$A$ block rests on a rough inclined plane making an angle of $30^o$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictional force on the block is $10\,N,$ the mass of the block (in $kg$) is (take $g = 10\,m/s^2$)

Four numbers are chosen at random from $\{1, 2, 3, \ldots, 40\}$. The probability that they are not consecutive is:

Anoxygenic photosynthesis is characteristic of

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$, the rise in temperature of the gas in $B$ is (in $~K$)

On addition of $1 \ mL$ solution of $10\% \ NaCl$ to $10 \ mL$ gold sol in the presence of $0.025 \ g$ of starch,the coagulation is just prevented. The gold number of starch is:

An engine is supposed to operate between two reservoirs at temperatures $727^{\circ}C$ and $227^{\circ}C$. The maximum possible efficiency of such an engine is: