NTA JEE Main 26th June 2022 Shift 2

A ball is projected vertically upward with an initial velocity of $$50$$ m s$$^{-1}$$ at $$t = 0$$ s. At $$t = 2$$ s, another ball is projected vertically upward with same velocity. At $$t =$$ ______ s, second ball will meet the first ball.
$$(g = 10$$ m s$$^{-2})$$

A system to 10 balls each of mass $$2$$ kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $$7^{th}$$ and $$8^{th}$$ ball is ______ N when $$6^{th}$$ ball just leaves the table.

A batsman hits back a ball of mass $$0.4$$ kg straight in the direction of the bowler without changing its initial speed of $$15$$ m s$$^{-1}$$. The impulse imparted to the ball is ______ N s.

A geyser heats water flowing at a rate of $$2.0$$ kg per minute from $$30°$$C to $$70°$$C. If geyser operates on a gas burner, the rate of combustion of fuel will be ______ g min$$^{-1}$$.
[Heat of combustion $$= 8 \times 10^3$$ J g$$^{-1}$$, Specific heat of water $$= 4.2$$ J g$$^{-1}$$ °C$$^{-1}$$]

A heat engine operates with the cold reservoir at temperature $$324$$ K. The minimum temperature of the hot reservoir, if the heat engine takes $$300$$ J heat from the hot reservoir and delivers $$180$$ J heat to the cold reservoir per cycle, is ______ K.

A set of $$20$$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $$4$$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is ______ Hz.

Two $$10$$ cm long, straight wires, each carrying a current of $$5$$ A are kept parallel to each other. If each wire experienced a force of $$10^{-5}$$ N, then separation between the wires is ______ cm.

A small bulb is placed at the bottom of a tank containing water to a depth of $$\sqrt{7}$$ m. The refractive index of water is $$\frac{4}{3}$$. The area of the surface of water through which light from the bulb can emerge out is $$x\pi$$ m$$^2$$. The value of $$x$$ is ______

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength $$6630$$ Å is $$0.42$$ V. If the threshold frequency is $$x \times 10^{13}$$ s, where $$x$$ is (nearest integer): (Given, speed light $$= 3 \times 10^8$$ m s$$^{-1}$$, Planck's constant $$= 6.63 \times 10^{-34}$$ J s)

A travelling microscope is used to determine the refractive index of a glass slab. If $$40$$ divisions are there in $$1$$ cm on main scale and $$50$$ Vernier scale divisions are equal to $$49$$ main scale divisions, then least count of the travelling microscope is ______ $$\times 10^{-6}$$ m.