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
2023 session2_06apr_shift2

17 maths questions

Q61 Complex Numbers Argand & Loci Solving Complex Equations with Geometric Interpretation View
Let $a \neq b$ be two non-zero real numbers. Then the number of elements in the set $X = \left\{ z \in C : \operatorname{Re}\left(az^{2} + bz\right) = a$ and $\operatorname{Re}\left(bz^{2} + az\right) = b\right\}$ is equal to
(1) 0
(2) 1
(3) 3
(4) 2
Q62 Complex Numbers Argand & Loci Circle Equation and Properties via Complex Number Manipulation View
For $\alpha, \beta, z \in \mathbb{C}$ and $\lambda > 1$, if $\sqrt{\lambda - 1}$ is the radius of the circle $|z - \alpha|^{2} + |z - \beta|^{2} = 2\lambda$, then $|\alpha - \beta|$ is equal to $\_\_\_\_$.
Q63 Permutations & Arrangements Dictionary Order / Rank of a Permutation View
All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is
(1) 576
(2) 578
(3) 580
(4) 582
Q64 Combinations & Selection Selection with Group/Category Constraints View
The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is $\_\_\_\_$.
Q65 Number Theory GCD, LCM, and Coprimality View
If $\operatorname{gcd}(m, n) = 1$ and $1^{2} - 2^{2} + 3^{2} - 4^{2} + \ldots + (2021)^{2} - (2022)^{2} + (2023)^{2} = 1012m^{2}n$ then $m^{2} - n^{2}$ is equal to
(1) 240
(2) 200
(3) 220
(4) 180
Q66 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
If $(20)^{19} + 2(21)(20)^{18} + 3(21)^{2}(20)^{17} + \ldots + 20(21)^{19} = k(20)^{19}$, then $k$ is equal to $\_\_\_\_$.
Q67 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
If the coefficients of $x^{7}$ in $\left(ax^{2} + \frac{1}{2bx}\right)^{11}$ and $x^{-7}$ in $\left(ax - \frac{1}{3bx^{2}}\right)^{11}$ are equal, then
(1) $729ab = 32$
(2) $32ab = 729$
(3) $64ab = 243$
(4) $243ab = 64$
Q68 Proof True/False Justification View
Among the statements: $(S1): 2023^{2022} - 1999^{2022}$ is divisible by 8. $(S2): 13(13)^{n} - 11n - 13$ is divisible by 144 for infinitely many $n \in \mathbb{N}$
(1) Only $(S2)$ is correct
(2) Only $(S1)$ is correct
(3) Both $(S1)$ and $(S2)$ are correct
(4) Both $(S1)$ and $(S2)$ are incorrect
Q69 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
The value of $\tan 9^{\circ} - \tan 27^{\circ} - \tan 63^{\circ} + \tan 81^{\circ}$ is $\_\_\_\_$.
Q70 Circles Area and Geometric Measurement Involving Circles View
If the tangents at the points $P$ and $Q$ on the circle $x^{2} + y^{2} - 2x + y = 5$ meet at the point $R\left(\frac{9}{4}, 2\right)$, then the area of the triangle $PQR$ is
(1) $\frac{5}{4}$
(2) $\frac{13}{8}$
(3) $\frac{5}{8}$
(4) $\frac{13}{4}$
Q71 Conic sections Eccentricity or Asymptote Computation View
Let the eccentricity of an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is reciprocal to that of the hyperbola $2x^{2} - 2y^{2} = 1$. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is $\_\_\_\_$.
Q72 Sequences and series, recurrence and convergence Convergence proof and limit determination View
$\lim_{n \rightarrow \infty} \left\{\left(2^{\frac{1}{2}} - 2^{\frac{1}{3}}\right)\left(2^{\frac{1}{2}} - 2^{\frac{1}{5}}\right) \ldots \left(2^{\frac{1}{2}} - 2^{\frac{1}{2n+1}}\right)\right\}$ is equal to
(1) 1
(2) 0
(3) $\sqrt{2}$
(4) $\frac{1}{\sqrt{2}}$
Q73 Proof True/False Justification View
Among the statements $(S1): (p \Rightarrow q) \vee ((\sim p) \wedge q)$ is a tautology $(S2): (q \Rightarrow p) \Rightarrow ((\sim p) \wedge q)$ is a contradiction
(1) Neither $(S1)$ and $(S2)$ is True
(2) Both $(S1)$ and $(S2)$ are True
(3) Only $(S2)$ is True
(4) Only $(S1)$ is True
Q74 Measures of Location and Spread View
If the mean and variance of the frequency distribution
$x_{i}$246810121416
$f_{i}$44$\alpha$158$\beta$45

are 9 and 15.08 respectively, then the value of $\alpha^{2} + \beta^{2} - \alpha\beta$ is $\_\_\_\_$.
Q75 Circles Circle Identification and Classification View
In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons who speak only English is $\alpha$ and the number of persons who speaks only Hindi is $\beta$, then the eccentricity of the ellipse $25\left(\beta^{2}x^{2} + \alpha^{2}y^{2}\right) = \alpha^{2}\beta^{2}$ is
(1) $\frac{\sqrt{119}}{12}$
(2) $\frac{\sqrt{117}}{12}$
(3) $\frac{3\sqrt{15}}{12}$
(4) $\frac{\sqrt{129}}{12}$
Q76 Matrices Matrix Power Computation and Application View
Let $P$ be a square matrix such that $P^{2} = I - P$. For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $P^{\alpha} + P^{\beta} = \gamma I - 29P$ and $P^{\alpha} - P^{\beta} = \delta I - 13P$, then $\alpha + \beta + \gamma - \delta$ is equal to
(1) 18
(2) 40
(3) 22
(4) 24
Q77 Matrices Linear System and Inverse Existence View
For the system of equations $x + y + z = 6$ $x + 2y + \alpha z = 10$ $x + 3y + 5z = \beta$, which one of the following is NOT true?
(1) System has no solution for $\alpha = 3, \beta = 24$
(2) System has a unique solution for $\alpha = -3, \beta = 14$
(3) System has infinitely many solutions for $\alpha = 3, \beta = 14$
(4) System has a unique solution for $\alpha = 3, \beta = 14$