JEE MAIN 2013 Previous Year Questions (PYQs) – Page 1 of 3
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Let A and B be two sets containing 2 elements and 4 elements respectively. The
number of subsets of AXB having 3 or more elements is :
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Solution
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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Solution
$\displaystyle \lim_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :
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Solution
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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Solution
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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4
Solution
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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Solution
If $\int f(x)\,dx=\psi(x)$, then $\int x^{5}f(x^{3})\,dx$ is equal to
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Solution
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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Solution
If $y=\sec(\tan^{-1}x)$, then $\dfrac{dy}{dx}$ at $x=1$ is equal to :
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Solution
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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Solution
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