JEE Main 2006 Physics Paper: AIEEE

In an $AC$ generator, a coil with $N$ turns, all of the same area $A$ and total resistance $R,$ rotates with frequency $\omega$ in a magnetic field $B.$ The maximum value of $emf$ generated in the coil is

In a series resonant $LCR$ circuit, the voltage across $R$ is $100$ volts and $R = 1\text{ k}\Omega$ with $C = 2\ \mu\text{F}.$ The resonant frequency $\omega$ is $200\text{ rad/s}$. At resonance the voltage across $L$ is

An alpha nucleus of energy $\frac{1}{2}mv^2$ bombards a heavy nuclear target of charge $Ze$. Then the distance of closest approach for the alpha nucleus will be proportional to

Consider a two particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the center of mass through a distance $d,$ by what distance should the second particle is moved, so as to keep the center of mass at the same position?

An electric bulb is rated $220$ volt - $100$ watt. The power consumed by it when operated on $110$ volt will be

A thermocouple is made from two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is kept cold, then, an electric current will

The Kirchhoff's first law $\left(\sum i = 0\right)$ and second law $\left(\sum iR = \sum E\right)$, where the symbols have their usual meanings, are respectively based on

The current $I$ drawn from the $5$ volt source will be

A material 'B' has twice the specific resistance of 'A'. A circular wire made of 'B' has twice the diameter of a wire made of 'A'. Then for the two wires to have the same resistance, the ratio $\ell_B/\ell_A$ of their respective lengths must be

The resistance of bulb filament is $100\ \Omega$ at a temperature of $100^\circ\text{C}.$ If its temperature coefficient of resistance be $0.005$ per $^\circ\text{C}$, its resistance will become $200\ \Omega$ at a temperature of

In a Wheatstone's bridge, three resistance $P, Q$ and $R$ connected in the three arms and the fourth arm is formed by two resistances $S_1$ and $S_2$ connected in parallel. The condition for the bridge to be balanced will be

The threshold frequency for a metallic surface corresponds to an energy of $6.2\text{ eV}$ and the stopping potential for a radiation incident on this surface is $5\text{ V.}$ The incident radiation lies in

The time taken by a photoelectron to come out after the photon strikes is approximately

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $\mathrm{I}$ of the photocell varies as follows

An inductor $(L = 100\text{ mH})$, a resistor $(R = 100\,\Omega)$ and a battery $(E = 100\text{ V})$ are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circuiting the points $A$ and $B$. The current in the circuit $1\text{ ms}$ after the short circuit is

The flux linked with a coil at any instant $\text{'}t\text{'}$ is given by

$\phi = 10t^{2} - 50t + 250$

The induced $emf$ at $t = 3\text{ s}$ is

The $rms$ value of the electric field of the light coming from the Sun is $720\text{ N/C}.$ The average total energy density of the electromagnetic wave is

An electric dipole is placed at an angle of $30^\circ$ to a non-uniform electric field. The dipole will experience

Two spherical conductors $A$ and $B$ of radii $1\text{ mm}$ and $2\text{ mm}$ are separated by a distance of $5\text{ cm}$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is

Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2 - V_1 = 20\text{ V}.$ (i.e., plate $2$ is at a higher potential). The plates are separated by $d = 0.1\text{ m}$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1.$ What is its speed when it hits plate $2$?

$\left(e = 1.6 \times 10^{-19}\text{ C},\ m_e = 9.11 \times 10^{-31}\text{ kg}\right)$

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $TK$, evaluate the total radiant power incident on Earth at a distance $r$ from the Sun

Where r0 is the radius of the Earth and $\sigma$ is Stefan's constant.

Needles $N_1, N_2$ and $N_3$ are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will

A wire elongates by $l\text{ mm}$ when a LOAD $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in $\text{mm}$)

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies as $v = \alpha\sqrt{x}$. The displacement of the particle varies with time as

A long solenoid has $200$ turns per $cm$ and carries a current $i.$ The magnetic field at its center is $6.28 \times 10^{-2}\ Weber/m^2.$ Another long solenoid has $100$ turns per $cm$ and it carries a current $\frac{i}{3}$. The value of the magnetic field at its center is

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

The $\text{'}rad\text{'}$ is the correct unit used to report the measurement of

When ${}_{3}Li^{7}$ nuclei are bombarded by protons, and the resultant nuclei are ${}_{4}Be^{8}$, the emitted particles will be

If the binding energy per nucleon in ${}^{7}_{3}Li$ and ${}^{4}_{2}He$ nuclei are $5.60\text{ MeV}$ and $7.06\text{ MeV}$ respectively, then in the reaction

$p + {}^{7}_{3}Li \rightarrow 2\,{}^{4}_{2}He$

energy of proton must be

The energy spectrum of $\beta$-particles [ number $N(E)$ as a function of $\beta$-energy $E$ ] emitted from a radioactive source is

Starting from the origin a body oscillates simple harmonically with a period of $2\text{ s}$ After what time will its kinetic energy be $75\%$ of the total energy?

The maximum velocity of a particle, executing simple harmonic motion with an amplitude $7\text{ mm},$ is $4.4\text{ m/s}.$ The period of oscillation is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega.$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The refractive index of a glass is $1.520$ for red light and $1.525$ for blue light. Let $D_1$ and $D_2$ be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then,

A thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $\omega' =$

Four point masses, each of value $m,$ are placed at the corners of a square $ABCD$ of side $l$. The moment of inertia of this system about an axis passing through $A$ and parallel to $BD$ is

A force of $-F\hat{k}$ acts on $O,$ the origin of the coordinate system. The torque about the point $(1,-1)$ is

If the lattice constant of this semiconductor is decreased, then which of the following is correct?

If the ratio of the concentration of electrons to that of holes in a semiconductor is $\frac{7}{5}$ and the ratio of currents is $\frac{7}{4},$ then what is the ratio of their drift velocities?

In a common base mode of a transistor, the collector current is $5.488\,mA$ for an emitter current of $5.60\,mA.$ The value of the base current amplification factor $(\beta)$ will be

A solid which is not transparent to visible light and whose conductivity increases with temperature is formed by

In the following, which one of the diodes is reverse biased?

The circuit has two oppositively connected ideal diodes in parallel. What is the current following in the circuit?

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0,$ while Box contains one mole of helium at temperature $\left(\frac{7}{3}\right)T_0.$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, $T_f$ in terms of $T_0$ is

The work of $146\text{ kJ}$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^\circ\text{C}.$ The gas is $\left(R = 8.3\text{ J mol}^{-1}\text{ K}^{-1}\right)$

Which of the following units denotes the dimension $\frac{ML^2}{Q^2}$, where $Q$ denotes the electric charge?

If the terminal speed of a sphere of gold (density $= 19.5\ kg/m^{3}$) is $0.2\ m/s$ in a viscous liquid (density $= 1.5\ kg/m^{3}$, find the terminal speed of a sphere of silver (density $= 10.5\ kg/m^{3}$) of the same size in the same liquid

A whistle producing sound waves of frequencies $9500\text{ Hz}$ and above is approaching a stationary person with speed $v\text{ ms}^{-1}.$ The velocity of sound in air is $300\text{ ms}^{-1}.$ If the person can hear frequencies upto a maximum of $10{,}000\text{ Hz},$ the maximum value of $v$ upto which he can hear whistle is

A string is stretched between fixed points separated by $75.0\text{ cm.}$ It is observed to have resonant frequencies of $420\text{ Hz}$ and $315\text{ Hz}$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is

A mass of $M\text{ kg}$ is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of $45^\circ$ with the initial vertical direction is

The potential energy of a $1\text{ kg}$ particle free to move along the $x$-axis is given by $V(x) = \left(\frac{x^4}{4} - \frac{x^2}{2}\right)\text{ J}$. The total mechanical energy of the particle is $2\text{ J}.$ Then, the maximum speed (in $\text{m/s}$) is

A particle of mass $100\text{ g}$ is thrown vertically upwards with a speed of $5\text{ m/s}$. The work done by the force of gravity during the time the particle goes up is

A ball of mass $0.2\text{ kg}$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2\text{ m}$ while applying the force and the ball goes upto $2\text{ m}$ height further, find the magnitude of the force. (consider $g = 10\text{ m/s}^2$ ).