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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Let $T_{n}$ be the number of all possible triangles formed by joining vertices
of an $n$-sided regular polygon. If $T_{…
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
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 $x$-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)
The equation of the circle passing through the foci of the ellipse
$\dfrac{x^{2}}{16}+\dfrac{y^{2}}{9}=1$, and having c…
Topic: JEE Main 2013 (Offline)
If $y=\sec(\tan^{-1}x)$, then $\dfrac{dy}{dx}$ at $x=1$ is equal to :
Topic: JEE Main 2013 (Offline)
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 :
Topic: JEE Main 2013 (Offline)
If $\int f(x)\,dx=\psi(x)$, then $\int x^{5}f(x^{3})\,dx$ is equal to
Topic: JEE Main 2013 (Offline)
Statement-1 : The value of the integral
$\displaystyle \int_{\pi/6}^{\pi/3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\pi…
Topic: JEE Main 2013 (Offline)
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…
Topic: JEE Main 2013 (Offline)
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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 …
Topic: JEE Main 2013 (Offline)
If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg\left(\frac{1+z}{1+z^2}\right)$ equals :
Topic: JEE Main 2013 (Offline)
$ \text{The expression } \dfrac{\tan A}{1-\cot A,} + \dfrac{\cot A}{1-\tan A,} \text{ can be written as:} $
Topic: JEE Main 2013 (Offline)
If the vectors $\overrightarrow {AB} = 3\widehat i + 4\widehat k$ and $\overrightarrow {AC} = 5\widehat i - 2\widehat…
Topic: JEE Main 2013 (Offline)
If the lines ${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$ and ${{x - 1} \over k} = {{y - 4} \over 2…
Topic: JEE Main 2013 (Offline)
