Solved papers for JEE Main & Advanced AIEEE Solved Paper-2012

done AIEEE Solved Paper-2012 Total Questions - 30

• question_answer1) A wooden wheel of radius R is made of two semicircular parts (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 presses 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:   AIEEE  Solved  Paper-2012
  A)
  \[2\pi SY\alpha \Delta T\]                               
  done clear
  B)
  \[SY\alpha \,\Delta T\]
  done clear
  C)
  \[\pi SY\alpha \,\Delta T\]                              
  done clear
  D)
  \[2SY\alpha \,\Delta T\]
  done clear
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• question_answer2) The figure shows an experimental plot discharging of a capacitor in an RC circuit. The time constant \[\tau \] of this circuit lies between:   AIEEE  Solved  Paper-2012
  A)
  150 sec and 200 sec           
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  B)
  0 and 50 sec
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  C)
  50 sec and 100 sec              
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  D)
  100 sec and 150 sec
  done clear
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• question_answer3) In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as function of distance from the centre. The graph which would correspond to the above will be :   AIEEE  Solved  Paper-2012
  A)
    
  done clear
  B)
    
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  C)
    
  done clear
  D)
   
  done clear
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• question_answer4) An electromagnetic wave in vacuum has the electric and magnetic field \[\vec{E}\] and \[\vec{B}\], which are always perpendicular to each other. The direction of polarization is given by \[\vec{X}\] and that of wave propagation by \[\vec{k}\]. Then.   AIEEE  Solved  Paper-2012
  A)
   \[\vec{X}||\vec{B}\] and \[\vec{k}||\vec{B}\times \vec{E}\]       
  done clear
  B)
   \[\vec{X}||\vec{E}\] and \[\vec{k}||\vec{E}\times \vec{B}\]
  done clear
  C)
  \[\vec{X}||\vec{B}\] and \[\vec{k}||\vec{E}\times \vec{B}\]
  done clear
  D)
   \[\vec{X}||\vec{E}\] and \[\vec{k}||\vec{B}\times \vec{E}\]
  done clear
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• question_answer5) 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 averatge life time of the pendulum is (assuming damping is small) in seconds :   AIEEE  Solved  Paper-2012
  A)
  \[\frac{0.693}{b}\]                             
  done clear
  B)
  b
  done clear
  C)
  \[\frac{1}{b}\]                                      
  done clear
  D)
  \[\frac{2}{b}\]
  done clear
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• question_answer6) Hydrogen atom is excieted 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:   AIEEE  Solved  Paper-2012
  A)
  2                                                
  done clear
  B)
  3
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  C)
  5                                                
  done clear
  D)
  6
  done clear
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• question_answer7) 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 :   AIEEE  Solved  Paper-2012
  A)
   developement of air current when the plate is placed.
  done clear
  B)
  induction of electrical charge on the plate
  done clear
  C)
  shielding of magnetic lines of force as aluminium is a paramagnetic material.
  done clear
  D)
  Electromagnetic induction in the aluminium plate giving rise to electromagnetic damping.
  done clear
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• question_answer8) 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:   AIEEE  Solved  Paper-2012
  A)
  \[6.4\times {{10}^{11}}\] Joules   
  done clear
  B)
  \[6.4\times {{10}^{8}}\] Joules
  done clear
  C)
  \[6.4\times {{10}^{9}}\] Joules     
  done clear
  D)
  \[6.4\times {{10}^{10}}\] Joules
  done clear
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• question_answer9) Helium gas goes through a cycle ABCDA (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)                  AIEEE  Solved  Paper-2012
  A)
  15.4%                      
  done clear
  B)
  9.1%
  done clear
  C)
  10.5%                      
  done clear
  D)
  12.5%
  done clear
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• question_answer10) 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 \[{{I}_{m}}\] be the maximum intensity, the resultant intensity ? when they interfere at phase difference ? is given by :   AIEEE  Solved  Paper-2012
  A)
  \[\frac{{{I}_{m}}}{9}(4+5\cos \phi )\]         
  done clear
  B)
  \[\frac{{{I}_{m}}}{3}\left( 1+2{{\cos }^{2}}\frac{\phi }{2} \right)\]
  done clear
  C)
  \[\frac{{{I}_{m}}}{5}\left( 1+4{{\cos }^{2}}\frac{\phi }{2} \right)\]
  done clear
  D)
   \[\frac{{{I}_{m}}}{9}\left( 1+8{{\cos }^{2}}\frac{\phi }{2} \right)\]
  done clear
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• question_answer11) A liquid in a beaker has temperature \[\theta (t)\] at time t and \[{{\theta }_{0}}\] is temperature of surroundings, then according to Newton's law of cooling the correct graph between \[{{\log }_{e}}(\theta -{{\theta }_{0}})\] and t is :   AIEEE  Solved  Paper-2012
  A)
              
  done clear
  B)
   
  done clear
  C)
           
  done clear
  D)
   
  done clear
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• question_answer12) A particle of mass m is at rest at the origin at time\[t=0\]. It is subjected to a force \[F(t)={{F}_{0}}{{e}^{-bt}}\] in the \[x\] direction. Its speed v(t) is depicted by which of the following curves?   AIEEE  Solved  Paper-2012
  A)
          
  done clear
  B)
   
  done clear
  C)
              
  done clear
  D)
   
  done clear
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• question_answer13) Two electric bulbs marked 25W- 220V and 100W - 220 V are connected in series to a 440 V supply. Which of the bulbs will fuse?   AIEEE  Solved  Paper-2012
  A)
  both                                        
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  B)
  100W
  done clear
  C)
  25W                                         
  done clear
  D)
  neither 
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• question_answer14) 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 :   AIEEE  Solved  Paper-2012
  A)
  6%                                            
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  B)
  zero
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  C)
  1%                                            
  done clear
  D)
  3%
  done clear
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• question_answer15) A boy can throw a stone up to amaximum height of 10m. The maximum horizontal distance that the boy can throw the same stone up to will be:   AIEEE  Solved  Paper-2012
  A)
  \[20\sqrt{2}\] m                  
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  B)
  10 m
  done clear
  C)
  \[10\sqrt{2}\] m                  
  done clear
  D)
  20m
  done clear
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• question_answer16) This equation has statement 1 and Statement 2. Of the four choices given the Statements, choose the one that 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.   AIEEE  Solved  Paper-2012
  A)
  Statement 1 is false, Statement 2 is true.
  done clear
  B)
   Statement 1 is true, Statement 2 is false
  done clear
  C)
  Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for statement 1
  done clear
  D)
  Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation o Statement 1
  done clear
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• question_answer17) 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 :                AIEEE  Solved  Paper-2012
  A)
  0.0125 \[N{{m}^{-1}}\]                     
  done clear
  B)
   0.1 \[N{{m}^{-1}}\]
  done clear
  C)
  0.05 \[N{{m}^{-1}}\]                          
  done clear
  D)
  0.025 \[N{{m}^{-1}}\]
  done clear
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• question_answer18) A charge Q is uniformly distributed over the surface of non-condcting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity\[\omega \]. As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. if we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure :   AIEEE  Solved  Paper-2012
  A)
            
  done clear
  B)
    
  done clear
  C)
             
  done clear
  D)
   
  done clear
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• question_answer19) Truth table for system of four NAND gates as shown in figure is :                AIEEE  Solved  Paper-2012
  A)

  A	B	Y
  0	0	0
  0	1	1
  1	0	1
  1	1	0

  done clear
  B)
   

  A	B	Y
  0	0	0
  0	1	0
  1	0	1
  1	1	1

  done clear
  C)
   

  A	B	Y
  0	0	1
  0	1	1
  1	0	0
  1	1	0

  done clear
  D)
   

  A	B	Y
  0	0	1
  0	1	0
  1	0	0
  1	1	1

  done clear
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• question_answer20) 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 500m. 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 :   AIEEE  Solved  Paper-2012
  A)
   80 km                     
  done clear
  B)
  16 km
  done clear
  C)
  40 km                      
  done clear
  D)
  64 km
  done clear
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• question_answer21) 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 \[=9\times {{10}^{-31}}kg\])   AIEEE  Solved  Paper-2012
  A)
  0.73 MeV                               
  done clear
  B)
  7.10 MeV
  done clear
  C)
  6.30 MeV                               
  done clear
  D)
  5.4 MeV
  done clear
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• question_answer22) A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be :   AIEEE  Solved  Paper-2012
  A)
  efficiency of carnot engine cannot be made larger than 50%
  done clear
  B)
  1200 K
  done clear
  C)
  750 K                                        
  done clear
  D)
  600 K
  done clear
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• question_answer23) 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 \[{{S}_{1}}\], will be more than that on \[{{S}_{2}}\]Statement 2:  \[{{k}_{1}}<{{k}_{2}}\]   AIEEE  Solved  Paper-2012
  A)
  Statement 1 is false, Statement 2 is true.
  done clear
  B)
  Statement 1 is true, Statement 2 is false
  done clear
  C)
  Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for statement 1
  done clear
  D)
  Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1
  done clear
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• question_answer24) Two cars of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are moving in circles of radii \[{{r}_{1}}\] and \[{{r}_{2}}\], respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is :   AIEEE  Solved  Paper-2012
  A)
  \[{{m}_{1}}{{r}_{1}}:{{m}_{2}}{{r}_{2}}\]                  
  done clear
  B)
  \[{{m}_{1}}:{{m}_{2}}\]
  done clear
  C)
  \[{{r}_{1}}:{{r}_{2}}\]                                        
  done clear
  D)
  \[1:1\]
  done clear
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• question_answer25) A cylindrical tube, open at both ends, has a fundamental frequncy, 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 :   AIEEE  Solved  Paper-2012
  A)
  \[f\]                                        
  done clear
  B)
  \[f/2\]
  done clear
  C)
  \[3f/4\]                   
  done clear
  D)
  \[2f\]
  done clear
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• question_answer26) 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 on film?   AIEEE  Solved  Paper-2012
  A)
  7.2 m
  done clear
  B)
  2.4 m
  done clear
  C)
  3.2 m                                       
  done clear
  D)
  5.6 m
  done clear
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• question_answer27) 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)   AIEEE  Solved  Paper-2012
  A)
  \[\frac{{{({{m}_{1}}+{{m}_{2}})}^{2}}{{n}^{2}}{{h}^{2}}}{2m_{1}^{2}m_{2}^{2}{{r}^{2}}}\]                
  done clear
  B)
  \[\frac{{{n}^{2}}{{h}^{2}}}{2({{m}_{1}}+{{m}_{2}}){{r}^{2}}}\]
  done clear
  C)
               \[\frac{2{{n}^{2}}{{h}^{2}}}{({{m}_{1}}+{{m}_{2}}){{r}^{2}}}\]                        
  done clear
  D)
               \[\frac{({{m}_{1}}+{{m}_{2}}){{n}^{2}}{{h}^{2}}}{2{{m}_{1}}{{m}_{2}}{{r}^{2}}}\]
  done clear
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• question_answer28) 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 :   AIEEE  Solved  Paper-2012
  A)
  58.59 degree                        
  done clear
  B)
  58.77 degree
  done clear
  C)
  58.65 degree                        
  done clear
  D)
  59 degree
  done clear
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• question_answer29) This questions 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 unioformly positive charge density \[\rho \].As a result of this uniform charge distribution there is a finite value of electric potential at the centre 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 \[\frac{q\rho }{3{{\varepsilon }_{0}}}\]. Statement-2: The electric field at a distance r \[(r<R)\] from the centre of the sphere is \[\frac{\rho r}{3{{\varepsilon }_{0}}}\]   AIEEE  Solved  Paper-2012
  A)
  Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of statement-1.
  done clear
  B)
  Statement 1 is true Statement 2 is false.
  done clear
  C)
  Statement 1 is false Statement 2 is true.
  done clear
  D)
  Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
  done clear
  View Answer play_arrow

• question_answer30) Proton, Deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively \[{{r}_{p}},{{r}_{d}}\] and \[{{r}_{\alpha }}\]. Which one of the following relation is correct?   AIEEE  Solved  Paper-2012
  A)
  \[{{r}_{\alpha }}={{r}_{p}}={{r}_{d}}\]                       
  done clear
  B)
  \[{{r}_{\alpha }}={{r}_{p}}<{{r}_{d}}\]
  done clear
  C)
  \[{{r}_{\alpha }}>{{r}_{d}}>{{r}_{p}}\]                       
  done clear
  D)
  \[{{r}_{\alpha }}={{r}_{d}}>{{r}_{p}}\]
  done clear
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