NTA JEE Main 9th January 2019 Shift 2

A particle is executing simple harmonic motion (SHM) of amplitude $$A$$, along the $$x$$-axis, about $$x = 0$$. When its potential Energy (PE) equal kinetic energy (KE), the position of the particle will be:

A rod of mass $$M$$ and length $$2L$$ is suspended at its middle by a wire. It exhibits torsional oscillations. If two masses, each of mass $$m$$, are attached at a distance $$L/2$$ from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio $$m/M$$ is close to:

A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km h$$^{-1}$$. If the wave speed is 330 m s$$^{-1}$$, the frequency heard by the running person shall be close to:

Charge is distributed within a sphere of radius $$R$$ with a volume charge density $$\rho(r) = \frac{A}{r^2}e^{-\frac{2r}{a}}$$, where $$A$$ and $$a$$ are constants. If $$Q$$ is the total charge of this charge distribution, the radius $$R$$ is:

Two point charges $$q_1(\sqrt{10}$$ $$\mu$$C) and $$q_2(-25$$ $$\mu$$C) are placed on the $$x$$-axis at $$x = 1$$ m and $$x = 4$$ m respectively. The electric field (in V/m) at a point $$y = 3$$ m on $$y$$-axis is, [Take $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ N m$$^2$$C$$^{-2}$$]

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $$K_1$$, $$K_2$$, $$K_3$$, $$K_4$$ arranged as shown in the figure. The effective dielectric constant $$K$$ will be:

A carbon resistance has a following colour code. What is the value of the resistance?

GOY Golden

In the given circuit the internal resistance of the 18V cell is negligible. If $$R_1 = 400$$ $$\Omega$$, $$R_3 = 100$$ $$\Omega$$ and $$R_4 = 500$$ $$\Omega$$ and the reading of an ideal voltmeter across $$R_4$$ is 5 V, then the value of $$R_2$$ will be:

A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron $$= 1.6 \times 10^{-19}$$ C)

One of the two identical conducting wires of length $$L$$ is bent in the form of a circular loop and the other one into a circular coil of $$N$$ identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop $$(B_L)$$ to that at the centre of the coil $$(B_C)$$, i.e. $$\frac{B_L}{B_C}$$ will be: