Solved papers for JEE Main & Advanced AIEEE Solved Paper-2010

done AIEEE Solved Paper-2010 Total Questions - 30

• question_answer1) Directions Q. No. 1 are based on the following paragraph. An initially parallel cylindrical beam travels in a medium of refractive index \[\mu (I)={{\mu }_{0}}+{{\mu }_{2}}I,\] where \[{{\mu }_{0}}\] and \[{{\mu }_{2}}\] are positive constants and \[I\] is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The initial shape of the wavefront of the beam is -     AIEEE  Solved  Paper-2010
  A)
  planar
  done clear
  B)
  convex
  done clear
  C)
  concave
  done clear
  D)
  convex near the axis and concave near the periphery
  done clear
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• question_answer2) Directions Q. No. 2 are based on the following paragraph. An initially parallel cylindrical beam travels in a medium of refractive index \[\mu (I)={{\mu }_{0}}+{{\mu }_{2}}I,\] where \[{{\mu }_{0}}\] and \[{{\mu }_{2}}\] are positive constants and \[I\] is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The speed of light in the medium is ?       AIEEE  Solved  Paper-2010
  A)
  maximum on the axis of the beam
  done clear
  B)
  minimum on the axis of the beam
  done clear
  C)
  the same everywhere in the beam
  done clear
  D)
  directly proportional to the intensity I
  done clear
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• question_answer3) Directions Q. No. 3 are based on the following paragraph. An initially parallel cylindrical beam travels in a medium of refractive index \[\mu (I)={{\mu }_{0}}+{{\mu }_{2}}I,\] where \[{{\mu }_{0}}\] and \[{{\mu }_{2}}\] are positive constants and \[I\] is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. As the beam enters the medium, it will -       AIEEE  Solved  Paper-2010
  A)
  travel as a cylindrical beam
  done clear
  B)
  diverge
  done clear
  C)
  converge
  done clear
  D)
  diverge near the axis and converge near the periphery
  done clear
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• question_answer4) Directions Q. No. 4 are based on the following paragraph. A nucleus of mass \[M+\Delta m\] is at rest and decays into two daughter nuclei of equal mass \[\frac{M}{2}\] each. Speed of light is c. The speed of daughter nuclei is ?       AIEEE  Solved  Paper-2010
  A)
  \[c\sqrt[{}]{\frac{\Delta m}{M+\Delta m}}\]       
  done clear
  B)
  \[c\frac{\Delta m}{M+\Delta m}\]           
  done clear
  C)
  \[c\sqrt[{}]{\frac{2\Delta m}{M}}\]         
  done clear
  D)
  \[c\sqrt[{}]{\frac{\Delta m}{M}}\]
  done clear
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• question_answer5) Directions Q. No. 5 are based on the following paragraph. A nucleus of mass \[M+\Delta m\] is at rest and decays into two daughter nuclei of equal mass \[\frac{M}{2}\] each. Speed of light is c.   The binding energy per nucleon for the parent nucleus is\[{{E}_{1}}\]and that for the daughter nuclei is\[{{E}_{2}}\]. Then ?       AIEEE  Solved  Paper-2010
  A)
  \[{{E}_{1}}=2{{E}_{2}}\]
  done clear
  B)
  \[{{E}_{2}}=2{{E}_{1}}\]
  done clear
  C)
  \[{{E}_{1}}>{{E}_{2}}\]  
  done clear
  D)
  \[{{E}_{2}}>{{E}_{1}}\]
  done clear
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• question_answer6) Directions: Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is\[{{V}_{0}}\]and the maximum kinetic energy of the photoelectrons is\[{{K}_{max}}\]. When the ultraviolet light is replaced by X-rays, both\[{{V}_{0}}\]and\[{{K}_{max}}\] increase. Statement-2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because the range of frequencies present in the incident light. Directions: Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.       AIEEE  Solved  Paper-2010
  A)
  Statement-1 is true, Statement-2 is false.
  done clear
  B)
  Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1
  done clear
  C)
  Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
  done clear
  D)
  Statement-1 is false, Statement-2 is true.
  done clear
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• question_answer7) Directions: Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement- 2: Principle of conservation of momentum holds true for all kinds of collisions. Directions: Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.       AIEEE  Solved  Paper-2010
  A)
  Statement-1 is true, Statement-2 is false.
  done clear
  B)
  Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1
  done clear
  C)
  Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
  done clear
  D)
  Statement-1 is false, Statement-2 is true.
  done clear
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• question_answer8)   The figure shows the position - time (x - t) graph of one-dimensional motion of the body of mass 0.4 kg. The magnitude of each impulse is ?       AIEEE  Solved  Paper-2010
  A)
  0.2 Ns                   
  done clear
  B)
  0.4 Ns   
  done clear
  C)
  0.8 Ns   
  done clear
  D)
  1.6 Ns
  done clear
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• question_answer9)   Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line XX? is given by -       AIEEE  Solved  Paper-2010
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
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• question_answer10)   A ball is made of a material of density \[\rho \] where \[{{\rho }_{oil}}<\rho <{{\rho }_{water}}\]with\[{{\rho }_{oil}}\]and\[{{\rho }_{water}}\] representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?       AIEEE  Solved  Paper-2010
  A)
                         
  done clear
  B)
  
  done clear
  C)
   
  done clear
  D)
        
  done clear
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• question_answer11)   A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field\[\overrightarrow{E}\]at the centre O is ?     AIEEE  Solved  Paper-2010
  A)
  \[\frac{q}{2{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}\]                        
  done clear
  B)
  \[\frac{q}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}\]        
  done clear
  C)
         \[-\frac{q}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}\]
  done clear
  D)
         \[-\frac{q}{2{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}\]
  done clear
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• question_answer12)   A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is-       AIEEE  Solved  Paper-2010
  A)
  0.25                       
  done clear
  B)
  0.5                         
  done clear
  C)
         0.75       
  done clear
  D)
         0.99
  done clear
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• question_answer13)   The respective number of significant figures for the numbers 23.023, 0.0003 and\[2.1\times {{10}^{3}}\] are -       AIEEE  Solved  Paper-2010
  A)
  4, 4, 2   
  done clear
  B)
         5, 1, 2    23.023 significant fig. 5 0.0003 significant fig. 1 \[2.1\times {{10}^{3}}\]significant fig. 2
  done clear
  C)
         5, 1, 5   
  done clear
  D)
         5, 5, 2
  done clear
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• question_answer14)   The combination of gates shown below yields     AIEEE  Solved  Paper-2010
  A)
  NAND gate                        
  done clear
  B)
  OR gate
  done clear
  C)
  NOT gate            
  done clear
  D)
         XOR gate
  done clear
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• question_answer15)   If a source of power 4 kW produces\[{{10}^{20}}\]photons/second, the radiation belongs to a part of the spectrum called ?       AIEEE  Solved  Paper-2010
  A)
  \[\gamma -\]rays            
  done clear
  B)
         X-rays  
  done clear
  C)
         ultraviolet rays
  done clear
  D)
         microwaves
  done clear
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• question_answer16)   A radioactive nucleus (initial mass number A and atomic number Z) emits 3 α-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be ?       AIEEE  Solved  Paper-2010
  A)
  \[\frac{A-Z-4}{Z-2}\]      
  done clear
  B)
         \[\frac{A-Z-8}{Z-4}\]
  done clear
  C)
  \[\frac{A-Z-4}{Z-8}\]      
  done clear
  D)
         \[\frac{A-Z-12}{Z-4}\]
  done clear
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• question_answer17) Let there be a spherically symmetric charge distribution with charge density varying as\[\rho (r)={{\rho }_{0}}\left( \frac{5}{4}-\frac{r}{R} \right)\]up to\[r=R,\]and\[\rho (r)=0\]for\[r>R,\]where r is the distance from the origin. The electric field at a distance \[r(r<R)\]from the origin is given by ?       AIEEE  Solved  Paper-2010
  A)
  \[\frac{{{\rho }_{0}}r}{3{{\varepsilon }_{0}}}\left( \frac{5}{4}-\frac{r}{R} \right)\]
  done clear
  B)
         \[\frac{4\pi {{\rho }_{0}}r}{3{{\varepsilon }_{0}}}\left( \frac{5}{3}-\frac{r}{R} \right)\]
  done clear
  C)
         \[\frac{{{\rho }_{0}}r}{4{{\varepsilon }_{0}}}\left( \frac{5}{3}-\frac{r}{R} \right)\]
  done clear
  D)
         \[\frac{4{{\rho }_{0}}r}{3{{\varepsilon }_{0}}}\left( \frac{5}{4}-\frac{r}{R} \right)\]
  done clear
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• question_answer18)   In a series LCR circuit\[R=200\,\,\Omega \]and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by\[30{}^\circ \]. On taking out the inductor from the circuit the current leads the voltage by \[30{}^\circ \]. The power dissipated in the LCR circuit is ?       AIEEE  Solved  Paper-2010
  A)
  242 W   
  done clear
  B)
         305 W                   
  done clear
  C)
  210 W   
  done clear
  D)
         Zero W
  done clear
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• question_answer19)   In the circuit shown below, the key K is closed at\[t=0.\]the current through the battery is ?       AIEEE  Solved  Paper-2010
  A)
  \[\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}\]at \[t=0\]and \[\frac{V}{{{R}_{2}}}\]at\[t=\infty \]
  done clear
  B)
  \[\frac{V{{R}_{1}}{{R}_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}}\]at \[t=0\]and \[\frac{V}{{{R}_{2}}}\]at \[t=\infty \]
  done clear
  C)
  \[\frac{V}{{{R}_{2}}}\]at\[t=0\]and \[\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}\]at\[t=\infty \]
  done clear
  D)
  \[\frac{V}{{{R}_{2}}}\]at \[t=0\]and \[\frac{V{{R}_{1}}{{R}_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}}\]at\[t=\infty \]
  done clear
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• question_answer20)   A particle is moving with velocity ) \[\overrightarrow{v}=K(y\hat{i}+x\hat{j})\]where K is a constant. The general equation for its path is ?       AIEEE  Solved  Paper-2010
  A)
  \[{{y}^{2}}={{x}^{2}}+constant\]
  done clear
  B)
  \[y={{x}^{2}}+constant\]
  done clear
  C)
  \[{{y}^{2}}=x+constant\]
  done clear
  D)
  \[xy=constant\]
  done clear
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• question_answer21)   Let C be the capacitance of a capacitor discharging through a resistor R. Suppose\[{{t}_{1}}\]is the time taken for the energy stored in the capacitor to reduce to half its initial value and \[{{t}_{2}}\]is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio \[{{t}_{1}}/{{t}_{2}}\]will be ?       AIEEE  Solved  Paper-2010
  A)
  2             
  done clear
  B)
                         1                             
  done clear
  C)
         \[\frac{1}{2}\]                   
  done clear
  D)
         \[\frac{1}{4}\]
  done clear
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• question_answer22)   A rectangular loop has a sliding connector PQ of length\[l\]and resistance\[R\,\Omega \]and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents\[{{I}_{1}},{{I}_{2}}\]and I are ?       AIEEE  Solved  Paper-2010
  A)
  \[{{I}_{1}}={{I}_{2}}=\frac{B/v}{6R},I=\frac{B/v}{3R}\]
  done clear
  B)
  \[{{I}_{1}}=-{{I}_{2}}=\frac{B/v}{R},I=\frac{2B/v}{R}\]
  done clear
  C)
  \[{{I}_{1}}={{I}_{2}}=\frac{B/v}{3R},I=\frac{2B/v}{3R}\]
  done clear
  D)
  \[{{I}_{1}}={{I}_{2}}=I=\frac{B/v}{R}\]
  done clear
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• question_answer23)   The equation of a wave on a string of linear mass density\[0.04\text{ }kg\text{ }{{m}^{1}}\]is given by\[y=0.02\] (m) \[\sin \left[ 2\pi \left( \frac{t}{0.04(s)}-\frac{x}{0.50(m)} \right) \right]\].The tension in the string is ?       AIEEE  Solved  Paper-2010
  A)
  6.25 N  
  done clear
  B)
         4.0 N     
  done clear
  C)
         12.5 N  
  done clear
  D)
         0.5 N
  done clear
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• question_answer24) Two fixed frictionless inclined planes making an angle\[30{}^\circ \]and\[60{}^\circ \]with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?       AIEEE  Solved  Paper-2010
  A)
  \[4.9\text{ }m{{s}^{2}}\]in vertical direction
  done clear
  B)
  \[4.9\text{ }m{{s}^{2}}\] in horizontal direction
  done clear
  C)
  \[9.8\text{ }m{{s}^{2}}\]in vertical direction
  done clear
  D)
  Zero
  done clear
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• question_answer25) For a particle in uniform circular motion, the acceleration\[\overrightarrow{a}\]at a point\[P(R,\text{ }\theta )\]on the circle of radius R is (Here\[\theta \]is measured from the x-axis)       AIEEE  Solved  Paper-2010
  A)
  \[\frac{{{v}^{2}}}{R}\hat{i}+\frac{{{v}^{2}}}{R}\hat{j}\]  
  done clear
  B)
         \[-\frac{{{v}^{2}}}{R}\cos \theta \hat{i}+\frac{{{v}^{2}}}{R}\sin \theta \hat{j}\]
  done clear
  C)
  \[-\frac{{{v}^{2}}}{R}sin\theta \hat{i}+\frac{{{v}^{2}}}{R}\cos \theta \hat{j}\]     
  done clear
  D)
  \[-\frac{{{v}^{2}}}{R}\cos \theta \hat{i}-\frac{{{v}^{2}}}{R}sin\theta \hat{j}\]
  done clear
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• question_answer26)   A small particle of mass m is projected at an angle\[\theta \]with the x-axis with an initial velocity \[{{v}_{0}}\] in the\[x-y\]plane as shown in the figure. At a time \[t<\frac{{{v}_{0}}\sin \theta }{g},\] the angular momentum of the particle is ?       AIEEE  Solved  Paper-2010
  A)
  \[\frac{1}{2}mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{i}\]      
  done clear
  B)
  \[-mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{j}\]         
  done clear
  C)
  \[mg{{v}_{0}}t\cos \theta \hat{k}\]
  done clear
  D)
         \[-\frac{1}{2}mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{k}\]
  done clear
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• question_answer27)   Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of\[30{}^\circ \]with each other. When suspended in a liquid of density\[0.8\text{ }g\text{ }c{{m}^{3}},\] the angle remains the same. If density of the material of the sphere is\[1.6\text{ }g\text{ }c{{m}^{3}},\] the dielectric constant of the liquid is ?       AIEEE  Solved  Paper-2010
  A)
  1                                             
  done clear
  B)
  4                             
  done clear
  C)
         3                                             
  done clear
  D)
  2
  done clear
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• question_answer28)   A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length\[s={{t}^{3}}+5,\]where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of 'P' when\[t=2s\] is nearly.       AIEEE  Solved  Paper-2010
  A)
  \[14\text{ }m/{{s}^{2}}\]
  done clear
  B)
                         \[13\text{ }m/{{s}^{2}}\]             
  done clear
  C)
         \[12\text{ }m/{{s}^{2}}\]             
  done clear
  D)
         \[7.2\text{ }m/{{s}^{2}}\]
  done clear
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• question_answer29)   The potential energy function for the force between two atoms in a diatomic molecule is approximately given by \[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\]where a and b are constants and\[x\]is the distance between the atoms. If the dissociation energy of the molecule is \[D=[U(x=\infty )-{{U}_{at\,equilibrium}}],D\]is ?       AIEEE  Solved  Paper-2010
  A)
  \[\frac{{{b}^{2}}}{6a}\] 
  done clear
  B)
                         \[\frac{{{b}^{2}}}{2a}\]                 
  done clear
  C)
         \[\frac{{{b}^{2}}}{12a}\]               
  done clear
  D)
         \[\frac{{{b}^{2}}}{4a}\]
  done clear
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• question_answer30)   Two conductors have the same resistance at \[0{}^\circ C\]but their temperature coefficients of resistance are\[{{\alpha }_{1}}\]and\[{{\alpha }_{2}}\]. the respective temperature coefficients of their series and parallel combinations are nearly ?       AIEEE  Solved  Paper-2010
  A)
  \[\frac{{{\alpha }_{1}}+{{\alpha }_{2}}}{2},\frac{{{\alpha }_{1}}+{{\alpha }_{2}}}{2}\]        
  done clear
  B)
  \[\frac{{{\alpha }_{1}}+{{\alpha }_{2}}}{2},{{\alpha }_{1}}+{{\alpha }_{2}}\]
  done clear
  C)
  \[{{\alpha }_{1}}+{{\alpha }_{2}},\frac{{{\alpha }_{1}}+{{\alpha }_{2}}}{2}\]          
  done clear
  D)
  \[{{\alpha }_{1}}+{{\alpha }_{2}},\frac{{{\alpha }_{1}}{{\alpha }_{2}}}{{{\alpha }_{1}}+{{\alpha }_{2}}}\]
  done clear
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