The average degree of freedom per molecule of a gas is $6$. The gas performs $25 \, J$ of work while expanding at constant pressure. The heat absorbed by the gas is ...... $J$.

Which of the following statements regarding the nature of physical laws is $NOT$ correct?

When ethanol is reacted with $PCl_5$,it gives $A$,$POCl_3$,and $HCl$. The reaction of $A$ with silver nitrite $(AgNO_2)$ gives the major product $(B)$ and $AgCl$. What are $A$ and $B$ respectively?

The kinetic energy of an electron and a proton is $10^{-32} \ J$. Then the relation between their de-Broglie wavelengths is

Let $\alpha \neq 1$ be a real root of the equation $x^3-ax^2+ax-1=0$,where $a \neq -1$ is a real number. Then,a root of this equation,among the following,is

$A$ block of mass $m$ is placed on a surface with a vertical cross-section given by $y = \frac{x^3}{6}$. If the coefficient of friction is $0.5$,the maximum height above the ground at which the block can be placed without slipping is