jee-main

Papers (169)
2025
session1_22jan_shift1 25 session1_22jan_shift2 25 session1_23jan_shift1 25 session1_23jan_shift2 25 session1_24jan_shift1 25 session1_24jan_shift2 25 session1_28jan_shift1 25 session1_28jan_shift2 25 session1_29jan_shift1 29 session1_29jan_shift2 25
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 session1_09jan_shift1

22 maths questions

Q21 Variable acceleration (1D) Inverse/implicit relationship between position and time View
The distance $x$ covered by a particle in one dimensional motion varies with time $t$ as $x ^ { 2 } = a t ^ { 2 } + 2 b t + c$. If the acceleration of the particle depends on $x$ as $x ^ { - n }$, where $n$ is an integer, the value of $n$ is $\_\_\_\_$
Q23 Circular Motion 1 Maximum Speed/Tension from String Breaking Limit View
A body of mass $\mathrm { m } = 10 \mathrm {~kg}$ is attached to one end of a wire of length 0.3 m . What is the maximum angular speed (in $\mathrm { rad } \mathrm { s } ^ { - 1 }$ ) with which it can be rotated about its other end in a space station without breaking the wire? [Breaking stress of wire $( \sigma ) = 4.8 \times 10 ^ { 7 } \mathrm {~N} \mathrm {~m} ^ { - 2 }$ and area of cross-section of the wire $= 10 ^ { - 2 } \mathrm {~cm} ^ { 2 }$ ]
Q51 Solving quadratics and applications Counting solutions or configurations satisfying a quadratic system View
The number of real roots of the equation, $e ^ { 4 x } + e ^ { 3 x } - 4 e ^ { 2 x } + e ^ { x } + 1 = 0$ is:
(1) 1
(2) 3
(3) 2
(4) 4
Q52 Complex Numbers Argand & Loci Intersection of Loci and Simultaneous Geometric Conditions View
Let $z$ be a complex number such that $\left| \frac { z - i } { z + 2 i } \right| = 1$ and $| z | = \frac { 5 } { 2 }$. Then, the value of $| z + 3 i |$ is
(1) $\sqrt { 10 }$
(2) $\frac { 7 } { 2 }$
(3) $\frac { 15 } { 4 }$
(4) $2 \sqrt { 3 }$
Q53 Permutations & Arrangements Forming Numbers with Digit Constraints View
If the number of five digit numbers with distinct digits and 2 at the $10 ^ { \text {th} }$ place is $336 k$, then $k$ is equal to:
(1) 4
(2) 6
(3) 7
(4) 8
Q54 Geometric Sequences and Series Sum of an Infinite Geometric Series (Direct Computation) View
The product $2 ^ { \frac { 1 } { 4 } } \bullet 4 ^ { \frac { 1 } { 16 } } \bullet 8 ^ { \frac { 1 } { 48 } } \bullet 16 ^ { \frac { 1 } { 128 } } \bullet \ldots$ to $\infty$ is equal to:
(1) $2 ^ { \frac { 1 } { 2 } }$
(2) $2 ^ { \frac { 1 } { 4 } }$
(3) 1
(4) 2
Q55 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
The value of $\cos ^ { 3 } \left( \frac { \pi } { 8 } \right) \cdot \cos \left( \frac { 3 \pi } { 8 } \right) + \sin ^ { 3 } \left( \frac { \pi } { 8 } \right) \cdot \sin \left( \frac { 3 \pi } { 8 } \right)$ is:
(1) $\frac { 1 } { \sqrt { 2 } }$
(2) $\frac { 1 } { 2 \sqrt { 2 } }$
(3) $\frac { 1 } { 2 }$
(4) $\frac { 1 } { 4 }$
Q56 Circles Tangent Lines and Tangent Lengths View
A circle touches the $y$-axis at the point $( 0,4 )$ and passes through the point $( 2,0 )$. Which of the following lines is not a tangent to this circle?
(1) $4 x - 3 y + 17 = 0$
(2) $3 x - 4 y - 24 = 0$
(3) $3 x + 4 y - 6 = 0$
(4) $4 x + 3 y - 8 = 0$
Q57 Conic sections Eccentricity or Asymptote Computation View
If $e _ { 1 }$ and $e _ { 2 }$ are the eccentricities of the ellipse $\frac { x ^ { 2 } } { 18 } + \frac { y ^ { 2 } } { 4 } = 1$ and the hyperbola $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1$ respectively and $\left( e _ { 1 } , e _ { 2 } \right)$ is a point on the ellipse $15 x ^ { 2 } + 3 y ^ { 2 } = k$, then the value of $k$ is equal to
(1) 16
(2) 17
(3) 15
(4) 14
Q58 Proof Direct Proof of a Stated Identity or Equality View
Negation of the statement: $\sqrt { 5 }$ is an integer or 5 is irrational is:
(1) $\sqrt { 5 }$ is not an integer 5 is not irrational
(2) $\sqrt { 5 }$ is not an integer and 5 is not irrational
(3) $\sqrt { 5 }$ is irrational or 5 is an integer
(4) $\sqrt { 5 }$ is an integer and 5 irrational
Q59 Measures of Location and Spread View
Let the observation $x _ { i } ( 1 \leq i \leq 10 )$ satisfy the equations $\sum _ { i = 1 } ^ { 10 } \left( x _ { i } - 5 \right) = 10 , \sum _ { i = 1 } ^ { 10 } \left( x _ { i } - 5 \right) ^ { 2 } = 40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations, $x _ { 1 } - 3 , x _ { 2 } - 3 , \ldots , x _ { 10 } - 3$, then the ordered pair $( \mu , \lambda )$ is equal to:
(1) $( 3,3 )$
(2) $( 6,3 )$
(3) $( 6,6 )$
(4) $( 3,6 )$
Q60 3x3 Matrices Determinant of Parametric or Structured Matrix View
If $A = \left[ \begin{array} { c c c } 1 & 1 & 2 \\ 1 & 3 & 4 \\ 1 & - 1 & 3 \end{array} \right] , B = \mathrm{adj}\, A$ and $C = 3 A$, then $\frac { | \mathrm{adj}\, B | } { | C | }$ is equal to
(1) 8
(2) 16
(3) 72
(4) 2
Q61 Vectors: Lines & Planes Coplanarity and Relative Position of Planes View
If for some $\alpha$ and $\beta$ in $R$, the intersection of the following three planes $x + 4 y - 2 z = 1$ $x + 7 y - 5 z = \beta$ $x + 5 y + \alpha z = 5$ is a line in $R ^ { 3 }$, then $\alpha + \beta$ is equal to:
(1) 0
(2) 10
(3) 2
(4) - 10
Q62 Curve Sketching Finding Parameters for Continuity View
$f ( x ) = \left\{ \begin{array} { c l } \frac { \sin ( a + 2 ) x + \sin x } { x } & ; x < 0 \\ b & ; x = 0 \\ \frac { \left( x + 3 x ^ { 2 } \right) ^ { 1 / 3 } - x ^ { 1 / 3 } } { x ^ { 1 / 3 } } & ; x > 0 \end{array} \right.$ is continuous at $x = 0$, then $a + 2 b$ is equal to:
(1) 1
(2) - 1
(3) 0
(4) - 2
Q63 Applied differentiation Convexity and inflection point analysis View
Let $f$ be any function continuous on $[ a , b ]$ and twice differentiable on $( a , b )$. If all $x \in ( a , b ) , f ^ { \prime } ( x ) > 0$ and $f ^ { \prime \prime } ( x ) < 0$, then for any $c \in ( a , b ) , \frac { f ( c ) - f ( a ) } { f ( b ) - f ( c ) }$
(1) $\frac { b + a } { b - a }$
(2) 1
(3) $\frac { b - c } { c - a }$
(4) $\frac { c - a } { b - c }$
Q64 Connected Rates of Change Reverse-Engineering a Geometric Quantity from Given Rates View
A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 \mathrm {~cm} ^ { 3 } / \mathrm { min }$. When the thickness of ice is 5 cm , then the rate (in $\mathrm { cm } / \mathrm { min }$.) at which of the thickness of ice decreases, is:
(1) $\frac { 5 } { 6 \pi }$
(2) $\frac { 1 } { 54 \pi }$
(3) $\frac { 1 } { 36 \pi }$
(4) $\frac { 1 } { 18 \pi }$
Q65 Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition View
The integral $\int \frac { d x } { ( x + 4 ) ^ { \frac { 8 } { 7 } } ( x - 3 ) ^ { \frac { 6 } { 7 } } }$ is equal to: (where $C$ is a constant of integration)
(1) $\left( \frac { x - 3 } { x + 4 } \right) ^ { \frac { 1 } { 7 } } + C$
(2) $\left( \frac { x - 3 } { x + 4 } \right) ^ { \frac { - 1 } { 7 } } + C$
(3) $\frac { 1 } { 2 } \left( \frac { x - 3 } { x + 4 } \right) ^ { \frac { 3 } { 7 } } + C$
(4) $- \frac { 1 } { 13 } \left( \frac { x - 3 } { x + 4 } \right) ^ { \frac { - 13 } { 7 } } + C$
Q66 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
If for all real triplets $( a , b , c ) , f ( x ) = a + b x + c x ^ { 2 }$; then $\int _ { 0 } ^ { 1 } f ( x ) d x$ is equal to:
(1) $2 \left\{ 3 f ( 1 ) + 2 f \left( \frac { 1 } { 2 } \right) \right\}$
(2) $\frac { 1 } { 2 } \left\{ f ( 1 ) + 3 f \left( \frac { 1 } { 2 } \right) \right\}$
(3) $\frac { 1 } { 3 } \left\{ f ( 0 ) + f \left( \frac { 1 } { 2 } \right) \right\}$
(4) $\frac { 1 } { 6 } \left\{ f ( 0 ) + f ( 1 ) + 4 f \left( \frac { 1 } { 2 } \right) \right\}$
Q67 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View
The value of $\int _ { 0 } ^ { 2 \pi } \frac { x \sin ^ { 8 } x } { \sin ^ { 8 } x + \cos ^ { 8 } x } d x$ is equal to:
(1) $2 \pi$
(2) $2 \pi ^ { 2 }$
(3) $\pi ^ { 2 }$
(4) $4 \pi$
Q68 Indefinite & Definite Integrals Antiderivative Verification and Construction View
If $f ^ { \prime } ( x ) = \tan ^ { - 1 } ( \sec x + \tan x ) , - \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$ and $f ( 0 ) = 0$, then $f ( 1 )$ is equal to:
(1) $\frac { \pi + 1 } { 4 }$
(2) $\frac { 1 } { 4 }$
(3) $\frac { \pi - 1 } { 4 }$
(4) $\frac { \pi + 2 } { 4 }$
Q69 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
Let $D$ be the centroid of the triangle with vertices $( 3 , - 1 ) , ( 1,3 )$ and $( 2,4 )$. Let P be the point of intersection of the lines $x + 3 y - 1 = 10$ and $3 x - y + 1 = 0$. Then, the line passing through the points $D$ and P also passes through the point:
(1) $( - 9 , - 6 )$
(2) $( 9,7 )$
(3) $( 7,6 )$
(4) $( - 9 , - 7 )$
Q70 Negative Binomial Distribution View
In a box, there are 20 cards, out of which 10 are labelled as $A$ and the remaining 10 are labelled as $B$. Cards are drawn at random, one after the other and with replacement, till a second $A$ card is obtained. The probability that the second $A$ card appears before the third $B$ card is:
(1) $\frac { 9 } { 16 }$
(2) $\frac { 11 } { 16 }$
(3) $\frac { 13 } { 16 }$
(4) $\frac { 15 } { 16 }$