$A$ coordination complex contains $Co^{3+}$,$Cl^{-}$,and $NH_3$. When dissolved in water,one mole of this complex gives a total of $3$ moles of ions. The complex is

The value of $\cos 15^{\circ} \cos 7.5^{\circ} \sin 7.5^{\circ}$ is

Which of the following is not a peroxo acid?

Select the correct option on the basis of the following sentences regarding a gland's function:
$(I)$ Hormones increase alertness.
$(II)$ Hormones increase the heart beat.
$(III)$ Stimulate the breakdown of glycogen.
$(IV)$ Stimulate the breakdown of lipids and proteins.

If a line in space makes angles $\alpha, \beta,$ and $\gamma$ with the coordinate axes,then the value of $\cos 2\alpha + \cos 2\beta + \cos 2\gamma + \sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ is equal to:

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $PQ$ is about ........ $kg-m^2.$