A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force $${W \over 20}$$ on the car. While moving uphill on the road at a speed of 10 ms⁻¹, the car needs power P. If it needs power $${p \over 2}$$ while moving downhill at speed v then value of $$\upsilon $$ is :

In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $$\theta $$ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction $$\mu $$_min between the mass and the inclined surface such that the mass does not move is :

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and aplane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of :