$A$ cannon shell fired breaks into two equal parts at its highest point. One part retraces its path to the cannon with kinetic energy $E_1$,and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is:

The rate of disintegration of a fixed quantity of a radioactive element can be increased by

$50 \, g$ of copper is heated to increase its temperature by $10 \, ^\circ C$. If the same quantity of heat is given to $10 \, g$ of water,the rise in its temperature is ........ $^\circ C$ (Specific heat of copper $= 420 \, J \cdot kg^{-1} \cdot ^\circ C^{-1}$,Specific heat of water $= 4200 \, J \cdot kg^{-1} \cdot ^\circ C^{-1}$)

If $EAN$ of central metal cation $M^{2+}$ in a non-chelating complex is $36$ and atomic number of metal $M$ is $26$,then the number of monodentate ligands in this complex is:

The bond dissociation energy of $B-F$ in $BF_3$ is $646 \ kJ \ mol^{-1}$ whereas that of $C-F$ in $CF_4$ is $515 \ kJ \ mol^{-1}$. The correct reason for higher $B-F$ bond dissociation energy as compared to that of $C-F$ is

If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle of $\frac{3 \pi}{4}$ with the positive $X$-axis,then the value of $f^{\prime}(3)$ is