NTA JEE Main 20th July 2021 Shift 2

A body of mass $$m$$ is launched up on a rough inclined plane making an angle of 30$$^\circ$$ with the horizontal. The coefficient of friction between the body and plane is $$\frac{\sqrt{x}}{5}$$ if the time of ascent is half of the time of descent. The value of $$x$$ is ___.

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $$\frac{\sqrt{x}}{2}$$. Then, the value of $$x$$ is ___.

A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is ___.

One mole of an ideal gas at 27 $$^\circ$$C is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be ___ $$\times 10^{-1}$$ J. [Given, $$R = 8.3$$ J mole$$^{-1}$$ K, ln 2 = 0.6931] (Round off to the nearest integer)

In the given figure switches $$S_1$$ and $$S_2$$ are in open condition. The resistance across $$ab$$ when the switches $$S_1$$ and $$S_2$$ are closed is ___ $$\Omega$$.

A series LCR circuit of $$R = 5$$ $$\Omega$$, $$L = 20$$ mH and $$C = 0.5$$ $$\mu$$F is connected across an AC supply of 250 V, having variable frequency. The power dissipated at resonance condition is ___ $$\times 10^2$$ W.

A certain metallic surface is illuminated by monochromatic radiation of wavelength $$\lambda$$. The stopping potential for photoelectric current for this radiation is $$3V_0$$. If the same surface is illuminated with a radiation of wavelength $$2\lambda$$, the stopping potential is $$V_0$$. The threshold wavelength of this surface for photoelectric effect is ___ $$\lambda$$.

A radioactive substance decays to $$\left(\frac{1}{16}\right)^{th}$$ of its initial activity in 80 days. The half life of the radioactive substance expressed in days is ___.

A zener diode having zener voltage 8 V and power dissipation rating of 0.5 W is connected across a potential divider arranged with maximum potential drop across zener diode as shown in the diagram. The value of protective resistance $$R_p$$ is ___ $$\Omega$$.

For the forward biased diode characteristics shown in the figure, the dynamic resistance at $$I_D = 3$$ mA will be ___ $$\Omega$$.