JEE Main 2019 Physics Paper: 12 Apr, Shift 1

An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength $\lambda$, energy $E = \frac{1240\text{ eV}}{\lambda(\text{in nm})}$):

Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K1, K2 and K3. The first capacitor is filled as shown in fig.I, and the second one is filled as shown in fig II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E1 refers to capacitor (I) and E2 to capacitor (II)):

To verify Ohm's law, a student connects the voltmeter across the battery as, shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained:

If V0 is almost zero, identify the correct statement:

The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is:

A galvanometer of resistance 100 $\Omega$ has 50 divisions on its scale and has sensitivitv of 20 $\mu$A/division. It is to be converted to a voltmeter with three ranges of 0-2V, 0-10 V and 0-20 V. The appropriate circuit to do so is

The stopping potential V0 (in volt) as a function of frequency ($v$) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be: (Given: Planck’s constant (h) = 6.63 × 10–34 Js, electron charges e = 1.6 × 10–19 C)

The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of 1 cm s-1. At some instant, a part of L is in a uniform magnetic field of 1 T, perpendicular to the plane of the loop. If the resistance of L is 1.7 $\Omega$, the current in the loop at that instant will be close to:

An electromagnetic wave is represented by the electric field $\vec{E} = E_0\hat{n}\sin\left[\omega t + (6y - 8z)\right]$. Taking unit vectors in x, y and z directions to be $\hat{i}, \hat{j}, \hat{k}$, the direction of propagation $\hat{s}$, is:

A point dipole $\vec{p} = -p_0\hat{x}$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Take V= 0 at infinity)

Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $\vec{P}$as shown. In this case:

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If B1 and B2 are respectively the total magnetic field due to the earth at the two places, then the ratio $\frac{B_1}{B_2}$ is best given by:

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40 $\pi$ rad s–1 about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 × 10–9 T, then the charge carried by the ring is close to ($\mu$0 = 4$\pi$ × 10–7 N/A2 ).

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is -

The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x2. If it were launched at an angle $\theta$0 with speed v0 then (g = 10 ms–2):

A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to: (Refractive index of water = 1.33)

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $\theta$0. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his center of mass moves by a distance $\ell$($\ell$ << L), is close to;

A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $\left(\frac{\sigma_0}{r}\right)$, then the radius of gyration of the disc about its axis passing through the centre is:

A uniform rod of length $\ell$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?

The transfer characteristic curve of a transistor, having input and output resistance 100 $\Omega$ and 100 k$\Omega$ respectively is shown in the figure. The voltage and power gain, are respectively:

The truth table for the circuit given in the fig. is:

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is –180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is:

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? (R = 8.3 J/mol K)

When M1 gram of ice at –10oC (specific heat = 0.5 cal g–1oC–1) is added to M2 gram of water at 50°C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g–1 is:

At 40o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40oC to 20oC it regains its original length of 0.2 m. The value of M is close to: (Coefficient of linear expansion and Young’s modulus of brass are 10–5 /oC and 1011 N/m 2, respectively; g= 10 ms–2)

Which of the following combinations has the dimension of electrical resistance ($\epsilon$0 is the permittivity of vacuum and $\mu$0 is the permeability of vacuum)?

A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency $v$. The value of $v$ is close to: (Speed of sound in water =1500 ms–1)

A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – $\omega$t + $\phi$). Its snapshot at t = 0 is given in the figure.

For this wave, the phase $\phi$ is:

The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength 5000 $\text{Å}$ is used, the minimum separation between two points, to be seen as distinct, will be:

In a double slit experiment, when a thin film of thickness t having refractive index $\mu$. is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ($\lambda$ is the wavelength of the light used):