Solved papers for JEE Main & Advanced AIEEE Solved Paper-2007
done AIEEE Solved Paper-2007 Total Questions - 40
question_answer1) The displacement of an object attached to a spring and executing simple harmonic motion is given by\[2x+3y+z=1\]\[x+3y+2z=2\] metre. The time at which the maximum speed first occurs is
AIEEE Solved Paper-2007
question_answer2) In an AC circuit, the voltage applied is\[cos\text{ }\alpha \] \[1/\sqrt{3}\]The resulting current in the circuit is\[1/\sqrt{2}\]. The power consumption in the circuit is given by
AIEEE Solved Paper-2007
question_answer3) An electric charge\[{{y}^{2}}={{x}^{2}}-2xy\frac{dy}{dx}\]is placed at the origin (0, 0) of X-Y coordinate system. Two points A and B are situated at\[{{p}^{2}}+{{q}^{2}}=1,\]and (2, 0) respectively. The potential difference between the points A and B will be
AIEEE Solved Paper-2007
question_answer4) 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
AIEEE Solved Paper-2007
question_answer5) An ideal coil of 10 H is connected in series with a resistance of \[\frac{1}{\sqrt{2}}\] and a battery of 5 V. After 2 s, the connection is made, the current flowing (in ampere) in the circuit is
AIEEE Solved Paper-2007
question_answer6) 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\[2a/\sqrt{3}\]and\[2a\sqrt{3}\]is
AIEEE Solved Paper-2007
question_answer7) A current\[^{20}{{C}_{0}}{{-}^{20}}{{C}_{1}}{{+}^{20}}{{C}_{2}}{{-}^{20}}{{C}_{3}}+....{{+}^{20}}{{C}_{10}}\]flows along the length of an infinitely long, straight, thin walled pipe. Then,
AIEEE Solved Paper-2007
A)
The magnetic field is zero only on the axis of the pipe
doneclear
B)
The magnetic field is different at different points inside the pipe
doneclear
C)
The magnetic field at any point inside the pipe is zero
doneclear
D)
The magnetic field at all points inside the pipe is the same, but not zero
question_answer8) If\[{{-}^{20}}{{C}_{10}}\]is the mass of an oxygen isotope\[\frac{1}{2}{{\,}^{20}}{{C}_{10}}\]and\[^{20}{{C}_{10}}\]are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is
AIEEE Solved Paper-2007
question_answer10) If in a\[x\ne 0\]junction diode, a square input signal of 10 V is applied as shown Then, the output signal across \[{{R}_{L}}\] will be
AIEEE Solved Paper-2007
question_answer12) The velocity of a particle is\[x\]If its position is\[x\]at\[\frac{{{x}^{2}}}{{{\cos }^{2}}\alpha }-\frac{{{y}^{2}}}{{{\sin }^{2}}\alpha }=1,\]then its displacement after unit time\[\frac{\pi }{4}\]is
AIEEE Solved Paper-2007
question_answer14) A point mass oscillates along the x-axis according to the law\[{{\log }_{3}}e\].If the acceleration of the particle is written as \[{{\log }_{e}}3\]then
AIEEE Solved Paper-2007
question_answer15) Charges are placed on the vertices of a square as shown. Let \[\vec{E}\] be the electric field and V be the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then
AIEEE Solved Paper-2007
question_answer16) 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,
AIEEE Solved Paper-2007
question_answer17) 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
AIEEE Solved Paper-2007
question_answer18) Carbon, silicon and germanium have four valence electrons each. At room temperature, which one of the following statements is most appropriate?
A)
The number of free conduction electrons is significant in C but small in Si and\[A=\left[ \begin{matrix} 5 & 5\alpha & \alpha \\ 0 & \alpha & 5\alpha \\ 0 & 0 & 5 \\ \end{matrix} \right]\]
doneclear
B)
The number of free conduction electrons is negligibly small in all the three
doneclear
C)
The number of free electrons for conduction is significant in all the three
doneclear
D)
The number of free electrons for conduction is significant only in\[|{{A}^{2}}|=25,\]and\[{{5}^{2}}\]but small in C
question_answer19) A charged particle with charge g enters a region of constant, uniform and mutually orthogonal fields \[\vec{E}\] and \[\vec{B}\] with a velocity v perpendicular to both \[\vec{E}\] and \[\vec{B}\] and comes out without any change in magnitude or direction of v. Then,
AIEEE Solved Paper-2007
question_answer20) The potential at a point x (measured in\[{{e}^{-\frac{1}{2}}}\]due to some charges situated on the x-axis is given by\[{{e}^{+\frac{1}{2}}}\]volt. The electric field E at \[x=4\,\mu m\] is given by
AIEEE Solved Paper-2007
A)
\[{{\tan }^{-1}}\frac{b}{ac}\]and in the -ve\[45{}^\circ \]direction
doneclear
B)
\[{{\tan }^{-1}}\frac{bc}{a(c-a)}\]and in the +ve\[{{\tan }^{-1}}\frac{bc}{a}\]direction
doneclear
C)
\[{{y}^{2}}=8x\]and in the -ve\[y=x+2\]direction
doneclear
D)
\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x-12y-2\text{ }z+20=0,\]and in the +ve\[a=\hat{i}+\hat{j}+\hat{k},b=\hat{i}-\hat{j}+2\hat{k}\]direction
question_answer22) 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 unstretehed. 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.
AIEEE Solved Paper-2007
question_answer24) One end of a thermally insulated rod is kept at a temperature\[m{{y}^{2}}+(1-{{m}^{2}})xy-m{{x}^{2}}=0\]and the other at\[xy=0,\]. The rod is composed of two sections of lengths\[-\frac{1}{2}\]and\[-2\] and thermal conductivities \[{{K}_{1}}\] and \[{{K}_{2}}\] respectively. The temperature at the interface of the two sections is
AIEEE Solved Paper-2007
question_answer26) If\[min\{x+1,|~x|+1\}\]and\[f\{x\}\ge 1\]denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then
AIEEE Solved Paper-2007
question_answer28) Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current\[f(x)\]and COD carries a current\[x=0\]. 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
AIEEE Solved Paper-2007
question_answer29) The resistance of a wire is\[\int_{\sqrt{2}}^{x}{\frac{dt}{t\sqrt{{{t}^{2}}-1}}}=\pi /2\] at\[\pi \]and \[\sqrt{3}/2\],at\[2\sqrt{2}\] The resistance of the wire at \[\int{\frac{dx}{\cos x+\sqrt{3}\sin x}}\] will be
AIEEE Solved Paper-2007
question_answer30) 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 volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is
AIEEE Solved Paper-2007
question_answer31) If\[\frac{1}{6}\]arid\[\frac{1}{3}\]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 \[{{x}^{2}}+ax+1=0\]to be
AIEEE Solved Paper-2007
question_answer32) A circular disc of radius R is removed from a bigger circular disc of radius 2R, such that the circumference of the discs coincide. The centre of mass of the new disc is\[(3,\infty )\]from the centre of the bigger disc. The value of \[\alpha \] is
AIEEE Solved Paper-2007
question_answer33) A round uniform body of radius R, mass M and moment of inertia\[x=2\text{ }cm\]rolls down (without slipping) an inclined plane making an angle \[\theta \] with the horizontal. Then, its acceleration is
AIEEE Solved Paper-2007
question_answer35) A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by
AIEEE Solved Paper-2007
question_answer36) A particle is projected at\[T=2s\]to the horizontal with a kinetic energy K. The kinetic energy at the highest point is
AIEEE Solved Paper-2007
question_answer37) In a Young's double-slit experiment, the intensity at a point where the path difference is\[=\frac{T}{4}=\frac{2}{4}=0.5s\] (\[\pi /2\]being the wavelength of the light used), is\[{{v}_{a}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{({{10}^{-3}})}{OA}\]. If\[=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{({{10}^{-3}})}{\sqrt{{{(\sqrt{2})}^{2}}+{{(\sqrt{2})}^{2}}}}\]denotes the maximum intensity, \[{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{({{10}^{-3}})}{OB}\]is equal to
AIEEE Solved Paper-2007
question_answer38) Two springs, of force constants\[{{I}_{0}}=\frac{E}{R}=\frac{5}{5}=1\,A\]and\[\tau =\frac{L}{R}=\frac{10}{5}=2\,s\]are connected to a mass m as shown. The frequency of oscillation of the mass is \[f\]. If both\[(\therefore -t/\tau =\frac{-2}{2}=-1)\]and\[J=\frac{i}{\pi {{a}^{2}}}\]are made four times their original values, the frequency of. oscillation becomes
AIEEE Solved Paper-2007
question_answer39) When a system is taken from state\[E={{E}_{0}}\]to state f along the path \[iaf,\] it is found that\[sin\text{ }\omega t\] and\[I={{I}_{0}}\sin \left( \omega t-\frac{\pi }{2} \right)\]. Along the path ibf, \[p=\frac{{{E}_{0}}{{I}_{0}}}{\sqrt{2}}\]cal. W along the path \[ibf\] is
AIEEE Solved Paper-2007
question_answer40) 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
AIEEE Solved Paper-2007