How many $mL$ of $1 \, M$ $H_2SO_4$ is required to neutralize $10 \, mL$ of $1 \, M$ $NaOH$ solution?

The shadow of a tower standing on a level ground is found to be $60 \ m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is

Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied,$\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system.

Process	Condition
$(I)$ Adiabatic	$(A)$ $\Delta W = 0$
$(II)$ Isothermal	$(B)$ $\Delta Q = 0$
$(III)$ Isochoric	$(C)$ $\Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$
$(IV)$ Isobaric	$(D)$ $\Delta U = 0$

If $\frac{x^2}{(x^2 + a^2)(x^2 + b^2)} = K \left( \frac{a^2}{x^2 + a^2} - \frac{b^2}{x^2 + b^2} \right)$,then $K =$

Charges of $+\frac{10}{3} \times 10^{-9} \text{ C}$ are placed at each of the four corners of a square of side $8 \text{ cm}$. The potential at the intersection of the diagonals is:

What is the final product obtained by the reduction of glycerol with hydriodic acid $(HI)$?