jee-main

Papers (169)
2025
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2024
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2023
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2022
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2021
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2020
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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
2013 25apr

13 maths questions

Q2 Projectiles Projectile from a Non-Inertial or Moving Frame View
The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $R _ { 0 } = 40 \mathrm {~m}$. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $\mathrm { v } = 20 \mathrm {~m} / \mathrm { s }$ on a horizontal surface? $\left( \mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 } \right)$
(1) $30 ^ { \circ }$
(2) $60 ^ { \circ }$
(3) $75 ^ { \circ }$
(4) $45 ^ { \circ }$
Q5 Newton's laws and connected particles Atwood machine and pulley systems View
Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $\mathrm { M } = 2 \mathrm {~m}$, then the stress produced in the wire is:
(1) $\frac { 2 \mathrm { mg } } { 3 \mathrm {~A} }$
(2) $\frac { 4 \mathrm { mg } } { 3 \mathrm {~A} }$
(3) $\frac { \mathrm { mg } } { \mathrm { A } }$
(4) $\frac { 3 \mathrm { mg } } { 4 \mathrm {~A} }$
Q10 Simple Harmonic Motion View
A uniform cylinder of length L and mass $M$ having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be:
(1) Smaller than $2\pi \left[ \frac { M } { ( k + A\sigma g ) } \right] ^ { 1/2 }$
(2) $2\pi \sqrt { \frac { M } { k } }$
(3) Larger than $2\pi \left[ \frac { M } { ( k + A\sigma g ) } \right] ^ { 1/2 }$
(4) $2\pi \left[ \frac { M } { ( k + A\sigma g ) } \right] ^ { 1/2 }$
Q61 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
If $p$ and $q$ are non-zero real numbers and $\alpha ^ { 3 } + \beta ^ { 3 } = - p , \alpha \beta = q$, then a quadratic equation whose roots are $\frac { \alpha ^ { 2 } } { \beta } , \frac { \beta ^ { 2 } } { \alpha }$ is :
(1) $p x ^ { 2 } - q x + p ^ { 2 } = 0$
(2) $q x ^ { 2 } + p x + q ^ { 2 } = 0$
(3) $p x ^ { 2 } + q x + p ^ { 2 } = 0$
(4) $q x ^ { 2 } - p x + q ^ { 2 } = 0$
Q62 Complex Numbers Argand & Loci True/False or Multiple-Statement Verification View
Let $z$ satisfy $| z | = 1$ and $z = 1 - \bar { z }$. Statement $1 : z$ is a real number. Statement 2 : Principal argument of z is $\frac { \pi } { 3 }$
(1) Statement 1 is true Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
(2) Statement 1 is false; Statement 2 is true.
(3) Statement 1 is true, Statement 2 is false.
(4) Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
Q63 Permutations & Arrangements Forming Numbers with Digit Constraints View
5-digit numbers are to be formed using $2,3,5,7,9$ without repeating the digits. If $p$ be the number of such numbers that exceed 20000 and $q$ be the number of those that lie between 30000 and 90000, then $p : q$ is:
(1) $6 : 5$
(2) $3 : 2$
(3) $4 : 3$
(4) $5 : 3$
Q64 Geometric Sequences and Series Arithmetic-Geometric Sequence Interplay View
Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common difference six. If first and last terms of this sequence are equal, then the last term is:
(1) 16
(2) 8
(3) 4
(4) 2
Q65 Sequences and Series Evaluation of a Finite or Infinite Sum View
The value of $1^{2} + 3^{2} + 5^{2} + \cdots + 25^{2}$ is:
(1) 2925
(2) 1469
(3) 1728
(4) 1456
Q66 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
If for positive integers $r > 1 , n > 2$, the coefficients of the $( 3r ) ^ { \text {th} }$ and $( r + 2 ) ^ { \text {th} }$ powers of $x$ in the expansion of $( 1 + x ) ^ { 2n }$ are equal, then $n$ is equal to:
(1) $2r + 1$
(2) $2r - 1$
(3) $3r$
(4) $r + 1$
Q67 Standard trigonometric equations Trigonometric equation with algebraic or logarithmic coupling View
Let $\mathrm { A } = \{ \theta : \sin ( \theta ) = \tan ( \theta ) \}$ and $\mathrm { B } = \{ \theta : \cos ( \theta ) = 1 \}$ be two sets. Then:
(1) $\mathrm { A } = \mathrm { B }$
(2) $A \not\subset B$
(3) $B \not\subset A$
(4) $A \subset B$ and $B - A \neq \phi$
Q68 Straight Lines & Coordinate Geometry Reflection and Image in a Line View
If the image of point $\mathrm { P } ( 2,3 )$ in a line L is $\mathrm { Q } ( 4,5 )$, then the image of point $\mathrm { R } ( 0,0 )$ in the same line is:
(1) $( 2,2 )$
(2) $( 4,5 )$
(3) $( 3,4 )$
(4) $( 7,7 )$
Q69 Reciprocal Trig & Identities View
Let $x \in ( 0,1 )$. The set of all $x$ such that $\sin ^ { -1 } x > \cos ^ { -1 } x$, is the interval:
(1) $\left( \frac { 1 } { 2 } , \frac { 1 } { \sqrt { 2 } } \right)$
(2) $\left( \frac { 1 } { \sqrt { 2 } } , 1 \right)$
(3) $( 0,1 )$
(4) $\left( 0 , \frac { \sqrt { 3 } } { 2 } \right)$
Q70 Circles Circle Equation Derivation View
Statement 1: The only circle having radius $\sqrt { 10 }$ and a diameter along line $2x + y = 5$ is $x ^ { 2 } + y ^ { 2 } - 6x + 2y = 0$. Statement 2: $2x + y = 5$ is a normal to the circle $x ^ { 2 } + y ^ { 2 } - 6x + 2y = 0$.
(1) Statement 1 is false; Statement 2 is true.
(2) Statement 1 is true; Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(3) Statement 1 is true; Statement 2 is false.
(4) Statement 1 is true; Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.