NTA JEE Main 25th January 2023 Shift 1

Match List I with List II
List - I                        List - II
A. Surface tension       I. kg m$$^{-1}$$ s$$^{-1}$$
B. Pressure                 II. kg m s$$^{-1}$$
C. Viscosity                III. kg m$$^{-1}$$ s$$^{-2}$$
D. Impulse                  IV. kg s$$^{-2}$$
Choose the correct answer from the options given below:

A car travels a distance of $$x$$ with speed $$v_1$$ and then same distance $$x$$ with speed $$v_2$$ in the same direction. The average speed of the car is:

A car is moving with a constant speed of 20 m s$$^{-1}$$ in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be: (Take g = 10 m s$$^{-2}$$)

An object of mass 8 kg is hanging from one end of a uniform rod $$CD$$ of mass 2 kg and length 1 m, is pivoted at its end $$C$$ on a vertical wall as shown in the figure. It is supported by a cable $$AB$$ such that the system is in equilibrium. The tension in the cable is: (Take $$g = 10$$ m s$$^{-2}$$)

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately) (take $$g = 10$$ ms$$^{-2}$$, radius of earth = 6400 km)

$$T$$ is the time period of simple pendulum on the earth's surface. Its time period becomes $$xT$$ when taken to a height $$R$$ (equal to earth's radius) above the earth's surface. Then, the value of $$x$$ will be:

A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is 22°C. How long it will take to cool from 75°C to 69°C?

A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be:

The root mean square velocity of molecules of gas is

A parallel plate capacitor has plate area 40 cm$$^2$$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is: