Solved papers for JEE Main & Advanced JEE Main Paper (Held On 22 April 2013)

done JEE Main Paper (Held On 22 April 2013) Total Questions - 30

• question_answer1) Orbits of a particle moving in a circle are such that the perimeter of orbit equals an integer number of de - Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will therefore be proportional to:     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[{{n}^{2}}\]                                         
  done clear
  B)
   \[n\]
  done clear
  C)
   \[{{n}^{1/2}}\]                                     
  done clear
  D)
   \[{{n}^{1/4}}\]
  done clear
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• question_answer2) Two blocks of mass \[{{M}_{1}}=20\,kg\] and \[{{\operatorname{M}}_{2}}=12\operatorname{K}\operatorname{g},\] are connected by a metal rod of mass 8 kg. The system is pulled vertically up applying a force of 480 N as shown. The tension at mid-point of the rod is:   JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[144\] N                             
  done clear
  B)
   \[96\] N
  done clear
  C)
   \[240\] N                             
  done clear
  D)
   \[192\] N
  done clear
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• question_answer3) An LCR circuit as shown in the figure is connected to voltage source \[{{\operatorname{V}}_{\operatorname{ac}}}\] whose frequency can be varied. The frequency, at which the voltage across the resistor is maximum, is:   JEE Main  Online Paper (Held On 22 April 2013)
  A)
   902 Hz                  
  done clear
  B)
   143 Hz
  done clear
  C)
   23 Hz                    
  done clear
  D)
   345 Hz
  done clear
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• question_answer4) A body stars from rest on a long inclined plane of slope\[{{45}^{o}}\]. The coefficient of friction between the body and the plane varies as \[\mu =0.3\,x,\] where \[x\] is distance travelled down the down the plane. The body will have maximum speed (for g=10 m/\[{{\text{s}}^{\text{2}}}\]) when \[x\]= :     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   9.8 m
  done clear
  B)
   27 m
  done clear
  C)
   12 m                                     
  done clear
  D)
   3.33 ms
  done clear
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• question_answer5) A and B are two sources generating sound waves. A listener is situated at C. The frequency of the source at A is 500 Hz A, now, moves towards C with a speed 4 m/s. The number of beats heard at C is 6. When A moves away from C with speed 4 m/s, the number of beats heard at C is 18. The speed of sound is 340 m/s. The frequency of the source at B is:                     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   500 Hz                  
  done clear
  B)
   506 Hz
  done clear
  C)
   512 Hz                  
  done clear
  D)
   494 Hz
  done clear
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• question_answer6) A dc source of emf \[{{E}_{1}}=100\,V\] and internal resistance \[\operatorname{r}=0.5\Omega ,\] a storage battery of emf \[{{\operatorname{E}}_{2}}=90\operatorname{V}\] and an external resistance R are connected as shown in figure. For what value of R no current will pass through the battery?                   JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[5.5\,\,\Omega \]                              
  done clear
  B)
   \[3.5\,\,\Omega \]
  done clear
  C)
   \[4.5\,\,\Omega \]                              
  done clear
  D)
   \[2.5\,\,\Omega \]
  done clear
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• question_answer7) The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is :(mass of the moon \[=7.36\times {{10}^{22}}\,kg\], radius of the moon?s orbit \[=3.8\times {{10}^{8}}\,m\])     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[6.73\times {{10}^{-5}}\operatorname{m}/{{\operatorname{s}}^{2}}\] 
  done clear
  B)
   \[6.73\times {{10}^{-.3}}\operatorname{m}/{{\operatorname{s}}^{2}}\]
  done clear
  C)
   \[6.73\times {{10}^{-.2}}\operatorname{m}/{{\operatorname{s}}^{2}}\]
  done clear
  D)
   \[6.73\times {{10}^{-.4}}\operatorname{m}/{{\operatorname{s}}^{2}}\]
  done clear
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• question_answer8) An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its initial value. If the final pressure of gas is 128 atmosphers, the value of \['\gamma '\] the gas is:     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   1.5                                        
  done clear
  B)
   1.4
  done clear
  C)
   1.3                                        
  done clear
  D)
   1.6
  done clear
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• question_answer9) A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of \[{{30}^{0}}\] with the horizontal. The ball strikes the ground at B. What is the value of the distance AB?                 (Moment of inertia of spherical shell of mass m and radius R about its diameter \[=\frac{2}{3}{{\operatorname{mR}}^{2}})\]   JEE Main  Online Paper (Held On 22 April 2013)
  A)
   1.87 m                  
  done clear
  B)
   2.08  m
  done clear
  C)
   1.57 m                  
  done clear
  D)
   1.77 m
  done clear
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• question_answer10) The dimensions of angular momentum, latent heat and capacitance are, respectively.     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{1}}{{\operatorname{A}}^{2}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{2}}\]
  done clear
  B)
   \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{4}}{{\operatorname{A}}^{2}}\]
  done clear
  C)
   \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},\operatorname{M}{{\operatorname{L}}^{2}}\operatorname{T}{{\operatorname{A}}^{2}}\]
  done clear
  D)
   \[\operatorname{M}{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-1}},{{\operatorname{L}}^{2}}{{\operatorname{T}}^{-2}},{{\operatorname{M}}^{-1}}{{\operatorname{L}}^{-2}}{{\operatorname{T}}^{4}}{{\operatorname{A}}^{2}}\]
  done clear
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• question_answer11) Air of density 1.2 \[\operatorname{Kg}{{\operatorname{m}}^{-3}}\] is blowing across the horizontal wings of on aero plane in such a way that its speeds above and below the wings are \[150\,\,m{{s}^{-1}}\]and \[100\,\,m{{s}^{-1}}\],  respectively. The pressure difference between the upper and lower     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[60\operatorname{N}{{\operatorname{m}}^{-2}}\]                   
  done clear
  B)
   \[180\operatorname{N}{{\operatorname{m}}^{-2}}\]
  done clear
  C)
   \[7500\operatorname{N}{{\operatorname{m}}^{-2}}\]                              
  done clear
  D)
   \[12500\operatorname{N}{{\operatorname{m}}^{-2}}\]
  done clear
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• question_answer12) 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: In Young?s double slit experiment, the number of fringes observed in the filed of view is small with longer wave length of light and is large with shorter wave length of light.                 Statement 2: In the double slit experiment the fringe width depends directly on the wave length of light.     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   Statement 1 is true Statement 2 is true and the Statement 2 is not the correct explanation of the Statement 1
  done clear
  B)
   Statement 1 is false and the Statement 2 is true
  done clear
  C)
   Statement 1 true and statement 2 is true and the Statement 2 is true explanation of the Statement 1
  done clear
  D)
   Statement 1 is true and the Statement 2 is false
  done clear
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• question_answer13) To find the resistance of galvanometer by the half deflection method the following circuit is used with resistances \[{{\operatorname{R}}_{1}}=9970\Omega ,{{\operatorname{R}}_{2}}=30\Omega \] and \[{{\operatorname{R}}_{3}}=0\]. The deflection in the galvanometer is d. With \[{{\operatorname{R}}_{3}}=107\Omega \]the deflection changed to \[\frac{\operatorname{d}}{2}.\] The galvanometer resistance is approximately:                    JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[107\Omega \]                  
  done clear
  B)
   \[137\Omega \]
  done clear
  C)
   \[107/2\Omega \]                              
  done clear
  D)
   \[77\,\Omega \]
  done clear
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• question_answer14) The focal length of the objective and the eyepiece of a telescope are 50 cm and 5 cm respectively. If the telescope is focused for distinct vision on a scale distant 2m from its objective, then its magnifying power will be:     JEE Main  Online Paper (Held On 22 April 2013)
  A)
  \[-4\]                                     
  done clear
  B)
  \[-8\]
  done clear
  C)
  \[+8\]                                    
  done clear
  D)
  \[-2\]
  done clear
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• question_answer15) In a series L-C-R circuit, \[\text{C}=\text{1}{{0}^{-11}}\] Farad, \[\text{L}=\text{1}{{0}^{-5}}\] Henry and \[\text{R}=100\] Ohm, when a constant D.C. voltage E is applied to the circuit, the capacitor acquires a charge \[\text{1}{{\text{0}}^{-9}}\operatorname{C}.\] The D.C. source is replaced by a sinusoidal voltage source in which the peak voltage \[{{\operatorname{E}}_{0}}\] is equal to the constant D.C voltage E. At resonance the peak value of the charge acquired by the capacitor will be :   JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[{{10}^{-15}}\operatorname{C}\]                  
  done clear
  B)
   \[{{10}^{-6}}\operatorname{C}\]
  done clear
  C)
   \[{{10}^{-10}}\operatorname{C}\]                  
  done clear
  D)
   \[{{10}^{-8}}\operatorname{C}\]
  done clear
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• question_answer16) A point charge of magnitude + \[1\mu C\] is fixed at (0, 0, 0). An isolated uncharged spherical conductor, is fixed with its center at (4, 0, 0). The potential and the induced electric field at the sphere is :     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[1.8\times {{10}^{5}}\] and \[-5.625\times {{10}^{6}}\,V/m\]
  done clear
  B)
   \[0\operatorname{V}\] and \[0\operatorname{V}/\operatorname{m}\]
  done clear
  C)
   \[2.25\times {{10}^{5}}\operatorname{V}\] and \[-5.625\times {{10}^{6}}\operatorname{V}/\operatorname{m}\]
  done clear
  D)
   \[2.25\times {{10}^{5}}\operatorname{V}\] and V/m
  done clear
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• question_answer17) A uniform wire (Young?s modulus\[2\times {{10}^{11}}{{\operatorname{Nm}}^{-2}}\]) is subjected to longitudinal tensile stress of\[5\times {{10}^{7}}{{\operatorname{Nm}}^{-2}}\]. If the  overall volume change in the wire is 0.02%, the fractional decrease in the radius of the wire is close to:     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[1.0\times {{10}^{-4}}\]                   
  done clear
  B)
   \[1.5\times {{10}^{-4}}\]
  done clear
  C)
   \[0.25\times {{10}^{-4}}\]                 
  done clear
  D)
   \[5\times {{10}^{-4}}\]
  done clear
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• question_answer18) The half ? life of a radioactive element A is the same as the mean-life of another radioactive element B. Initially both substances have the same number of atoms, then :     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   A and B both decay at the same rate always
  done clear
  B)
   A and B will decay at the same rate initially
  done clear
  C)
   A will decay at a faster rate B initially
  done clear
  D)
   B will decay at faster rate A initially
  done clear
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• question_answer19) A Ball projected from ground at an angle of \[{{45}^{0}}\] just clears a wall in front. If point of projection is 4m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is:     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   4.4 m                    
  done clear
  B)
   2.4 m
  done clear
  C)
   3.6 m                                    
  done clear
  D)
   1.6 m
  done clear
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• question_answer20) A plane electromagnetic wave in a non-magnetic dielectric medium is given by \[\overset{\to }{\mathop{\operatorname{E}}}\,={{\overset{\to }{\mathop{\operatorname{E}}}\,}_{0}}\]\[(4\times {{10}^{-7}}x-50t)\] with distance being in meter and time in seconds. The dielectric constant of the medium is :   JEE Main  Online Paper (Held On 22 April 2013)
  A)
   2.4                                        
  done clear
  B)
   5.8
  done clear
  C)
   8.2                                        
  done clear
  D)
   4.8
  done clear
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• question_answer21) To establish an instantaneous current of 2 A through a \[1\mu \operatorname{F}\] capacitor; the potential difference across the capacitor plates should be changed at the rate of :   JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[2\times {{10}^{4}}\operatorname{V}/s\]                    
  done clear
  B)
  \[4\times {{10}^{6}}\operatorname{V}/s\]
  done clear
  C)
   \[2\times {{10}^{6}}\operatorname{V}/s\]                    
  done clear
  D)
   \[4\times {{10}^{4}}\operatorname{V}/s\]
  done clear
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• question_answer22) Choose the correct sketch of the magnetic field lies of a circular current loop shown by the dot  and the cross \[\otimes \]      JEE Main  Online Paper (Held On 22 April 2013)
  A)
   
  done clear
  B)
    
  done clear
  C)
   
  done clear
  D)
    
  done clear
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• question_answer23) Two small equal point charges of magnitude q are suspended from a common point on the ceiling by insulating massless strings of equal lengths. They come to equilibrium with each string making angle \[\theta \] from the vertical. If the mass of each charge is m, then the electrostatic potential at the centre of line joining them will be \[\left( \frac{1}{4\pi {{\in }_{0}}}=\operatorname{k} \right).\]     JEE Main  Online Paper (Held On 22 April 2013)
  A)
  \[2\sqrt{\operatorname{k}\operatorname{mg}\tan \theta }\]   
  done clear
  B)
   \[\sqrt{\operatorname{k}\operatorname{mg}\tan \theta }\]
  done clear
  C)
   \[4\sqrt{\operatorname{k}\operatorname{mg}/\tan \theta }\]
  done clear
  D)
   \[4\sqrt{\operatorname{k}\operatorname{mg}\,\,\tan \theta }\]
  done clear
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• question_answer24) The image of an illuminated square is obtained on screen with the help of a converging lens. The distance of the square of the square from the lens is 40 cm. The area of the image is 9 times that of the square. The focal length of the lens is :     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   36 cm                   
  done clear
  B)
   27 cm
  done clear
  C)
   60 cm                   
  done clear
  D)
   30 cm
  done clear
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• question_answer25) A certain amount of gas is taken through a cyclic process (A B C D A) that has two isobars, one isochore and one isothermal. The cycle can be represented on a P-V indicator diagram as:     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
          
  done clear
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• question_answer26)                 Figure shows a circuit in which three identical diodes are used. Each diode has forward resistance of 20 \[\Omega \] and infinite backward resistance. Resistors \[{{\operatorname{R}}_{1}}={{\operatorname{R}}_{2}}={{\operatorname{R}}_{3}}=50\Omega \]. Battery voltage is 6 V. The current though \[{{\operatorname{R}}_{3}}\].     JEE Main  Online Paper (Held On 22 April 2013)
  A)
    50 mA                 
  done clear
  B)
   100 mA
  done clear
  C)
    60 mA                 
  done clear
  D)
   25 mA
  done clear
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• question_answer27) A mass m = 1.0kg is put on a flat pan attached to vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500 N/m. What is the amplitude A of the motion, so that the mass m tends to get detached from the pan? (Take g = 10 m/\[{{\operatorname{s}}^{2}}\]). The spring is stiff enough so that it does not get distorted during the motion.                   JEE Main  Online Paper (Held On 22 April 2013)
  A)
   \[\operatorname{A}>2.0\operatorname{cm}\]                           
  done clear
  B)
   \[\operatorname{A}=2.0\operatorname{cm}\]
  done clear
  C)
   \[\operatorname{A}<2.0\operatorname{cm}\]                           
  done clear
  D)
   \[\operatorname{A}<1.5\operatorname{cm}\]
  done clear
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• question_answer28) A current \[i\] is flowing in a straight conductor of length L. The magnetic induction at a point on its axis at a distance \[\frac{\operatorname{L}}{4}\]  from its centre will be:     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   Zero                      
  done clear
  B)
   \[\frac{{{\mu }_{0}}\operatorname{i}}{2\pi L}\]
  done clear
  C)
   \[\frac{{{\mu }_{0}}\operatorname{i}}{\sqrt{2L}}\]                      
  done clear
  D)
   \[\frac{4{{\mu }_{0}}\operatorname{i}}{\sqrt{5}\,\pi L}\]
  done clear
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• question_answer29) This question has Statement-1 and Statement-2. Of four choices given after the Statements, choose the one that best describes the two Statements.                 Statement 1: Short wave transmission is achieved due to the total internal reflection of the e-m wave from an appropriate height in the ionosphere.                 Statement 2: Refractive index of a plasma is independent of the frequency of e-m waves.     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   Statement 1 is true, Statement 2 is false
  done clear
  B)
   Statement 1 is false, Statement 2 is true
  done clear
  C)
   Statement 1 is true, Statement 2 is true but Statement 2 is not the correct explanation of Statement 1
  done clear
  D)
   Statement 1 is true, Statement 2 is true but Statement 2 is the correct explanation of Statement 1
  done clear
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• question_answer30) Given that 1g of water in liquid phase has volume  \[\text{1c}{{\text{m}}^{3}}\]and in vopour phase \[\text{1671}\,\,\text{c}{{\text{m}}^{3}}\] at atmospheric pressure and the latent heat of vaporization of water is 2256 J/g; the change in the internal energy in Joules for 1 g of water at 373 K when it changes from liquid phase to vapour phase at the same temperature is:     JEE Main  Online Paper (Held On 22 April 2013)
  A)
   2256                     
  done clear
  B)
   167
  done clear
  C)
   2089                     
  done clear
  D)
   1
  done clear
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