Consider the three forces acting at O and in equilibrium as shown in the figure. Which of the following equations is/are CORRECT?

I. P\(_1\) cos \(\theta_1\) = p\(_1\) cos \(\theta_2\)

II. P\(_3\) = P\(_1\) cos \(\theta_4\)  + P\(_2 cos_2\)

III. P\(_1 \sin \theta_1 = P_2 \sin \theta_2\)

The refractive index of a liquid is 1.5. If the velocity of light in vacuum is 3.0 x 10\(^8ms^{-1}\), the velocity of light in the liquid is 

A ship travelling towards a cliff receives the echo of its whistle after 3.5 seconds. A short while later, it receives the echo after 2.5 seconds. If the speed of sound in air under the prevalling condition is 250ms -1, how much closer is the ship to the cliff?

Which of the following statements about defects of vision is/are CORRECT? 

I. For a long sighted person, close objects appear blurred

II. For a short sighted person, distant objects appear blurred 

III. Short sight is corrected by using a pair of converging lenses 

Which of the following conditions are necessary and sufficient for total internal reflection to take place at the boundary between two optical media?

I. Light is passing from optical denser medium to optically less dense medium

II. Light is passing from optically less dense medium to optically denser medium

III. Angle of incidence is greater than a certain critical value

IV. Angle of incidence is lesser  than a certain critical value