The alum used for purifying water is

An ideal gas expands isothermally from volume $V_1$ to $V_2$ and is then compressed to the original volume $V_1$ adiabatically. If the initial pressure is $P_1$ and the final pressure is $P_3$,and the total work done is $W$,then:

Two blocks of masses $1 ~kg$ and $2 ~kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 ~N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 ~m/s^2$.

Which of the following factors does $NOT$ favor the formation of an electrovalent (ionic) bond?

If the area of an equilateral triangle inscribed in the circle $x^2+y^2+10x+12y+c=0$ is $27\sqrt{3}$ sq. units,then $c$ is equal to:

$A$ simple pendulum of mass $200\, g$ and length $100\, cm$ is moved aside until the string makes an angle of $60^\circ$ with the vertical. The kinetic and potential energies of the bob,when the string is inclined at $30^\circ$ to the vertical,are