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
2022 session1_24jun_shift1

20 maths questions

Q2 Projectiles Finding Angle of Projection from Given Conditions View
A projectile is projected with velocity of $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle $\theta$ with the horizontal. After $t$ seconds its inclination with horizontal becomes zero. If $R$ represents horizontal range of the projectile, the value of $\theta$ will be : [use $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ ]
(1) $\frac { 1 } { 2 } \sin ^ { - 1 } \left( \frac { 5 t ^ { 2 } } { 4 R } \right)$
(2) $\frac { 1 } { 2 } \sin ^ { - 1 } \left( \frac { 4 R } { 5 t ^ { 2 } } \right)$
(3) $\tan ^ { - 1 } \left( \frac { 4 t ^ { 2 } } { 5 R } \right)$
(4) $\cot ^ { - 1 } \left( \frac { R } { 20 t ^ { 2 } } \right)$
Q3 Circular Motion 1 Maximum Speed/Tension from String Breaking Limit View
A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N . If the maximum speed with which the stone can revolve is $\frac { K } { \pi } \mathrm { rev } \min ^ { - 1 }$. The value of $K$ is : (Assume the string is massless and un-stretchable)
(1) 400
(2) 300
(3) 600
(4) 800
Q4 Friction Deceleration and Stopping Distance on a Horizontal Surface View
A block of mass 10 kg starts sliding on a surface with an initial velocity of $9.8 \mathrm {~ms} ^ { - 1 }$. The coefficient of friction between the surface and block is 0.5 . The distance covered by the block before coming to rest is :[use $\mathrm { g } = 9.8 \mathrm {~ms} ^ { - 2 }$ ]
(1) 9.8 m
(2) 4.9 m
(3) 12.5 m
(4) 19.6 m
Q5 Work done and energy Work done by constant or variable force via integration View
A particle experiences a variable force $\overrightarrow { \mathrm { F } } = \left( 4 x \hat { i } + 3 y ^ { 2 } \hat { j } \right)$ in a horizontal $x - y$ plane. Assume distance in meters and force is newton. If the particle moves from point $( 1,2 )$ to point $( 2,3 )$ in the $x - y$ plane, then Kinetic Energy changes by :
(1) 25 J
(2) 50 J
(3) 12.5 J
(4) 0 J
Q21 Constant acceleration (SUVAT) Vertical projection (up or down) from a height View
From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s . A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s . A third ball released, from the rest from the same location, will reach the ground in $\_\_\_\_$ s.
Q23 Moments View
A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be $x \times 10 ^ { - 2 } \mathrm {~kg}$. The value of $x$ is $\_\_\_\_$ .
Q61 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3 x ^ { 2 } + \lambda x - 1 = 0$ is 15 , then $6 \left( \alpha ^ { 3 } + \beta ^ { 3 } \right) ^ { 2 }$ is equal to
(1) 46
(2) 36
(3) 24
(4) 18
Q62 Complex Numbers Argand & Loci Intersection of Loci and Simultaneous Geometric Conditions View
Let $A = \{ z \in \mathrm { C } : 1 \leqslant | z - ( 1 + i ) | \leqslant 2 \}$ and $B = \{ z \in A : | z - ( 1 - i ) | = 1 \}$. Then, $B$
(1) is an empty set
(2) contains exactly two elements
(3) contains exactly three elements
(4) is an infinite set
Q63 Arithmetic Sequences and Series Counting or Combinatorial Problems on APs View
If $\left\{ a _ { i } \right\} _ { i = 1 } ^ { \mathrm { n } }$, where $n$ is an even integer, is an arithmetic progression with common difference 1 , and $\sum _ { i = 1 } ^ { n } a _ { i } = 192 , \sum _ { i = 1 } ^ { \frac { n } { 2 } } a _ { 2 i } = 120$, then $n$ is equal to
(1) 18
(2) 36
(3) 96
(4) 48
Q64 Number Theory Modular Arithmetic Computation View
The remainder when $3 ^ { 2022 }$ is divided by 5 is
(1) 1
(2) 2
(3) 3
(4) 4
Q65 Standard trigonometric equations Evaluate trigonometric expression given a constraint View
Let $\mathrm { S } = \left\{ \theta \in [ - \pi , \pi ] - \left\{ \pm \frac { \pi } { 2 } \right\} : \sin \theta \tan \theta + \tan \theta = \sin 2 \theta \right\}$. If $T = \sum _ { \theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal to
(1) $7 + \sqrt { 3 }$
(2) 5
(3) $8 + \sqrt { 3 }$
(4) 9
Q66 Circles Circle Equation Derivation View
Let $x ^ { 2 } + y ^ { 2 } + A x + B y + C = 0$ be a circle passing through ( 0,6 ) and touching the parabola $y = x ^ { 2 }$ at ( 2,4 ). Then $A + C$ is equal to
(1) 16
(2) $\frac { 88 } { 5 }$
(3) 72
(4) - 8
Q67 Conic sections Tangent and Normal Line Problems View
Let $\lambda x - 2 y = \mu$ be a tangent to the hyperbola $a ^ { 2 } x ^ { 2 } - y ^ { 2 } = b ^ { 2 }$. Then $\left( \frac { \lambda } { a } \right) ^ { 2 } - \left( \frac { \mu } { b } \right) ^ { 2 }$ is equal to
(1) - 2
(2) - 4
(3) 2
(4) 4
Q68 Proof True/False Justification View
The number of choices for $\Delta \in \{ \wedge , \vee , \Rightarrow , \Leftrightarrow \}$, such that $( p \Delta q ) \Rightarrow ( ( p \Delta \sim q ) \vee ( ( \sim p ) \Delta q ) )$ is a tautology, is
(1) 1
(2) 2
(3) 3
(4) 4
Q69 Matrices Determinant and Rank Computation View
Let $S = \{ \sqrt { n } : 1 \leqslant n \leqslant 50$ and $n$ is odd $\}$. Let $a \in S$ and $A = \left[ \begin{array} { r r r } 1 & 0 & a \\ - 1 & 1 & 0 \\ - a & 0 & 1 \end{array} \right]$. If $\Sigma _ { a \in S } \operatorname { det } ( \operatorname { adj } A ) = 100 \lambda$, then $\lambda$ is equal to
(1) 218
(2) 221
(3) 663
(4) 1717
Q70 Matrices Linear System and Inverse Existence View
The number of values of $\alpha$ for which the system of equations $x + y + z = \alpha$ $\alpha x + 2 \alpha y + 3 z = - 1$ $x + 3 \alpha y + 5 z = 4$ is inconsistent, is
(1) 0
(2) 1
(3) 2
(4) 3
Q71 Reciprocal Trig & Identities View
The set of all values of $k$ for which $\left( \tan ^ { - 1 } x \right) ^ { 3 } + \left( \cot ^ { - 1 } x \right) ^ { 3 } = \mathrm { k } \pi ^ { 3 } , x \in R$, is the interval
(1) $\left[ \frac { 1 } { 32 } , \frac { 7 } { 8 } \right)$
(2) $\left( \frac { 1 } { 24 } , \frac { 13 } { 16 } \right)$
(3) $\left[ \frac { 1 } { 48 } , \frac { 13 } { 16 } \right]$
(4) $\left[ \frac { 1 } { 32 } , \frac { 9 } { 8 } \right)$
Q72 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
The domain of $f ( x ) = \frac { \cos ^ { - 1 } \left( \frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 9 } \right) } { \log \left( x ^ { 2 } - 3 x + 2 \right) }$ is
(1) $x \in \left[ \frac { - 1 } { 2 } , 1 \right) \cup ( 2 , \infty ) - \{ 3 \}$
(2) $x \in \left[ \frac { - 1 } { 2 } , 1 \right] \cup ( 2 , \infty ) - \{ 3 \}$
(3) $x \in \left( \frac { - 1 } { 2 } , 1 \right) \cup [ 2 , \infty ) - \{ 3 \}$
(4) $x \in \left[ \frac { - 1 } { 2 } , 1 \right) \cup [ 2 , \infty ) - \{ 3 \}$
Q73 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions View
For the function $f ( x ) = 4 \log _ { e } ( x - 1 ) - 2 x ^ { 2 } + 4 x + 5 , x > 1$, which one of the following is NOT correct?
(1) $f ( x )$ is increasing in $( 1,2 )$ and decreasing in $( 2 , \infty )$
(2) $f ( x ) = - 1$ has exactly two solutions
(3) $f ^ { \prime } ( \mathrm { e } ) - f ^ { \prime \prime } ( 2 ) < 0$
(4) $f ( x ) = 0$ has a root in the interval $( e , e + 1 )$
Q74 Tangents, normals and gradients Find tangent line with a specified slope or from an external point View
If the tangent at the point $\left( x _ { 1 } , y _ { 1 } \right)$ on the curve $y = x ^ { 3 } + 3 x ^ { 2 } + 5$ passes through the origin, then $\left( x _ { 1 } , y _ { 1 } \right)$ does NOT lie on the curve