JEE Main 2016 Physics Paper

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4\ \mu\text{F}$ and $9\ \mu\text{F}$ capacitors), at a point distance $30\text{ m}$ from it, would equal:

A galvanometer having a coil resistance of $100\ \Omega$ gives a full scale deflection, when a currect of $1\text{ mA}$ is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of $10\text{ A},$ is:

Radiation of wavelength $\lambda,$ is incident on a photocell. The fastest emitted electron has speed $v.$ If the wavelength is changed to $\frac{3\lambda}{4},$ the speed of the fastest emitted electron will be:

Arrange the following electromagnetic radiations per quantum in the order of increasing energy: A: Blue light B: Yellow light

C: X-ray D: Radiowave.

The region between two concentric spheres of radii $a$ and $b,$ respectively (see figure), has volume charge density $\rho = \frac{A}{r},$ where $A$ is a constant and $r$ is the distance from the center. At the center of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is:

A satellite is revolving in a circular orbit at a height $'h'$ from the earth's surface (radius of earth $R;\ h << R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to: (Neglect the effect of atmosphere.)

Hysteresis loops for two magnetic materials $A$ and $B$ are given below:

These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use:

Two identical wires $A$ and $B,$ each of length $\text{'}l\text{'}$, carry the same current $I$. Wire $A$ is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side $\text{'}a\text{'}$. If $B_A$ and $B_B$ are the values of magnetic fields at the centres of the circle and square respectively, then the ratio $\frac{B_A}{B_B}$ is:

Half-lives of two radioactive elements $A$ and $B$ are $20$ minutes and $40$ minutes, respectively. Initially, the samples have equal number of nuclei. After $80$ minutes, the ratio of decayed number of $A$ and $B$ nuclei will be:

A particle performs simple harmonic motion with amplitude $A.$ Its speed is trebled at the instant that it is at a distance $\frac{2A}{3}$ from equilibrium position. The new amplitude of the motion is:

An observer looks at a distant tree of height $10\text{ m}$ with a telescope of magnifying power of $20$ To the observer the tree appears:

In an experiment for determination of refractive index of glass of a prism by $i - \delta$ plot, it was found that a ray incident at angle $35^\circ$, suffers a deviation of $40^\circ$ and that it emerges at angle $79^\circ$ In that case which of the following is closest to the maximum possible value of the refractive index?

A roller is made by joining together two cones at their vertices $O$. It is kept on two rails $AB$ and $CD$, which are placed asymmetrically (see figure), with its axis perpendicular to $CD$ and its center $O$ at the center of line joining $AB$ and $CD$ (see figure). It is given a light push so that it starts rolling with its center $O$ moving parallel to $CD$ in the direction shown. As it moves, the roller will tend to:

The temperature dependence of resistance of $\text{Cu}$ and undoped $\text{Si}$ in the temperature range $300 - 400\text{ K},$ is best described by:

For a common emitter configuration, if $\alpha$ and $\beta$ have their usual meanings, the incorrect relationship between $\alpha$ and $\beta$ is:

If $a, b, c, d$ are inputs to a gate and $x$ is its output, then, as per the following time graph, the gate is:

Identify the semiconductor devices whose characteristics are given below, in the order $(a), (b), (c), (d)$:

$\text{'}n\text{'}$ moles of an ideal gas undergoes a process $A \rightarrow B$ as shown in the figure. The maximum temperature of the gas during the process will be:

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^{n} =$ constant, then $n$ is given by (Here $C_p$ and $C_v$ are molar specific heat at constant pressure and constant volume, respectively:

A pendulum clock loses $12\text{ s}$ a day if the temperature is $40^{\circ}\text{C}$ and gains $4\text{ s}$ a day if the temperature is $20^{\circ}\text{C}.$ The temperature at which the clock will show correct time, and the co-efficient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively:

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:

A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:

A uniform string of length $20\text{ m}$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is: (take $g = 10\text{ ms}^{-2}$)

The box of a pin hole camera, of length $L,$ has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength $\lambda$ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say $b_{\min}$) when:

A person trying to lose weight by burning fat lifts a mass of $10\text{ kg}$ upto a height of $1\text{ m}\ 1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times 10^{7}\text{ J}$ of energy per $\text{kg}$ which is converted to mechanical energy with a $20\%$ efficiency rate. Take $g = 9.8\text{ ms}^{-2}$:

A point particle of mass $m,$ moves along the uniformly rough track $PQR$ as shown in the figure. The coefficient of friction, between the particle and the rough track equals $\mu.$ The particle is released, from rest from the point $P$ and it comes to rest at point $R.$ The energies, lost by the ball, over the parts, $PQ$ and $QR$, of the track, are equal to each other, and no energy is lost when particle changes direction from $PQ$ to $QR$.

The value of the coefficient of friction $\mu$ and the distance $x\ (= QR),$ are, respectively close to: