$A$ parallel plate capacitor with air as medium between the plates has a capacitance of $10\,\mu F$. The area of the capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constants $k_1 = 2$ and $k_2 = 4$. The capacitance of the system will now be.......$\mu F$.

An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant,the springs are relaxed. The left mass is displaced to the left and the right mass is displaced to the right by the same distance and released. The resulting collision is elastic. The time period of the oscillations of the system is

When a positively charged particle enters a uniform magnetic field with uniform velocity,its trajectory can be :
$(1)$ a straight line
$(2)$ a circle
$(3)$ a helix

The most stable conformation of ethylene glycol is

When did $R.H. Whittaker$ propose the five-kingdom classification system?

The equation of the plane passing through the point $(1, 2, -3)$ and perpendicular to the planes $3x + y - 2z = 5$ and $2x - 5y - z = 7$ is: