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
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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 09apr

14 maths questions

Q4 Forces, equilibrium and resultants View
A uniform sphere of weight $W$ and radius 5 cm is being held by a string as shown in the figure. The tension in the string will be :
(1) $12 \frac { \mathrm {~W} } { 5 }$
(2) $5 \frac { \mathrm {~W} } { 12 }$
(3) $13 \frac { \mathrm {~W} } { 5 }$
(4) $13 \frac { \mathrm {~W} } { 12 }$
Q11 Simple Harmonic Motion View
Two simple pendulums of length 1 m and 4 m respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed number of oscillations equal to:
(1) 2
(2) 7
(3) 5
(4) 3
Q61 Discriminant and conditions for roots Parameter range for specific root conditions (location/count) View
The values of ' $a$ ' for which one root of the equation $x ^ { 2 } - ( a + 1 ) x + a ^ { 2 } + a - 8 = 0$ exceeds 2 and the other is lesser than 2 , are given by :
(1) $3 < a < 10$
(2) $a \geq 10$
(3) $- 2 < a < 3$
(4) $a \leq - 2$
Q62 Complex Numbers Arithmetic Modulus Computation View
If $Z _ { 1 } \neq 0$ and $Z _ { 2 }$ be two complex numbers such that $\frac { Z _ { 2 } } { Z _ { 1 } }$ is a purely imaginary number, then $\left| \frac { 2 Z _ { 1 } + 3 Z _ { 2 } } { 2 Z _ { 1 } - 3 Z _ { 2 } } \right|$ is equal to:
(1) 2
(2) 5
(3) 3
(4) 1
Q63 Combinations & Selection Selection with Group/Category Constraints View
A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :
(1) 40
(2) 41
(3) 16
(4) 32
Q64 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
Let $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$ be an A.P, such that $\frac { a _ { 1 } + a _ { 2 } + \ldots + a _ { p } } { a _ { 1 } + a _ { 2 } + a _ { 3 } + \ldots + a _ { q } } = \frac { p ^ { 3 } } { q ^ { 3 } } ; p \neq q$. Then $\frac { a _ { 6 } } { a _ { 21 } }$ is equal to:
(1) $\frac { 41 } { 11 }$
(2) $\frac { 31 } { 121 }$
(3) $\frac { 11 } { 41 }$
(4) $\frac { 121 } { 1861 }$
Q65 Sequences and Series Evaluation of a Finite or Infinite Sum View
The sum of the series: $1 + \frac { 1 } { 1 + 2 } + \frac { 1 } { 1 + 2 + 3 } + \ldots\ldots$. upto 10 terms, is:
(1) $\frac { 18 } { 11 }$
(2) $\frac { 22 } { 13 }$
(3) $\frac { 20 } { 11 }$
(4) $\frac { 16 } { 9 }$
Q66 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
The ratio of the coefficient of $x ^ { 15 }$ to the term independent of $x$ in the expansion of $\left( x ^ { 2 } + \frac { 2 } { x } \right) ^ { 15 }$ is:
(1) $7 : 16$
(2) $7 : 64$
(3) $1 : 4$
(4) $1 : 32$
Q67 Reciprocal Trig & Identities View
A value of $x$ for which $\sin \left( \cot ^ { - 1 } ( 1 + x ) \right) = \cos \left( \tan ^ { - 1 } x \right)$, is :
(1) $- \frac { 1 } { 2 }$
(2) 1
(3) 0
(4) $\frac { 1 } { 2 }$
Q68 Straight Lines & Coordinate Geometry Reflection and Image in a Line View
A light ray emerging from the point source placed at $\mathrm { P } ( 1,3 )$ is reflected at a point Q in the axis of $x$. If the reflected ray passes through the point $R ( 6,7 )$, then the abscissa of $Q$ is:
(1) 1
(2) 3
(3) $\frac { 7 } { 2 }$
(4) $\frac { 5 } { 2 }$
Q69 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
If the three lines $x - 3 y = p , a x + 2 y = q$ and $a x + y = r$ form a right-angled triangle then :
(1) $a ^ { 2 } - 9 a + 18 = 0$
(2) $a ^ { 2 } - 6 a - 12 = 0$
(3) $a ^ { 2 } - 6 a - 18 = 0$
(4) $a ^ { 2 } - 9 a + 12 = 0$
Q70 Circles Circle Equation Derivation View
If each of the lines $5 x + 8 y = 13$ and $4 x - y = 3$ contains a diameter of the circle $x ^ { 2 } + y ^ { 2 } - 2 \left( a ^ { 2 } - 7 a + 11 \right) x - 2 \left( a ^ { 2 } - 6 a + 6 \right) y + b ^ { 3 } + 1 = 0$, then :
(1) $a = 5$ and $b \notin ( - 1,1 )$
(2) $a = 1$ and $b \notin ( - 1,1 )$
(3) $a = 2$ and $b \notin ( - \infty , 1 )$
(4) $a = 5$ and $b \in ( - \infty , 1 )$
Q71 Differential equations Higher-Order and Special DEs (Proof/Theory) View
Statement-1: The slope of the tangent at any point P on a parabola, whose axis is the axis of $x$ and vertex is at the origin, is inversely proportional to the ordinate of the point P. Statement-2: The system of parabolas $y ^ { 2 } = 4 a x$ satisfies a differential equation of degree 1 and order 1.
(1) Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.
(2) Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for statement-1.
(3) Statement-1 is true; Statement-2 is false.
(4) Statement-1 is false; Statement-2 is true.
Q72 Conic sections Fixed Point or Collinearity Proof for Line through Conic View
Equation of the line passing through the points of intersection of the parabola $x ^ { 2 } = 8 y$ and the ellipse $\frac { x ^ { 2 } } { 3 } + y ^ { 2 } = 1$ is :
(1) $y - 3 = 0$
(2) $y + 3 = 0$
(3) $3 y + 1 = 0$
(4) $3 y - 1 = 0$