 12 22apr 5 23apr 14 25apr 13
2012
07may 17 12may 21 19may 14 26may 17 offline 30
2011
jee-main_2011.pdf 18
2010
jee-main_2010.pdf 6
2009
jee-main_2009.pdf 2
2008
jee-main_2008.pdf 4
2007
jee-main_2007.pdf 38
2006
jee-main_2006.pdf 15
2005
jee-main_2005.pdf 25
2004
jee-main_2004.pdf 22
2003
jee-main_2003.pdf 8
2002
jee-main_2002.pdf 12
2013 07apr

29 maths questions

Q61 Sign Change & Interval Methods View
The real number $k$ for which the equation, $2x^3 + 3x + k = 0$ has two distinct real roots in $[0,1]$ belongs to
(1) lies between - 1 and 0 .
(2) does not exist.
(3) lies between 1 and 2 .
(4) lies between 2 and 3 .
Q62 Discriminant and conditions for roots Root relationships and Vieta's formulas View
If the equations $x^2 + 2x + 3 = 0$ and $ax^2 + bx + c = 0, a, b, c \in R$, have a common root, then $a : b : c$ is:
(1) $1 : 3 : 2$
(2) $3 : 1 : 2$
(3) $1 : 2 : 3$
(4) $3 : 2 : 1$
Q63 Complex Numbers Argand & Loci Trigonometric/Polar Form and De Moivre's Theorem View
If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg\left(\frac{1+z}{1+\bar{z}}\right)$ can be equal to (given $z \neq -1$)
(1) $\theta$
(2) $\pi - \theta$
(3) $-\theta$
(4) $\frac{\pi}{2} - \theta$
Q64 Combinations & Selection Geometric Combinatorics View
Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1} - T_n = 10$, then the value of $n$ is:
(1) 10
(2) 8
(3) 5
(4) 7
Q65 Arithmetic Sequences and Series Properties of AP Terms under Transformation View
If $x, y, z$ are positive numbers in A.P. and $\tan^{-1}x, \tan^{-1}y$ and $\tan^{-1}z$ are also in A.P., then which of the following is correct.
(1) $6x = 3y = 2z$
(2) $6x = 4y = 3z$
(3) $x = y = z$
(4) $2x = 3y = 6z$
Q66 Arithmetic Sequences and Series Telescoping or Non-Standard Summation Involving an AP View
The sum of first 20 terms of the sequence $0.7, 0.77, 0.777, \ldots\ldots$, is:
(1) $\frac{7}{81}\left(179 + 10^{-20}\right)$
(2) $\frac{7}{9}\left(99 + 10^{-20}\right)$
(3) $\frac{7}{81}\left(179 - 10^{-20}\right)$
(4) $\frac{7}{9}\left(99 - 10^{-20}\right)$
Q67 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
The term independent of $x$ in the expansion of $\left(\frac{x+1}{x^{2/3} - x^{1/3} + 1} - \frac{x-1}{x - x^{1/2}}\right)^{10}$ is
(1) 210
(2) 310
(3) 4
(4) 120
Q68 Trig Proofs Trigonometric Identity Simplification View
The expression $\frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A}$ can be written as:
(1) $\tan A + \cot A$
(2) $\sec A + \operatorname{cosec} A$
(3) $\sin A \cos A + 1$
(4) $\sec A \operatorname{cosec} A + 1$
Q69 Straight Lines & Coordinate Geometry Reflection and Image in a Line View
A ray of light along $x + \sqrt{3}y = \sqrt{3}$ gets reflected upon reaching $X$-axis, the equation of the reflected ray is
(1) $y = \sqrt{3}x - \sqrt{3}$
(2) $\sqrt{3}y = x - 1$
(3) $y = x + \sqrt{3}$
(4) $\sqrt{3}y = x - \sqrt{3}$
Q70 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
The $x$-coordinate of the incentre of the triangle that has the coordinates of midpoints of its sides as $(0,1)$, $(1,1)$ and $(1,0)$ is
(1) $1 + \sqrt{2}$
(2) $1 - \sqrt{2}$
(3) $2 + \sqrt{2}$
(4) $2 - \sqrt{2}$
Q71 Circles Circle Equation Derivation View
The circle passing through $(1, -2)$ and touching the axis of $x$ at $(3, 0)$ also passes through the point
(1) $(5, -2)$
(2) $(-2, 5)$
(3) $(-5, 2)$
(4) $(2, -5)$
Q72 Circles Tangent Lines and Tangent Lengths View
Given: A circle, $2x^2 + 2y^2 = 5$ and a parabola, $y^2 = 4\sqrt{5}x$. Statement-I: An equation of a common tangent to these curves is $y = x + \sqrt{5}$. Statement-II: If the line, $y = mx + \frac{\sqrt{5}}{m}$ $(m \neq 0)$ is their common tangent, then $m$ satisfies $m^4 - 3m^2 + 2 = 0$.
(1) Statement-I is true; Statement-II is false.
(2) Statement-I is false; Statement-II is true.
(3) Statement-I is true; Statement-II is true; Statement-II is a correct explanation for Statement-I.
(4) Statement-I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I.
Q73 Circles Circle Equation Derivation View
The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$, and having centre at $(0, 3)$ is
(1) $x^2 + y^2 - 6y - 5 = 0$
(2) $x^2 + y^2 - 6y + 5 = 0$
(3) $x^2 + y^2 - 6y - 7 = 0$
(4) $x^2 + y^2 - 6y + 7 = 0$
Q74 Chain Rule Limit Evaluation Involving Composition or Substitution View
The value of $\lim_{x \rightarrow 0} \frac{(1 - \cos 2x)(3 + \cos x)}{x \tan 4x}$ is equal to
(1) 1
(2) 2
(3) $-\frac{1}{4}$
(4) $\frac{1}{2}$
Q76 Measures of Location and Spread View
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
(1) mode
(2) variance
(3) mean
(4) median
Q77 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) $\frac{p^2 + q^2}{p^2 \cos\theta + q^2 \sin\theta}$
(2) $\frac{\left(p^2 + q^2\right)\sin\theta}{(p\cos\theta + q\sin\theta)^2}$
(3) $\frac{\left(p^2 + q^2\right)\sin\theta}{p\cos\theta + q\sin\theta}$
(4) $\frac{p^2 + q^2\cos\theta}{p\cos\theta + q\sin\theta}$
Q78 Combinations & Selection Subset Counting with Set-Theoretic Conditions View
Let $A$ and $B$ be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ having 3 or more elements is:
(1) 219
(2) 211
(3) 256
(4) 220
Q79 Matrices Determinant of Parametric or Structured Matrix View
If $P = \left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$, then $\alpha$ is equal to
(1) 5
(2) 0
(3) 4
(4) 11
Q80 Simultaneous equations View
The number of values of $k$, for which the system of equations: $(k+1)x + 8y = 4k$ $kx + (k+3)y = 3k - 1$ has no solution, is:
(1) 2
(2) 3
(3) Infinite
(4) 1
Q81 Chain Rule Chain Rule with Composition of Explicit Functions View
If $y = \sec\left(\tan^{-1}x\right)$, then $\frac{dy}{dx}$ at $x = 1$ is equal to
(1) 1
(2) $\sqrt{2}$
(3) $\frac{1}{\sqrt{2}}$
(4) $\frac{1}{2}$
Q82 Tangents, normals and gradients Find tangent line with a specified slope or from an external point View
The intercepts on the $x$-axis made by tangents to the curve, $y = \int_0^x |t|\, dt, x \in R$, which are parallel to the line $y = 2x$, are equal to
(1) $\pm 3$
(2) $\pm 4$
(3) $\pm 1$
(4) $\pm 2$
Q83 Integration by Parts Multiple-Choice Primitive Identification View
If $\int f(x)\, dx = \psi(x)$, then $\int x^5 f\left(x^3\right) dx$, is equal to
(1) $\frac{1}{3}x^3 \psi\left(x^3\right) - \int x^2 \psi\left(x^3\right) dx + c$
(2) $\frac{1}{3}\left[x^3 \psi\left(x^3\right) - \int x^3 \psi\left(x^3\right) dx\right] + c$
(3) $\frac{1}{3}\left[x^3 \psi\left(x^3\right) - \int x^2 \psi\left(x^3\right) dx\right] + c$
(4) $\frac{1}{3}x^3 \psi\left(x^3\right) - 3\int x^3 \psi\left(x^3\right) dx + c$
Q84 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View
Statement-I: The value of the integral $\int_{\pi/6}^{\pi/3} \frac{dx}{1 + \sqrt{\tan x}}$ is equal to $\frac{\pi}{6}$. Statement-II: $\int_a^b f(x)\, dx = \int_a^b f(a + b - x)\, dx$.
(1) Statement-I is true; Statement-II is false.
(2) Statement-I is false; Statement-II is true.
(3) Statement-I is true; Statement-II is true; Statement-II is a correct explanation for Statement-I.
(4) Statement-I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I.
Q85 Areas by integration View
The area (in square units) bounded by the curves $y = \sqrt{x}$, $2y - x + 3 = 0$, $X$-axis and lying in the first quadrant is
(1) 18 sq. units
(2) $\frac{27}{4}$ sq. units
(3) 9 sq. units
(4) 36 sq. units
Q86 Applied differentiation Applied modeling with differentiation View
At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production $P$ w.r.t. additional number of workers $x$ is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm employs 25 more workers, then the new level of production of items is
(1) 3500
(2) 4500
(3) 2500
(4) 3000
Q87 Vectors 3D & Lines Magnitude of Vector Expression View
If the vectors $\overrightarrow{AB} = 3\hat{i} + 4\hat{k}$ and $\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a triangle $ABC$, then the length of the median through $A$ is:
(1) $\sqrt{33}$
(2) $\sqrt{45}$
(3) $\sqrt{18}$
(4) $\sqrt{72}$
Q88 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 have
(1) exactly two values.
(2) exactly three values.
(3) any value.
(4) exactly one value.
Q89 Vectors 3D & Lines Shortest Distance Between Two Lines View
Distance between two parallel planes $2x + y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is
(1) $\frac{7}{2}$
(2) $\frac{9}{2}$
(3) $\frac{3}{2}$
(4) $\frac{5}{2}$
Q90 Binomial Distribution Compute Cumulative or Complement Binomial Probability View
A multiple choice examination has 5 questions. Each question has three alternative answers out of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is:
(1) $\frac{11}{3^5}$
(2) $\frac{10}{3^5}$
(3) $\frac{17}{3^5}$
(4) $\frac{13}{3^5}$