$A$ compound $X$ with molecular formula $C_3H_8O$ can be oxidised to a compound $Y$ with the molecular formula $C_3H_6O_2$. $X$ is most likely to be

An ideal gas is taken through the cycle $A \to B \to C \to A$,as shown in the figure. If the net heat supplied to the gas in the cycle is $5 \ J$,the work done by the gas in the process $C \to A$ is ....... $J$.

$A$ metal nitrate reacts with $KI$ to give a black precipitate which on addition of excess of $KI$ converts into an orange-colored solution. The cation of the metal nitrate is

In an intrinsic semiconductor at room temperature,the number of electrons and holes are:

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now,the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result,the particles move towards each other on the surface. The magnitude of acceleration,when the separation between them becomes $2x$,is

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is: