The value of $\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} - 1 = $

The potential energy of a particle oscillating along the $x-$axis is given as $U = 20 + (x - 2)^2$,where $U$ is in $joules$ and $x$ is in $meters$. The total mechanical energy of the particle is $36 \, J$. The maximum kinetic energy of the particle is ............... $J$.

If a spherical balloon has a variable diameter $3x + \frac{9}{2}$,then the rate of change of its volume with respect to $x$ is

The coefficient of $x^k$ in the expansion of $\frac{1-2x-x^2}{e^{-x}}$ is

The energy that should be added to an electron,to reduce its de-Broglie wavelength from $10^{-10} \ m$ to $0.5 \times 10^{-10} \ m$,will be

Celestite is a mineral of which of the following?