NTA JEE Main 9th January 2019 Shift 2

The position co-ordinates of a particle moving in a 3D coordinate system is given by
$$x = a\cos\omega t$$
$$y = a\sin\omega t$$
and $$z = a\omega t$$
The speed of the particle is:

Expression for time in terms of $$G$$ (universal gravitational constant), $$h$$ (Planck constant) and $$c$$ (speed of light) is proportional to:

In a car race on straight road, car A takes a time $$t$$ less than car $$B$$ at the finish and passes finishing point with a speed $$v$$ more than that of car $$B$$. Both the cars start from rest and travel with constant acceleration $$a_1$$ and $$a_2$$ respectively. Then $$v$$ is equal to:

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45$$^{\circ}$$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ($$g = 10$$ m s$$^{-2}$$)

A force acts on a 2 kg object so that its position is given as a function of time as $$x = 3t^2 + 5$$. What is the work done by this force in first 5 seconds?

A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle of 30$$^{\circ}$$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s$$^{-1}$$) will be: ($$g = 10$$ ms$$^{-2}$$)

The energy required to take a satellite to a height $$h$$ above the Earth surface (radius of Earth $$= 6.4 \times 10^3$$ km) is $$E_1$$, and the kinetic energy required for the satellite to be in a circular orbit at this height is $$E_2$$. The value of $$h$$ for which $$E_1$$ and $$E_2$$ are equal, is:

The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m$$^3$$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:

Two carnot engines $$A$$ and $$B$$ are operated in series. The first one, $$A$$, receives heat at $$T_1 (= 600K)$$ and rejects to a reservoir at temperature $$T_2$$. The second engine $$B$$ receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $$T_3 (= 400K)$$. Calculate the temperature $$T_2$$ if the work outputs of the two engines are equal:

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature, 27$$^{\circ}$$C. The amount of heat transferred to the gas, so that R.M.S. velocity of molecules is doubled, is about. [$$R = 8.3$$ J (K mole)$$^{-1}$$]