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
2019 session2_09apr_shift2

29 maths questions

Q61 Solving quadratics and applications Optimization or extremal value of an expression via completing the square View
If $m$ is chosen in the quadratic equation $\left( m ^ { 2 } + 1 \right) x ^ { 2 } - 3 x + \left( m ^ { 2 } + 1 \right) ^ { 2 } = 0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is:
(1) $4 \sqrt { 3 }$
(2) $10 \sqrt { 5 }$
(3) $8 \sqrt { 3 }$
(4) $8 \sqrt { 5 }$
Q62 Complex Numbers Arithmetic Identifying Real/Imaginary Parts or Components View
Let $z \in C$ be such that $| z | < 1$. If $\omega = \frac { 5 + 3 z } { 5 ( 1 - z ) }$, then:
(1) $5 R e ( \omega ) > 1$
(2) $5 \operatorname { Im } ( \omega ) < 1$
(3) $5 R e ( \omega ) > 4$
(4) $4 \operatorname { Im } ( \omega ) > 5$
Q63 Arithmetic Sequences and Series Summation of Derived Sequence from AP View
The sum of the series $1 + 2 \times 3 + 3 \times 5 + 4 \times 7 + \ldots$ upto $11 ^ { \text {th} }$ term is:
(1) 945
(2) 916
(3) 946
(4) 915
Q64 Arithmetic Sequences and Series Counting or Combinatorial Problems on APs View
Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square, whose each side contains exactly 2 balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is
(1) 262
(2) 190
(3) 225
(4) 157
Q65 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its $11^{\text{th}}$ term is:
(1) $- 25$
(2) $- 35$
(3) $25$
(4) $- 36$
Q66 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
If some three consecutive coefficients in the binomial expansion of $( x + 1 ) ^ { n }$ in powers of $x$ are in the ratio $2 : 15 : 70$, then the average of these three coefficients is:
(1) 227
(2) 964
(3) 625
(4) 232
Q67 Trig Proofs Trigonometric Identity Simplification View
The value of $\sin 10 ^ { \circ } \sin 30 ^ { \circ } \sin 50 ^ { \circ } \sin 70 ^ { \circ }$ is:
(1) $\frac { 1 } { 36 }$
(2) $\frac { 1 } { 16 }$
(3) $\frac { 1 } { 18 }$
(4) $\frac { 1 } { 32 }$
Q68 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation View
If the two lines $x + ( a - 1 ) y = 1$ and $2 x + a ^ { 2 } y = 1 , ( a \in R - \{ 0,1 \} )$ are perpendicular, then the distance of their point of intersection from the origin is
(1) $\frac { 2 } { \sqrt { 5 } }$
(2) $\frac { \sqrt { 2 } } { 5 }$
(3) $\frac { 2 } { 5 }$
(4) $\sqrt { \frac { 2 } { 5 } }$
Q69 Circles Area and Geometric Measurement Involving Circles View
A rectangle is inscribed in a circle with a diameter lying along the line $3 y = x + 7$. If the two adjacent vertices of the rectangle are $( - 8,5 )$ and $( 6,5 )$, then the area of the rectangle (in sq. units) is:
(1) 72
(2) 98
(3) 56
(4) 84
Q70 Circles Tangent Lines and Tangent Lengths View
The common tangent to the circles $x ^ { 2 } + y ^ { 2 } = 4$ and $x ^ { 2 } + y ^ { 2 } + 6 x + 8 y - 24 = 0$ also passes through the point:
(1) $( 4 , - 2 )$
(2) $( - 4,6 )$
(3) $( 6 , - 2 )$
(4) $( - 6,4 )$
Q71 Circles Circles Tangent to Each Other or to Axes View
The area (in sq. units) of the smaller of the two circles that touch the parabola, $y ^ { 2 } = 4 x$ at the point $( 1,2 )$ and the $x$-axis is
(1) $8 \pi ( 3 - 2 \sqrt { 2 } )$
(2) $8 \pi ( 2 - \sqrt { 2 } )$
(3) $4 \pi ( 3 + \sqrt { 2 } )$
(4) $4 \pi ( 2 - \sqrt { 2 } )$
Q72 Circles Tangent Lines and Tangent Lengths View
If the tangent to the parabola $y ^ { 2 } = x$ at a point $( \alpha , \beta ) , ( \beta > 0 )$ is also a tangent to the ellipse, $x ^ { 2 } + 2 y ^ { 2 } = 1$ then $\alpha$ is equal to:
(1) $\sqrt { 2 } - 1$
(2) $2 \sqrt { 2 } + 1$
(3) $\sqrt { 2 } + 1$
(4) $2 \sqrt { 2 } - 1$
Q73 Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions View
If $f ( x ) = [ x ] - \left[ \frac { x } { 4 } \right] , x \in R$, where $[ x ]$ denotes the greatest integer function, then:
(1) $\lim _ { x \rightarrow 4 + } f ( x )$ exists but $\lim _ { x \rightarrow 4 - } f ( x )$ does not exist
(2) $f$ is continuous at $x = 4$
(3) $\lim _ { x \rightarrow 4 - } f ( x )$ exists but $\lim _ { x \rightarrow 4 + } f ( x )$ does not exist
(4) Both $\lim _ { x \rightarrow 4 - } f ( x )$ and $\lim _ { x \rightarrow 4 + } f ( x )$ exist but are not equal
Q75 Measures of Location and Spread View
The mean and the median of the following ten numbers in increasing order $10,22,26,29,34 , x , 42,67,70 , y$ are 42 and 35 respectively, then $\frac { y } { x }$ is equal to:
(1) $\frac { 9 } { 4 }$
(2) $\frac { 7 } { 3 }$
(3) $\frac { 7 } { 2 }$
(4) $\frac { 8 } { 3 }$
Q76 Sine and Cosine Rules Heights and distances / angle of elevation problem View
Two poles standing on a horizontal ground are of heights $5 m$ and $10 m$ respectively. The line joining their tops makes an angle of $15 ^ { \circ }$ with the ground. Then the distance (in $m$) between the poles, is
(1) $10 ( \sqrt { 3 } - 1 )$
(2) $\frac { 5 } { 2 } ( 2 + \sqrt { 3 } )$
(3) $5 ( 2 + \sqrt { 3 } )$
(4) $5 ( \sqrt { 3 } + 1 )$
Q77 Matrices Matrix Algebra and Product Properties View
The total number of matrices $A = \left( \begin{array} { c c c } 0 & 2 y & 1 \\ 2 x & y & - 1 \\ 2 x & - y & 1 \end{array} \right) , ( x , y \in R , x \neq y )$ for which $A ^ { T } A = 3 I _ { 3 }$ is:
(1) 6
(2) 3
(3) 4
(4) 2
Q78 Matrices Linear System and Inverse Existence View
If the system of equations $2 x + 3 y - z = 0 , x + k y - 2 z = 0$ and $2 x - y + z = 0$ has a non-trivial solution $( x , y , z )$, then $\frac { x } { y } + \frac { y } { z } + \frac { z } { x } + k$ is equal to
(1) $- \frac { 1 } { 4 }$
(2) $\frac { 1 } { 2 }$
(3) $- 4$
(4) $\frac { 3 } { 4 }$
Q79 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
The domain of the definition of the function $f ( x ) = \frac { 1 } { 4 - x ^ { 2 } } + \log _ { 10 } \left( x ^ { 3 } - x \right)$ is:
(1) $( - 1,0 ) \cup ( 1,2 ) \cup ( 2 , \infty )$
(2) $( 1,2 ) \cup ( 2 , \infty )$
(3) $( - 2 , - 1 ) \cup ( - 1,0 ) \cup ( 2 , \infty )$
(4) $( - 1,0 ) \cup ( 1,2 ) \cup ( 3 , \infty )$
Q80 Curve Sketching Finding Parameters for Continuity View
If the function $f ( x ) = \left\{ \begin{array} { l } a | \pi - x | + 1 , x \leq 5 \\ b | x - \pi | + 3 , x > 5 \end{array} \right.$ is continuous at $x = 5$, then the value of $a - b$ is:
(1) $\frac { 2 } { 5 - \pi }$
(2) $\frac { - 2 } { \pi + 5 }$
(3) $\frac { 2 } { \pi + 5 }$
(4) $\frac { 2 } { \pi - 5 }$
Q81 Connected Rates of Change Volume/Height Related Rates for Containers and Solids View
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $\tan ^ { - 1 } \left( \frac { 1 } { 2 } \right)$. Water is poured into it at a constant rate of $5$ cubic $\mathrm { m } / \mathrm { min }$. Then the rate (in $\mathrm { m } / \mathrm { min }$), at which the level of water is rising at the instant when the depth of water in the tank is $10 m$; is:
(1) $\frac { 1 } { 10 \pi }$
(2) $\frac { 1 } { 15 \pi }$
(3) $\frac { 1 } { 5 \pi }$
(4) $\frac { 2 } { \pi }$
Q82 Standard Integrals and Reverse Chain Rule Integral Equation to Determine a Function Value View
If $\int e ^ { \sec x } \left( \sec x \tan x f ( x ) + \left( \sec x \tan x + \sec ^ { 2 } x \right) \right) d x = e ^ { \sec x } f ( x ) + C$, then a possible choice of $f ( x )$ is:
(1) $\sec x - \tan x - \frac { 1 } { 2 }$
(2) $\sec x + \tan x + \frac { 1 } { 2 }$
(3) $x \sec x + \tan x + \frac { 1 } { 2 }$
(4) $\sec x + x \tan x - \frac { 1 } { 2 }$
Q83 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
The value of the integral $\int _ { 0 } ^ { 1 } x \cot ^ { - 1 } \left( 1 - x ^ { 2 } + x ^ { 4 } \right) d x$ is
(1) $\frac { \pi } { 4 } - \frac { 1 } { 2 } \log _ { e } 2$
(2) $\frac { \pi } { 4 } - \log _ { e } 2$
(3) $\frac { \pi } { 2 } - \log _ { e } 2$
(4) $\frac { \pi } { 2 } - \frac { 1 } { 2 } \log _ { e } 2$
Q84 Indefinite & Definite Integrals Finding a Function from an Integral Equation View
If $f : R \rightarrow R$ is a differentiable function and $f ( 2 ) = 6$, then $\lim _ { x \rightarrow 2 } \int _ { 6 } ^ { f ( x ) } \frac { 2 t d t } { ( x - 2 ) }$ is:
(1) 0
(2) $2 f ^ { \prime } ( 2 )$
(3) $24 f ^ { \prime } ( 2 )$
(4) $12 f ^ { \prime } ( 2 )$
Q85 Areas by integration View
The area (in sq. units) of the region $A = \left\{ ( x , y ) : \frac { y ^ { 2 } } { 2 } \leq x \leq y + 4 \right\}$ is:
(1) 30
(2) 18
(3) $\frac { 53 } { 3 }$
(4) 16
Q86 Differential equations First-Order Linear DE: General Solution View
If $\cos x \frac { d y } { d x } - y \sin x = 6 x , \left( 0 < x < \frac { \pi } { 2 } \right)$ and $y \left( \frac { \pi } { 3 } \right) = 0$, then $y \left( \frac { \pi } { 6 } \right)$ is equal to
(1) $- \frac { \pi ^ { 2 } } { 4 \sqrt { 3 } }$
(2) $\frac { \pi ^ { 2 } } { 2 \sqrt { 3 } }$
(3) $- \frac { \pi ^ { 2 } } { 2 }$
(4) $- \frac { \pi ^ { 2 } } { 2 \sqrt { 3 } }$
Q87 Vectors Introduction & 2D Angle or Cosine Between Vectors View
If a unit vector $\vec { a }$ makes angles $\frac { \pi } { 3 }$ with $\hat { i } , \frac { \pi } { 4 }$ with $\hat { j }$ and $\theta \in ( 0 , \pi )$ with $\widehat { k }$, then a value of $\theta$ is:
(1) $\frac { 5 \pi } { 6 }$
(2) $\frac { 5 \pi } { 12 }$
(3) $\frac { \pi } { 4 }$
(4) $\frac { 2 \pi } { 3 }$
Q88 Vectors 3D & Lines Distance from a Point to a Line (Show/Compute) View
The vertices $B$ and $C$ of a $\triangle A B C$ lie on the line, $\frac { x + 2 } { 3 } = \frac { y - 1 } { 0 } = \frac { z } { 4 }$ such that $B C = 5$ units. Then the area (in sq. units) of this triangle, given the point $A ( 1 , - 1,2 )$, is
(1) 6
(2) $2 \sqrt { 34 }$
(3) $\sqrt { 34 }$
(4) $5 \sqrt { 17 }$
Q89 Vectors: Lines & Planes Distance Computation (Point-to-Plane or Line-to-Line) View
Let $P$ be the plane, which contains the line of intersection of the planes, $x + y + z - 6 = 0$ and $2 x + 3 y + z + 5 = 0$ and it is perpendicular to the $x y$-plane. Then the distance of the point $( 0,0,256 )$ from $P$ is equal to:
(1) $205 \sqrt { 5 }$ units
(2) $\frac { 17 } { \sqrt { 5 } }$ units
(3) $\frac { 11 } { \sqrt { 5 } }$ units
(4) $63 \sqrt { 5 }$ units
Q90 Probability Definitions Probability Using Set/Event Algebra View
Two newspapers $A$ and $B$ are published in a city. It is known that $25 \%$ of the city population reads $A$ and $20 \%$ reads $B$ while $8 \%$ reads both $A$ and $B$. Further, 30\% of those who read $A$ but not $B$ look into advertisements and $40 \%$ of those who read $B$ but not $A$ also look into advertisements, while $50 \%$ of those who read both $A$ and $B$ look into advertisements. Then the percentage of the population who look into advertisements is:
(1) 13.5
(2) 12.8
(3) 13.9
(4) 13