Solved papers for JEE Main & Advanced JEE Main Paper (Held On 10 April 2015)

done JEE Main Paper (Held On 10 April 2015) Total Questions - 30

• question_answer1) A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it is rolling without slipping then the value of 'F' is: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[ma\]                                   
  done clear
  B)
  \[2 ma\]
  done clear
  C)
   \[\frac{5}{3}\]                                  
  done clear
  D)
   \[\frac{3}{2}ma\]
  done clear
  View Answer play_arrow

• question_answer2) When current in a coil changes from 5 A to 2 A in 0.1 s, an average voltage of 50 V is produced. The self-inductance of the coils is: JEE Main Online Paper (Held On 10 April 2015)
  A)
   3H                                         
  done clear
  B)
   1.67 H
  done clear
  C)
   6 H                                        
  done clear
  D)
   0.67 H
  done clear
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• question_answer3) If a body moving in a circular path maintains constant speed of \[\frac{3}{2}ma\], then which of the following correctly describes relation between acceleration and radius? JEE Main Online Paper (Held On 10 April 2015)
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
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• question_answer4) An electromagnetic wave travelling in the x-direction has frequency of \[2\times {{10}^{14}}Hz\]and electric field amplitude of \[27V{{m}^{-1}}.\]From the options given below, which one describes the magnetic field for this wave? JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\overset{\to }{\mathop{B}}\,(x.t)=(9\times {{10}^{-8}}T)\hat{i}\] \[\sin \left[ 2\pi (1.5\times {{10}^{-8}}x-2\times {{10}^{14}}t) \right]\]
  done clear
  B)
  \[\overset{\to }{\mathop{B}}\,(x,t)=(3\times {{10}^{-8}}T)\hat{j}\] \[\sin \left[ 1.5\times {{10}^{-6}}x-2\times {{10}^{14}}t) \right]\]
  done clear
  C)
  \[\overset{\to }{\mathop{B}}\,(x,t)=(3\times {{10}^{-8}}T)\hat{j}\] \[\sin \left[ 2\pi (1.5\times {{10}^{-8}}x-2\times {{10}^{14}}t) \right]\]
  done clear
  D)
  \[\overset{\to }{\mathop{B}}\,(x,t)=(9\times {{10}^{-8}}T)\hat{k}\] \[\sin \left[ 2\pi (1.5\times {{10}^{-6}}x-2\times {{10}^{14}}t) \right]\]
  done clear
  E)
   None of the above
  done clear
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• question_answer5) A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R << L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing  Is t and its distance from the galaxy?s axis is r, then: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[T\propto {{r}^{2}}\]                    
  done clear
  B)
  \[T\propto r\]
  done clear
  C)
  \[{{T}^{2}}\propto {{r}^{3}}\]                     
  done clear
  D)
  \[T\propto \sqrt{r}\]
  done clear
  View Answer play_arrow

• question_answer6) If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter\[\frac{2}{\sqrt{\pi }}cm\]then the Reynolds number for the flow is (density of water \[={{10}^{3}}kg/{{m}^{3}}\]and viscosity of water \[={{10}^{-3}}Pa.s\]) close to: JEE Main Online Paper (Held On 10 April 2015)
  A)
   11,000                 
  done clear
  B)
   5500
  done clear
  C)
   550                                       
  done clear
  D)
   1100
  done clear
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• question_answer7) If two  glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\frac{4T}{R}\]                                
  done clear
  B)
  \[\frac{2T}{R}\]
  done clear
  C)
   \[\frac{T}{2R}\]                                               
  done clear
  D)
  \[\frac{T}{4R}\]
  done clear
  E)
   None of the above
  done clear
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• question_answer8) A thin disc of radius b = 2a has a concentric hole of radius \['\sigma '\] in it (see figure). It carries uniform surface charge 'w' on it. If the electric field on its axis at height 'h' (h<<a) from its centre is given as \['C\overset{\scriptscriptstyle\smile}{h}'\]then value  of ?C? is: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\frac{\sigma }{a{{\varepsilon }_{0}}}\]                               
  done clear
  B)
  \[\frac{\sigma }{4a{{\varepsilon }_{0}}}\]
  done clear
  C)
  \[\frac{\sigma }{2a{{\varepsilon }_{0}}}\]                             
  done clear
  D)
  \[\frac{\sigma }{8a{{\varepsilon }_{0}}}\]
  done clear
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• question_answer9) If the capacitance of a Nano capacitor is measured in tern-is of a unit V made by combining the electronic charge 'e', Bohr radius \['{{a}_{0}}',\] Planck's constant 'h' and speed of light 'c' then : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[u=\frac{hc}{{{e}^{2}}{{a}_{0}}}\]                          
  done clear
  B)
  \[u=\frac{{{e}^{2}}h}{c{{a}_{0}}}\]
  done clear
  C)
  \[u=\frac{{{e}^{2}}{{a}_{0}}}{hc}\]                          
  done clear
  D)
  \[u=\frac{{{e}^{2}}c}{h{{a}_{0}}}\]
  done clear
  View Answer play_arrow

• question_answer10) Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about one of its diagonals, then : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[I=\frac{m{{a}^{2}}}{12}\]                         
  done clear
  B)
  \[I>\frac{m{{a}^{2}}}{12}\]
  done clear
  C)
   \[I=\frac{m{{a}^{2}}}{24}\]                        
  done clear
  D)
  \[\frac{m{{a}^{2}}}{24}<I<\frac{m{{a}^{2}}}{12}\]
  done clear
  View Answer play_arrow

• question_answer11) A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is \[\theta \], then\[\theta \], is close to : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[{{60}^{o}}\]                                    
  done clear
  B)
  \[{{15}^{o}}\]
  done clear
  C)
   \[{{1}^{o}}\]                                     
  done clear
  D)
  \[{{30}^{o}}\]
  done clear
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• question_answer12) Suppose the drift velocity Vi in a material varied with the applied electric field E as \[{{\upsilon }_{d}}\propto \sqrt{E}.\]Then V - I graph for a wire made of such a material is best given by : JEE Main Online Paper (Held On 10 April 2015)
  A)
  
  done clear
  B)
                 
  done clear
  C)
  
  done clear
  D)
  
  done clear
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• question_answer13) In an unbiased n-p Junction electrons diffuse from n - region to p - region because : JEE Main Online Paper (Held On 10 April 2015)
  A)
   only electrons move from n to p  holes in p- region and not the vice - versa
  done clear
  B)
   holes in p - region attract them
  done clear
  C)
   electrons travel across the junction due to potential difference
  done clear
  D)
   electron concentration in n - region is more as compared to that in p-region
  done clear
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• question_answer14) A simple harmonic oscillator of angular frequency \[2rad\,{{s}^{-1}}\]is acted upon by an external force F = sint N. If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is proportional to: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\sin t+\frac{1}{2}\cos 2t\]        
  done clear
  B)
  \[\sin t-\frac{1}{2}\sin 2t\]
  done clear
  C)
   \[\cot t-\frac{1}{2}\sin 2t\]        
  done clear
  D)
  \[\sin t+\frac{1}{2}\sin 2t\]
  done clear
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• question_answer15) A parallel beam of electrons travelling in x-direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum \[{{p}_{y}}\] in the y-direction then for a majority of electrons passing through the slit (h is Planck's constant) : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[|{{p}_{y}}|d>h\]                         
  done clear
  B)
  \[|{{p}_{y}}|d>>h\]
  done clear
  C)
  \[|{{p}_{y}}|d<h\]                         
  done clear
  D)
  \[|{{p}_{y}}|d\simeq h\]
  done clear
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• question_answer16) In the circuits  and  switches \[{{S}_{1}}\] and \[{{S}_{2}}\] are closed at t = 0 and are kept closed for a long time. '1'he variation of currents in the two circuits for \[t\ge 0\] are roughly shown by (figures are schematic and not drawn to scale) : JEE Main Online Paper (Held On 10 April 2015)
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
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• question_answer17) A proton (mass m) accelerated by a potential difference V flies through a uniform transverse magnetic field B. The field occupies a region of space by width 'd?. If \['\alpha '\] be the angle of deviation of proton from initial direction of motion (see figure), the value of sin a will be : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[{{q}^{V}}\sqrt{\frac{Bd}{2m}}\]                            
  done clear
  B)
  \[Bd\sqrt{\frac{q}{2mV}}\]
  done clear
  C)
  \[\frac{B}{2}\sqrt{\frac{qd}{mV}}\]                        
  done clear
  D)
  \[\frac{B}{d}\sqrt{\frac{q}{2mV}}\]
  done clear
  View Answer play_arrow

• question_answer18) de-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to \[(|e|=1.6\times {{10}^{-19}}C,{{m}_{e}}=9.1\times {{10}^{-31}}kg,h=6.6\times {{10}^{-34}}Js)\] JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[0.5\,\overset{\text{o}}{\mathop{\text{A}}}\,\]            
  done clear
  B)
  \[1.7\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  C)
  \[2.4\,\overset{\text{o}}{\mathop{\text{A}}}\,\]          
  done clear
  D)
  \[1.2\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
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• question_answer19) Diameter of a steel ball is measured using a Vernier callipers which lias divisions of cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as :

  S. No.	MS (cm)	VS divisions
  1.	0.5	8
  2.	0.5	4
  3.	0.5	6

  If the zero error is - 0.03 cm, then mean corrected diameter is : JEE Main Online Paper (Held On 10 April 2015)
  A)
   0.56 cm
  done clear
  B)
   0.53 cm
  done clear
  C)
    0.52 cm
  done clear
  D)
   0.59 cm
  done clear
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• question_answer20) If one were to apply Bohr model to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the nth  level will be : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[n\left( \frac{hqB}{2\pi m} \right)\]                      
  done clear
  B)
  \[n\left( \frac{hqB}{8\pi m} \right)\]
  done clear
  C)
   \[n\left( \frac{hqB}{4\pi m} \right)\]                     
  done clear
  D)
  \[n\left( \frac{hqB}{\pi m} \right)\]
  done clear
  View Answer play_arrow

• question_answer21) x and y displacements of a particle are given as x(t)=a \[\sin \omega t\] and \[y(t)=a\sin 2\omega t.\] Its trajectory will look like : JEE Main Online Paper (Held On 10 April 2015)
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
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• question_answer22) Shown in the figure are two point charges +Q and -Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If \[{{\sigma }_{1}}\] is the surface charge on the inner surface and \[{{Q}_{1}}\] net charge on it and \[{{\sigma }_{2}}\] the surface charge on the outer surface and \[{{Q}_{2}}\] net charge on it then : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[{{\sigma }_{1}}\ne 0,{{Q}_{1}}=0\] \[{{\sigma }_{2}}\ne 0,{{Q}_{2}}=0\]
  done clear
  B)
  \[{{\sigma }_{1}}\ne 0,{{Q}_{1}}=0\] \[{{\sigma }_{2}}=0,{{Q}_{2}}=0\]
  done clear
  C)
  \[{{\sigma }_{1}}\ne 0,{{Q}_{1}}\ne 0\] \[{{\sigma }_{2}}\ne 0,{{Q}_{2}}\ne 0\]
  done clear
  D)
  \[{{\sigma }_{1}}=0,{{Q}_{1}}=0\] \[{{\sigma }_{2}}=0,{{Q}_{2}}=0\]
  done clear
  View Answer play_arrow

• question_answer23) A block of mass m=10 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of nails 50 g moving with speed r, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed \[\frac{\upsilon }{10}\] after being dropped from height H, then neglecting energy losses and taking \[g=10m{{s}^{-2}},\]the value of H is close to: JEE Main Online Paper (Held On 10 April 2015)
  A)
   0.2 km
  done clear
  B)
   0.4 km
  done clear
  C)
   0.5 km
  done clear
  D)
   0.3 km
  done clear
  E)
   None of the above
  done clear
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• question_answer24) A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance \[\left( \frac{x}{2} \right)\]from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity \[3m{{s}^{-1}}.\]The total initial energy of the spring is: JEE Main Online Paper (Held On 10 April 2015)
  A)
    15J
  done clear
  B)
   0.6 J
  done clear
  C)
   0.8 J
  done clear
  D)
   0.3 J
  done clear
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• question_answer25) A bat moving at \[10m{{s}^{-1}}\] towards a wall sends a sound signal of ROOO Hz towards it. On reflection it hears a sound of frequency f. The value of f in Hz is dose to (speed of sound \[=320m{{s}^{-1}}\]) JEE Main Online Paper (Held On 10 April 2015)
  A)
   8516
  done clear
  B)
   8000
  done clear
  C)
    8424
  done clear
  D)
   8258
  done clear
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• question_answer26) An ideal gas goes through a reversible cycle \[a\to b\to c\to d\]has the V - T diagram shown below. Process \[d\to a\]and \[b\to c\] are adiabatic. The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) : JEE Main Online Paper (Held On 10 April 2015)
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
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• question_answer27) A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15 A. If it is equivalent to a magnet of the same size and magnetization \[\overset{\to }{\mathop{M}}\,\](magnetic moment/volume), then \[|\overset{\to }{\mathop{M}}\,|\]is: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[30000\,A{{m}^{-1}}\]                 
  done clear
  B)
  \[3\pi \,A{{m}^{-1}}\]
  done clear
  C)
  \[30000\pi \,A{{m}^{-1}}\]          
  done clear
  D)
  \[300\,A{{m}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer28) In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as \[{{T}^{q}}.\] A good estimate for q is : JEE Main Online Paper (Held On 10 April 2015)
  A)
   1                                            
  done clear
  B)
  \[\frac{1}{4}\]
  done clear
  C)
  \[\frac{1}{2}\]                                   
  done clear
  D)
   2
  done clear
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• question_answer29) You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm- The radius of curvature of the mirror would then be : JEE Main Online Paper (Held On 10 April 2015)
  A)
  -24 cm                  
  done clear
  B)
   24 cm
  done clear
  C)
   60 cm                  
  done clear
  D)
   30 cm
  done clear
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• question_answer30) A 10V battery with internal resistance \[1\Omega \]and a 15 V battery with internal resistance \[0.6\Omega \] are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to : JEE Main Online Paper (Held On 10 April 2015)
  A)
   11.9 V                  
  done clear
  B)
   13.1 V
  done clear
  C)
   12.5 V                  
  done clear
  D)
   24.5 V
  done clear
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