# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2005

### done AIEEE Solved Paper-2005

• question_answer1) A projectile can have the same range R for two angles of projection. If${{t}_{1}}$and${{t}_{2}}$are the times of flights in the two cases, then the product of the two times of flights is proportional to       AIEEE  Solved  Paper-2005

A) ${{R}^{2}}$

B) $\frac{1}{{{R}^{2}}}$

C)        $\frac{1}{R}$

D)        $R$

• question_answer2) An annular ring with inner and outer radii${{R}_{1}}$and${{R}_{2}}$is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring,$\frac{{{F}_{1}}}{{{F}_{2}}}$is     AIEEE  Solved  Paper-2005

A) $\frac{{{R}_{2}}}{{{R}_{1}}}$

B)        ${{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}$

C)        1

D)        $\frac{{{R}_{1}}}{{{R}_{2}}}$

• question_answer3) A smooth block is released at rest on a$45{}^\circ$incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is     AIEEE  Solved  Paper-2005

A) ${{\mu }_{k}}=1-\frac{1}{{{n}^{2}}}$

B) ${{\mu }_{k}}=\sqrt{1-\frac{1}{{{n}^{2}}}}$

C)        ${{\mu }_{s}}=1-\frac{1}{{{n}^{2}}}$

D)        ${{\mu }_{s}}=\sqrt{1-\frac{1}{{{n}^{2}}}}$

• question_answer4) The upper half of an inclined plane with inclination$\phi$is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by     AIEEE  Solved  Paper-2005

A) $2\sin \phi$

B)        $2\cos \phi$

C)        $2\tan \phi$

D)        $\tan \phi$

• question_answer5) A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?     AIEEE  Solved  Paper-2005

A) 3.0 cm

B)                        2.0 cm

C)        1.5 cm

D)        1.0 cm

• question_answer6) Out of the following pairs, which one does not have identical dimensions?     AIEEE  Solved  Paper-2005

A) Angular momentum and Planck's constant

B) Impulse and momentum

C) Moment of inertia and moment of a force

D) Work and torque

• question_answer7) The relation between time t and distance$x$is $t=a{{x}^{2}}+bx,$where a and b are constants. The acceleration is       AIEEE  Solved  Paper-2005

A) $-2ab{{v}^{2}}$

B)        $2b{{v}^{3}}$

C)        $-2a{{v}^{3}}$

D)        $2a{{v}^{2}}$

• question_answer8) A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance travelled is 15 S, then       AIEEE  Solved  Paper-2005

A) $S=ft$

B)        $S=\frac{1}{6}f{{t}^{2}}$

C)        $S=\frac{1}{2}f{{t}^{2}}$

D)        $S=\frac{1}{4}f{{t}^{2}}$

• question_answer9) A particle is moving eastwards with a velocity of$5m{{s}^{-1}}$. In 10 s, the velocity changes to$5\text{ }m{{s}^{-1}}$northwards.  The average acceleration in this time is     AIEEE  Solved  Paper-2005

A) $\frac{1}{\sqrt{2}}m{{s}^{-2}}$towards north-east

B) $\frac{1}{2}m{{s}^{-2}}$towards north

C) zero

D) $\frac{1}{\sqrt{2}}m{{s}^{-2}}$towards north-west

• question_answer10) A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at$2m/{{s}^{2}}$. He peaches the ground with a speed of 3 m/s. At what height, did he bail out?     AIEEE  Solved  Paper-2005

A) 91 m

B)        182 m

C) 293 m

D)        111 m

• question_answer11) A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration a to keep the block stationary. Then, a is equal to AIEEE  Solved  Paper-2005

A) $g/tan\alpha$

B)        $g\text{ }\cos ec\alpha$

C)        $g$

D)        $g\text{ }tan\alpha$

• question_answer12) A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is     AIEEE  Solved  Paper-2005

A) 40 m/s

B)                       20 m/s

C)        10 m/s

D)        $10\sqrt{30}\,m/s$

• question_answer13) A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass$\frac{1}{3}$M and a body C of mass$\frac{2}{3}$M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards     AIEEE  Solved  Paper-2005

A) depends on height of breaking

B) does not shift

C) body C

D) body B

• question_answer14) The moment of inertia of uniform semi-circular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is     AIEEE  Solved  Paper-2005

A) $\frac{1}{4}M{{r}^{2}}$

B)                        $\frac{2}{5}M{{r}^{2}}$

C)        $M{{r}^{2}}$

D)                        $\frac{1}{2}M{{r}^{2}}$

• question_answer15) A particle of mass 0.3 kg is subjected to a force $F=-\text{ }kx$with$k=15\text{ }N/m.$What will be its initial acceleration, if it is released from a point 20 cm away from the origin?     AIEEE  Solved  Paper-2005

A) $3\text{ }m/{{s}^{2}}$

B)       $15\text{ }m/{{s}^{2}}$

C)        $5\text{ }m/{{s}^{2}}$

D)        $\text{10 }m/{{s}^{2}}$

• question_answer16) The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is AIEEE  Solved  Paper-2005

A) $\sqrt{MK}L$

B) $\frac{k{{L}^{2}}}{2M}$

C) zero

D)        $\frac{M{{L}^{2}}}{k}$

• question_answer17) A mass m moves with a velocity v and collides   inelastically   with   another identical mass. After collision the 1st mass moves with velocity$\frac{v}{\sqrt{3}}$in a direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision.     AIEEE  Solved  Paper-2005

A) $v$

B)                        $\sqrt{3}v$

C)        $\frac{2}{\sqrt{3}}v$

D)        $\frac{v}{\sqrt{3}}$

• question_answer18) A 20 cm long capillary tube is dipped, in water. The water rises upto 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be     AIEEE  Solved  Paper-2005

A) 8cm

B)                        10cm

C)        4cm

D)        20cm

• question_answer19) If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is     AIEEE  Solved  Paper-2005

A) $2{{S}^{2}}Y$

B)                        $\frac{{{S}^{2}}}{2Y}$

C)        $\frac{2Y}{{{S}^{2}}}$

D)        $\frac{S}{2Y}$

• question_answer20) Average density of the earth     AIEEE  Solved  Paper-2005

A) does not depend on g

B) is a complex function of g

C) is directly proportional to g

D) is inversely proportional to g

• question_answer21) A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time, is given by     AIEEE  Solved  Paper-2005

A) $\frac{m{{v}^{2}}}{{{T}^{2}}}t$

B)        $\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}$

C)        $\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}$

D)        $\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}$

• question_answer22) Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped, is$[{{\mu }_{k}}=0.5]$     AIEEE  Solved  Paper-2005

A) 800m

B) 1000m

C)        100m

D)        400m

• question_answer23) Which of the following is incorrect regarding  the first law of thermodynamics?     AIEEE  Solved  Paper-2005

A) It is not applicable to any cyclic process

B) It is a restatement of the principle of conservation of energy

C) It introduces the concept of the internal energy

D) It introduces the concept of the entropy

• question_answer24) AT shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C. AIEEE  Solved  Paper-2005

A) $\frac{2}{3}l$

B)                        $\frac{3}{2}l$

C)        $\frac{4}{3}l$

D)        $l$

• question_answer25) The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?                   AIEEE  Solved  Paper-2005

A) $d=\frac{h}{2}$

B)                                        $d=\frac{3h}{2}$

C)        $d=2h$

D)        $d=h$

• question_answer26) A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere. (You may take $G=6.67\times {{10}^{-11}}N{{m}^{2}}/k{{g}^{2}}$)     AIEEE  Solved  Paper-2005

A) $13.34\times {{10}^{-10}}J$

B) $3.33\times {{10}^{-10}}J$

C)        $6.67\times {{10}^{-9}}J$

D)        $6.67\times {{10}^{-10}}J$

• question_answer27) A gaseous mixture consists of 16 g of helium and 16 g of oxygen/The ratio$\frac{{{C}_{p}}}{{{C}_{v}}}$ of the mixture is     AIEEE  Solved  Paper-2005

A) 1.59

B)        1.62

C)        1.4

D)        1.54

• question_answer28) The intensity of gamma radiation from a given source is$I$. On passing through 36 mm of lead, it is reduced to $I/8$. The thickness of lead, which will reduce the intensity to $I/2$ will be     AIEEE  Solved  Paper-2005

A) 6mm

B) 9mm

C)        18mm

D)        12mm

• question_answer29) The  electrical  conductivity  of  a semiconductor     increases     when electromagnetic radiation of wavelength shorter than 2480 nm, is incident on it. The bandgap for the semiconductor is     AIEEE  Solved  Paper-2005

A) 1.1 eV

B)                                        2.5 eV

C)                        0.5 eV

D)                        0.7 eV

• question_answer30) A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 0.5m away, the number of electrons emitted by photocathode would     AIEEE  Solved  Paper-2005

A) decrease by a factor of 4

B) increase by a factor of 4

C) decrease by a factor of 2

D) increase by a factor of 2

• question_answer31) Starting with a sample of pure$^{66}Cu,$ 7/8 of it decays into Zn in 15 min. The corresponding half-life is     AIEEE  Solved  Paper-2005

A) 10 min

B)        15 min

C)        5 min

D)        $7\frac{1}{2}$ min

• question_answer32) If radius of the$_{13}^{27}Al$ nucleus is estimated to be $3.6\text{ }fm,$then the radius of $_{52}^{125}Te$nucleus be nearly     AIEEE  Solved  Paper-2005

A) 6fm

B)        8fm

C)        4fm

D)        5fm

• question_answer33) The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is AIEEE  Solved  Paper-2005

A) 1/2

B)                       1/4

C)        1/3

D)        2/3

• question_answer34) The figure shows a system of two concentric spheres of radii${{r}_{1}},{{r}_{2}}$and kept at temperatures ${{T}_{1}},{{T}_{2}},$respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to AIEEE  Solved  Paper-2005

A) $\frac{({{r}_{2}}-{{r}_{1}})}{({{r}_{1}}{{r}_{2}})}$

B)        $\ln \left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)$

C)        $\frac{{{r}_{1}}{{r}_{2}}}{({{r}_{2}}-{{r}_{1}})}$

D)        $({{r}_{2}}-{{r}_{1}})$

• question_answer35) A system goes from A to B via two processes and II as shown in figure. If$\Delta {{U}_{1}}$and$\Delta {{U}_{2}}$are the changes in internal energies in the processes I and II respectively, then AIEEE  Solved  Paper-2005

A) $\Delta {{U}_{1}}=\Delta {{U}_{2}}$

B) relation between$\Delta {{U}_{1}}$and$\Delta {{U}_{2}}$cannot be determined

C) $\Delta {{U}_{2}}>\Delta {{U}_{1}}$

D) $\Delta {{U}_{2}}<\Delta {{U}_{1}}$

• question_answer36) The function ${{\sin }^{2}}\,(\omega t)$ represents     AIEEE  Solved  Paper-2005

A) a periodic, but not simple harmonic motion with a period $2\pi /\omega$

B) a periodic, but not simple harmonic motion with a period $\pi /\omega$

C) a simple harmonic motion with a period $2\pi /\omega$

D) a simple harmonic motion with a period $\pi /\omega$

• question_answer37) A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is     AIEEE  Solved  Paper-2005

A) hyperbola

B)                        circle

C) straight line

D) parabola

• question_answer38) Two simple harmonic motions are represented by the equations ${{y}_{1}}=0.1\sin \left( 100\pi t+\frac{\pi }{3} \right)$and${{y}_{2}}=0.1\,\cos \pi t.$ The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is     AIEEE  Solved  Paper-2005

A) $\frac{-\pi }{6}$

B)                        $\frac{\pi }{3}$

C)        $\frac{-\pi }{3}$

D)        $\frac{\pi }{6}$

• question_answer39) A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the water surface, the radius of this circle (in cm) is     AIEEE  Solved  Paper-2005

A) $36\sqrt{7}$

B)                        $\frac{36}{\sqrt{7}}$

C)        $36\sqrt{5}$

D)        $4\sqrt{5}$

• question_answer40) Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]     AIEEE  Solved  Paper-2005

A) 5 m

B) 1 m

C)        6 m

D)        3 m

• question_answer41) A thin glass (refractive index 1.5) lens has optical power of - 5 D in air. Its optical power in a liquid medium with refractive index 1.6 will be     AIEEE  Solved  Paper-2005

A) 1 D

B)                                        -1 D

C)        25 D

D)        - 25 D

• question_answer42) The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy? AIEEE  Solved  Paper-2005

A) III

B)                        IV

C)                        I

D)        II

• question_answer43) If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor     AIEEE  Solved  Paper-2005

A) $\frac{1}{2}$

B)                       2

C)        $\frac{1}{\sqrt{2}}$

D)        $\sqrt{2}$

• question_answer44) In a common base amplifier, the phase difference between the input signal voltage and output voltage is     AIEEE  Solved  Paper-2005

A) $\frac{\pi }{4}$

B) $\pi$

C)        zero

D)        $\frac{\pi }{2}$

• question_answer45) In a full wave rectifier, circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would be     AIEEE  Solved  Paper-2005

A) 50 Hz

B)                                        25 Hz

C)        100 Hz

D)        70.7 Hz

• question_answer46) A nuclear transformation is denoted, by$X(n,\text{ }\alpha )\to _{3}^{7}Li$. Which of the following is the nucleus of element X?             AIEEE  Solved  Paper-2005

A) $_{6}^{12}C$

B) $_{5}^{10}B$

C) $_{5}^{9}B$

D)        $_{4}^{11}Be$

• question_answer47) A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions per milliampere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 V, the resistance in Ohm's needed to be connected in series with the coil will be     AIEEE  Solved  Paper-2005

A) ${{10}^{3}}$

B)                                        ${{10}^{5}}$

C)        99995

D)        9995

• question_answer48) Two voltameters, one of copper and another of silver, are joined in parallel. When a total charge q flows through the voltameters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are${{z}_{1}}$and${{z}_{2}}$respectively, the charge which flows through the silver voltameter is     AIEEE  Solved  Paper-2005

A) $\frac{q}{1+\frac{{{z}_{1}}}{{{z}_{2}}}}$

B)                                        $\frac{q}{1+\frac{{{z}_{2}}}{{{z}_{1}}}}$

C)        $q\frac{{{z}_{1}}}{{{z}_{2}}}$

D)        $q\frac{{{z}_{2}}}{{{z}_{1}}}$

• question_answer49) In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be AIEEE  Solved  Paper-2005

A) $200\,\Omega$

B)       $100\,\Omega$

C)        $500\,\Omega$

D)        $1000\,\Omega$

• question_answer50) Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are${{R}_{1}}$and${{R}_{2}}({{R}_{2}}>{{R}_{1}})$.   If   the   potential difference across the source having internal resistance${{R}_{2}}$is zero, then     AIEEE  Solved  Paper-2005

A) $R=\frac{{{R}_{2}}({{R}_{1}}+{{R}_{2}})}{({{R}_{2}}-{{R}_{1}})}$

B) $R={{R}_{2}}-{{R}_{1}}$

C)        $R=\frac{{{R}_{1}}{{R}_{2}}}{({{R}_{1}}+{{R}_{2}})}$

D) $R=\frac{{{R}_{1}}{{R}_{2}}}{({{R}_{2}}-{{R}_{1}})}$

• question_answer51) A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by $\Delta T,$ the potential difference V across the capacitance is     AIEEE  Solved  Paper-2005

A) $\sqrt{\frac{2mC\Delta T}{s}}$

B)        $\frac{mC\Delta T}{s}$

C)        $\frac{ms\Delta T}{C}$

D)        $\sqrt{\frac{2ms\Delta T}{C}}$

• question_answer52) One conducting 17-tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed v, then the emf induced in the circuit in terms of B, l and v, where l is the width of each tube, will be AIEEE  Solved  Paper-2005

A) $BIl$

B)                        $-BIl$

C)        zero

D)        $2\,BIl$

• question_answer53) A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be     AIEEE  Solved  Paper-2005

A) doubled

B)                        four times

C)        one-fourth

D)        halved

• question_answer54) Two thin, long, parallel wires, separated by a distance d carry a current of i ampere in the same direction. They will     AIEEE  Solved  Paper-2005

A) attract each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi d)}$

B) repel each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi d)}$

C) attract each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi {{d}^{2}})}$

D) repel each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi {{d}^{2}})}$

• question_answer55) When an unpolarised light of intensity${{I}_{0}}$is incident on a polarising sheet, the intensity of the light which does not get transmitted is -     AIEEE  Solved  Paper-2005

A) $\frac{1}{2}{{l}_{0}}$

B)        $\frac{1}{4}{{l}_{0}}$

C) zero

D)        ${{l}_{0}}$

• question_answer56) A charged ball B hangs from a silk thread S, which makes an angle $\theta$ with a large charged conducting sheet as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to AIEEE  Solved  Paper-2005

A) $\cos \theta$

B)                        $\cot \theta$

C)                        $\sin \theta$

D)        $\tan \theta$

• question_answer57) Two point charges$+8q$and$-2q$are located at$x=0$and$x=L$respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero, is     AIEEE  Solved  Paper-2005

A) 2L

B)                        L/4

C)        8L

D)        4L

• question_answer58) Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are $+\text{ }q$and$-\text{ }q$. The potential difference between the centres of the two rings is     AIEEE  Solved  Paper-2005

A) $\frac{qR}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

B) $\frac{q}{2\pi {{\varepsilon }_{0}}}\left[ \frac{1}{R}-\frac{1}{\sqrt{{{R}^{2}}+{{d}^{2}}}} \right]$

C) zero

D) $\frac{q}{4\pi {{\varepsilon }_{0}}}\left[ \frac{1}{R}-\frac{1}{\sqrt{{{R}^{2}}+{{d}^{2}}}} \right]$

• question_answer59) A parallel plate capacitor is made by stacking  n  equally  spaced  plates connected alternatively. If the capacitance between any two adjacent plates is C, then the resultant capacitance is     AIEEE  Solved  Paper-2005

A) $(n-1)C$

B)        $(n+1)C$

C)        C

D)        $nC$

• question_answer60) When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats/s are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats/s are heard. If the frequency of for k 1 is 200 Hz, then what was the original frequency of fork 2?     AIEEE  Solved  Paper-2005

A) 200 Hz

B)                        202 Hz

C)        196 Hz

D)        204 Hz

• question_answer61) If a simple harmonic motion is represented by $\frac{{{d}^{2}}x}{d{{t}^{2}}}+\alpha x=0,$ its time period is     AIEEE  Solved  Paper-2005

A) $\frac{2\pi }{\alpha }$

B)                        $\frac{2\pi }{\sqrt{\alpha }}$

C)        $2\pi \alpha$

D)        $2\pi \sqrt{\alpha }$

• question_answer62) The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would     AIEEE  Solved  Paper-2005

A) first increase and then decrease to the original value

B) first decrease and then increase to the original value

C) remain unchanged

D) increase towards a saturation value

• question_answer63) An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?   AIEEE  Solved  Paper-2005

A) Zero

B)                        0.5%

C)        5%

D)        20%

• question_answer64) If${{I}_{0}}$is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?     AIEEE  Solved  Paper-2005

A) $2\,{{l}_{0}}$

B)                       $4{{l}_{0}}$

C) ${{l}_{0}}$

D)        $\frac{{{l}_{0}}}{2}$

• question_answer65) Two concentric coils each of radius equal to$2\pi$cm are placed at right angles to each other. 3 A and 4 A are the currents flowing in each coil respectively. The magnetic induction in $Wb/{{m}^{2}}$at the centre   of   the   coils , will   be $({{\mu }_{0}}=4\pi \times {{10}^{-7}}Wb/Am)$     AIEEE  Solved  Paper-2005

A) $12\times {{10}^{-5}}$

B)        ${{10}^{-5}}$

C)        $5\times {{10}^{-5}}$

D)        $7\times {{10}^{-5}}$

• question_answer66) A coil of inductance 300 mH and resistance$2\Omega$. are connected to a source of voltage 2V. The current reaches half of its steady state value in     AIEEE  Solved  Paper-2005

A) 0.05s

B)        0.1s

C)        0.15s

D)        0.3s

• question_answer67) The self-inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of     AIEEE  Solved  Paper-2005

A) $4\mu F$

B)                       $8\mu F$

C)        $1\mu F$

D)        $2\mu F$

• question_answer68) An energy source will supply a constant current into the load, if its internal resistance is     AIEEE  Solved  Paper-2005

A) equal to the resistance of the load

B) very large as compared to the load resistance

C) zero

D) non-zero but less than the resistance of the load

• question_answer69) A circuit has a resistance of$12\,\Omega$and an impedance of$15\,\Omega$. The power factor of the circuit will be     AIEEE  Solved  Paper-2005

A) 0.8

B)        0.4

C)        1.25

D)        0.125

• question_answer70) The phase difference between the alternating current and emf is$\pi /2$. Which of the following cannot be the constituent of the circuit?             AIEEE  Solved  Paper-2005

A) C alone

B)        R, L

C)        L, C

D)        L alone

• question_answer71) A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then     AIEEE  Solved  Paper-2005

A) its velocity will decrease

B) its velocity will increase

C) it will turn towards right of direction of motion

D) it will turn towards left of direction of motion

• question_answer72) A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is     AIEEE  Solved  Paper-2005

A) $\frac{2\pi mq}{B}$

B)        $\frac{2\pi {{q}^{2}}B}{m}$

C)        $\frac{2\pi qB}{m}$

D)        $\frac{2\pi m}{qB}$

• question_answer73) In a potentiometer experiment, the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of Q, the balancing length becomes 120 cm. The internal resistance of the cell is     AIEEE  Solved  Paper-2005

A) $1\,\Omega$

B)                        $0.5\,\Omega$

C)        $4\,\Omega$

D)        $2\,\Omega$

• question_answer74) The resistance of hot tungsten filament is about 10 times the cold resistance. What will be the resistance of 100 W and 200 V lamp, when not in use?     AIEEE  Solved  Paper-2005

A) $40\,\Omega$

B)                                        $20\,\Omega$

C)        $400\,\Omega$

D)        $200\,\Omega$

• question_answer75) A magnetic needle is kept in a non-uniform magnetic   field.   It experiences     AIEEE  Solved  Paper-2005

A) a torque but not a force

B) neither a force nor a torque

C) a force and a torque

D) a force but not a torque

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