The thermally most stable compound is:

If $\frac{{}^{n+2} C_6}{{}^{n-2} C_2} = 11$,then $n$ satisfies the equation

$A$ reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^{\circ} C$,the efficiency of the engine is doubled. The temperatures of the source and sink are

The longest distance of the point $(a, 0)$ from the curve $2 x^2+y^2=2 x$ is

Two bodies are thrown up at angles of $45^{\circ}$ and $60^{\circ}$,respectively,with the horizontal. If both bodies attain the same vertical height,then the ratio of velocities with which these are thrown is:

$A$ 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 $g = 10 \, m/s^2$)