NTA JEE Main 28th June 2022 Shift 2

A car covers $$AB$$ distance with first one-third at velocity $$v_1$$ m s$$^{-1}$$, second one-third at $$v_2$$ m s$$^{-1}$$ and last one-third at $$v_3$$ m s$$^{-1}$$. If $$v_3 = 3v_1$$, $$v_2 = 2v_1$$ and $$v_1 = 11$$ m s$$^{-1}$$, then the average velocity of the car is ______ m s$$^{-1}$$.

A uniform disc with mass $$M = 4$$ kg and radius $$R = 10$$ cm is mounted on a fixed horizontal axle as shown in figure. A block with mass $$m = 2$$ kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ______ N.
(Take $$g = 10$$ ms$$^{-2}$$)

A liquid of density 750 kg m$$^{-3}$$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from $$A_1 = 1.2 \times 10^{-2}$$ m$$^2$$ to $$A_2 = \frac{A_1}{2}$$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ______ $$\times 10^{-3}$$ m$$^3$$ s$$^{-1}$$.

A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ______ cm.
(Velocity of sound in air is 340 ms$$^{-1}$$)

A capacitor $$C_1$$ of capacitance 5 $$\mu$$F is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor $$C_2$$ of capacitance 10 $$\mu$$F as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor $$C_2$$ is ______ $$\mu$$C.

All resistances in figure are 1 $$\Omega$$ each. The value of current '$$I$$' is $$\frac{a}{5}$$ A. The value of $$a$$ is ______.

In the given circuit, the magnitude of $$V_L$$ and $$V_C$$ are twice that of $$V_R$$. Given that $$f = 50$$ Hz, the inductance of the coil is $$\frac{1}{K\pi}$$ mH. The value of $$K$$ is ______.

In a Young's double slit experiment, an angular width of the fringe is 0.35° on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index $$\frac{7}{5}$$, is $$\frac{1}{\alpha}$$. The value of $$\alpha$$ is ______.

A Zener of breakdown voltage $$V_Z = 8$$ V and maximum Zener current, $$I_{ZM} = 10$$ mA is subjected to an input voltage $$V_i = 10$$ V with series resistance $$R = 100$$ $$\Omega$$. In the given circuit $$R_L$$ represents the variable load resistance. The ratio of maximum and minimum value of $$R_L$$ is ______.

A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is $$\frac{x}{121}$$%. The value of $$x$$ is ______.