jee-main

Papers (169)
2025
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2024
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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_03sep_shift1

21 maths questions

Q21 Work done and energy Work-energy applied to launching or projecting objects View
A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of $F$ (in N) is $\left( g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 } \right)$
Q51 Discriminant and conditions for roots Parameter range for specific root conditions (location/count) View
Consider the two sets: $A = \left\{ m \in R : \right.$ both the roots of $x ^ { 2 } - ( m + 1 ) x + m + 4 = 0$ are real $\}$ and $B = [ - 3,5 )$
Which of the following is not true?
(1) $A - B = ( - \infty , - 3 ) \cup ( 5 , \infty )$
(2) $A \cap B = \{ - 3 \}$
(3) $B - A = ( - 3,5 )$
(4) $A \cup B = R$
Q52 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
If $\alpha$ and $\beta$ are the roots of the equation $x ^ { 2 } + p x + 2 = 0$ and $\frac { 1 } { \alpha }$ and $\frac { 1 } { \beta }$ are the roots of the equation $2 x ^ { 2 } + 2 q x + 1 = 0$, then $\left( \alpha - \frac { 1 } { \alpha } \right) \left( \beta - \frac { 1 } { \beta } \right) \left( \alpha + \frac { 1 } { \beta } \right) \left( \beta + \frac { 1 } { \alpha } \right)$ is equal to:
(1) $\frac { 9 } { 4 } \left( 9 + q ^ { 2 } \right)$
(2) $\frac { 9 } { 4 } \left( 9 - q ^ { 2 } \right)$
(3) $\frac { 9 } { 4 } \left( 9 + p ^ { 2 } \right)$
(4) $\frac { 9 } { 4 } \left( 9 - p ^ { 2 } \right)$
Q53 Arithmetic Sequences and Series Find Common Difference from Given Conditions View
If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is
(1) $\frac { 1 } { 6 }$
(2) $\frac { 1 } { 5 }$
(3) $\frac { 1 } { 4 }$
(4) $\frac { 1 } { 7 }$
Q54 Permutations & Arrangements Factorial and Combinatorial Expression Simplification View
The value of $\left( 2 \cdot { } ^ { 1 } P _ { 0 } - 3 \cdot { } ^ { 2 } P _ { 1 } + 4 \cdot { } ^ { 3 } P _ { 2 } - \right.$ up to $51 ^ { \text {th} }$ term $) + ( 1 ! - 2 ! + 3 ! -$ up to $51 ^ { \text {th} }$ term) is equal to
(1) $1 - 51 ( 51 )$ !
(2) $1 + ( 51 )$ !
(3) $1 + ( 52 )$ !
(4) 1
Q55 Binomial Theorem (positive integer n) Count Integral or Rational Terms in a Binomial Expansion View
If the number of integral terms in the expansion of $\left( 3 ^ { \frac { 1 } { 2 } } + 5 ^ { \frac { 1 } { 8 } } \right) ^ { n }$ is exactly 33, then the least value of $n$ is
(1) 264
(2) 128
(3) 256
(4) 248
Q56 Conic sections Chord Properties and Midpoint Problems View
Let P be a point on the parabola, $y ^ { 2 } = 12 x$ and N be the foot of the perpendicular drawn from $P$, on the axis of the parabola. A line is now drawn through the mid-point $M$ of $P N$, parallel to its axis which meets the parabola at $Q$. If the $y$-intercept of the line NQ is $\frac { 4 } { 3 }$, then:
(1) $P N = 4$
(2) $M Q = \frac { 1 } { 3 }$
(3) $M Q = \frac { 1 } { 4 }$
(4) $P N = 3$
Q57 Conic sections Equation Determination from Geometric Conditions View
A hyperbola having the transverse axis of length, $\sqrt { 2 }$ has the same foci as that of the ellipse, $3 x ^ { 2 } + 4 y ^ { 2 } = 12$ then this hyperbola does not pass through which of the following points?
(1) $\left( \frac { 1 } { \sqrt { 2 } } , 0 \right)$
(2) $\left( - \sqrt { \frac { 3 } { 2 } } , 1 \right)$
(3) $\left( 1 , - \frac { 1 } { \sqrt { 2 } } \right)$
(4) $\left( \sqrt { \frac { 3 } { 2 } } , \frac { 1 } { \sqrt { 2 } } \right)$
Q58 Curve Sketching Limit Computation from Algebraic Expressions View
Let $[ t ]$ denote the greatest integer $\leq t$. If $\lambda \varepsilon R - \{ 0,1 \} , \quad \lim _ { x \rightarrow 0 } \left| \frac { 1 - x + | x | } { \lambda - x + [ x ] } \right| = L$, then $L$ is equal to
(1) 1
(2) 2
(3) $\frac { 1 } { 2 }$
(4) 0
Q59 Proof Direct Proof of a Stated Identity or Equality View
The proposition $p \rightarrow \sim ( p \wedge \sim q )$ is equivalent to:
(1) $q$
(2) $( \sim p ) \vee q$
(3) $( \sim p ) \wedge q$
(4) $( \sim p ) \vee ( \sim q )$
Q60 Measures of Location and Spread View
For the frequency distribution: Variate $( x ) : x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots , x _ { 15 }$ Frequency $( f ) : f _ { 1 } , f _ { 2 } , f _ { 3 } , \ldots , f _ { 15 }$ where $0 < x _ { 1 } < x _ { 2 } < x _ { 3 } < \ldots < x _ { 15 } = 10$ and $\sum _ { i = 1 } ^ { 15 } f _ { i } > 0$, the standard deviation cannot be
(1) 4
(2) 1
(3) 6
(4) 2
Q61 Matrices Determinant and Rank Computation View
If $\Delta = \left| \begin{array} { c c c } x - 2 & 2 x - 3 & 3 x - 4 \\ 2 x - 3 & 3 x - 4 & 4 x - 5 \\ 3 x - 5 & 5 x - 8 & 10 x - 17 \end{array} \right| = A x ^ { 3 } + B x ^ { 2 } + C x + D$, then $B + C$ is equal to:
(1) $- 1$
(2) $1$
(3) $- 3$
(4) $9$
Q62 Addition & Double Angle Formulae Addition/Subtraction Formula Evaluation View
$2 \pi - \left( \sin ^ { - 1 } \frac { 4 } { 5 } + \sin ^ { - 1 } \frac { 5 } { 13 } + \sin ^ { - 1 } \frac { 16 } { 65 } \right)$ is equal to:
(1) $\frac { \pi } { 2 }$
(2) $\frac { 5 \pi } { 4 }$
(3) $\frac { 3 \pi } { 2 }$
(4) $\frac { 7 \pi } { 4 }$
Q63 Implicit equations and differentiation Second derivative via implicit differentiation View
If $y ^ { 2 } + \log _ { e } \left( \cos ^ { 2 } x \right) = y , \quad x \in \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ then:
(1) $y \prime \prime ( 0 ) = 0$
(2) $| y \prime ( 0 ) | + | y \prime \prime ( 0 ) | = 1$
(3) $| y \prime \prime ( 0 ) | = 2$
(4) $| y \prime ( 0 ) | + | y \prime \prime ( 0 ) | = 3$
Q64 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions View
The function, $f ( x ) = ( 3 x - 7 ) x ^ { \frac { 2 } { 3 } } , x \in \mathrm { R }$, is increasing for all $x$ lying in
(1) $( - \infty , 0 ) \cup \left( \frac { 14 } { 15 } , \infty \right)$
(2) $( - \infty , 0 ) \cup \left( \frac { 3 } { 7 } , \infty \right)$
(3) $\left( - \infty , \frac { 14 } { 15 } \right)$
(4) $\left( - \infty , - \frac { 14 } { 15 } \right) \cup ( 0 , \infty )$
Q65 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View
$\int _ { - \pi } ^ { \pi } | \pi - | \mathrm { x } | | \mathrm { d } x$ is equal to
(1) $\sqrt { 2 } \pi ^ { 2 }$
(2) $2 \pi ^ { 2 }$
(3) $\pi ^ { 2 }$
(4) $\frac { \pi ^ { 2 } } { 2 }$
Q66 Areas Between Curves Area Between Curves with Parametric or Implicit Region Definition View
The area (in sq. units) of the region $\left\{ ( x , y ) : 0 \leq y \leq x ^ { 2 } + 1,0 \leq y \leq x + 1 , \frac { 1 } { 2 } \leq x \leq 2 \right\}$ is
(1) $\frac { 23 } { 16 }$
(2) $\frac { 79 } { 24 }$
(3) $\frac { 79 } { 16 }$
(4) $\frac { 23 } { 6 }$
Q67 Differential equations Solving Separable DEs with Initial Conditions View
The solution curve of the differential equation, $\left( 1 + e ^ { - x } \right) \left( 1 + y ^ { 2 } \right) \frac { d y } { d x } = y ^ { 2 }$ which passes through the point $( 0,1 )$, is
(1) $y ^ { 2 } + 1 = y \left( \log _ { e } \left( \frac { 1 + e ^ { - x } } { 2 } \right) + 2 \right)$
(2) $y ^ { 2 } + 1 = y \left( \log _ { e } \left( \frac { 1 + e ^ { x } } { 2 } \right) + 2 \right)$
(3) $y ^ { 2 } = 1 + y \log _ { e } \left( \frac { 1 + e ^ { x } } { 2 } \right)$
(4) $y ^ { 2 } = 1 + y \log _ { e } \left( \frac { 1 + e ^ { - x } } { 2 } \right)$
Q68 Vectors: Lines & Planes Perpendicular/Orthogonal Projection onto a Plane View
The foot of the perpendicular drawn from the point $( 4,2,3 )$ to the line joining the points $( 1 , - 2,3 )$ and $( 1,1,0 )$ lies on the plane
(1) $2 x + y - z = 1$
(2) $x - y - 2 z = 1$
(3) $x - 2 y + z = 1$
(4) $x + 2 y - z = 1$
Q69 Vectors 3D & Lines MCQ: Relationship Between Two Lines View
The lines $\vec { r } = ( \hat { i } - \hat { j } ) + l ( 2 \hat { i } + \widehat { k } )$ and $\vec { r } = ( 2 \hat { i } - \hat { j } ) + m ( \hat { i } + \hat { j } - \widehat { k } )$
(1) Do not intersect for any values of $l$ and $m$
(2) Intersect for all values of $l$ and $m$
(3) Intersect when $l = 2$ and $m = \frac { 1 } { 2 }$
(4) Intersect when $l = 1$ and $m = 2$
Q70 Conditional Probability Combinatorial Conditional Probability (Counting-Based) View
A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared at least once is
(1) $\frac { 1 } { 4 }$
(2) $\frac { 1 } { 3 }$
(3) $\frac { 1 } { 8 }$
(4) $\frac { 1 } { 9 }$