In an adiabatic change,the pressure and temperature of a monoatomic gas are related as $P \propto T^C$,where $C$ equals

Three taps $A, B, C$ fill up a tank independently in $10 \, h$,$20 \, h$,and $30 \, h$,respectively. Initially,the tank is empty. Exactly one pair of taps is open during each hour,and every pair of taps is open for at least one hour. What is the minimum number of hours required to fill the tank?

Considering ideal gas behavior, the expansion work done $(in kJ )$ when $144 g$ of water is electrolyzed completely under constant pressure at $300 K$ is $...$ .
Use: Universal gas constant $( R )=8.3 J K ^{-1} mol^{-1}$; Atomic mass $($in amu$)$: $H =1, O =16$

The solution set of $(5+4 \cos \theta)(2 \cos \theta+1)=0$ in the interval $[0, 2 \pi]$ is:

Which of the following on thermal decomposition produces both basic and acidic oxides?

In the following diagram,the charge and potential difference across $8\, \mu F$ capacitance will be nearly