JEE Main 2014 Physics Paper: 12 Apr, Shift 1

A sinusoidal voltage V(t) = 100 sin (500t) is applied across a pure inductance of L = 0.02 H. The current through the coil is:

The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors 3 $\Omega$, 9 $\Omega$ and 9 $\Omega$ and a capacitor 5.0 $\mu$F.

How much is the current I in the circuit in steady state?

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation:

K(x) = K0 + $\lambda$x ($\lambda$ = a constant)

The capacitance C, of this capacitor, would be related to its 'vacuum' capacitance C0 as per relation:

In the experiment of calibration of voltmeter, a standard cell of e.m.f. 1.1 volt is balanced against 440 cm of potentiometer wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding reading of voltmeter is 0.5 volt. The error in the reading of voltmeter will be:

A beam of light has two wavelengths 4972 $\text{\AA}$ and 6216 $\text{\AA}$ with a total intensity of 3.6 $\times$ 10$-$3 Wm${}^{-2}$ equally distributed among the two wavelengths. The beam falls normally on an area of 1 cm2 of a clean metallic surface of work function 2.3 eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photo electrons liberated in 2s is approximately:

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:

A spherically symmetric charge distribution is characterised by a charge density having the following variation:

$\rho$(r) = $\rho$0 $\left(1 - \frac{r}{R}\right)$ for r < R

$\rho$(r) = 0 for r $\geq$ R

Where r is the distance from the center of the charge distribution and $\rho$0 is a constant. The electric field at an internal point (r < R) is:

A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius 'a'. The time in which it will be emptied is:

Two hypothetical planets of masses m1 and m2 are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is 'd'?

(Speed of m1 is $v$1 and that of m2 is $v$2)

At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms${}^{-1}$. The gas is:

Steel ruptures when a shear of 3.5 $\times$ 108 N m−2 is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly:

A Person climbs up a stalled escalator in 60 s. If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator?

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B1, at its center when a current I passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field B2 at the centre of the loops when current I/3 passes through it. The ratio B1: B2 is:

A positive charge 'q' of mass 'm' is moving along the + x axis. We wish to apply a uniform magnetic field B for time $\Delta$t so that the charge reverses its direction crossing the y axis at a distance d. Then:

A piece of bone of an animal from a ruin is found to have 14C activity of 12 disintegrations per minute per gm of its carbon content. The 14C activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die? (Given half life of 14C is t1/2 = 5760 years)

Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants?

The refractive index of the material of a concave lens is $\mu$. It is immersed in a medium of refractive index $\mu$1. A parallel beam of light is incident on the lens. The path of the emergent rays when $\mu$1 > $\mu$ is:

A particle is moving in a circular path of radius a, with a constant velocity $v$ as shown in the figure. The center of circle is marked by 'C'. The angular momentum from the origin O can be written as:

For LED's to emit light in visible region of electromagnetic light, it should have energy band gap in the range of:

Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S the change in total surface area, T is the surface tension and P atmospheric pressure, which of the following relation is correct?

A Carnot engine absorbs 1000 J of heat energy from a reservoir at 127oC and rejects 600 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be:

From the following combinations of physical constant (expressed through their usual symbols) the only combination, that would have the same value in different systems of unit, is:

A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed $v$. The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz, The source A receives waves, reflected from ground, of frequency nearly: (Speed of sound = 343 m/s)

Interference pattern is observed at 'P' due to superimposition of two rays coming out from a source 'S' as shown in the figure. The value of $'l'$ for which maxima is obtained at 'P' is: (R is perfect reflecting surface):

In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength. If wavelength of red light is 6600 $\text{Å}$, then wavelength of first maximum will be:

A spring of unstretched length $l$ has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity $v$ is: