The least positive integer $n$ for which $(1+i)^n=(1-i)^n$ is

In almost all Indian metropolitan cities like Delhi,the major atmospheric pollutant$(s)$ is/are:

Two particles undergo $SHM$ along parallel lines with the same time period $(T)$ and equal amplitudes. At a particular instant,one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time:

If one end of the diameter is $(1, 1)$ and the other end lies on the line $x + y = 3$,then the locus of the centre of the circle is

$A$ spherically symmetric gravitational system of particles has a mass density $\rho = \begin{cases} \rho_0 & \text{for } r \leq R \\ 0 & \text{for } r > R \end{cases}$ where $\rho_0$ is a constant. $A$ test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r$ $(0 < r < \infty)$ from the centre of the system is represented by:

$\int_{-1}^1 \frac{\cosh x}{1+e^{2 x}} d x$ is equal to :