Helium gas undergoes a cycle $ABCDA$ (consisting of two isochoric and two isobaric lines) as shown in the figure. The efficiency of this cycle is nearly ..... $\%$ (Assume the gas to be close to an ideal gas).

The plane faces of two identical plano-convex lenses,each having a focal length of $40 \, cm$,are placed against each other to form a biconvex lens. The distance from this lens at which an object must be placed to obtain a real,inverted image with magnification $-1$ is ...... $cm$.

The refracting angle of a prism is $A$ and the refractive index of the material of the prism is $\cot(A/2)$. Then the angle of minimum deviation is

Which of the following allotropes of carbon is isomorphous with crystalline silicon?

The foot of the perpendicular from $(0,2,3)$ to the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ is

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,what is its new time period in seconds?