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
2016 03apr

30 maths questions

Q61 Arithmetic Sequences and Series Arithmetic-Geometric Hybrid Problem View
If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is: (1) $\frac{8}{5}$ (2) $\frac{4}{3}$ (3) $1$ (4) $\frac{7}{4}$
Q62 Sequences and Series Evaluation of a Finite or Infinite Sum View
If the sum of the first ten terms of the series $\left(1\frac{3}{5}\right)^{2}+\left(2\frac{2}{5}\right)^{2}+\left(3\frac{1}{5}\right)^{2}+4^{2}+\left(4\frac{4}{5}\right)^{2}+\ldots$, is $\frac{16}{5} m$, then $m$ is equal to: (1) 102 (2) 101 (3) 100 (4) 99
Q63 Matrices Determinant and Rank Computation View
If $A = \begin{pmatrix} 5a & -b \\ 3 & 2 \end{pmatrix}$ and $A$ adj $A = A A^{T}$, then $5a + b$ is equal to: (1) $-1$ (2) $5$ (3) $4$ (4) $13$
Q64 Matrices Linear System and Inverse Existence View
The system of linear equations \begin{align*} x + \lambda y - z &= 0 \lambda x - y - z &= 0 x + y - \lambda z &= 0 \end{align*} has a non-trivial solution for: (1) infinitely many values of $\lambda$ (2) exactly one value of $\lambda$ (3) exactly two values of $\lambda$ (4) exactly three values of $\lambda$
Q65 Matrices Determinant and Rank Computation View
If $A = \begin{pmatrix} 2 & -3 \\ -4 & 1 \end{pmatrix}$, then adj$(3A^2 + 12A)$ is equal to: (1) $\begin{pmatrix} 72 & -84 \\ -63 & 51 \end{pmatrix}$ (2) $\begin{pmatrix} 51 & 63 \\ 84 & 72 \end{pmatrix}$ (3) $\begin{pmatrix} 51 & 84 \\ 63 & 72 \end{pmatrix}$ (4) $\begin{pmatrix} 72 & -63 \\ -84 & 51 \end{pmatrix}$
Q66 Quadratic trigonometric equations View
The number of distinct real roots of the equation $\tan^{2}x - \sec^{10}x + 1 = 0$ in the interval $\left(0, \frac{\pi}{3}\right)$ is: (1) 0 (2) 1 (3) 2 (4) 3
Q67 Complex Numbers Arithmetic Systems of Equations via Real and Imaginary Part Matching View
A value of $\theta$ for which $\frac{2+3i\sin\theta}{1-2i\sin\theta}$ is purely imaginary, is: (1) $\frac{\pi}{3}$ (2) $\frac{\pi}{6}$ (3) $\sin^{-1}\left(\frac{\sqrt{3}}{4}\right)$ (4) $\sin^{-1}\left(\frac{1}{\sqrt{3}}\right)$
Q68 Stationary points and optimisation Geometric or applied optimisation problem View
A wire of length 2 units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then: (1) $2x = (\pi + 4)r$ (2) $(4-\pi)x = \pi r$ (3) $x = 2r$ (4) $2x = r$
Q69 Straight Lines & Coordinate Geometry Section Ratio and Division of Segments View
A straight line through origin $O$ meets the lines $3y = 10 - 4x$ and $8x + 6y + 5 = 0$ at points $A$ and $B$ respectively. Then $O$ divides the segment $AB$ in the ratio: (1) $2:3$ (2) $1:2$ (3) $4:1$ (4) $3:4$
Q70 Circles Circle Equation Derivation View
Let $P$ be the point on the parabola, $y^2 = 8x$ which is at a minimum distance from the centre $C$ of the circle, $x^2 + (y+6)^2 = 1$. Then the equation of the circle, passing through $C$ and having its centre at $P$ is: (1) $x^2 + y^2 - 4x + 8y + 12 = 0$ (2) $x^2 + y^2 - x + 4y - 12 = 0$ (3) $x^2 + y^2 - \frac{x}{4} + 2y - 24 = 0$ (4) $x^2 + y^2 - 4x + 9y + 18 = 0$
Q71 Conic sections Eccentricity or Asymptote Computation View
The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is: (1) $\frac{4}{3}$ (2) $\frac{4}{\sqrt{3}}$ (3) $\frac{2}{\sqrt{3}}$ (4) $\sqrt{3}$
Q72 Areas Between Curves Area Involving Conic Sections or Circles View
The area (in sq. units) of the region $\{(x,y): y^2 \geq 2x$ and $x^2 + y^2 \leq 4x, x \geq 0, y \geq 0\}$ is: (1) $\pi - \frac{4\sqrt{2}}{3}$ (2) $\pi - \frac{8}{3}$ (3) $\pi - \frac{4}{3}$ (4) $\frac{\pi}{2} - \frac{2\sqrt{2}}{3}$
Q73 Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition View
The integral $\int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx$ is equal to: (1) $\frac{-x^{10}}{2(x^5+x^3+1)^2} + C$ (2) $\frac{x^{10}}{2(x^5+x^3+1)^2} + C$ (3) $\frac{-x^5}{(x^5+x^3+1)^2} + C$ (4) $\frac{x^5}{2(x^5+x^3+1)^2} + C$
Q74 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
The integral $\int_{\pi/4}^{3\pi/4} \frac{dx}{1+\cos x}$ is equal to: (1) $-1$ (2) $-2$ (3) $2$ (4) $4$
Q75 First order differential equations (integrating factor) View
If a curve $y = f(x)$ passes through the point $(1,-1)$ and satisfies the differential equation, $y(1+xy)dx = x\,dy$, then $f\left(-\frac{1}{2}\right)$ is equal to: (1) $-\frac{2}{5}$ (2) $-\frac{4}{5}$ (3) $\frac{2}{5}$ (4) $\frac{4}{5}$
Q76 Measures of Location and Spread View
If the standard deviation of the numbers $2, 3, a$ and $11$ is $3.5$, then which of the following is true? (1) $3a^2 - 26a + 55 = 0$ (2) $3a^2 - 32a + 84 = 0$ (3) $3a^2 - 34a + 91 = 0$ (4) $3a^2 - 23a + 44 = 0$
Q77 Independent Events View
Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die $B$ shows up two and $E_3$ is the event that the sum of dice $A$ and $B$ is odd, then which of the following statements is NOT true? (1) $E_1$ and $E_3$ are independent. (2) $E_1$, $E_2$ and $E_3$ are independent. (3) $E_1$ and $E_2$ are independent. (4) $E_2$ and $E_3$ are independent.
Q78 Standard trigonometric equations Solve trigonometric equation for solutions in an interval View
If $0 \leq x < 2\pi$, then the number of real values of $x$, which satisfy the equation $\cos x + \cos 2x + \cos 3x + \cos 4x = 0$ is: (1) 3 (2) 5 (3) 7 (4) 9
Q79 Vectors: Cross Product & Distances View
Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\sqrt{3}}{2}(\vec{b}+\vec{c})$. If $\vec{b}$ is not parallel to $\vec{c}$, then the angle between $\vec{a}$ and $\vec{b}$ is: (1) $\frac{3\pi}{4}$ (2) $\frac{\pi}{2}$ (3) $\frac{2\pi}{3}$ (4) $\frac{5\pi}{6}$
Q80 Vectors: Lines & Planes Parallelism Between Line and Plane or Constraint on Parameters View
If the line $\frac{x-3}{2} = \frac{y+2}{-1} = \frac{z+4}{3}$ lies in the plane $lx + my - z = 9$, then $l^2 + m^2$ is equal to: (1) 18 (2) 5 (3) 2 (4) 26
Q81 Vectors: Lines & Planes Distance Computation (Point-to-Plane or Line-to-Line) View
The distance of the point $(1, -5, 9)$ from the plane $x - y + z = 5$ measured along the line $x = y = z$ is: (1) $3\sqrt{10}$ (2) $10\sqrt{3}$ (3) $\frac{10}{\sqrt{3}}$ (4) $\frac{20}{3}$
Q82 Proof Direct Proof of a Stated Identity or Equality View
The Boolean expression $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$ is equivalent to: (1) $\sim p \wedge q$ (2) $p \wedge q$ (3) $p \vee q$ (4) $p \vee \sim q$
Q83 Proof Direct Proof of a Stated Identity or Equality View
The contrapositive of the following statement, ``If the side of a square doubles, then its area increases four times'', is: (1) If the area of a square increases four times, then its side is not doubled. (2) If the area of a square does not increase four times, then its side is not doubled. (3) If the area of a square does not increase four times, then its side is doubled. (4) If the side of a square is not doubled, then its area does not increase four times.
Q84 Differentiating Transcendental Functions Compute derivative of transcendental function View
For $x \in \mathbb{R}$, $f(x) = |\log 2 - \sin x|$ and $g(x) = f(f(x))$, then: (1) $g'(0) = \cos(\log 2)$ (2) $g'(0) = -\cos(\log 2)$ (3) $g$ is differentiable at $x=0$ and $g'(0) = -\sin(\log 2)$ (4) $g$ is not differentiable at $x=0$
Q85 Small angle approximation View
$\lim_{x \to \pi/2} \frac{\cot x - \cos x}{(\pi - 2x)^3}$ equals: (1) $\frac{1}{24}$ (2) $\frac{1}{16}$ (3) $\frac{1}{8}$ (4) $\frac{1}{4}$
Q86 Tangents, normals and gradients Normal or perpendicular line problems View
Consider $f(x) = \tan^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right)$, $x \in \left(0, \frac{\pi}{2}\right)$. A normal to $y = f(x)$ at $x = \frac{\pi}{6}$ also passes through the point: (1) $(0, 0)$ (2) $\left(0, \frac{2\pi}{3}\right)$ (3) $\left(\frac{\pi}{6}, 0\right)$ (4) $\left(\frac{\pi}{4}, 0\right)$
Q87 Curve Sketching Number of Solutions / Roots via Curve Analysis View
The number of distinct real roots of the equation $x^4 - 4x^3 + 12x^2 + x - 1 = 0$ is: (1) 2 (2) 3 (3) 0 (4) 4
Q88 Solving quadratics and applications Counting solutions or configurations satisfying a quadratic system View
The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x - 60} = 1$ is: (1) 3 (2) $-4$ (3) 6 (4) 5
Q89 Matrices Determinant and Rank Computation View
If $\alpha$, $\beta \neq 0$, and $f(n) = \alpha^n + \beta^n$ and $$\begin{vmatrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4) \end{vmatrix} = K(1-\alpha)^2(1-\beta)^2(\alpha-\beta)^2,$$ then $K$ is equal to: (1) $\alpha\beta$ (2) $\frac{1}{\alpha\beta}$ (3) 1 (4) $-1$
Q90 Permutations & Arrangements Dictionary Order / Rank of a Permutation View
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is: (1) 46th (2) 59th (3) 52nd (4) 58th