NTA JEE Main 24th June 2022 Shift 1

From the top of a tower, a ball is thrown vertically upward which reaches the ground in $$6$$ s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in $$1.5$$ s. A third ball released, from the rest from the same location, will reach the ground in ______ s.

A ball of mass $$100$$ g is dropped from a height $$h = 10$$ cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $$\frac{h}{2}$$. The spring constant is ______ N m$$^{-1}$$
(Use $$g = 10$$ m s$$^{-2}$$)

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass $$10$$ g are put one on the top of the other at the $$10.0$$ cm mark the scale is found to be balanced at $$40.0$$ cm mark. The mass of the metre scale is found to be $$x \times 10^{-2}$$ kg. The value of $$x$$ is ______.

$$0.056$$ kg of Nitrogen is enclosed in a vessel at a temperature of $$127°$$C. The amount of heat required to double the speed of its molecules is ______ kcal.
(Take $$R = 2$$ cal mole$$^{-1}$$ K$$^{-1}$$)

In a potentiometer arrangement, a cell gives a balancing point at $$75$$ cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is $$3 : 2$$, the difference in the balancing length of the potentiometer wire in above two cases will be ______ cm.

As shown in the figure an inductor of inductance $$200$$ mH is connected to an AC source of emf $$220$$ V and frequency $$50$$ Hz. The instantaneous voltage of the source is $$0$$ V when the peak value of current is $$\frac{\sqrt{a}}{\pi}$$ A. The value of $$a$$ is ______.

Two identical thin biconvex lenses of focal length $$15$$ cm and refractive index $$1.5$$ are in contact with each other. The space between the lenses is filled with a liquid of refractive index $$1.25$$. The focal length of the combination is ______ cm.

Sodium light of wavelengths $$650$$ nm and $$655$$ nm is used to study diffraction at a single slit of aperture $$0.5$$ mm. The distance between the slit and the screen is $$2.0$$ m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is ______ $$\times 10^{-5}$$ m.

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is $$v_1$$. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes $$v_2$$. If $$v_2 = xv_1$$, the value of $$x$$ will be ______.

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of $$10$$ mV is added to the base-emitter voltage, the base current changes by $$10\mu$$A and the collector current changes by $$1.5$$ mA. The load resistance is $$5$$ k$$\Omega$$. The voltage gain of the transistor will be ______.