JEE MAIN 2015 Previous Year Questions (PYQs) – Page 2 of 2
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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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Solution
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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4
Solution
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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Solution
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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Solution
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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4
Solution
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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Solution
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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Solution
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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Solution
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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Solution
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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Solution
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