JEE Main 2004 Physics Paper: AIEEE

Alternating current can not be measured by $\text{D.C.}$ ammeter because

In a $LCR$ circuit capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchaged, the inductance should be changed from $L$ to

In an $LCR$ series $\text{a.c.}$ circuit, the voltage across each of the components, $L, C$ and $R$ is $50\text{ V}$. The voltage across the $L\text{-}C$ combination will be:

An $\alpha$-particle of energy $5\text{ MeV}$ is scattered through $180^\circ$ by a fixed uranium nucleus. The distance of closest approach is of the order of

Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?

The resistance of the series combination of two resistances is $S.$ When they are joined in parallel the total resistance is $P.$ If $S = nP$ then the minimum possible value of $n$ is

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of $\frac{4}{3}$ and $\frac{2}{3}$, then the ratio of the current passing through the wires will be

The total current supplied to the circuit by the battery is

The electrochemical equivalent of a metal is $3.3 \times 10^{-7}\text{ kg}$ per Coulomb. The mass of the metal liberated at the cathode when a $3\text{ A}$ current is passed for $2$ seconds will be

The thermo $\text{emf}$ of a thermocouple varies with temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts where the ratio $a/b$ is $700^\circ\text{C}.$ If the cold junction is kept at $0^\circ\text{C},$ then the neutral temperature is

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

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 $l_B/l_A$ of their respective lengths must be

Thermistors are usually made of

In a meter bridge experiment null point is obtained at $20\text{ cm}$, from one end of the wire when resistance $X$ is balanced against another resistance $Y.$ If $X < Y$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $4X$ against $Y$

The work function of a substance is $4.0\text{ eV}.$ The longest wavelength of light that can cause photo- electron emission from this substance is approximately.

According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal $Vs$ the frequency of the incident radiation gives a straight line whose slope

A coil having $n$ turns and resistance $R\Omega$ is connected with a galvanometer of resistance $4R\Omega.$ This combination is moved in time $t$ seconds from a magnetic field $W_1$ weber to $W_2$ weber. The induced current in the circuit is

A metal conductor of length $1\text{ m}$ rotates vertically about one of its ends at angular velocity $5$ radians per second. If the horizontal component of earth's magnetic field is $0.2 \times 10^{-4}\text{ T},$ then the $e.m.f.$ developed between the two ends of the conductor is

In a uniform magnetic field of induction $B$ a wire in the form of a semicircle of radius $r$ rotates about the diameter of the circle with an angular frequency $\omega.$ The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $R,$ the mean power generated per period of rotation is

A radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

An electromagnetic wave of frequency $\nu = 3.0\text{ MHz}$ passes from vacuum into a dielectric medium with permittivity $\epsilon = 4.0.$ Then

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that of $B$ but uncharged is brought in contact with $B,$ then brought in contact with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is

Four charges equal to -$Q$ are placed at the four corners of a square and a charge $q$ is at its center. If the system is in equilibrium the value of $q$ is

A charged particle $q$ is shot towards another charged particle $Q$ which is fixed, with a speed $v$. It approaches $Q$ upto a closest distance $r$ and then returns. If $q$ were given a speed of $2v$ the closest distance of approach would be

A charged oil drop is suspended in a uniform field of $3 \times 10^{4}\text{ V/m}$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $= 9.9 \times 10^{-15}\text{ kg}$ and $g = 10\text{ m/s}^2$)

If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

The time period of an earth satellite in circular orbit is independent of

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x,$ respectively, are $T_2$ and $T_1\ (T_2 > T_1).$ The rate of heat transfer through the slab, in a steady state is $\left(\frac{A(T_2-T_1)K}{x}\right) f,$ with $f$ equal to

If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on earth to what it was previously will be

Two masses $m_1 = 5\text{ kg}$ and $m_2 = 4.8\text{ kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? $\left(g = 9.8\text{ m/s}^{2}\right)$

A block rests on a rough inclined plane making an angle of $30^\circ$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictional force on the block is $10\text{ N},$ the mass of the block (in $\text{kg}$) is $(\text{take } g = 10\text{ m/s}^{2})$

The materials suitable for making electromagnets should have

Curie temperature is the temperature above which

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $2\text{ s.}$ The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be

A wire fixed at the upper end stretches by length $l$ by applying a force $F.$ The work done in stretching is

An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in $\frac{T}{3}$ seconds?

A current $i$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $B.$ It is then bent into a circular loop of $n$ turns. The magnetic field at the center of the coil will be

The magnetic field due to a current carrying circular loop of radius $3\text{ cm}$ at a point on the axis at a distance of $4\text{ cm}$ from the centre is $54\ \mu\text{T}.$ What will be its value at the center of loop?

Two long conductors, separated by a distance $d$ carry current $I_1$ and $I_2$ in the same direction. They exert a force $F$ on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is

The binding energy per nucleon of deuteron $\left({}^{2}_{1}H\right)$ and helium nucleus $\left({}^{4}_{2}He\right)$ is $1.1\text{ MeV}$ and $7\text{ MeV}$ respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is

A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $2 : 1$ The ratio of their nuclear sizes will be

In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_1$ of the force while the energy is maximum for a frequency $\omega_2$ of the force; then

A particle of mass $m$ is attached to a spring (of spring constant $k$) and has a natural angular frequency $\omega_0.$ An external force $F(t)$ proportional to $\cos\omega t\ (\omega \neq \omega_0)$ is applied to the oscillator. The time displacement of the oscillator will be proportional to

The total energy of particle, executing simple harmonic motion is

The bob of a simple pendulum executes simple harmonic motion in water with a period $t,$ while the period of oscillation of the bob is $t_0$ in air. Neglecting frictional force of water and given that the density of the bob is $(4/3) \times 1000\text{ kg/m}^{3}.$ What relationship between $t$ and $t_0$ is true

A particle at the end of a spring executes $\text{S.H.M.}$ with a period $t_1$. While the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$ then

A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed $\frac{v_0}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection θ?

A plano convex lens of refractive index $1.5$ and radius of curvature $30\text{ cm}$ is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of size of the object

A light ray is incident perpendicularly to one face of a $90^\circ$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $45^\circ$, we conclude that the refractive index $n$

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

One solid sphere $A$ and another hollow sphere $B$ are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $I_A$ and $I_B$ such that

The manifestation of band structure in solids is due to

A piece of copper and another of germanium are cooled from room temperature to $77\text{ K},$ the resistance of

When $npn$ transistor is used as an amplifer

For a transistor amplifier in common emitter configuration for load impedance of $1\text{ k}\Omega\ (h_{fe} = 50$ and $h_{oe} = 25\ \mu\text{A/V})$ the current gain is

When $p\text{-}n$ junction diode is forward biased then

If two soap bubbles of different radii are connected by a tube

Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $(T_1, T_2),$ volume $(V_1, V_2)$ and pressure $(P_1, P_2)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

Which of the following statements is correct for any thermodynamic system?

One mole of ideal monatomic gas $(\gamma = 5/3)$ is mixed with one mole of diatomic gas $(\gamma = 7/5)$. What is $\gamma$ for the mixture? $\gamma$ Denotes the ratio of specific heat at constant pressure, to that at constant volume

Time taken by a $836\text{ W}$ heater to heat one litre of water from $10^{\circ}\text{C}$ to $40^{\circ}\text{C}$ is

Which one of the following represents the correct dimensions of the coefficient of viscosity?

If $\vec{A} \times \vec{B} = \vec{B} \times \vec{A}$, then the angle between A and B is

Spherical balls of radius $R$ are falling in a viscous fluid of viscosity $\eta$ with a velocity $v.$ The retarding viscous force acting on the spherical ball is

The displacement $y$ of a particle in a medium can be expressed as, $y = 10^{-6}\sin\left(100t + 20x + \frac{\pi}{4}\right)\text{ m}$ where $t$ is in second and $x$ in meter. The speed of the wave is

The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index $n$) is:

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment, is:

A uniform chain of length $2\text{ m}$ is kept on a table such that a length of $60\text{ cm}$ hangs freely from the edge of the table. The total mass of the chain is $4\text{ kg}.$ What is the work done in pulling the entire chain on the table?

A body of mass $\text{'}m\text{'},$ accelerates uniformly from rest to $\text{'}v_1\text{'}$ in time $T$. The instantaneous power delivered to the body as a function of time is given by

A force $\vec{F} = \left(5\vec{i} + 3\vec{j} + 2\vec{k}\right)\text{ N}$ is applied over a particle which displaces it from its origin to the point $\vec{r} = \left(2\vec{i} - \vec{j}\right)\text{ m}$ The work done on the particle in joules is

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to