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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN 2013 PYQ

JEE MAIN PYQ 2013
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A\times B$ having 3 or more elements is :





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JEE MAIN PYQ 2013
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?





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JEE MAIN PYQ 2013
$\displaystyle \lim_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :





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JEE MAIN PYQ 2013
At present, a firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ w.r.t. additional number of workers $x$ is given by $\dfrac{dP}{dx}=100-12\sqrt{x}$. If the firm employs $25$ more workers, then the new level of production of items is :





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JEE MAIN PYQ 2013
The area (in square units) bounded by the curves $y=\sqrt{x}$, $2y-x+3=0$, $x$-axis, and lying in the first quadrant is :





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JEE MAIN PYQ 2013
Statement-1 : The value of the integral $\displaystyle \int_{\pi/6}^{\pi/3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\pi/6$ Statement-2 : $\displaystyle \int_{a}^{b}f(x)\,dx=\int_{a}^{b}f(a+b-x)\,dx$.





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JEE MAIN PYQ 2013
If $\int f(x)\,dx=\psi(x)$, then $\int x^{5}f(x^{3})\,dx$ is equal to





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JEE MAIN PYQ 2013
If $x,y,z$ are in A.P. and $\tan^{-1}x,\tan^{-1}y$ and $\tan^{-1}z$ are also in A.P., then :





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JEE MAIN PYQ 2013
If $y=\sec(\tan^{-1}x)$, then $\dfrac{dy}{dx}$ at $x=1$ is equal to :





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JEE MAIN PYQ 2013
The equation of the circle passing through the foci of the ellipse $\dfrac{x^{2}}{16}+\dfrac{y^{2}}{9}=1$, and having centre at $(0,3)$ is :





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JEE MAIN PYQ 2013
The $x$-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0,1)$, $(1,1)$ and $(1,0)$ is :





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JEE MAIN PYQ 2013
A ray of light along $x+\sqrt{3}\,y=\sqrt{3}$ gets reflected upon reaching $X$-axis, the equation of the reflected ray is :





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JEE MAIN PYQ 2013
The term independent of $x$ in expansion of $\left(\dfrac{x+1}{x^{2/3}-x^{1/3}+1}-\dfrac{x-1}{x-x^{1/2}}\right)^{10}$ is





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JEE MAIN PYQ 2013
Let $T_{n}$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1}-T_{n}=10$, then the value of $n$ is :





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JEE MAIN PYQ 2013
If the equations $x^{2}+2x+3=0$ and $ax^{2}+bx+c=0$, $a,b,c\in\mathbb{R}$, have a common root, then $a:b:c$ is





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JEE MAIN PYQ 2013
The real number $k$ for which the equation $2x^{3}+3x+k=0$ has two distinct real roots in $[0,1]$





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JEE MAIN PYQ 2013
The number of values of $k$, for which the system of equations : $\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \cr {kx + \left( {k + 3} \right)y = 3k - 1} \cr } $





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JEE MAIN PYQ 2013
If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg\left(\frac{1+z}{1+z^2}\right)$ equals :





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JEE MAIN PYQ 2013
$ \text{The expression } \dfrac{\tan A}{1-\cot A,} + \dfrac{\cot A}{1-\tan A,} \text{ can be written as:} $





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JEE MAIN PYQ 2013
If the vectors $\overrightarrow {AB} = 3\widehat i + 4\widehat k$ and $\overrightarrow {AC} = 5\widehat i - 2\widehat j + 4\widehat k$ are the sides of a triangle $ABC,$ then the length of the median through $A$ is :





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JEE MAIN PYQ 2013
If the lines ${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$ and ${{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}$ are coplanar, then $k$ can have :





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