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
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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
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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
2019 session2_08apr_shift2

29 maths questions

Q61 Arithmetic Sequences and Series Arithmetic-Geometric Hybrid Problem View
If three distinct numbers $a , b , c$ are in G.P. and the equations $a x ^ { 2 } + 2 b x + c = 0$ and $d x ^ { 2 } + 2 e x + f = 0$ have a common root, then which one of the following statements is correct?
(1) $\frac { d } { a } , \frac { e } { b } , \frac { f } { c }$ are in A.P.
(2) $d , e , f$ are in A.P.
(3) $d , e , f$ are in G.P.
(4) $\frac { d } { a } , \frac { e } { b } , \frac { f } { c }$ are in G.P.
Q62 Discriminant and conditions for roots Parameter range for no real roots (positive definite) View
The number of integral values of $m$ for which the equation, $1 + m ^ { 2 } x ^ { 2 } - 21 + 3 m x + 1 + 8 m = 0$ has no real root, is
(1) 2
(2) 3
(3) Infinitely many
(4) 1
Q63 Complex Numbers Arithmetic Powers of i or Complex Number Integer Powers View
If $z = \frac { \sqrt { 3 } } { 2 } + \frac { i } { 2 }$ $( i = \sqrt { - 1 } )$, then $1 + i z + z ^ { 5 } + i z ^ { 8 }$ is equal to:
(1) - 1
(2) 1
(3) 0
(4) $- 1 + 2 i ^ { 9 }$
Q64 Permutations & Arrangements Forming Numbers with Digit Constraints View
The number of four-digit numbers strictly greater than 4321 that can be formed using the digit $0,1,2,3,4,5$ (repetition of digits is allowed) is:
(1) 360
(2) 288
(3) 306
(4) 310
Q65 Arithmetic Sequences and Series Summation of Derived Sequence from AP View
The sum $\sum _ { k = 1 } ^ { 20 } k \frac { 1 } { 2 ^ { k } }$ is equal to
(1) $1 - \frac { 11 } { 3 ^ { 20 } }$
(2) $2 - \frac { 21 } { 2 ^ { 20 } }$
(3) $2 - \frac { 3 } { 2 ^ { 17 } }$
(4) $2 - \frac { 11 } { 2 ^ { 19 } }$
Q66 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
If the fourth term in the binomial expansion of $\sqrt { x ^ { \frac { 1 } { 1 + \log _ { 10 } x } } } + x ^ { \frac { 1 } { 12 } }$ is equal to 200 , and $x > 1$, then the value of $x$ is
(1) 100
(2) $10 ^ { 4 }$
(3) $10 ^ { 3 }$
(4) 10
Q67 Straight Lines & Coordinate Geometry Slope and Angle Between Lines View
Suppose that the points $( h , k )$, $( 1,2 )$ and $( - 3,4 )$ lie on the line $L _ { 1 }$. If a line $L _ { 2 }$ passing through the points $( h , k )$ and $( 4,3 )$ is perpendicular to $L _ { 1 }$, then $\frac { k } { h }$ equals:
(1) $- \frac { 1 } { 7 }$
(2) 3
(3) 0
(4) $\frac { 1 } { 3 }$
Q68 Circles Area and Geometric Measurement Involving Circles View
The tangent and the normal lines at the point $( \sqrt { 3 } , 1 )$ to the circle $x ^ { 2 } + y ^ { 2 } = 4$ and the $x$-axis form a triangle. The area of this triangle (in square units) is:
(1) $\frac { 1 } { 3 }$
(2) $\frac { 2 } { \sqrt { 3 } }$
(3) $\frac { 4 } { \sqrt { 3 } }$
(4) $\frac { 1 } { \sqrt { 3 } }$
Q69 Circles Intersection of Circles or Circle with Conic View
The tangent to the parabola $y ^ { 2 } = 4 x$ at the point where it intersects the circle $x ^ { 2 } + y ^ { 2 } = 5$ in the first quadrant, passes through the point:
(1) $\left( \frac { 1 } { 4 } , \frac { 3 } { 4 } \right)$
(2) $\left( - \frac { 1 } { 3 } , \frac { 4 } { 3 } \right)$
(3) $\left( - \frac { 1 } { 4 } , \frac { 1 } { 2 } \right)$
(4) $\left( \frac { 3 } { 4 } , \frac { 7 } { 4 } \right)$
Q70 Circles Area and Geometric Measurement Involving Circles View
In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at $( 0 , 5 \sqrt { 3 } )$, then the length of its latus rectum is:
(1) 6
(2) 10
(3) 8
(4) 5
Q71 Circles Tangent Lines and Tangent Lengths View
If the eccentricity of the standard hyperbola passing through the point $( 4 , 6 )$ is 2 , then the equation of the tangent to the hyperbola at $( 4 , 6 )$ is:
(1) $2 x - 3 y + 10 = 0$
(2) $x - 2 y + 8 = 0$
(3) $3 x - 2 y = 0$
(4) $2 x - y - 2 = 0$
Q72 Chain Rule Limit Involving Derivative Definition of Composed Functions View
Let $f : R \rightarrow R$ be a differentiable function satisfying $f ^ { \prime } ( 3 ) + f ^ { \prime } ( 2 ) = 0$. Then $\lim _ { x \rightarrow 0 } \left( \frac { 1 + f ( 3 + x ) - f ( 3 ) } { 1 + f ( 2 - x ) - f ( 2 ) } \right)$ is equal to
(1) 1
(2) e
(3) $e ^ { 2 }$
(4) $e ^ { - 1 }$
Q74 Measures of Location and Spread View
A student scores the following marks in five tests: $45,54,41,57,43$. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:
(1) $\frac { 10 } { 3 }$
(2) $\frac { 100 } { 3 }$
(3) $\frac { 10 } { \sqrt { 3 } }$
(4) $\frac { 100 } { \sqrt { 3 } }$
Q75 Straight Lines & Coordinate Geometry Perspective, Projection, and Applied Geometry View
Two vertical poles of height, $20 m$ and $80 m$ stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is:
(1) 16
(2) 12
(3) 18
(4) 15
Q76 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
If the lengths of the sides of a triangle are in A.P and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is:
(1) $3 : 4 : 5$
(2) $5 : 6 : 7$
(3) $5 : 9 : 13$
(4) $4 : 5 : 6$
Q77 Polynomial Division & Manipulation View
Let the numbers $2 , b , c$ be in an A.P. and $A = \begin{pmatrix} 2 & b & c \\ 4 & b^2 & c^2 \end{pmatrix}$. If $\det ( A ) \in [ 2,16 ]$, then $c$ lies in the interval:
(1) $[2,3]$
(2) $[4,6]$
(3) $\left[3, 2 + 2 ^ { \frac { 3 } { 4 } }\right]$
(4) $\left[2 + 2 ^ { \frac { 3 } { 4 } } , 4\right]$
Q78 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
If the system of linear equations $$\begin{aligned} & x - 2 y + k z = 1 \\ & 2 x + y + z = 2 \\ & 3 x - y - k z = 3 \end{aligned}$$ has a solution $( x , y , z )$, $z \neq 0$, then $( x , y )$ lies on the straight line whose equation is:
(1) $4 x - 3 y - 4 = 0$
(2) $3 x - 4 y - 4 = 0$
(3) $3 x - 4 y - 1 = 0$
(4) $4 x - 3 y - 1 = 0$
Q79 Exponential Functions Functional Equation with Exponentials View
Let $f ( x ) = a ^ { x }$ $( a > 0 )$ be written as $f ( x ) = f _ { 1 } ( x ) + f _ { 2 } ( x )$, where $f _ { 1 } ( x )$ is an even function and $f _ { 2 } ( x )$ is an odd function. Then $f _ { 1 } ( x + y ) + f _ { 1 } ( x - y )$ equals:
(1) $2 f _ { 1 } ( x ) f _ { 1 } ( y )$
(2) $2 f _ { 1 } ( x + y ) f _ { 1 } ( x - y )$
(3) $2 f _ { 1 } ( x ) f _ { 2 } ( y )$
(4) $2 f _ { 1 } ( x + y ) f _ { 2 } ( x - y )$
Q80 Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions View
Let $f : [ - 1,3 ] \rightarrow \mathrm { R }$ be defined as $$f ( x ) = \begin{cases} |x| + [x], & -1 \leq x < 1 \\ x + |x|, & 1 \leq x < 2 \\ x + [x], & 2 \leq x \leq 3 \end{cases}$$ where $[t]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is discontinuous at:
(1) Only one point
(2) Only two points
(3) Four or more points
(4) Only three points
Q81 Chain Rule Chain Rule with Composition of Explicit Functions View
If $f ( 1 ) = 1 , f ^ { \prime } ( 1 ) = 3$, then the derivative of $f ( f ( f ( x ) ) ) + ( f ( x ) ) ^ { 2 }$ at $x = 1$ is:
(1) 9
(2) 12
(3) 15
(4) 33
Q82 Stationary points and optimisation Geometric or applied optimisation problem View
The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is:
(1) $\sqrt { 3 }$
(2) $\frac { 2 } { 3 } \sqrt { 3 }$
(3) $\sqrt { 6 }$
(4) $2 \sqrt { 3 }$
Q83 Differential equations Solving Separable DEs with Initial Conditions View
Given that the slope of the tangent to a curve $y = y ( x )$ at any point $( x , y )$ is $\frac { 2 y } { x ^ { 2 } }$. If the curve passes through the centre of the circle $x ^ { 2 } + y ^ { 2 } - 2 x - 2 y = 0$, then its equation is
(1) $x ^ { 2 } \log _ { e } | y | = - 2 ( x - 1 )$
(2) $x \log _ { e } | y | = 2 ( x - 1 )$
(3) $x \log _ { e } | y | = - 2 ( x - 1 )$
(4) $x \log _ { e } | y | = x - 1$
Q84 Integration by Substitution Substitution to Transform Integral Form (Show Transformed Expression) View
If $\int \frac { d x } { x ^ { 3 } \left( 1 + x ^ { 6} \right) ^ { \frac { 2 } { 3 } } } = x f ( x ) \left( 1 + x ^ { 6} \right)^{ \frac { 1 } { 3 } } + C$, where $C$ is a constant of integration, then the function $f ( x )$ is equal to
(1) $\frac { 3 } { x ^ { 2 } }$
(2) $- \frac { 1 } { 2 x ^ { 3 } }$
(3) $- \frac { 1 } { 6 x ^ { 3 } }$
(4) $- \frac { 1 } { 2 x ^ { 2 } }$
Q85 Indefinite & Definite Integrals Finding a Function from an Integral Equation View
Let $f ( x ) = \int _ { 0 } ^ { x } g ( t ) \, dt$, where $g$ is a non-zero even function. If $f ( x + 5 ) = g ( x )$, then $\int _ { 0 } ^ { x } f ( t ) \, dt$ equals
(1) $\int _ { 5 } ^ { x + 5 } g ( t ) \, dt$
(2) $\int _ { x + 5 } ^ { 5 } g ( t ) \, dt$
(3) $5 \int _ { x + 5 } ^ { 5 } g ( t ) \, dt$
(4) $2 \int _ { 5 } ^ { x + 5 } g ( t ) \, dt$
Q86 Areas by integration View
Let $S ( \alpha ) = \{ ( x , y ) : y ^ { 2 } \leq x , 0 \leq x \leq \alpha \}$ and $A ( \alpha )$ is area of the region $S ( \alpha )$. If for a $\lambda$, $0 < \lambda < 4$, $A ( \lambda ) : A ( 4 ) = 2 : 5$, then $\lambda$ equals:
(1) $4 \left( \frac { 2 } { 5 } \right) ^ { \frac { 1 } { 3 } }$
(2) $2 \left( \frac { 4 } { 25 } \right) ^ { \frac { 1 } { 3 } }$
(3) $4 \left( \frac { 4 } { 25 } \right) ^ { \frac { 1 } { 3 } }$
(4) $2 \left( \frac { 2 } { 5 } \right)$
Q87 Vectors Introduction & 2D Optimization of a Vector Expression View
Let $\vec { a } = 3 \hat { i } + 2 \hat { j } + x \hat { k }$ and $\vec { b } = \hat { i } - \hat { j } + \hat { k }$, for some real $x$. Then the condition for $| \vec { a } \times \vec { b } | = r$ to follow
(1) $0 < r \leq \sqrt { \frac { 3 } { 2 } }$
(2) $r \geq 5 \sqrt { \frac { 3 } { 2 } }$
(3) $\sqrt { \frac { 3 } { 2 } } < r \leq 3 \sqrt { \frac { 3 } { 2 } }$
(4) $3 \sqrt { \frac { 3 } { 2 } } < r < 5 \sqrt { \frac { 3 } { 2 } }$
Q88 Vectors: Lines & Planes Find Cartesian Equation of a Plane View
The vector equation of the plane through the line of intersection of the planes $x + y + z = 1$ and $2 x + 3 y + 4 z = 5$ which is perpendicular to the plane $x - y + z = 0$ is
(1) $\vec { r } \times ( \hat { i } + \hat { k } ) + 2 = 0$
(2) $\vec { r } \cdot ( \hat { i } - \hat { k } ) - 2 = 0$
(3) $\vec { r } \times ( \hat { i } - \hat { k } ) + 2 = 0$
(4) $\vec { r } \cdot ( \hat { i } - \hat { k } ) + 2 = 0$
Q89 Vectors 3D & Lines Section Division and Coordinate Computation View
If a point $R ( 4 , y , z )$ lies on the line segment joining the points $P ( 2 , - 3 , 4 )$ and $Q ( 8 , 0 , 10 )$, then the distance of $R$ from the origin is
(1) $2 \sqrt { 21 }$
(2) $\sqrt { 53 }$
(3) 6
(4) $2 \sqrt { 14 }$
Q90 Binomial Distribution Find Minimum n for a Probability Threshold View
The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least $90 \%$ is:
(1) 2
(2) 4
(3) 5
(4) 3