Solved papers for JEE Main & Advanced AIEEE Solved Paper-2011

done AIEEE Solved Paper-2011 Total Questions - 30

• question_answer1) A carnot engine operation between temperatrues \[{{T}_{1}}\] and \[{{T}_{2}}\] has efficiency \[\frac{1}{6}\]. When \[{{T}_{2}}\] is lowered by 62 K, its efficiency increases to\[\frac{1}{3}\]. Then \[{{T}_{1}}\] and \[{{T}_{2}}\] are respectively   AIEEE  Solved  Paper-2011    
  A)
  310 K and 248 K   
  done clear
  B)
  372 K and 310 K
  done clear
  C)
  372 K and 330 K   
  done clear
  D)
  330 K and 268 K
  done clear
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• question_answer2) A pulley of radius 2 m is rotated about its axis by a force \[F=(20\,t-5{{t}^{2}})\] newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg \[{{m}^{2}}\], the number of rotations made by the pulley before its direction of motion if reversed is   AIEEE  Solved  Paper-2011
  A)
  More than 9
  done clear
  B)
  Less than 3
  done clear
  C)
  More than 3 but less than 6
  done clear
  D)
   More than 6 but less than 9
  done clear
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• question_answer3) Three perfect gases at absolute temperatures \[{{T}_{1}},{{T}_{2}}\] and \[{{T}_{3}}\] are mixed. The masses of molecules are \[{{m}_{1}},{{m}_{2}}\] and \[{{m}_{3}}\] and the number of molecules are \[{{n}_{1}},{{n}_{2}}\] and \[{{n}_{3}}\] respectively. Assuming no loss of energy, the final temperature of the mixture is   AIEEE  Solved  Paper-2011
  A)
   \[\frac{n_{1}^{2}T_{1}^{2}+n_{2}^{2}T_{2}^{2}+n_{3}^{2}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}\]  
  done clear
  B)
   \[\frac{{{T}_{1}}+{{T}_{2}}+{{T}_{3}}}{3}\]
  done clear
  C)
   \[\frac{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}}\]
  done clear
  D)
   \[\frac{{{n}_{1}}T_{1}^{2}+{{n}_{2}}T_{2}^{2}+{{n}_{3}}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}\]
  done clear
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• question_answer4) A boat is moving due east in a region where the earth's magnetic field is \[5.0\times {{10}^{-5}}N{{A}^{-1}}\] due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is \[1.50\,m{{s}^{-1}}\], the magnitude of the induced emf in the wire of aerial is   AIEEE  Solved  Paper-2011
  A)
  \[0.15\] mV                           
  done clear
  B)
  1 mV
  done clear
  C)
  \[0.75\] mV                           
  done clear
  D)
  \[0.50\] mV
  done clear
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• question_answer5) A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect the angular speed of the disc   AIEEE  Solved  Paper-2011
  A)
  First increase and then decrease
  done clear
  B)
  Remains unchanged
  done clear
  C)
  Continuously decreases
  done clear
  D)
  Continuously increases
  done clear
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• question_answer6) Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance \[d(d<<l)\] apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance \[x\] between them   AIEEE  Solved  Paper-2011
  A)
  \[v\propto x\]                     
  done clear
  B)
  \[v\propto {{x}^{-\frac{1}{2}}}\]
  done clear
  C)
  \[v\propto {{x}^{-1}}\]                     
  done clear
  D)
  \[v\propto {{x}^{\frac{1}{2}}}\]
  done clear
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• question_answer7) 100 g of water is heated from \[{{30}^{o}}C\] to \[{{50}^{o}}C\]. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K)   AIEEE  Solved  Paper-2011
  A)
  \[2.1\] kJ                                
  done clear
  B)
  \[4.2\] kJ
  done clear
  C)
  \[8.4\] kJ
  done clear
  D)
  84 kJ
  done clear
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• question_answer8) The half life of a radioactive substance is 20 minutes. The approximate time interval \[({{t}_{2}}-{{t}_{1}})\] between the time \[{{t}_{2}}\] when \[\frac{2}{3}\] of its has decayed and time \[{{t}_{1}}\] when \[\frac{1}{3}\] of its had decayed is   AIEEE  Solved  Paper-2011
  A)
  28 min                     
  done clear
  B)
   7 min
  done clear
  C)
  14 min                     
  done clear
  D)
   20 min
  done clear
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• question_answer9) Energy required for the electron excitation in\[L{{i}^{++}}\] from the first to the third Bohr orbit is   AIEEE  Solved  Paper-2011
  A)
  \[122.4\] eV                          
  done clear
  B)
  \[12.1\] eV
  done clear
  C)
  \[36.3\] eV                            
  done clear
  D)
  \[108.8\] eV
  done clear
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• question_answer10) The electrostatic potential inside a charged spherical ball is given by \[\phi =an{{r}^{2}}+b\] where r is the distance from the centre; a, b are constants. Then the charge density inside the ball is   AIEEE  Solved  Paper-2011
  A)
  \[-6\,\,a{{\varepsilon }_{0}}\]                       
  done clear
  B)
  \[-24\,\pi \,a{{\varepsilon }_{0}}\gamma \]
  done clear
  C)
  \[-6\,a{{\varepsilon }_{0}}\gamma \]                        
  done clear
  D)
  \[-24\,\,\pi \,a{{\varepsilon }_{0}}\gamma \]
  done clear
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• question_answer11) Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution \[=0.03\,\,N{{m}^{-1}}\])   AIEEE  Solved  Paper-2011
  A)
  \[0.4\,\,\pi \] m J                
  done clear
  B)
  \[4\,\,\pi \] m J
  done clear
  C)
               \[0.2\,\,\pi \] m J                                
  done clear
  D)
               \[2\,\,\pi \] m J
  done clear
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• question_answer12) A resistor 'R' and \[2\mu F\] capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed. (\[{{\log }_{10}}2.5=0.4\])   AIEEE  Solved  Paper-2011
  A)
  \[3.3\times {{10}^{7}}\Omega \]                 
  done clear
  B)
  \[1.3\times {{10}^{4}}\Omega \]
  done clear
  C)
  \[1.7\times {{10}^{5}}\Omega \]                 
  done clear
  D)
  \[2.7\times {{10}^{6}}\Omega \]
  done clear
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• question_answer13) A current I flows in an infinitely long wire with corss section in the form of a semi-circular ring of raidus R. The magnitude of the magnetic induction along its axis is   AIEEE  Solved  Paper-2011
  A)
  \[\frac{{{\mu }_{0}}I}{4\pi R}\]                                     
  done clear
  B)
  \[\frac{{{\mu }_{0}}I}{{{\pi }^{2}}R}\]
  done clear
  C)
  \[\frac{{{\mu }_{0}}I}{2{{\pi }^{2}}R}\]                      
  done clear
  D)
   \[\frac{{{\mu }_{0}}I}{2\pi R}\]
  done clear
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• question_answer14) An object, moving with a speed of \[6.25\,m/s\], is decelerated at a rate given by \[\frac{dv}{dt}=-2.5\sqrt{v}\]where v is the instantaneous speed. The time taken by the object, to come to rest, would be   AIEEE  Solved  Paper-2011
  A)
               8 s                                             
  done clear
  B)
               1 s
  done clear
  C)
  2 s                                             
  done clear
  D)
  4 s
  done clear
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• question_answer15) Direction: The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the covex surface of a plane-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (coNvex) surface and the bottom (glass plate) surface of the film. Statement-1:       When light reflects from the                                 air-glass plate interface, the reflected wave suffers a phase change of \[\pi \]. Statement-2:        The centre of the interference                                    pattern is dark.   AIEEE  Solved  Paper-2011
  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 and Statement-2 is the correct explanation of Statement-1
  done clear
  D)
  Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
  done clear
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• question_answer16) Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is   AIEEE  Solved  Paper-2011
  A)
  \[-\frac{9Gm}{r}\]                              
  done clear
  B)
   Zero
  done clear
  C)
  \[-\frac{4Gm}{r}\]                              
  done clear
  D)
   \[-\frac{6Gm}{r}\]
  done clear
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• question_answer17) 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:        Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals. Statement-2:        The state of ionosphere varies from hour to hour, day to day and season to season.   AIEEE  Solved  Paper-2011
  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 and Statement-2 is the correct explanation of Statement-1
  done clear
  D)
   Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
  done clear
  View Answer play_arrow

• question_answer18) A fully charged capacitor C with initial charge \[{{q}_{0}}\] is connected to a coil of self inductance L at \[t=0\]. The time at which the energy is stored equally between the electric and the magnetic fields is   AIEEE  Solved  Paper-2011
  A)
  \[\sqrt{LC}\]                         
  done clear
  B)
  \[\pi \sqrt{LC}\]
  done clear
  C)
  \[\frac{\pi }{4}\sqrt{LC}\]                
  done clear
  D)
  \[2\pi \sqrt{LC}\]
  done clear
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• question_answer19) 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:        A metallic surface is irradiated by a monochromatic light of frequency \[v>{{v}_{0}}\] (the threshold frequency). The maximum kinetic energy and the stopping potential are \[{{K}_{\max }}\] and \[{{V}_{0}}\] respectively. If the frequency incident on the surface is doubled, both the\[{{K}_{\max }}\] and \[{{V}_{0}}\] are also doubled. Statement-2:        The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.   AIEEE  Solved  Paper-2011
  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 and Statement-2 is a correct explanation for Statement-1
  done clear
  D)
  Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
  done clear
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• question_answer20) Water is flowing continuously from a tap having an internal diameter \[8\times {{10}^{-3}}m\]. The water velocity as it leaves the tap is \[0.4\,m{{s}^{-1}}\]. The diameter of the water stream at a distance \[2\times {{10}^{-1}}m\] below the tap is close to   AIEEE  Solved  Paper-2011
  A)
  \[3.6\times {{10}^{-3}}m\]                             
  done clear
  B)
  \[5.0\times {{10}^{-3}}m\]
  done clear
  C)
  \[7.5\times {{10}^{-3}}m\]                             
  done clear
  D)
  \[9.6\times {{10}^{-3}}m\]
  done clear
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• question_answer21) A mass M, attached to a horizontal spring, executes S.H.M. with amplitude \[{{A}_{1}}\]. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude \[{{A}_{2}}\]. The ratio of\[\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right)\]is   AIEEE  Solved  Paper-2011
  A)
  \[{{\left( \frac{M+m}{M} \right)}^{1/2}}\]                              
  done clear
  B)
  \[\frac{M}{M+m}\]
  done clear
  C)
                \[\frac{M+m}{M}\]                          
  done clear
  D)
               \[{{\left( \frac{M}{M+m} \right)}^{1/2}}\]
  done clear
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• question_answer22) Two particles are executing simple harmonic motion of the same amplitude A and frequency \[\omega \] along the x-axis. Their mean position is separated by distance \[{{X}_{0}}({{X}_{0}}>A)\]. If the maximum separation between them is \[({{X}_{0}}+A)\], the phase difference between their motion is   AIEEE  Solved  Paper-2011
  A)
  \[\frac{\pi }{6}\]                                  
  done clear
  B)
  \[\frac{\pi }{2}\]
  done clear
  C)
               \[\frac{\pi }{3}\]                                  
  done clear
  D)
               \[\frac{\pi }{4}\]
  done clear
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• question_answer23) If a wire is stretched to make it 0.1% longer, its resistance will   AIEEE  Solved  Paper-2011
  A)
  Decrease by 0.05%            
  done clear
  B)
  Increase by 0.05%
  done clear
  C)
  Increase by 0.2%
  done clear
  D)
  Decrease by 0.2%
  done clear
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• question_answer24) A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the  fountain that gets wet is   AIEEE  Solved  Paper-2011
  A)
  \[\pi \frac{{{v}^{2}}}{{{g}^{2}}}\]                                 
  done clear
  B)
  \[\pi \frac{{{v}^{2}}}{g}\]
  done clear
  C)
  \[\pi \frac{{{v}^{4}}}{{{g}^{2}}}\]                                 
  done clear
  D)
  \[\frac{\pi }{2}\frac{{{v}^{4}}}{{{g}^{2}}}\]
  done clear
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• question_answer25) A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats\[\gamma \]. It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by   AIEEE  Solved  Paper-2011
  A)
  \[\frac{(\gamma -1)}{2R}M{{v}^{2}}K\]                    
  done clear
  B)
  \[\frac{(\gamma -1)}{2(\gamma +1)R}M{{v}^{2}}K\]
  done clear
  C)
  \[\frac{(\gamma -1)}{2\gamma R}M{{v}^{2}}K\]                  
  done clear
  D)
  \[\frac{\gamma M{{v}^{2}}}{2R}K\]
  done clear
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• question_answer26) A screw gauge gives the following reading when used to measure the diameter of a wire.              Main scale reading:                            0 mm Circular scale reading:                        52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.              The diameter of wire from the above data is   AIEEE  Solved  Paper-2011
  A)
  0.005 cm                 
  done clear
  B)
  0.52 cm
  done clear
  C)
  0.052 cm                 
  done clear
  D)
  0.026 cm
  done clear
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• question_answer27) A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is   AIEEE  Solved  Paper-2011
  A)
  \[\frac{g}{3}\]                                      
  done clear
  B)
  \[\frac{3}{2}g\]
  done clear
  C)
  g                                                
  done clear
  D)
  \[\frac{2}{3}g\]
  done clear
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• question_answer28) The transverse displacement \[y(x,t)\] of a wave on a string is given by \[y(x,t)={{e}^{-\left( a{{x}^{2}}+b{{t}^{2}}+2\sqrt{ab}xt \right)}}\] This represents a   AIEEE  Solved  Paper-2011
  A)
  Standing wave of frequency \[\frac{1}{\sqrt{b}}\]
  done clear
  B)
  Wave moving in \[+x\] direction with speed \[\sqrt{\frac{a}{b}}\]
  done clear
  C)
  Wave moving in \[-x\] direction with speed \[\sqrt{\frac{b}{a}}\]
  done clear
  D)
  Standing wave of frequency \[\sqrt{b}\]
  done clear
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• question_answer29) A car is fitted with a convex side-view mirror of focal length 20 cm. A second car \[2.5\] m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is   AIEEE  Solved  Paper-2011
  A)
  15 m/s                     
  done clear
  B)
  \[\frac{1}{10}m/s\]
  done clear
  C)
  \[\frac{1}{15}m/s\]                            
  done clear
  D)
  10 m/s
  done clear
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• question_answer30) Let the \[x-z\] plane be the boundary between two transparent media. Medium 1 in \[z\ge 0\] has a refractive index of 2 and medium 2 with \[z>0\] has a refractive index of 3. A ray of light in medium 1 given by the vector \[\vec{A}=6\sqrt{3}\hat{i}+8\sqrt{3}\hat{j}-10\hat{k}\] is incident on the plane of separation. The angle of refraction in medium 2 is   AIEEE  Solved  Paper-2011
  A)
  \[{{75}^{o}}\]                                       
  done clear
  B)
  \[{{30}^{o}}\]
  done clear
  C)
  \[{{45}^{o}}\]                                       
  done clear
  D)
  \[{{60}^{o}}\]   
  done clear
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