AIEEE 2012 Question Paper with Solutions

A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; It is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to :

A liquid in a beaker has temperature $\theta \left( t \right)$ at time $t$ and ${\theta _0}$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between ${\log _e}\left( {\theta - {\theta _0}} \right)$ and $t$ is :

In a uniformly charged sphere of total charge $Q$ and radius $R,$ the electric field $E$ is plotted as function of distance from the center. The graph which would correspond to the above will be:

This question has statement- $1$ and statement- $2.$ Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.

Statement- $1:$ When a charge $q$ is take from the centre of the surface of the sphere its potential energy changes by ${{q\rho } \over {3{\varepsilon _0}}}$
Statement- $2:$ The electric field at a distance $r\left( {r < R} \right)$ from the center of the sphere is ${{\rho r} \over {3{\varepsilon _0}}}.$

A radar has a power of $1kW$ and is operating at a frequency of $10$ $GHz.$ It is located on a mountain top of height $500$ $m.$ The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth $= 6.4 \times {10^6}m$) is :

If a simple pendulum has significant amplitude (up to a factor of $1/e$ of original ) only in the period between $t = 0s\,\,to\,\,t = \tau \,s,$ then $\tau \,$ may be called the average life of the pendulum When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with $b$ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :

A Carnot engine, whose efficiency is $40\%$, takes in heat from a source maintained at a temperature of $500$ $K.$ It is desired to have an engine of efficiency $60\% .$ Then, the intake temperature for the same exhaust (sink) temperature must be :

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements, choose the one that best describes the two Statements.

If two springs ${S_1}$ and ${S_2}$ of force constants ${k_1}$ and ${k_2}$, respectively, are stretched by the same force, it is found that more work is done on spring ${S_1}$ than on spring ${S_2}$.

STATEMENT 1: If stretched by the same amount work done on ${S_1}$, Work done on ${S_1}$ is more than ${S_2}$
STATEMENT 2: ${k_1} < {k_2}$

A particle of mass $m$ is at rest at the origin at time $t=0.$ It is subjected to a force $F\left( t \right) = {F_0}{e^{ - bt}}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

A wooden wheel of radius $R$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area $S$ and length $L.$ $L$ is slightly less than $2\pi R.$ To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it process the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Young's modulus is $Y,$ the force that one part of the wheel applies on the other part is :

The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $\tau$ of this circuit lies between

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times {10^{ - 2}}\,\,N$ (see figure). The length of the slider is $30$ $cm$ and its weight negligible. The surface tension of the liquid film is

The mass of a spaceship is $1000$ $kg.$ It is to be launched from the earth's surface out into free space. The value of $g$ and $R$ (radius of earth ) are $10\,m/{s^2}$ and $6400$ $km$ respectively. The required energy for this work will be:

Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, denuteron and alpha particle are respectively ${r_p},{r_d}$ and ${r_\alpha }$. Which one of the following relation is correct?

In Young's double slit experiment , one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If ${{\rm I}_m}$ be the maximum intensity, the resultant intensity ${\rm I}$ when they interfere at phase difference $\phi$ is given by :

A cylindrical tube, open at both ends, has a fundamental frequency, $f,$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron $= 1.6725 \times {10^{ - 27}}kg,$ mass of proton $= 1.6725 \times {10^{ - 27}}\,kg,$ mass of electron $= 9 \times {10^{ - 31}}\,kg$ ).

A diatomic molecule is made of two masses ${m_1}$ and ${m_2}$ which are separated by a distance $r.$ If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by: ($n$ is an integer)

Two cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is

This question has Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement 1 : Davisson - Germer experiment established the wave nature of electrons.

Statement 2 : If electrons have wave nature, they can interfere and show diffraction.

A charge $Q$ is uniformly distributed over the surface of non-conducting disc of radius $R.$ The disc rotates about an axis perpendicular to its plane and passing through its center with an angular velocity $\omega .$ As a result of this rotation a magnetic field of induction $B$ is obtained at the center of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and very the radius of the disc then the variation of the magnetic induction at the center of the disc will be represented by the figure :

Helium gas goes through a cycle $ABCD$ (consisting of two isochoric and isobaric lines) as shown in figure efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)

An electromagnetic wave in vacuum has the electric and magnetic field $\mathop E\limits^ \to$and $\mathop B\limits^ \to$, which are always perpendicular to each other. The direction of polarization is given by $\mathop X\limits^ \to$ and that of wave propagation by $\mathop k\limits^ \to$. Then

Truth table for system of four $NAND$ gates as shown in figure is:

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

An object $2.4$ $m$ in front of a lens forms a sharp image on a film $12$ $cm$ behind the lens. A glass plate $1$ $cm$ thick, of refractive index $1.50$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus of film?

Two electric bulbs marked $25W$ $-$ $220$ $V$ and $100W$ $-$ $220V$ are connected in series to a $440$ $V$ supply. Which of the bulbs will fuse?

Hydrogen atom is excited from ground state to another state with principal quantum number equal to $4.$ Then the number of spectral lines in the emission spectra will be :

A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading: 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data