$A$ $500 \ kg$ car takes a round turn of radius $50 \ m$ with a velocity of $36 \ km/h$. The centripetal force acting on the car is (in $N$)

If $|a|=4, |b|=5, |a-b|=3$ and $\theta$ is the angle between the vectors $a$ and $b$, then $\tan^2 \theta=$

According to Hess's law,the heat of reaction depends upon:

The function $f: R \rightarrow R$ defined by $f(x)=\frac{x}{\sqrt{1+x^2}}$ is ........

Three processes form a thermodynamic cycle as shown on the $P-V$ diagram for an ideal gas. Process $1 \to 2$ takes place at a constant temperature $(300\,K)$. Process $2 \to 3$ takes place at a constant volume. During this process,$40\,J$ of heat leaves the system. Process $3 \to 1$ is adiabatic and the temperature $T_3$ is $275\,K$. The work done by the gas during the process $3 \to 1$ is...... $J$.

$A$ gas at $27 ^oC$ has a volume $V$ and pressure $P$. On heating, its pressure is doubled and volume becomes three times. The resulting temperature of the gas will be ....... $^oC$.