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 session1_07jan_shift2

17 maths questions

Q21 Forces, equilibrium and resultants View
The sum of two forces $\overrightarrow { \mathrm { P } }$ and $\overrightarrow { \mathrm { Q } }$ is $\overrightarrow { \mathrm { R } }$ such that $| \overrightarrow { \mathrm { R } } | = | \overrightarrow { \mathrm { P } } |$. Find the angle between resultant of $2 \overrightarrow { \mathrm { P } }$ and $\overrightarrow { \mathrm { Q } }$ and $\overrightarrow { \mathrm { Q } }$.
Q22 Moments View
Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is $\mu = 0.4$, the maximum possible value of $100 \times \frac { b } { a }$ for a box not to topple before moving is $\_\_\_\_$
Q51 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
Let $\alpha$ and $\beta$ be the roots of the equation $x ^ { 2 } - x - 1 = 0$. If $p _ { k } = ( \alpha ) ^ { k } + ( \beta ) ^ { k } , k \geq 1$, then which one of the following statements is not true?
(1) $p _ { 3 } = p _ { 5 } - p _ { 4 }$
(2) $p _ { 5 } = 11$
(3) $\left( p _ { 1 } + p _ { 2 } + p _ { 3 } + p _ { 4 } + p _ { 5 } \right) = 26$
(4) $p _ { 5 } = p _ { 2 } \cdot p _ { 3 }$
Q52 Complex Numbers Argand & Loci Algebraic Conditions for Geometric Properties (Real, Imaginary, Collinear) View
If $\frac { 3 + i \sin \theta } { 4 - i \cos \theta } , \theta \in [ 0,2 \pi ]$, is a real number, then an argument of $\sin \theta + i \cos \theta$ is
(1) $\pi - \tan ^ { - 1 } \left( \frac { 4 } { 3 } \right)$
(2) $\pi - \tan ^ { - 1 } \left( \frac { 3 } { 4 } \right)$
(3) $- \tan ^ { - 1 } \left( \frac { 3 } { 4 } \right)$
(4) $\tan ^ { - 1 } \left( \frac { 4 } { 3 } \right)$
Q53 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
Let $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$, be a G.P. such that $a _ { 1 } < 0 , a _ { 1 } + a _ { 2 } = 4$ and $a _ { 3 } + a _ { 4 } = 16$. If $\sum _ { i = 1 } ^ { 9 } a _ { i } = 4 \lambda$, then $\lambda$, is equal to.
(1) - 513
(2) - 171
(3) 171
(4) $\frac { 511 } { 3 }$
Q54 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
If the sum of the first 40 terms of the series, $3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + \ldots$. is $( 102 ) \mathrm { m }$, then m is equal to
(1) 20
(2) 25
(3) 5
(4) 10
Q55 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions View
The coefficient of $x ^ { 7 }$ in the expression $( 1 + x ) ^ { 10 } + x ( 1 + x ) ^ { 9 } + x ^ { 2 } ( 1 + x ) ^ { 8 } + \ldots + x ^ { 10 }$, is
(1) 210
(2) 330
(3) 120
(4) 420
Q56 Combinations & Selection Basic Combination Computation View
The number of ordered pairs $( r , k )$ for which $6 . { } ^ { 35 } C _ { r } = \left( k ^ { 2 } - 3 \right) . { } ^ { 36 } C _ { r + 1 }$, where $k$ is an integer is
(1) 3
(2) 2
(3) 6
(4) 4
Q57 Straight Lines & Coordinate Geometry Locus Determination View
The locus of the mid-points of the perpendiculars drawn from points on the line $x = 2 y$, to the line $x = y$, is.
(1) $2 x - 3 y = 0$
(2) $5 x - 7 y = 0$
(3) $3 x - 2 y = 0$
(4) $7 x - 5 y = 0$
Q58 Circles Tangent Lines and Tangent Lengths View
Let the tangents drawn from the origin to the circle, $x ^ { 2 } + y ^ { 2 } - 8 x - 4 y + 16 = 0$ touch it at the points $A$ and $B$. Then $( A B ) ^ { 2 }$ is equal to
(1) $\frac { 52 } { 5 }$
(2) $\frac { 56 } { 5 }$
(3) $\frac { 64 } { 5 }$
(4) $\frac { 32 } { 5 }$
Q59 Conic sections Equation Determination from Geometric Conditions View
If $3 x + 4 y = 12 \sqrt { 2 }$ is a tangent to the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { 9 } = 1$ for some $a \in R$, then the distance between the foci of the ellipse is
(1) $2 \sqrt { 7 }$
(2) 4
(3) $2 \sqrt { 5 }$
(4) $2 \sqrt { 2 }$
Q60 Proof Direct Proof of a Stated Identity or Equality View
Let $A , B , C$ and $D$ be four non-empty sets. The contrapositive statement of "If $A \subseteq B$ and $B \subseteq D$, then $A \subseteq C$" is
(1) If $A \nsubseteq C$, then $A \subseteq B$ and $B \subseteq D$
(2) If $A \subseteq C$, then $B \subset A$ and $D \subset B$
(3) If $A \nsubseteq C$, then $A \nsubseteq B$ and $B \subseteq D$
(4) If $A \nsubseteq C$, then $A \nsubseteq B$ or $B \nsubseteq D$
Q61 Matrices Determinant and Rank Computation View
Let $\mathrm { A } = \left[ a _ { i j } \right]$ and $\mathrm { B } = \left[ b _ { i j } \right]$ be two $3 \times 3$ real matrices such that $b _ { i j } = ( 3 ) ^ { ( i + j - 2 ) } a _ { i j }$, where $i , j = 1,2,3$. If the determinant of B is 81, then determinant of A is
(1) $\frac { 1 } { 3 }$
(2) 3
(3) $\frac { 1 } { 81 }$
(4) $\frac { 1 } { 9 }$
Q62 Implicit equations and differentiation Compute slope at a point via implicit differentiation (single-step) View
Let $y = y ( x )$ be a function of $x$ satisfying $y \sqrt { 1 - x ^ { 2 } } = k - x \sqrt { 1 - y ^ { 2 } }$ where $k$ is a constant and $y \left( \frac { 1 } { 2 } \right) = - \frac { 1 } { 4 }$. Then $\frac { d y } { d x }$ at $x = \frac { 1 } { 2 }$, is equal to
(1) $- \frac { \sqrt { 5 } } { 4 }$
(2) $- \frac { \sqrt { 5 } } { 2 }$
(3) $\frac { 2 } { \sqrt { 5 } }$
(4) $\frac { \sqrt { 5 } } { 2 }$
Q63 Applied differentiation Properties of differentiable functions (abstract/theoretical) View
The value of $c$, in the Lagrange's mean value theorem for the function $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 8 x + 11$, when $x \in [ 0,1 ]$, is
(1) $\frac { 4 - \sqrt { 5 } } { 3 }$
(2) $\frac { 4 - \sqrt { 7 } } { 3 }$
(3) $\frac { 2 } { 3 }$
(4) $\frac { \sqrt { 7 } - 2 } { 3 }$
Q64 Stationary points and optimisation Find critical points and classify extrema of a given function View
Let $f ( x )$ be a polynomial of degree 5 such that $x = \pm 1$ are its critical points. If $\lim _ { x \rightarrow 0 } \left( 2 + \frac { f ( x ) } { x ^ { 3 } } \right) = 4$, then which one of the following is not true?
(1) $f$ is an odd function
(2) $f ( 1 ) - 4 f ( - 1 ) = 4$
(3) $x = 1$ is a point of local minimum and $x = - 1$ is a point of local maximum
(4) $x = 1$ is a point of local maxima of $f$
Q65 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
The value of $\alpha$ for which $4 \alpha \int _ { - 1 } ^ { 2 } e ^ { - \alpha | x | } d x = 5$, is
(1) $\log _ { e } 2$
(2) $\log _ { e } \left( \frac { 3 } { 2 } \right)$
(3) $\log _ { e } \sqrt { 2 }$
(4) $\log _ { e } \left( \frac { 4 } { 3 } \right)$