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_02sep_shift1

19 maths questions

Q51 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
Let $\alpha$ and $\beta$ be the roots of the equation, $5x^{2} + 6x - 2 = 0$. If $S_{n} = \alpha^{n} + \beta^{n}, n = 1,2,3,\ldots$, then
(1) $6S_{6} + 5S_{5} = 2S_{4}$
(2) $5S_{6} + 6S_{5} + 2S_{4} = 0$
(3) $5S_{6} + 6S_{5} = 2S_{4}$
(4) $6S_{6} + 5S_{5} + 2S_{4} = 0$
Q52 Complex Numbers Arithmetic Trigonometric/Polar Form and De Moivre's Theorem View
The value of $\left( \frac{1 + \sin\frac{2\pi}{9} + i\cos\frac{2\pi}{9}}{1 + \sin\frac{2\pi}{9} - i\cos\frac{2\pi}{9}} \right)^{3}$ is
(1) $\frac{1}{2}(1 - i\sqrt{3})$
(2) $\frac{1}{2}(\sqrt{3} - i)$
(3) $-\frac{1}{2}(\sqrt{3} - i)$
(4) $-\frac{1}{2}(1 - i\sqrt{3})$
Q53 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
The sum of the first three terms of G.P is $S$ and their products is 27. Then all such $S$ lie in
(1) $(-\infty, -9] \cup [3, \infty)$
(2) $[-3, \infty)$
(3) $(-\infty, -3] \cup [9, \infty)$
(4) $(-\infty, 9]$
Q54 Geometric Sequences and Series Sum of an Infinite Geometric Series (Direct Computation) View
If $|x| < 1, |y| < 1$ and $x \neq 1$, then the sum to infinity of the following series $(x + y) + (x^{2} + xy + y^{2}) + (x^{3} + x^{2}y + xy^{2} + y^{3}) + \ldots$ is
(1) $\frac{x + y - xy}{(1 + x)(1 + y)}$
(2) $\frac{x + y + xy}{(1 + x)(1 + y)}$
(3) $\frac{x + y - xy}{(1 - x)(1 - y)}$
(4) $\frac{x + y + xy}{(1 - x)(1 - y)}$
Q55 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
Let $\alpha > 0, \beta > 0$ be such that $\alpha^{3} + \beta^{2} = 4$. If the maximum value of the term independent of $x$ in the binomial expansion of $\left(\alpha x^{\frac{1}{9}} + \beta x^{-\frac{1}{6}}\right)^{10}$ is $10k$, then $k$ is equal to
(1) 336
(2) 352
(3) 84
(4) 176
Q56 Conic sections Tangent and Normal Line Problems View
A line parallel to the straight line $2x - y = 0$ is tangent to the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{2} = 1$ at the point $(x_{1}, y_{1})$. Then $x_{1}^{2} + 5y_{1}^{2}$ is equal to
(1) 6
(2) 8
(3) 10
(4) 5
Q57 Proof Direct Proof of a Stated Identity or Equality View
The contrapositive of the statement ``If I reach the station in time, then I will catch the train'' is
(1) If I do not reach the station in time, then I will catch the train.
(2) If I do not reach the station in time, then I will not catch the train.
(3) If I will catch the train, then I reach the station in time.
(4) If I will not catch the train, then I do not reach the station in time.
Q58 Measures of Location and Spread View
Let $X = \{x \in N : 1 \leq x \leq 17\}$ and $Y = \{ax + b : x \in X$ and $a, b \in R, a > 0\}$. If mean and variance of elements of $Y$ are 17 and 216 respectively then $a + b$ is equal to
(1) 7
(2) $-7$
(3) $-27$
(4) 9
Q59 Composite & Inverse Functions Find or Apply an Inverse Function Formula View
If $R = \{(x, y) : x, y \in Z, x^{2} + 3y^{2} \leq 8\}$ is a relation on the set of integers $Z$, then the domain of $R^{-1}$ is
(1) $\{-2, -1, 1, 2\}$
(2) $\{0, 1\}$
(3) $\{-2, -1, 0, 1, 2\}$
(4) $\{-1, 0, 1\}$
Q60 Matrices True/False or Multiple-Select Conceptual Reasoning View
Let $A$ be a $2 \times 2$ real matrix with entries from $\{0, 1\}$ and $|A| \neq 0$. Consider the following two statements: $(P)$ If $A \neq I_{2}$, then $|A| = -1$ $(Q)$ If $|A| = 1$, then $\operatorname{tr}(A) = 2$ Where $I_{2}$ denotes $2 \times 2$ identity matrix and $\operatorname{tr}(A)$ denotes the sum of the diagonal entries of $A$. Then
(1) $(P)$ is false and $(Q)$ is true
(2) Both $(P)$ and $(Q)$ are false
(3) $(P)$ is true and $(Q)$ is false
(4) Both $(P)$ and $(Q)$ are true
Q61 Matrices Linear System and Inverse Existence View
Let $S$ be the set of all $\lambda \in R$ for which the system of linear equations $$2x - y + 2z = 2$$ $$x - 2y + \lambda z = -4$$ $$x + \lambda y + z = 4$$ has no solution. Then the set $S$
(1) Contains more than two elements
(2) Is an empty set
(3) Is a singleton
(4) Contains exactly two elements
Q62 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
The domain of the function $f(x) = \sin^{-1}\left(\frac{|x| + 5}{x^{2} + 1}\right)$ is $(-\infty, -a] \cup [a, \infty)$, then $a$ is equal to
(1) $\frac{\sqrt{17}}{2}$
(2) $\frac{\sqrt{17} - 1}{2}$
(3) $\frac{1 + \sqrt{17}}{2}$
(4) $\frac{\sqrt{17}}{2} + 1$
Q63 Differentiating Transcendental Functions Determine parameters from function or curve conditions View
If a function $f(x)$ defined by $$f(x) = \begin{cases} ae^{x} + be^{-x}, & -1 \leq x < 1 \\ cx^{2}, & 1 \leq x \leq 3 \\ ax^{2} + 2cx, & 3 < x \leq 4 \end{cases}$$ be continuous for some $a, b, c \in R$ and $f'(0) + f'(2) = e$, then the value of $a$ is
(1) $\frac{1}{e^{2} - 3e + 13}$
(2) $\frac{e}{e^{2} - 3e - 13}$
(3) $\frac{e}{e^{2} + 3e + 13}$
(4) $\frac{e}{e^{2} - 3e + 13}$
Q64 Tangents, normals and gradients Find tangent line with a specified slope or from an external point View
If the tangent to the curve $y = x + \sin y$ at a point $(a, b)$ is parallel to the line joining $\left(0, \frac{3}{2}\right)$ and $\left(\frac{1}{2}, 2\right)$, then
(1) $b = a$
(2) $|b - a| = 1$
(3) $|a + b| = 1$
(4) $b = \frac{\pi}{2} + a$
Q65 Stationary points and optimisation Determine parameters from given extremum conditions View
If $p(x)$ be a polynomial of degree three that has a local maximum value 8 at $x = 1$ and a local minimum value 4 at $x = 2$ then $p(0)$ is equal to
(1) 6
(2) $-12$
(3) 24
(4) 12
Q66 Tangents, normals and gradients Normal or perpendicular line problems View
Let $P(h, k)$ be a point on the curve $y = x^{2} + 7x + 2$, nearest to the line, $y = 3x - 3$. Then the equation of the normal to the curve at $P$ is
(1) $x + 3y + 26 = 0$
(2) $x + 3y - 62 = 0$
(3) $x - 3y - 11 = 0$
(4) $x - 3y + 22 = 0$
Q67 Areas Between Curves Area Involving Conic Sections or Circles View
Area (in sq. units) of the region outside $\frac{|x|}{2} + \frac{|y|}{3} = 1$ and inside the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$ is
(1) $6(\pi - 2)$
(2) $3(\pi - 2)$
(3) $3(4 - \pi)$
(4) $6(4 - \pi)$
Q68 Differential equations Solving Separable DEs with Initial Conditions View
Let $y = y(x)$ be the solution of the differential equation, $\frac{2 + \sin x}{y + 1} \cdot \frac{dy}{dx} = -\cos x, y > 0, y(0) = 1$. If $y(\pi) = a$ and $\frac{dy}{dx}$ at $x = \pi$ is $b$, then the ordered pair $(a, b)$ is equal to
(1) $\left(2, \frac{3}{2}\right)$
(2) $(1, -1)$
(3) $(1, 1)$
(4) $(2, 1)$
Q69 Vectors: Lines & Planes Find Cartesian Equation of a Plane View
The plane passing through the points $(1, 2, 1)$, $(2, 1, 2)$ and parallel to the line, $2x = 3y, z = 1$ also passes through the point
(1) $(0, 6, -2)$
(2) $(-2, 0, 1)$
(3) $(0, -6, 2)$
(4) $(2, 0, -1)$