NTA JEE Main 29th January 2023 Shift 1

A $$0.4$$ kg mass takes $$8$$ s to reach ground when dropped from a certain height $$P$$ above surface of earth. The loss of potential energy in the last second of fall is ______ J. [Take $$g = 10$$ m s$$^{-2}$$]

A solid sphere of mass $$2$$ kg is making pure rolling on a horizontal surface with kinetic energy $$2240$$ J. The velocity of centre of mass of the sphere will be ______ m s$$^{-1}$$.

A body cools from $$60°$$C to $$40°$$C in $$6$$ minutes. If, temperature of surroundings is $$10°$$C. Then, after the next 6 minutes, its temperature will be ______ °C.

Two simple harmonic waves having equal amplitudes of $$8$$ cm and equal frequency of $$10$$ Hz are moving along the same direction. The resultant amplitude is also $$8$$ cm. The phase difference between the individual waves is ______ degree.

A point charge $$q_1 = 4q_0$$ is placed at origin. Another point charge $$q_2 = -q_0$$ is placed at $$x = 12$$ cm. Charge of proton is $$q_0$$. The proton is placed on $$x$$-axis so that the electrostatic force on the proton in zero. In this situation, the position of the proton from the origin is ______ cm.

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field $$B = 0.8$$ T. When released the radius of the loop starts shrinking at a constant rate of $$2$$ cm s$$^{-1}$$. The induced emf in the loop at an instant when the radius of the loop is $$10$$ cm will be ______ mV.

In a Young's double slit experiment, two slits are illuminated with a light of wavelength $$800$$ nm. The line joining $$A_1P$$ is perpendicular to $$A_1A_2$$ as shown in the figure. If the first minimum is detected at $$P$$, the value of slits separation $$a$$ will be:

The distance of screen from slits $$D = 5$$ cm. Answer in mm.

As shown in figures, three identical polaroids $$P_1$$, $$P_2$$ and $$P_3$$ are placed one after another. The pass axis of $$P_2$$ and $$P_3$$ are inclined at angle of $$60°$$ and $$90°$$ with respect to axis of $$P_1$$. The source $$S$$ has an intensity of $$256$$ W m$$^{-2}$$. The intensity of light at point $$O$$ is ______ W m$$^{-2}$$.

A radioactive element $$^{242}_{92}$$X emits two $$\alpha$$-particles, one electron and two positrons. The product nucleus is represented by $$^{234}_{P}$$Y. The value of $$P$$ is ______.

In a metre bridge experiment the balance point is obtained if the gaps are closed by $$2$$ $$\Omega$$ and $$3$$ $$\Omega$$. A shunt of $$X$$ $$\Omega$$ is added to $$3$$ $$\Omega$$ resistor to shift the balancing point by $$22.5$$ cm. The value of $$X$$ is ______.