AIEEE 2003 (Physics) Mock Test

A particle of mass $M$ and charge $Q$ moving with velocity $\vec{v}$ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B$. The work done by the field when the particle completes one full circle is:

A particle of charge $-16\times 10^{-18}\text{C}$ moving with velocity $10\text{m/s}$ along the $x$ -axis enters a region where a magnetic field of induction $B$ is along the $y$ -axis, and an electric field of magnitude $10^4\text{V/m}$ is along the negative $z$ -axis. If the charged particle continues moving along the $x$ -axis, the magnitude of $B$ is:

A thin rectangular magnet suspended freely has a period of oscillation equal to $T$. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is $T^{\prime }$, the ratio $T^{\prime }/T$ is:

A magnetic needle lying parallel to a magnetic field requires $W$ units of work to turn it through $60^{\circ }$. The torque needed to maintain the needle in this position will be:

The magnetic lines of force inside a bar magnet:

Curie temperature is the temperature above which:

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $49\text{N}$, when the lift is stationary. If the lift moves downward with an acceleration of $5{\text{m/s}}^2$, the reading of the spring balance will be:

The length of a wire of a potentiometer is $100\text{cm}$, and the e.m.f. of its standard cell is $E$ volt. It is employed to measure the e.m.f. of a battery whose internal resistance is $0.5\Omega$. If the balance point is obtained at $l=30\text{cm}$ from the positive end, the e.m.f. of the battery is:

A strip of copper and another of germanium are cooled from room temperature to $80\text{K}$. The resistance of:

Consider telecommunication through optical fibres. Which of the following statements is not true?

The thermo e.m.f. of a thermo-couple is $25\mu {\text{V/}}^{\circ }\text{C}$ at room temperature. A galvanometer of $40\Omega$ resistance, capable of detecting current as low as $10^{-5}\text{A}$, is connected with the thermocouple. The smallest temperature difference that can be detected by this system is:

The negative $\text{Zn}$ pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by $0.13\text{g}$ in $30\text{minutes}$. If the electrochemical equivalent of $\text{Zn}$ and $\text{Cu}$ are $32.5$ and $31.5$ (arbitrary units or mass ratio) respectively, the increase in the mass of the positive $\text{Cu}$ pole in this time is:

Dimensions of $\frac{1}{{\mu }_0{ϵ}_0}$, where symbols have their usual meaning, are:

A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$, and another disc $Y$ of radius $4R$ is made from an iron plate of thickness $t/4$. The relation between the moment of inertia $I_X$ and $I_Y$ is:

The time period of a satellite of earth is $5\text{hours}$. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become:

A particle performing uniform circular motion has angular momentum $L$. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is:

Which of the following radiations has the least wavelength?

When ${}^{238}\text{U}$ nucleus originally at rest, decays by emitting an alpha particle having a speed $u$, the recoil speed of the residual nucleus is:

Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ respectively are released in free space with initial separation between their centres equal to $12R$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is:

The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the:

A car moving with a speed of $50\text{km/hr}$, can be stopped by brakes after at least $6\text{m}$. If the same car is moving at a speed of $100\text{km/hr}$, the minimum stopping distance is:

A boy playing on the roof of a $10\text{m}$ high building throws a ball with a speed of $10\text{m/s}$ at an angle of $30^{\circ }$ with the horizontal. How far from the throwing point will the ball be at the height of $10\text{m}$ from the ground? (Take $g=10{\text{m/s}}^2$)

An ammeter reads up to $1\text{A}$. Its internal resistance is $0.81\Omega$. To increase the range to $10\text{A}$, the value of the required shunt is:

The physical quantities not having same dimensions are:

Three forces start acting simultaneously on a particle moving with velocity $\vec{v}$. These forces are represented in magnitude and direction by the three sides of a triangle $ABC$ taken in order. The particle will now move with velocity:

If the electric flux entering and leaving an enclosed surface respectively is ${\varphi }_1$ and ${\varphi }_2$, the electric charge inside the surface will be:

A horizontal force of $10\text{N}$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is:

A marble block of mass $2\text{kg}$ lying on ice when given a velocity of $6\text{m/s}$ is stopped by friction in $10\text{s}$. The coefficient of friction is:

Consider the following two statements:(1) Linear momentum of a system of particles is zero.(2) Kinetic energy of system of particles is zero.

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon:

A block of mass $M$ is pulled along a horizontal friction surface by a rope of mass $m$. If a force $P$ is applied at the free end of the rope, the force exerted by the rope on the block is:

A light spring balance hangs from the hook of the other light spring balance and a block of mass $M\text{kg}$ hangs from the former one. Then the true statement about scale reading is:

A wire suspended vertically from one of its ends stretched by attaching weight of $200\text{N}$ to the lower end. The weight stretches the wire by $1\text{mm}$. Then the elastic energy stored in the wire is:

The escape velocity for a body projected vertically upwards from the surface of earth is $11\text{km/s}$. If the body is projected at an angle of $45^{\circ }$ with the vertical, the escape velocity will be:

A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period $T$. If the mass is increased by $m$, the time period becomes $5T/3$. Then the ratio $m/M$ is:

"Heat cannot by itself flow from a body at lower temperature to a body at higher temperature" is a statement of consequence of:

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2$ respectively. If the maximum velocities during oscillations are equal, the ratio of amplitudes of $A$ and $B$ is:

The length of a simple pendulum executing simple harmonic motion is increased by $21\%$. The percentage increase in the time period of the pendulum of increased length is:

The displacement $y$ of wave travelling in the $x$ -direction is given by $y=10^{-4}\sin (600t-2x+\pi /3)$ metres, where $x$ is in metres and $t$ in seconds. The speed of the wave-motion in $\text{m/s}$ is:

When the current changes from $+2\text{A}$ to $-2\text{A}$ in $0.05$ second, an e.m.f. of $8\text{V}$ is induced in a coil. The coefficient of self-induction of the coil is:

In an oscillating $LC$ circuit the maximum charge on the capacitor is $Q$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is:

The core of any transformer is laminated so as to:

Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r}$ and $\vec{\tau }$ be the torque of this force about the origin. Then:

A radioactive sample at any instant has its disintegration rate $5000\text{disintegrations per minute}$. After $5\text{minutes}$, the rate is $1250\text{disintegrations per minute}$. Then, the decay constant (per minute) is:

A nucleus with $Z=92$ emits the following in a sequence: $\alpha ,\alpha ,{\beta }^{-},{\beta }^{-},\alpha ,\alpha ,\alpha ,\alpha ,{\beta }^{-},{\beta }^{-},\alpha ,{\beta }^{+},{\beta }^{+},\alpha$. The $Z$ of the resulting nucleus is:

Two identical photo cathodes receive light of frequencies $f_1$ and $f_2$. If the velocities of the photoelectrons (of mass $m$) coming out are respectively $v_1$ and $v_2$, then:

Which of the following cannot be emitted by radioactive substance during their decay?

A $3\text{V}$ battery with negligible internal resistance is connected in a circuit as shown. (Circuit consists of three $3\Omega$ resistors, two in parallel, then in series with the third). The current $I$ in the circuit will be:

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor:

The displacement of a particle varies according to the relation $x=4(\cos \pi t+\sin \pi t)$. The amplitude of the particle is:

A thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the centre of the shell is:

The work done in placing a charge of $8\times 10^{-18}$ coulomb on a condenser of capacity $100$ micro-farad is:

The co-ordinates of a moving particle at any time $t$ are given by $x=\alpha t^3$ and $y=\beta t^3$. The speed of the particle at time $t$ is given by:

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_p/C_v$ for the gas is:

Which of the following parameters does not characterize the thermodynamic state of matter?

A carnot engine takes $3\times 10^6\text{cal}$ of heat from a reservoir at $627^{\circ }\text{C}$, and gives it to a sink at $27^{\circ }\text{C}$. The work done by the engine is:

A spring of spring constant $5\times 10^3\text{N/m}$ is stretched initially by $5\text{cm}$ from the unstretched position. Then the work required to stretch it further by another $5\text{cm}$ is:

A metal wire of linear mass density $9.8\text{g/m}$ is stretched with a tension of $10\text{kg-wt}$ between two rigid supports $1\text{metre}$ apart. The wire passes at its middle point between the poles of a magnet and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is:

A tuning fork of known frequency $256\text{Hz}$ makes $5$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:

A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as function of displacement $x$. Which of the following statement is true?

In the nuclear fusion reaction ${}_1^2\text{H}{+}_1^3\text{H}{\to }_2^4\text{He}+\text{n}$, given that the repulsive potential energy between the two nuclei is $7.7\times 10^{-14}\text{J}$, the temperature at which the gases must be heated to initiate the reaction is nearly: (Boltzmann’s constant $k=1.38\times 10^{-23}\text{J/K}$)

Which of the following atoms has the lowest ionization potential?

The wavelengths involved in the spectrum of deuterium (${}_1^2\text{D}$) are slightly different from that of hydrogen spectrum, because:

In the middle of the depletion layer of a reverse-biased p-n junction, the:

If the binding energy of the electron in a hydrogen atom is $13.6\text{eV}$, the energy required to remove the electron from the first excited state of ${\text{Li}}^{++}$ is:

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to:

A rocket with a lift-off mass $3.5\times 10^4\text{kg}$ is blasted upwards with an initial acceleration of $10{\text{m/s}}^2$. Then the initial thrust of the blast is:

To demonstrate the phenomenon of interference we require two sources which emit radiation of:

Three charges $-q_1$, $+q_2$ and $-q_3$ are placed as shown in the figure. ($-q_1$ at origin, $+q_2$ at $(b,0)$, $-q_3$ at $(a\cos \theta ,a\sin \theta )$). The $x$ -component of the force on $-q_1$ is proportional to:

A $220\text{volt}$, $1000\text{watt}$ bulb is connected across a $110\text{volt}$ mains supply. The power consumed will be:

The image formed by an objective of a compound microscope is:

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by:

To get three images of a single object, one should have two plane mirrors at an angle of:

According to Newton’s law of cooling, the rate of cooling of a body is proportional to $(\Delta \theta {)}^n$, where $\Delta \theta$ is the difference of the temperature of the body and the surroundings, and $n$ is equal to:

The length of a given cylindrical wire is increased by $100\%$. Due to the consequent decrease in diameter, the percentage change in the resistance of the wire will be: