The radius of Germanium $(Ge)$ nuclide is measured to be twice the radius of $_{4}^{9}\text{Be}$ . The number of nucleons in $Ge$ are

If the distance between the points $(a \cos \theta, a \sin \theta)$ and $(a \cos \phi, a \sin \phi)$ is $2a$,then $\theta$ is equal to

Water is flowing through a tube of non-uniform cross-section. The ratio of the radius at the entry and exit ends of the pipe is $3:2$. Then the ratio of velocities at the entry and exit of the liquid is

Two Carnot engines $A$ and $B$ are operated in succession. The first one,$A$,receives heat from a source at $T_1 = 800\, K$ and rejects heat to a sink at $T_2\, K$. The second engine,$B$,receives the heat rejected by the first engine and rejects heat to another sink at $T_3 = 300\, K$. If the work outputs of the two engines are equal,then the value of $T_2$ is ...... $K$.

Two fair dice are rolled. The probability of the sum of digits on their faces being greater than or equal to $10$ is

An aeroplane flying with uniform speed horizontally $1 \ km$ above the ground is observed at an elevation of $60^{\circ}$. After $10 \ s$,if the elevation is observed to be $30^{\circ}$,then the speed of the plane (in $km/h$) is