If $\int \frac{dx}{x^2+2x+2} = f(x) + c$, then $f(x)$ is equal to :

$A$ bus moving on a level road with a velocity $v$ can be stopped at a distance of $x$,by the application of a retarding force $F$. The load on the bus is increased by $25 \%$ by boarding the passengers. Now,if the bus is moving with the same speed and if the same retarding force is applied,the distance travelled by the bus before it stops is

Three identical bodies of equal mass $M$ each are moving along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each body is

The enthalpy change $(\Delta H)$ for the reaction,$N_{2(g)} + 3H_{2(g)} \rightarrow 2NH_{3(g)}$ is $-92.38 \ kJ$ at $298 \ K$. The internal energy change $\Delta U$ at $298 \ K$ is $... \ kJ$.

Which of the following fungi is not responsible for ringworm?

Molar volume $( V_m )$ of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_m$ as the variable. The ratio $($in $mol dm ^{-3} )$ of the coefficient of $V_m^2$ to the coefficient of $V_m$ for a gas having van der Waals constants $a=6.0 dm ^6 atm \ mol ^{-2}$ and $b=0.060 dm ^3 mol^{-1}$ at $300 K$ and $300 atm$ is $....$ .
Use: Universal gas constant $(R)=0.082 dm ^3 atm \ mol { }^{-1} K^{-1}$