Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio |ω2 |/|ω1 | = 1/4, have their centers 30 mm apart. The number of teeth on the driver (gear 1) is _______ .

(Answer in integer)

The figure shows a block of mass m = 20 kg attached to a pair of identical linear springs, each having a spring constant k = 1000 N/m. The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is _________ seconds. (Rounded off to two decimal places)

Take π = 3.14.

The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity 𝜔₁. A rigid bar PQ is pinned to the wheel at P while the end Q slides on the floor.

What is the angular velocity 𝜔₂ of the bar PQ?

A heat engine extracts heat (𝑄_H) from a thermal reservoir at a temperature of 1000 K and rejects heat (𝑄_L) to a thermal reservoir at a temperature of 100 K, while producing work (𝑊). Which one of the combinations of [𝑄_H, 𝑄_L and 𝑊] given is allowed?