NEET 1998 Physics Paper: AIPMT

A step-up transformer operates on a $230\text{ V}$ line and supplies current of $2\text{ A}$ to a load. The ratio of the primary and secondary windings is $1 : 25$. The current in the primary coil is

In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If $a_0$ is the radius of the ground state orbit, $m$ is the mass and $e$ is the charge on the electron, $\varepsilon_0$ is the vacuum permittivity, the speed of the electron is

Three equal resistors connected in series across a source of emf together dissipate $10$ watt of power. What will be the power dissipated in watt if the same resistors are connected in parallel across the same source of emf?

A $5^\circ\text{C}$ rise in temperature is observed in a conductor by passing a current. When the current is doubled the rise in temperature will be approximately

If nearly $10^{5}\text{ C}$ liberate $1\text{ g}$ equivalent of aluminium, then the amount of aluminium (equivalent weight 9) deposited through electrolysis in $20\text{ min}$ by a current of $50$ amp will be

A galvanometer having a resistance of $8$ ohm is shunted by a wire of resistance $2$ ohm. If the total current is $1\text{ A}$, the part of it passing through the shunt will be

The $21\text{ cm}$ radio wave emitted by hydrogen in interstellar space is due to the interaction called the hyperfine interaction in atomic hydrogen. The energy of the emitted wave is nearly

Light of wavelength $5000$ Å falls on a sensitive plate with photoelectric work function of $1.9\text{ eV}$. The kinetic energy of the photoelectron emitted will be

In a photo-emissive cell, with exciting wavelength $\lambda$, the fastest electron has speed $v$. If the exciting wavelength is changed to $3\lambda/4$, the speed of the fastest emitted electron will be

Two coils have a mutual inductance of $0.005\text{ H}$. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 10\text{ A}$ and $\omega = 100\pi\text{ rad/s}$. The maximum value of emf in the second coil is

A point $Q$ lies on the perpendicular bisector of an electrical dipole of dipole moment $p$. If the distance of $Q$ from the dipole is $r$ (much larger than the size of the dipole) then electric field at $Q$ is proportional to

A hollow insulated conducting sphere is given a positive charge of $10\ \mu\text{C}$. What will be the electric field at the centre of the sphere if its radius is $2\text{ m}$?

A particle of mass $m$ and charge $q$ is placed at rest in a uniform electric field $E$ and then released. The kinetic energy attained by the particle after moving a distance $y$ is

The radiant energy from the sun, incident normally at the surface of earth is $20\text{ kcal/m}^{2}\text{ min}$. What would have been the radiant energy, incident normally on the earth, if the sun had a temperature, twice of the present one?

A ball of mass $0.25\text{ kg}$ attached to the end of a string of length $1.96\text{ m}$ is moving in a horizontal circle. The string will break if the tension is more than $25\text{ N}$. What is the maximum speed with which the ball can be moved?

A mass of $1\text{ kg}$ is suspended by a thread. It is

(i) lifted up with an acceleration $4.9\text{ m/s}^{2}$,

(ii) lowered with an acceleration $4.9\text{ m/s}^{2}$.

The ratio of the tensions is

A $5000\text{ kg}$ rocket is set for vertical firing. The exhaust speed is $800\text{ m s}^{-1}$. To give an initial upward acceleration of $20\text{ m/s}^{2}$, the amount of gas ejected per second to supply the needed thrust will be ($g = 10\text{ m s}^{-2}$)

For protecting a sensitive equipment from the external magnetic field, it should be

A car moving with a speed of $40\text{ km/h}$ can be stopped by applying brakes after atleast $2\text{ m}$. If the same car is moving with a speed of $80\text{ km/h}$, what is the minimum stopping distance?

A coil of one turn is made of a wire of certain length and then from the same length a coil of two turns is made. If the same current is passed in both the cases, then the ratio of the magnetic induction at their centres will be

Two long parallel wires are at a distance of $1\text{ m}$. Both of them carry one ampere of current. The force of attraction per unit length between the two wires is

Half-lives of two radioactive substances $A$ and $B$ are respectively $20\text{ min}$ and $40\text{ min}$. Initially the samples of $A$ and $B$ have equal number of nuclei. After $80\text{ min}$ the ratio of remaining number of $A$ and $B$ nuclei is

Complete the equation for the following fission process:

${}_{92}\text{U}^{235} + {}_{0}n^{1} \longrightarrow {}_{38}\text{Sr}^{90} + \ldots\ldots$

Atomic weight of boron is $10.81$ and it has two isotopes ${}_{5}^{10}\text{B}$ and ${}_{5}^{11}\text{B}$. Then, the ratio of atoms of ${}_{5}^{10}\text{B}$ and ${}_{5}^{11}\text{B}$ in nature would be

A nucleus ${}_{n}X^{m}$ emits one $\alpha$ and two $\beta$ particles. The resulting nucleus is

A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force $F\sin\omega t$. If the amplitude of the particle is maximum for $\omega = \omega_1$ and the energy of the particle is maximum for $\omega = \omega_2$, then

(where $\omega_0 \rightarrow$ natural angular frequency of oscillations of particle)

Two simple pendulums of length $0.5\text{ m}$ and $2.0\text{ m}$ respectively are given small linear displacement in one direction at the same time. They will again be in the same phase when the pendulum of shorter length has completed oscillations

A mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n$. What will be the frequency of the system, if a mass $4m$ is suspended from the same spring?

Two particles $A$ and $B$ are connected by a rigid rod $AB$. The rod slides along perpendicular rails as shown here. The velocity of $A$ to the right is $10\text{ m/s}$. What is the velocity of $B$ when angle $\alpha = 60^\circ$?

The speed of a boat is $5\text{ km/h}$ in still water. It crosses a river of width $1.0\text{ km}$ along the shortest possible path in $15\text{ min}$. The velocity of the river water is (in $\text{km/h}$)

A luminous object is placed at a distance of $30\text{ cm}$ from the convex lens of focal length $20\text{ cm}$. On the other side of the lens, at what distance from the lens, a convex mirror of radius of curvature $10\text{ cm}$, be placed in order to have an upright image of the object coincident with it?

Light enters at an angle of incidence in a transparent rod of refractive index $n$. For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence?

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 diameter of the ring. The ring will now rotate with an angular velocity

$O$ is the centre of an equilateral triangle $ABC.\ F_1,\ F_2$ and $F_3$ are three forces acting along the sides $AB,\ BC$ and $AC$ as shown in figure. What should be the magnitude of $F_3$ so that the total torque about $O$ is zero?

A weightless ladder $20\text{ ft}$ long rests against a frictionless wall at an angle of $60^\circ$ from the horizontal. A $150$ pound man is $4\text{ ft}$ from the top of the ladder. A horizontal force is needed to keep it from slipping. Choose the correct magnitude of force from the following:

The transfer ratio $\beta$ of a transistor is $50$. The input resistance of the transistor when used in the common emitter configuration is $1\text{ k}\Omega$. The peak value of the collector AC current for an AC input voltage of $0.01\text{ V}$ peak is

Which one of the following gates will have an output of 1?

The truth table given below is for which gate?

The cause of the potential barrier in a $p\text{-}n$ diode is

A semi-conducting device is connected in a series in circuit with a battery and a resistance. A current is allowed to pass through the circuit. If the polarity of the battery is reversed, the current drops to almost zero. The device may be

We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system, which of the following statements is true?

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma$, the change in internal energy of a mass of gas, when the volume changes from $V$ to $2V$ at constant pressure $P$ is

A vehicle, with a horn of frequency $n$ is moving with a velocity of $30\text{ m/s}$ in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency $n + n_1$. Then (if the sound velocity in air is $300\text{ m/s}$)

A transverse wave is represented by the equation

$y = y_0\sin\frac{2\pi}{\lambda}(vt - x)$

For what value of $\lambda$ is the maximum particle velocity equal to two times the wave velocity?

A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance $1.21$ Å between them. The wavelength of the standing wave is

In a sinusoidal wave, the time required for a particular point, to move from maximum displacement to zero displacement is $0.170\text{ s}$. The frequency of the wave is

A force acts on a $3.0\text{ g}$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^2 + t^3$, where $x$ is in metre and $t$ in second. The work done during the first $4\text{ s}$ is