The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x² . If it were launched at an angle $$\theta $$₀ with speed v₀ then (g = 10 ms^–2) :

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K)

A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is dose to: (Refractive index of water = 1.33)

An electromagnetic wave is represented by the electric field $$\overrightarrow E = {E_0}\widehat n\sin \left[ {\omega t + \left( {6y - 8z} \right)} \right]$$ . Taking unit vectors in x, y and z directions to be $$\widehat i,\widehat j,\widehat k$$ , the direction of propagation $$\widehat s$$, is :