JEE Main 2007 Physics Paper: AIEEE

In an $\text{a.c.}$ circuit the voltage applied is $E = E_0\sin\omega t.$ The resulting current in the circuit is $I = I_0\sin\left(\omega t - \frac{\pi}{2}\right).$ The power consumption in the circuit is given by

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V$ volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be

A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs coincide. The center of mass of the new disc is $\alpha R$ from the center of the bigger disc. The value of $\alpha$ is

The resistance of a wire is $5$ ohm at $50^\circ\text{C}$ and $6$ ohm at $100^\circ\text{C}.$ The resistance of the wire at $0^\circ\text{C}$ will be

Photon of frequency $\nu$ has a momentum associated with it. If $c$ is the velocity of light, the momentum is

An ideal coil of $10\text{ H}$ is connected in series with a resistance of $5\,\Omega$ and a battery of $5\text{ V} \cdot 2$ second after the connection is made, the current flowing in ampere in the circuit is

Charges are placed on the vertices of a square as shown. Let $\vec{E}$be the electric field and $V$ the potential at the center. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, then

An electric charge $10^{-3}\,\mu\text{C}$ is placed at the origin $(0, 0)$ of $X - Y$ co-ordinate system. Two points $A$ and $B$ are situated at $\left(\sqrt{2}, \sqrt{2}\right)$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be

The potential at a point $x$ (measured in $\mu\text{m}$) due to some charges situated on the $x$-axis is given by $V(x) = 20/\left(x^2 - 4\right)$ volt

The electric field $E$ at $x = 4\ \mu\text{m}$ is given by

If $g_E$ and $g_M$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio

$\frac{\text{electronic charge on the moon}}{\text{electronic charge on the earth}}\ \text{to be}$

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of length $L_1$ and $L_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two section is

A block of mass $m$ is connected to another block of mass $M$ by a spring (massless) of spring constant $k.$ The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the force on the block of mass $m.$

The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

A long straight wire of radius $a$ carries a steady current $i.$ The current is uniformly distributed across its cross section. The ratio of the magnetic field at $a/2$ and $2a$ is

A current $I$ flows along the length of an infinitely long, straight, thin walled pipe. Then

Two identical conducting wires $AOB$ and $COD$ are placed at right angles to each other. The wire $AOB$ carries an electric current $I_1$ and $COD$ carries a current $I_2$. The magnetic field on a point lying at a distance $d$ from $O$, in a direction perpendicular to the plane of the wires $AOB$ and $COD$, will be given by

A charged particle moves through a magnetic field perpendicular to its direction. Then

A charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $\vec{E}$ and $\vec{B}$ with a velocity$\vec{v}$perpendicular to both $\vec{E}$and $\vec{B},$ and comes out without any change in magnitude or direction of$\vec{v}$. Then

The half-life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y.$ Initially they have the same number of atoms. Then

If $M_O$ is the mass of an oxygen isotope ${}_{8}O^{17}, M_p$ and $M_N$ are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is

In gamma ray emission from a nucleus

A particle of mass $m$ executes simple harmonic motion with amplitude a and frequency $v.$ The average kinetic energy during its motion from the position of equilibrium to the end is

A point mass oscillates along the $x$-axis according to the law $x = x_0 \cos(\omega t - \pi/4).$ If the acceleration of the particle is written as $a = A\cos(\omega t + \delta),$ then

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 \times 10^{-2}\cos \pi t$ metre. The time at which the maximum speed first occurs is

Two springs, of force constant $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f.$ If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes

Two lenses of power $-15\text{ D}$ and $+5\text{ D}$ are in contact with each other. The focal length of the combination is

Angular momentum of the particle rotating with a central force is constant due to

For the given uniform square lamina $ABCD$, whose center is $O,$

A round uniform body of radius $R,$ mass $M$ and moment of inertia $I$ rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is

Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate?

If in a $p\text{-}n$ junction diode, a square input signal of $10\text{ V}$ is applied as shown

Then the output signal across $R_L$ will be

A Carnot engine, having an efficiency of $\eta = 1/10$ as heat engine, is used as a refrigerator. If the work done on the system is $10\ J$, the amount of energy absorbed from the reservoir at lower temperature is

When a system is taken from state $i$ to state $f$ along the path iaf, it is found that $Q = 50$ cal and $W = 20\text{ cal}$. Along the path $ibf\ Q = 36\text{ cal}.\ W$ along the path $ibf$ is

If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

A sound absorber attenuates the sound level by $20\text{ dB}$. The intensity decreases by a factor of

In a Young's double slit experiment the intensity at a point where the path difference is $\frac{\lambda}{6}$ ( $\lambda$ being the wavelength of light used) is $I$. If $I_0$ denotes the maximum intensity, $\frac{I}{I_0}$ is equal to

A particle is projected at $60^\circ$ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is

A $2\text{ kg}$ block slides on a horizontal floor with a speed of $4\text{ m/s}.$ It strikes an uncompressed spring and compresses it till the block is motionless. The kinetic friction force is $15\text{ N}$ and spring constant is $10{,}000\text{ N/m}.$ The spring compresses by