jee-main

Papers (191)
2026
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2025
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2024
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2023
session1_01feb_shift1 28 session1_01feb_shift2 3 session1_24jan_shift1 11 session1_24jan_shift2 11 session1_25jan_shift1 29 session1_25jan_shift2 29 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 5 session1_30jan_shift2 27 session1_31jan_shift1 28 session1_31jan_shift2 15 session2_06apr_shift1 5 session2_06apr_shift2 16 session2_08apr_shift1 29 session2_08apr_shift2 13 session2_10apr_shift1 29 session2_10apr_shift2 16 session2_11apr_shift1 6 session2_11apr_shift2 8 session2_12apr_shift1 26 session2_13apr_shift1 24 session2_13apr_shift2 24 session2_15apr_shift1 19
2022
session1_24jun_shift1 19 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 14 session1_26jun_shift1 29 session1_26jun_shift2 24 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 4 session2_25jul_shift1 29 session2_25jul_shift2 20 session2_26jul_shift1 29 session2_26jul_shift2 23 session2_27jul_shift1 28 session2_27jul_shift2 29 session2_28jul_shift1 11 session2_28jul_shift2 29 session2_29jul_shift1 17 session2_29jul_shift2 18
2021
session1_24feb_shift1 9 session1_24feb_shift2 4 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 15 session2_16mar_shift1 29 session2_16mar_shift2 18 session2_17mar_shift1 21 session2_17mar_shift2 27 session2_18mar_shift1 18 session2_18mar_shift2 9 session3_20jul_shift1 29 session3_20jul_shift2 29 session3_22jul_shift1 9 session3_25jul_shift1 8 session3_25jul_shift2 14 session3_27jul_shift1 4 session3_27jul_shift2 7 session4_01sep_shift2 14 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 29 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 28 session1_07jan_shift2 20 session1_08jan_shift1 5 session1_08jan_shift2 11 session1_09jan_shift1 26 session1_09jan_shift2 16 session2_02sep_shift1 18 session2_02sep_shift2 16 session2_03sep_shift1 23 session2_03sep_shift2 8 session2_04sep_shift1 14 session2_04sep_shift2 27 session2_05sep_shift1 22 session2_05sep_shift2 29 session2_06sep_shift1 11 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 29 session1_10jan_shift2 14 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 29 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 5 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 30 15apr 28 15apr_shift1 28 15apr_shift2 6 16apr 19
2017
02apr 30 08apr 30 09apr 34
2016
03apr 28 09apr 29 10apr 30
2015
04apr 29 10apr 29 11apr 8
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 12 22apr 5 23apr 14 25apr 13
2012
07may 17 12may 21 19may 14 26may 17 offline 30
2011
jee-main_2011.pdf 18
2010
jee-main_2010.pdf 6
2009
jee-main_2009.pdf 2
2008
jee-main_2008.pdf 4
2007
jee-main_2007.pdf 38
2006
jee-main_2006.pdf 15
2005
jee-main_2005.pdf 25
2004
jee-main_2004.pdf 22
2003
jee-main_2003.pdf 8
2002
jee-main_2002.pdf 12
2012 07may

17 maths questions

Q61 Discriminant and conditions for roots Parameter range for specific root conditions (location/count) View
The value of k for which the equation $( K - 2 ) x ^ { 2 } + 8 x + K + 4 = 0$ has both roots real, distinct and negative is
(1) 6
(2) 3
(3) 4
(4) 1
Q62 Complex Numbers Arithmetic Modulus Inequalities and Bounds (Proof-Based) View
Let $Z _ { 1 }$ and $Z _ { 2 }$ be any two complex number. Statement 1: $\left| Z _ { 1 } - Z _ { 2 } \right| \geq \left| Z _ { 1 } \right| - \left| Z _ { 2 } \right|$ Statement 2: $\left| Z _ { 1 } + Z _ { 2 } \right| \leq \left| Z _ { 1 } \right| + \left| Z _ { 2 } \right|$
(1) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
(2) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
(3) Statement 1 is true, Statement 2 is false.
(4) Statement 1 is false, Statement 2 is true.
Q63 Combinations & Selection Basic Combination Computation View
If the number of 5-element subsets of the set $A = \left\{ a _ { 1 } , a _ { 2 } , \ldots , a _ { 20 } \right\}$ of 20 distinct elements is $k$ times the number of 5-element subsets containing $a _ { 4 }$, then $k$ is
(1) 5
(2) $\frac { 20 } { 7 }$
(3) 4
(4) $\frac { 10 } { 3 }$
Q64 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
The difference between the fourth term and the first term of a Geometrical Progression is 52. If the sum of its first three terms is 26, then the sum of the first six terms of the progression is
(1) 63
(2) 189
(3) 728
(4) 364
Q65 Arithmetic Sequences and Series Evaluation of a Finite or Infinite Sum View
The sum of the series $1 ^ { 2 } + 2.2 ^ { 2 } + 3 ^ { 2 } + 2.4 ^ { 2 } + 5 ^ { 2 } + 2.6 ^ { 2 } + \ldots . + 2 ( 2 m ) ^ { 2 }$ is
(1) $m ( 2 m + 1 ) ^ { 2 }$
(2) $m ^ { 2 } ( m + 2 )$
(3) $m ^ { 2 } ( 2 m + 1 )$
(4) $m ( m + 2 ) ^ { 2 }$
Q66 Generalised Binomial Theorem Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions View
If $f ( y ) = 1 - ( y - 1 ) + ( y - 1 ) ^ { 2 } - ( y - 1 ) ^ { 3 } + \ldots - ( y - 1 ) ^ { 17 }$ then the coefficient of $y ^ { 2 }$ in it is
(1) ${ } ^ { 17 } \mathrm { C } _ { 2 }$
(2) ${ } ^ { 17 } \mathrm { C } _ { 3 }$
(3) ${ } ^ { 18 } \mathrm { C } _ { 2 }$
(4) ${ } ^ { 18 } \mathrm { C } _ { 3 }$
Q67 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
If the straight lines $x + 3 y = 4,3 x + y = 4$ and $x + y = 0$ form a triangle, then the triangle is
(1) scalene
(2) equilateral triangle
(3) isosceles
(4) right angled isosceles
Q68 Simultaneous equations Collinearity and Concurrency View
The point of intersection of the lines $\left( a ^ { 3 } + 3 \right) x + a y + a - 3 = 0$ and $\left( a ^ { 5 } + 2 \right) x + ( a + 2 ) y + 2 a + 3 = 0$ (a real) lies on the $y$-axis for
(1) no value of $a$
(2) more than two values of $a$
(3) exactly one value of $a$
(4) exactly two values of $a$
Q69 Circles Circle Equation Derivation View
The equation of the circle passing through the point $( 1,2 )$ and through the points of intersection of $x ^ { 2 } + y ^ { 2 } - 4 x - 6 y - 21 = 0$ and $3 x + 4 y + 5 = 0$ is given by
(1) $x ^ { 2 } + y ^ { 2 } + 2 x + 2 y + 11 = 0$
(2) $x ^ { 2 } + y ^ { 2 } - 2 x + 2 y - 7 = 0$
(3) $x ^ { 2 } + y ^ { 2 } + 2 x - 2 y - 3 = 0$
(4) $x ^ { 2 } + y ^ { 2 } + 2 x + 2 y - 11 = 0$
Q70 Circles Tangent and Normal Line Problems View
Statement 1: $y = m x - \frac { 1 } { m }$ is always a tangent to the parabola, $y ^ { 2 } = - 4 x$ for all non-zero values of $m$. Statement 2: Every tangent to the parabola, $y ^ { 2 } = - 4 x$ will meet its axis at a point whose abscissa is nonnegative.
(1) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
(2) Statement 1 is false, Statement 2 is true.
(3) Statement 1 is true, Statement 2 is false.
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
Q71 Conic sections Equation Determination from Geometric Conditions View
If the eccentricity of a hyperbola $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$, which passes through $( K , 2 )$, is $\frac { \sqrt { 13 } } { 3 }$, then the value of $K ^ { 2 }$ is
(1) 18
(2) 8
(3) 1
(4) 2
Q74 Measures of Location and Spread View
The frequency distribution of daily working expenditure of families in a locality is as follows:
\begin{tabular}{ c } Expenditure
in ₹. $( x )$ :
& $0 - 50$ & $50 - 100$ & $100 - 150$ & $150 - 200$ & $200 - 250$ \hline
No. of
families $( f )$ :
& 24 & 33 & 37 & $b$ & 25 \hline \end{tabular}
If the mode of the distribution is Rs. 140, then the value of $b$ is
(1) 34
(2) 31
(3) 26
(4) 36
Q75 Straight Lines & Coordinate Geometry Perspective, Projection, and Applied Geometry View
If two vertical poles 20 m and 80 m high stand apart on a horizontal plane, then the height (in m) of the point of intersection of the lines joining the top of each pole to the foot of other is
(1) 16
(2) 18
(3) 50
(4) 15
Q76 Independent Events View
Let $X$ and $Y$ are two events such that $P ( X \cup Y ) = P ( X \cap Y )$. Statement 1: $P ( X \cap Y' ) = P ( X' \cap Y ) = 0$. Statement 2: $P ( X ) + P ( Y ) = 2 P ( X \cap Y )$
(1) Statement 1 is false, Statement 2 is true.
(2) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
(3) Statement 1 is true, Statement 2 is false.
(4) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
Q77 Matrices Determinant and Rank Computation View
If $A = \left( \begin{array} { c } \alpha - 1 \\ 0 \\ 0 \end{array} \right) , B = \left( \begin{array} { c } \alpha + 1 \\ 0 \\ 0 \end{array} \right)$ be two matrices, then $A B ^ { T }$ is a non-zero matrix for $| \alpha |$ not equal to
(1) 2
(2) 0
(3) 1
(4) 3
Q78 Simultaneous equations Linear System and Inverse Existence View
If the system of equations $$\begin{aligned} & x + y + z = 6 \\ & x + 2 y + 3 z = 10 \\ & x + 2 y + \lambda z = 0 \end{aligned}$$ has a unique solution, then $\lambda$ is not equal to
(1) 1
(2) 0
(3) 2
(4) 3
Q79 Composite & Inverse Functions Range and Image Set Determination View
The range of the function $f ( x ) = \frac { x } { 1 + | x | } , x \in R$, is
(1) $R$
(2) $( - 1,1 )$
(3) $R - \{ 0 \}$
(4) $[ - 1,1 ]$