Solved papers for JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

done JEE Main Paper (Held On 26 May 2012) Total Questions - 30

• question_answer1) Three positive charges of equal value q are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as in   JEE Main Online Paper (Held On 26-May-2012)        
  A)
                                                                         
  done clear
  B)
                        
  done clear
  C)
                                                                              
  done clear
  D)
                        
  done clear
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• question_answer2) In Young's double slit interference experiment, the slit widths are in the ratio 1: 25. Then the ratio of intensity at the maxima and minima in the interference pattern is   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   3:2                                        
  done clear
  B)
                          1:25
  done clear
  C)
                         9:4                                         
  done clear
  D)
                          1:5
  done clear
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• question_answer3) Which of the plots shown in the figure represents speed (v) of the electron in a hydrogen atom as a function of the principal quantum number (n)?   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   B
  done clear
  B)
                         D
  done clear
  C)
                         C                                            
  done clear
  D)
                         A
  done clear
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• question_answer4) A radio transmitter transmits at 830 kHz. At a certain distance from the transmitter magnetic field has amplitude \[4.82\times {{10}^{-11}}T.\]The electric field and the wavelength are respectively   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   0.014N/C, 36m
  done clear
  B)
                         0.14N/C, 36m
  done clear
  C)
                          0.14N/C, 360m
  done clear
  D)
                          0.014N/C, 360m
  done clear
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• question_answer5) A satellite moving with velocity v in a force free space collects stationary interplanetary dust at a rate of\[\frac{dM}{dt}=\alpha v\] where M is the mass (of satellite t+ dust) at that instant. The instantaneous acceleration of the satellite is   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[-\frac{\alpha {{v}^{2}}}{2M}\]                
  done clear
  B)
                         \[-\frac{\alpha {{v}^{2}}}{M}\]
  done clear
  C)
                         \[-\alpha {{v}^{2}}\]                       
  done clear
  D)
                         \[-\frac{2\alpha {{v}^{2}}}{M}\]
  done clear
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• question_answer6) Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires A and B respectively in opposite directions. Wire A is infinitely long and the length of the wire B is 2 m. The force acting on the conductor B, which is situated at 10 cm distance from A will be   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[8\times {{10}^{-5}}N\]                                
  done clear
  B)
                         \[5\times {{10}^{-5}}N\]
  done clear
  C)
                         \[8\pi \times {{10}^{-7}}N\]                        
  done clear
  D)
                         \[4\pi \times {{10}^{-7}}N\]
  done clear
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• question_answer7) 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: It is not possible to make a sphere of capacity 1 farad using a conducting material. Statement 2: It is possible for earth as its radius is\[6.4\times {{10}^{6}}m.\]   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
  done clear
  B)
                         Statement 1 is false, Statement 2 is true.
  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 true, Statement 2 is false.
  done clear
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• question_answer8) The resistance of a wire is R. It is bent at the middle by 180° and both the ends are twisted together to make a shorter wire. The resistance of the new wire is   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  2R                          
  done clear
  B)
                         R/2
  done clear
  C)
                         R/4                        
  done clear
  D)
                         R/S
  done clear
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• question_answer9) An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is (velocity of sound = 330 m/s)   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  125.00                                  
  done clear
  B)
                         93.75
  done clear
  C)
                          62.50                                   
  done clear
  D)
                         187.50
  done clear
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• question_answer10) The electrical resistance R of a conductor of length \[l\] and area of cross section a is given by\[R=\frac{\rho l}{a}\]where \['\rho '\]is the electrical resistivity. What is the dimensional formula for electrical conductivity' \['\sigma '\]which is reciprocal of resistivity?   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]\]         
  done clear
  B)
                         \[[M{{L}^{-3}}{{T}^{-3}}{{A}^{2}}]\]
  done clear
  C)
                         \[[M{{L}^{-3}}{{T}^{-3}}{{A}^{-2}}]\]       
  done clear
  D)
                         \[[{{M}^{-2}}{{L}^{3}}{{T}^{2}}{{A}^{-1}}]\]
  done clear
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• question_answer11) The frequency of X-rays;\[\gamma \text{-}\]rays and ultraviolet rays are respectively a, b and c then.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[a<b;b>c\]                       
  done clear
  B)
                         \[a>b;b>c\]
  done clear
  C)
                         \[a<b<c\]                           
  done clear
  D)
                         \[a=b=c\]
  done clear
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• question_answer12) The figure shows a combination of two NOT gates and a NOR gate. The combination is equivalent to a.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   NAND gate       
  done clear
  B)
                         NOR gate
  done clear
  C)
                         AND gate                            
  done clear
  D)
                         OR gate
  done clear
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• question_answer13) Photoelectrons are ejected from a metal when light of frequency u falls on it. Pick out the wrong statement from the following.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   No electrons are emitted if o is less than W/h, where W is the work function of the metal
  done clear
  B)
                          The ejection of the photoelectrons is instantaneous.
  done clear
  C)
                          The maximum energy of the photo electrons is\[h\upsilon .\]
  done clear
  D)
                         The maximum energy of the photoelectrons is independent of the intensity of the light.
  done clear
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• question_answer14) The counting rate observed from a radioactive source at t = 0 was 1600 counts \[{{s}^{-1}}.\], and t = 8 s, it was 100 counts \[{{s}^{-1}}.\]. The counting rate observe das counts \[{{s}^{-1}}.\] at t = 6 s will be.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  250                                        
  done clear
  B)
                         400
  done clear
  C)
                         300                                        
  done clear
  D)
                         200
  done clear
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• question_answer15) A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C. When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[\sqrt{\frac{2Gm}{r}\left( \sqrt{2}-1 \right)}\] 
  done clear
  B)
                         \[\sqrt{\frac{Gm}{r}}\]
  done clear
  C)
                         \[\sqrt{\frac{2Gm}{r}\left( 1-\frac{1}{\sqrt{2}} \right)}\]
  done clear
  D)
                         \[\sqrt{\frac{2Gm}{r}}\]
  done clear
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• question_answer16) A beam of light consisting of red, green and blue colours is incident on a right-angled prism on face AB. The refractive indices of the material for the above red, green and blue colours are 1.39, 1.44 and 1.47 respectively. A person looking on surface A C of the prism will see   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  no light
  done clear
  B)
                         green and blue colours
  done clear
  C)
                          red and green colours
  done clear
  D)
                          Red colour only
  done clear
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• question_answer17) The force \[\overset{\to }{\mathop{F}}\,=F\hat{i}\] on a particle of mass 2 kg, moving along the x-axis is given in the figure as a function of its position x. The particle is moving with a velocity of 5 m/s along the x-axis at x = 0. What is the kinetic energy of the particle at\[x=8m?\]   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  34J                                         
  done clear
  B)
                         34.5 J
  done clear
  C)
                         4.5J                                       
  done clear
  D)
                         29.4J
  done clear
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• question_answer18) The door of a working refrigerator is left open in a well insulated room. The temperature of air in the room will   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  decrease
  done clear
  B)
                          increase in winters and decrease in summers
  done clear
  C)
  remain the same             
  done clear
  D)
                         increase
  done clear
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• question_answer19) The terminal velocity of a small sphere of radius a in a viscous liquid is proportional to   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[{{a}^{2}}\]                                      
  done clear
  B)
                         \[{{a}^{3}}\]
  done clear
  C)
                         a                                             
  done clear
  D)
                         \[{{a}^{-1}}\]
  done clear
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• question_answer20) A stone of mass m, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by \[T=A{{r}^{n}},\]where A is a constant, r is the instantaneous radius of the circle. The value of n is equal to.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   -1                                          
  done clear
  B)
  -2
  done clear
  C)
  -4                           
  done clear
  D)
  -3
  done clear
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• question_answer21) The disturbance y (x, t) of a wave propagating in the positive x-direction is given by \[y=\frac{1}{1+{{x}^{2}}}\] at time t = 0 and by \[y=\frac{1}{\left[ 1+{{\left( x-1 \right)}^{2}} \right]}\]at t = 2 s, where x and y are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in m/s is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  2.0                                         
  done clear
  B)
  4.0
  done clear
  C)
  0.5                                         
  done clear
  D)
  1.0
  done clear
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• question_answer22) An ideal monatomic gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure \[{{P}_{i}}.\] If the same gas is expanded adiabatically to a volume 2V, the final pressure is \[{{P}_{a}}.\]The ratio \[\frac{{{P}_{a}}}{{{P}_{i}}}\]is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[{{2}^{-1/3}}\]                                
  done clear
  B)
  \[{{2}^{1/3}}\]
  done clear
  C)
  \[{{2}^{2/3}}\]                                  
  done clear
  D)
  \[{{2}^{-2/3}}\]
  done clear
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• question_answer23) A telescope of aperture \[3\times {{10}^{-2}}m\] diameter is focused on a window at 80 m distance fitted with a wire mesh of spacing \[2\times {{10}^{-3}}m\]. Given:\[\lambda =5.5\times {{10}^{-7}}m,\]which of the following is true for observing the mesh through the telescope?   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   Yes, it is possible with the same aperture size.
  done clear
  B)
  Possible also with an aperture half the present diameter.
  done clear
  C)
  No, it is not possible.
  done clear
  D)
  Given data is not sufficient.
  done clear
  View Answer play_arrow

• question_answer24) 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 charged particle is moving at right angle to a static magnetic field. During the motion the kinetic energy of the charge remains unchanged. Statement 2: Static magnetic field exert force on a moving charge in the direction perpendicular to the magnetic field.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  Statement 1 is false, Statement 2 is time.
  done clear
  B)
  Statement 1 is time, Statement 2 is time, Statement 2 is not the correct explanation of Statement 1.
  done clear
  C)
  Statement 1 is true. Statement 2 is false.
  done clear
  D)
  Statement 1 is time, Statement 2 is time, Statement 2 is the correct explanation of Statement 1.
  done clear
  View Answer play_arrow

• question_answer25) A ball is dropped vertically downwards from a height h above the ground. It hits the ground inelastically and bounces up vertically. Neglecting subsequent motion and air resistance, which of the following graph represents variation between speed (v) and height (h) correctly?   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   
  done clear
  B)
   
  done clear
  C)
                 
  done clear
  D)
   
  done clear
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• question_answer26) A thick-walled hollow sphere has outside radius\[{{R}_{0}}.\]It rolls down an incline without slipping and its speed at the bottom is \[{{v}_{0}}.\].Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be\[5{{v}_{0}}/4.\]The radius of gyration of the hollow sphere about an axis through its centre is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[3{{R}_{0}}/2\]               
  done clear
  B)
  \[3{{R}_{0}}/4\]
  done clear
  C)
  \[9{{R}_{0}}/16\]                             
  done clear
  D)
  \[3{{R}_{0}}\]
  done clear
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• question_answer27) In a cylindrical water tank, there are two small holes A and B on the wall at a depth of\[{{h}_{1}},\] from the surface of water and at a height of \[{{h}_{2}}\] from the bottom of water tank. Surface of water is at height of\[{{h}_{2}}\] from the bottom of water tank. Surface of water is at height H from the bottom of water tank. Water coming out from both holes strikes the ground at the same point S. Find the ratio of \[{{h}_{1}}\]and \[{{h}_{2}}\]   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  Depends on H
  done clear
  B)
  1:1
  done clear
  C)
  2:2                                         
  done clear
  D)
  1:2
  done clear
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• question_answer28) 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: If you push on a cart being pulled by a horse so that it does not move, the cart pushes you back with an equal and opposite force. Statement 2: The cart does not move because the force described in statement 1 cancel each other.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   Statement 1 is time, Statement 2 is time, Statement 2 is the correct explanation of Statement 1.
  done clear
  B)
  Statement 1 is false, Statement 2 is time.
  done clear
  C)
  Statement 1 is true. Statement 2 is false.
  done clear
  D)
  Statement 1 is time. Statement 2 is time, Statement 2 is not the correct explanation of Statement 1.
  done clear
  View Answer play_arrow

• question_answer29) In an experiment of potentiometer for measuring the internal resistance of primary cell a balancing length \[\ell \]is obtained on the potentiometer wire when the cell is open circuit. Now the cell is short circuited by a resistance R, If R is to be equal to the internal resistance of the cell the balancing length on the potentiometer wire will be.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[\ell \]                
  done clear
  B)
                         \[2\ell \]
  done clear
  C)
                          \[\ell /2\]           
  done clear
  D)
                         \[\ell /4\]
  done clear
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• question_answer30) The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the resonance frequency of the circuit is 10 kHz. When the container is filled with a gas, the resonance frequency changes by 50 Hz. The dielectric constant of the gas is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  1.001                                    
  done clear
  B)
                         2.001
  done clear
  C)
                         1.01                                       
  done clear
  D)
                         3.01
  done clear
  View Answer play_arrow