If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg\left(\frac{1+z}{1+z^2}\right)$ equals :

1

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)

2

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)

3

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)

4

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)

5

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)

6

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)

7

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)

8

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)

9

If $y=\sec(\tan^{-1}x)$, then $\dfrac{dy}{dx}$ at $x=1$ is equal to :

Topic: JEE Main 2013 (Offline)

10

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)

1

$ \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)

2

If the vectors $\overrightarrow {AB} = 3\widehat i + 4\widehat k$ and $\overrightarrow {AC} = 5\widehat i - 2\widehat…

Topic: JEE Main 2013 (Offline)

3

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)