jee-main

Papers (169)
2025
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2024
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2023
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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
2012 07may

18 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 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 Binomial Theorem (positive integer n) 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 Straight Lines & Coordinate Geometry 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 Conic sections 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
Q72 Small angle approximation View
$\lim _ { x \rightarrow 0 } \left( \frac { x - \sin x } { x } \right) \sin \left( \frac { 1 } { x } \right)$
(1) equals 1
(2) equals 0
(3) does not exist
(4) equals $-1$
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 Principle of Inclusion/Exclusion 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 Matrices 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 Curve Sketching 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) $[ - 1,1 ]$