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
2024 session1_30jan_shift2

29 maths questions

Q61 Complex numbers 2 Existence or counting of roots with specified properties View
If $z$ is a complex number, then the number of common roots of the equation $z^{1985} + z^{100} + 1 = 0$ and $z^3 + 2z^2 + 2z + 1 = 0$, is equal to:
(1) 1
(2) 2
(3) 0
(4) 3
Q62 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
Let $a$ and $b$ be two distinct positive real numbers. Let $11^{\text{th}}$ term of a GP, whose first term is $a$ and third term is $b$, is equal to $p^{\text{th}}$ term of another GP, whose first term is $a$ and fifth term is $b$. Then $p$ is equal to
(1) 20
(2) 25
(3) 21
(4) 24
Q63 Addition & Double Angle Formulae Determine Parameters from Conditions on Coefficients or Terms View
Suppose $28 - p,\ p,\ 70 - \alpha,\ \alpha$ are the coefficient of four consecutive terms in the expansion of $(1 + x)^n$. Then the value of $2\alpha - 3p$ equals
(1) 7
(2) 10
(3) 4
(4) 6
Q64 Straight Lines & Coordinate Geometry Addition/Subtraction Formula Evaluation View
For $\alpha, \beta \in \left(0, \frac{\pi}{2}\right)$ let $3\sin(\alpha + \beta) = 2\sin(\alpha - \beta)$ and a real number $k$ be such that $\tan\alpha = k\tan\beta$. Then the value of $k$ is equal to
(1) $-5$
(2) $5$
(3) $\frac{2}{3}$
(4) $-\frac{2}{3}$
Q65 Circles Determining coefficients from given conditions on function values or geometry View
If $x^2 - y^2 + 2hxy + 2gx + 2fy + c = 0$ is the locus of a point, which moves such that it is always equidistant from the lines $x + 2y + 7 = 0$ and $2x - y + 8 = 0$, then the value of $g + c + h - f$ equals
(1) 14
(2) 6
(3) 8
(4) 29
Q66 Circles Circle Equation Derivation View
Let $A(\alpha, 0)$ and $B(0, \beta)$ be the points on the line $5x + 7y = 50$. Let the point $P$ divide the line segment $AB$ internally in the ratio $7:3$. Let $3x - 25 = 0$ be a directrix of the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ and the corresponding focus be $S$. If from $S$, the perpendicular on the $x$-axis passes through $P$, then the length of the latus rectum of $E$ is equal to
(1) $\frac{25}{3}$
(2) $\frac{32}{9}$
(3) $\frac{25}{9}$
(4) $\frac{32}{5}$
Q67 Conic sections Triangle or Quadrilateral Area and Perimeter with Foci View
Let $P$ be a point on the hyperbola $H: \frac{x^2}{9} - \frac{y^2}{4} = 1$, in the first quadrant such that the area of triangle formed by $P$ and the two foci of $H$ is $2\sqrt{13}$. Then, the square of the distance of $P$ from the origin is
(1) 18
(2) 26
(3) 22
(4) 20
Q68 3x3 Matrices Matrix Algebraic Properties and Abstract Reasoning View
Let $R = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix}$ be a non-zero $3 \times 3$ matrix, where $x\sin\theta = y\sin\left(\theta + \frac{2\pi}{3}\right) = z\sin\left(\theta + \frac{4\pi}{3}\right) \neq 0$, $\theta \in (0, 2\pi)$. For a square matrix $M$, let Trace $M$ denote the sum of all the diagonal entries of $M$. Then, among the statements: I. Trace$(R) = 0$ II. If Trace$(\operatorname{adj}(\operatorname{adj}(R))) = 0$, then $R$ has exactly one non-zero entry.
(1) Both (I) and (II) are true
(2) Only (II) is true
(3) Neither (I) nor (II) is true
(4) Only (I) is true
Q69 Simultaneous equations View
Consider the system of linear equations $x + y + z = 5$, $x + 2y + \lambda^2 z = 9$ and $x + 3y + \lambda z = \mu$, where $\lambda, \mu \in R$. Then, which of the following statement is NOT correct?
(1) System has infinite number of solution if $\lambda = 1$
(2) System is inconsistent if $\lambda = 1$ and $\mu \neq 13$ and $\mu = 13$
(3) System has unique solution if $\lambda \neq 1$ and $\mu \neq 13$
(4) System is consistent if $\lambda \neq 1$ and $\mu = 13$
Q70 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
If the domain of the function $f(x) = \log_e\frac{2x+3}{4x^2+x-3} + \cos^{-1}\frac{2x-1}{x+2}$ is $(\alpha, \beta]$, then the value of $5\beta - 4\alpha$ is equal to
(1) 10
(2) 12
(3) 11
(4) 9
Q71 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
Let $f: R \rightarrow R$ be a function defined $f(x) = \frac{x}{(1 + x^4)^{1/4}}$ and $g(x) = f(f(f(f(x))))$, then $18\int_0^{\sqrt{2\sqrt{5}}} x^2 g(x)\, dx$
(1) 33
(2) 36
(3) 42
(4) 39
Q72 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
Let $a$ and $b$ be real constants such that the function $f$ defined by $$f(x) = \begin{cases} x^2 + 3x + a, & x \leq 1 \\ bx + 2, & x > 1 \end{cases}$$ be differentiable on $R$. Then, the value of $\int_{-2}^{2} f(x)\, dx$ equals
(1) $\frac{15}{6}$
(2) $\frac{19}{6}$
(3) 21
(4) 17
Q73 Stationary points and optimisation Recover a Function from a Composition or Functional Equation View
Let $f: R - \{0\} \rightarrow R$ be a function satisfying $f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)}$ for all $x, y$, $f(y) \neq 0$. If $f'(1) = 2024$, then
(1) $xf'(x) - 2024f(x) = 0$
(2) $xf'(x) + 2024f(x) = 0$
(3) $xf'(x) + f(x) = 2024$
(4) $xf'(x) - 2023f(x) = 0$
Q74 Applied differentiation Find absolute extrema on a closed interval or domain View
Let $f(x) = (x+3)^2(x-2)^3$, $x \in [-4, 4]$. If $M$ and $m$ are the maximum and minimum values of $f$, respectively in $[-4, 4]$, then the value of $M - m$ is:
(1) 600
(2) 392
(3) 608
(4) 108
Q75 Indefinite & Definite Integrals Substitution to Evaluate a Definite Integral (Numerical Answer) View
Let $y = f(x)$ be a thrice differentiable function on $(-5, 5)$. Let the tangents to the curve $y = f(x)$ at $(1, f(1))$ and $(3, f(3))$ make angles $\frac{\pi}{6}$ and $\frac{\pi}{4}$, respectively with positive $x$-axis. If $27\int_1^3 \left(f'(t)\right)^2 + 1\right) f''(t)\, dt = \alpha + \beta\sqrt{3}$ where $\alpha, \beta$ are integers, then the value of $\alpha + \beta$ equals
(1) $-14$
(2) 26
(3) $-16$
(4) 36
Q76 Indefinite & Definite Integrals Parameter Determination from Conditions View
Let $f: R \rightarrow R$ be defined $f(x) = ae^{2x} + be^x + cx$. If $f(0) = -1$, $f'(\log_e 2) = 21$ and $\int_0^{\log 4} (f(x) - cx)\, dx = \frac{39}{2}$, then the value of $|a + b + c|$ equals:
(1) 16
(2) 10
(3) 12
(4) 8
Q77 Vectors 3D & Lines Magnitude of Vector Expression View
Let $\vec{a} = \hat{i} + \alpha\hat{j} + \beta\hat{k}$, $\alpha, \beta \in R$. Let a vector $\vec{b}$ be such that the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$ and $|\vec{b}|^2 = 6$. If $\vec{a} \cdot \vec{b} = 3\sqrt{2}$, then the value of $(\alpha^2 + \beta^2)|\vec{a} \times \vec{b}|^2$ is equal to
(1) 90
(2) 75
(3) 95
(4) 85
Q78 Vectors 3D & Lines Magnitude of Vector Expression View
Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{b}| = 1$ and $|\vec{b} \times \vec{a}| = 2$. Then $|(\vec{b} \times \vec{a}) - \vec{b}|^2$ is equal to
(1) 3
(2) 5
(3) 1
(4) 4
Q79 Vectors 3D & Lines MCQ: Point Membership on a Line View
Let $L_1: \vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \lambda(\hat{i} - \hat{j} + 2\hat{k})$, $\lambda \in R$, $L_2: \vec{r} = (\hat{j} - \hat{k}) + \mu(3\hat{i} + \hat{j} + p\hat{k})$, $\mu \in R$ and $L_3: \vec{r} = \delta(l\hat{i} + m\hat{j} + n\hat{k})$, $\delta \in R$ be three lines such that $L_1$ is perpendicular to $L_2$ and $L_3$ is perpendicular to both $L_1$ and $L_2$. Then the point which lies on $L_3$ is
(1) $(-1, 7, 4)$
(2) $(-1, -7, 4)$
(3) $(1, 7, -4)$
(4) $(1, -7, 4)$
Q80 Conditional Probability Bayes' Theorem with Production/Source Identification View
Bag $A$ contains 3 white, 7 red balls and bag $B$ contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag $A$, if the ball drawn is white, is:
(1) $\frac{1}{4}$
(2) $\frac{1}{9}$
(3) $\frac{1}{3}$
(4) $\frac{3}{10}$
Q81 Sign Change & Interval Methods View
The number of real solutions of the equation $x\left(x^2 + 3|x| + 5|x-1| + 6|x-2|\right) = 0$ is $\underline{\hspace{1cm}}$.
Q82 Combinations & Selection Selection with Group/Category Constraints View
In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A, B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is $\underline{\hspace{1cm}}$.
Q83 Arithmetic Sequences and Series Evaluate a Summation Involving Binomial Coefficients View
Let $S_n$ be the sum to $n$-terms of an arithmetic progression $3, 7, 11, \ldots$, if $40 < \frac{6}{n(n+1)}\sum_{k=1}^{n} S_k < 42$, then $n$ equals $\underline{\hspace{1cm}}$.
Q84 Circles Infinite Series or Sequences Involving Circles View
Let $\alpha = \sum_{k=0}^{n} \frac{\binom{n}{k}^2}{k+1}$ and $\beta = \sum_{k=0}^{n-1} \frac{\binom{n}{k}\binom{n}{k+1}}{k+2}$. If $5\alpha = 6\beta$, then $n$ equals $\underline{\hspace{1cm}}$.
Q85 Measures of Location and Spread Chord Length and Chord Properties View
Consider two circles $C_1: x^2 + y^2 = 25$ and $C_2: (x - \alpha)^2 + y^2 = 16$, where $\alpha \in (5, 9)$. Let the angle between the two radii (one to each circle) drawn from one of the intersection points of $C_1$ and $C_2$ be $\sin^{-1}\frac{\sqrt{63}}{8}$. If the length of common chord of $C_1$ and $C_2$ is $\beta$, then the value of $(\alpha\beta)^2$ equals $\underline{\hspace{1cm}}$.
Q86 Measures of Location and Spread View
If the variance $\sigma^2$ of the data $$\begin{array}{cccccccc} x_i & 0 & 1 & 5 & 6 & 10 & 12 & 17 \\ f_i & 3 & 2 & 3 & 2 & 6 & 3 & 3 \end{array}$$ is $k$, then the value of $\lfloor k \rfloor$ is $\underline{\hspace{1cm}}$ (where $\lfloor \cdot \rfloor$ denotes the greatest integer function).
Q88 Areas by integration View
The area of the region enclosed by the parabola $(y-2)^2 = x - 1$, the line $x - 2y + 4 = 0$ and the positive coordinate axes is $\underline{\hspace{1cm}}$.
Q89 Differential equations Finding a DE from a Limit or Implicit Condition View
Let $Y = Y(X)$ be a curve lying in the first quadrant such that the area enclosed by the line $Y - y = Y'(x)(X - x)$ and the coordinate axes, where $(x, y)$ is any point on the curve, is always $\frac{-y^2}{2Y'(x)} + 1$, $Y'(x) \neq 0$. If $Y(1) = 1$, then $12\,Y(2)$ equals $\underline{\hspace{1cm}}$.
Q90 Vectors: Lines & Planes Multi-Part 3D Geometry Problem View
Let a line passing through the point $(-1, 2, 3)$ intersect the lines $L_1: \frac{x-1}{3} = \frac{y-2}{2} = \frac{z+1}{-2}$ at $M(\alpha, \beta, \gamma)$ and $L_2: \frac{x+2}{-3} = \frac{y-2}{-2} = \frac{z-1}{4}$ at $N(a, b, c)$. Then the value of $\frac{(\alpha + \beta + \gamma)^2}{(a + b + c)^2}$ equals $\underline{\hspace{1cm}}$.