NTA JEE Main 30th January 2023 Shift 2

As shown in the figure, a current of $$2$$ A flowing in an equilateral triangle of side $$4\sqrt{3}$$ cm. The magnetic field at the centroid $$O$$ of the triangle is:

(Neglect the effect of earth's magnetic field)

A current carrying rectangular loop $$PQRS$$ is made of a uniform wire. The length $$PR = QS = 5$$ cm and $$PQ = RS = 100$$ cm. If the ammeter current reading changes from $$I$$ to $$2I$$, then the ratio of the magnetic forces per unit length on the wire $$PQ$$ due to the wire $$RS$$ in the two cases respectively $$(f^I_{PQ} : f^{2I}_{PQ})$$ is:

In the given circuit, the rms value of current $$(I_{rms})$$ through the resistor $$R$$ is:

A thin prism $$P_1$$ with an angle $$6°$$ and made of glass of refractive index $$1.54$$ is combined with another prism $$P_2$$ made from glass of refractive index $$1.72$$ to produce dispersion without average deviation. The angle of prism $$P_2$$ is:

A point source of $$100$$ W emits light with $$5\%$$ efficiency. At a distance of $$5$$ m from the source, the intensity produced by the electric field component is:

An electron accelerated through a potential difference $$V_1$$ has a de-Broglie wavelength of $$\lambda$$. When the potential is changed to $$V_2$$, its de-Broglie wavelength increases by $$50\%$$. The value of $$\left(\frac{V_1}{V_2}\right)$$ is equal to:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The nuclear density of nuclides $$^{10}_5$$B, $$^{6}_3$$Li, $$^{56}_{26}$$Fe, $$^{20}_{10}$$Ne and $$^{209}_{83}$$Bi can be arranged as
$$\rho^N_{Bi} > \rho^N_{Fe} > \rho^N_{Ne} > \rho^N_{B} > \rho^N_{Li}$$
Reason R: The radius $$R$$ of nucleus is related to its mass number $$A$$ as $$R = R_0 A^{\frac{1}{3}}$$, where $$R_0$$ is a constant.
In the light of the above statement, choose the correct answer from the options given below:

The output $$Y$$ for the inputs $$A$$ and $$B$$ of circuit is given by
Truth table of the shown circuit is:

Match List I with List II

A stone tied to $$180$$ cm long string at its end is making $$28$$ revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $$\frac{1936}{x}$$ m s$$^{-2}$$. The value of $$x$$ ______. [Take $$\pi = \frac{22}{7}$$]