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 :

1

The number of integers greater than $6000$ that can be formed, using the digits $3,5,6,7$ and $8$, without repetition, …

Topic: JEE Main 2015 (Offline)

2

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…

Topic: JEE Main 2015 (Offline)

3

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0,…

Topic: JEE Main 2015 (Offline)

4

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 :

Topic: JEE Main 2015 (Offline)

5

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^{2}=8y$. If the point $P$ divides the line segment $OQ$ …

Topic: JEE Main 2015 (Offline)

6

Let $\tan^{-1}y=\tan^{-1}x+\tan^{-1}\left(\dfrac{2x}{1-x^{2}}\right)$, where $|x|

Topic: JEE Main 2015 (Offline)

7

Let $f(x)$ be a polynomial of degree four having extreme values at $x=1$ and $x=2$. If $\displaystyle \lim_{x\to 0}\lef…

Topic: JEE Main 2015 (Offline)

8

The set of all values of $\lambda$ for which the system of linear equations  $2x_{1}-2x_{2}+x_{3}=\lambda x_{…

Topic: JEE Main 2015 (Offline)

9

If $A=\begin{bmatrix} 1 & 2 & 2\\ 2 & 1 & -2\\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $AA^{T}=9I$…

Topic: JEE Main 2015 (Offline)

10

The integral $\displaystyle \int \frac{dx}{x^{2}(x^{4}+1)^{3/4}}$ equals :

Topic: JEE Main 2015 (Offline)

1

Let $A$ and $B$ be two sets containing four and two elements respectively. Then, the number of subsets of the set $A\ti…

Topic: JEE Main 2015 (Offline)