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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If $y=\sec(\tan^{-1}x)$, then $\dfrac{dy}{dx}$ at $x=1$ is equal to :
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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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If $\int f(x)\,dx=\psi(x)$, then $\int x^{5}f(x^{3})\,dx$ is equal to
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Statement-1 : The value of the integral
$\displaystyle \int_{\pi/6}^{\pi/3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\pi…
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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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At present, a firm is manufacturing $2000$ items. It is estimated that the rate of
change of production $P$ w.r.t. addi…
Topic: JEE Main 2013 (Offline)
$\displaystyle \lim_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :
Topic: JEE Main 2013 (Offline)
All the students of a class performed poorly in Mathematics. The teacher
decided to give grace marks of $10$ to each of…
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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 mor…
Topic: JEE Main 2013 (Offline)
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The $x$-coordinate of the incentre of the triangle that has the coordinates of
mid points of its sides as $(0,1)$, $(1,…
Topic: JEE Main 2013 (Offline)
A ray of light along $x+\sqrt{3}\,y=\sqrt{3}$ gets reflected upon reaching
$X$-axis, the equation of the reflected ray …
Topic: JEE Main 2013 (Offline)
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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Let $T_{n}$ be the number of all possible triangles formed by joining vertices
of an $n$-sided regular polygon. If $T_{…
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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
Topic: JEE Main 2013 (Offline)
The real number $k$ for which the equation $2x^{3}+3x+k=0$ has two distinct real roots in $[0,1]$
Topic: JEE Main 2013 (Offline)
The number of values of $k$, for which the system of equations : $\matrix{
{\left( {k + 1} \right)x + 8y = 4k} \cr …
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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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$ \text{The expression } \dfrac{\tan A}{1-\cot A,} + \dfrac{\cot A}{1-\tan A,} \text{ can be written as:} $
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If the vectors $\overrightarrow {AB} = 3\widehat i + 4\widehat k$ and $\overrightarrow {AC} = 5\widehat i - 2\widehat…
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