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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN 2015 PYQ

JEE MAIN PYQ 2015
If the function.

$g\left( x \right) = \left\{ {\matrix{ {k\sqrt {x + 1} ,} & {0 \le x \le 3} \cr {m\,x + 2,} & {3 < x \le 5} \cr } } \right.$

is differentiable, then the value of $k+m$ is :





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JEE MAIN PYQ 2015
The mean of the data set comprising of $16$ observations is $16$. If one of the observations valued $16$ is deleted and three new observations valued $3,4$ and $5$ are added to the data, then the mean of the resultant data is:





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JEE MAIN PYQ 2015
$\displaystyle \lim_{x\to 0} \frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :





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JEE MAIN PYQ 2015
Let $\alpha$ and $\beta$ be the roots of equation $x^{2}-6x-2=0$. If $a_{n}=\alpha^{n}-\beta^{n}$, for $n\ge 1$, then the value of $\dfrac{a_{10}-2a_{8}}{2a_{9}}$ is equal to :





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JEE MAIN PYQ 2015
If 12 different balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :





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JEE MAIN PYQ 2015
Let $y(x)$ be the solution of the differential equation $(x\log x)\dfrac{dy}{dx}+y=2x\log x,\;(x\ge 1).$ Then $y(e)$ is equal to :





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JEE MAIN PYQ 2015
The area (in sq. units) of the region described by $\{(x,y):y^{2}\le 2x \text{ and } y\ge 4x-1\}$ is :





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JEE MAIN PYQ 2015
The integral $\displaystyle \int_{2}^{4}\dfrac{\log x^{2}}{\log x^{2}+\log(36-12x+x^{2})}\,dx$ is equal to :





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JEE MAIN PYQ 2015
The integral $\displaystyle \int \frac{dx}{x^{2}(x^{4}+1)^{3/4}}$ equals :





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JEE MAIN PYQ 2015
If $A=\begin{bmatrix} 1 & 2 & 2\\ 2 & 1 & -2\\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $AA^{T}=9I$, where $I$ is $3\times 3$ identity matrix, then the ordered pair $(a,b)$ is equal to :





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JEE MAIN PYQ 2015
The set of all values of $\lambda$ for which the system of linear equations  
$2x_{1}-2x_{2}+x_{3}=\lambda x_{1}$  
$2x_{1}-3x_{2}+2x_{3}=\lambda x_{2}$  
$-x_{1}+2x_{2}=\lambda x_{3}$  
has a non-trivial solution  





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JEE MAIN PYQ 2015
Let $f(x)$ be a polynomial of degree four having extreme values at $x=1$ and $x=2$. If $\displaystyle \lim_{x\to 0}\left[1+\frac{f(x)}{x^{2}}\right]=3$, then $f(2)$ is equal to :





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JEE MAIN PYQ 2015
Let $\tan^{-1}y=\tan^{-1}x+\tan^{-1}\left(\dfrac{2x}{1-x^{2}}\right)$, where $|x|<\dfrac{1}{\sqrt{3}}$. Then a value of $y$ is :





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JEE MAIN PYQ 2015
Let $O$ be the vertex and $Q$ be any point on the parabola, $x^{2}=8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$, then locus of $P$ is :





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JEE MAIN PYQ 2015
Locus of the image of the point $(2,3)$ in the line $(2x-3y+4)+k(x-2y+3)=0,\;k\in\mathbb{R},$ is a :





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JEE MAIN PYQ 2015
The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0,0)$, $(0,41)$ and $(41,0)$ is :





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JEE MAIN PYQ 2015
If $m$ is the A.M. of two distinct real numbers $l$ and $n$ $(l,n>1)$ and $G_{1},G_{2}$ and $G_{3}$ are three geometric means between $l$ and $n$, then $G_{1}^{4}+2G_{2}^{4}+G_{3}^{4}$ equals :





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JEE MAIN PYQ 2015
The number of integers greater than $6000$ that can be formed, using the digits $3,5,6,7$ and $8$, without repetition, is :





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JEE MAIN PYQ 2015
A complex number $z$ is said to be unimodular if $|z|=1$. Suppose $z_{1}$ and $z_{2}$ are complex numbers such that $\dfrac{z_{1}-2z_{2}}{2-z_{1}\overline{z_{2}}}$ is unimodular and $z_{2}$ is not unimodular. Then the point $z_{1}$ lies on a :





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JEE MAIN PYQ 2015
Let $A$ and $B$ be two sets containing four and two elements respectively. Then, the number of subsets of the set $A\times B$, each having at least three elements, are :





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