Solved papers for JEE Main & Advanced JEE Main Solved Paper-2015

done JEE Main Solved Paper-2015 Total Questions - 30

• question_answer1) Distance of the centre of mass of a solid uniform cone from its vertex is \[{{z}_{0}}\]. If the radius of its base is R and its height is h then \[{{z}_{0}}\]is equal to : [JEE Main Solved Paper-2015 ]
  A)
  \[\frac{5h}{8}\]                                
  done clear
  B)
  \[\frac{3{{h}^{2}}}{8R}\]
  done clear
  C)
   \[\frac{{{h}^{2}}}{8R}\]                                
  done clear
  D)
  \[\frac{3h}{4}\]
  done clear
  View Answer play_arrow

• question_answer2) A red LED emits light at 0.1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1m from the diode is : [JEE Main Solved Paper-2015 ]
  A)
  5.48 V/m                             
  done clear
  B)
  7.75 V/m
  done clear
  C)
  1.73 V/m                             
  done clear
  D)
  2.45 V/m
  done clear
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• question_answer3) A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period change to \[{{T}_{M}}.\]If the Young's modulus of the material of the wire is Y then\[\frac{1}{Y}\]is equal to : (g = gravitational acceleration) [JEE Main Solved Paper-2015 ]
  A)
   \[\left[ 1-{{\left( \frac{{{T}_{M}}}{T} \right)}^{2}} \right]\frac{A}{Mg}\]
  done clear
  B)
   \[\left[ 1-{{\left( \frac{T}{{{T}_{M}}} \right)}^{2}} \right]\frac{A}{Mg}\]
  done clear
  C)
  \[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{A}{Mg}\] 
  done clear
  D)
  \[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{Mg}{A}\]
  done clear
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• question_answer4) For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly? (graph are schematic and not drawn to scale) [JEE Main Solved Paper-2015 ]
  A)
                                                 
  done clear
  B)
  
  done clear
  C)
                                                 
  done clear
  D)
  
  done clear
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• question_answer5) A train is moving on a straight track with speed \[20m{{s}^{-1}}.\]. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound \[=320m{{s}^{-1}}\] ) close to [JEE Main Solved Paper-2015 ]
  A)
  18%                                                       
  done clear
  B)
  24%                
  done clear
  C)
  6%                                                         
  done clear
  D)
  12%
  done clear
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• question_answer6) When 5V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons \[2.5\times {{10}^{-4}}m{{s}^{-1}}.\]If the electron density in the wire is \[8\times {{10}^{28}}{{m}^{-3}},\]the resistivity of the material is close to [JEE Main Solved Paper-2015 ]
  A)
  \[1.6\times {{10}^{-6}}\Omega m\]        
  done clear
  B)
  \[1.6\times {{10}^{-5}}\Omega m\]
  done clear
  C)
  \[1.6\times {{10}^{-8}}\Omega m\]        
  done clear
  D)
  \[1.6\times {{10}^{-7}}\Omega m\]
  done clear
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• question_answer7) 4 Two long current carrying thin wires, both with current I, and held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle \['\theta '\] with the vertical. If wires have mass \[\lambda \]per unit length then the value of I is : (g = gravitational acceleration) [JEE Main Solved Paper-2015 ]
  A)
  \[2\sqrt{\frac{\pi gL}{{{\mu }_{0}}}\tan \theta }\]            
  done clear
  B)
  \[\sqrt{\frac{\pi \lambda gL}{{{\mu }_{0}}}\tan \theta }\]
  done clear
  C)
  \[\sin \theta \sqrt{\frac{\pi \lambda gL}{{{\mu }_{0}}\cos \theta }}\]      
  done clear
  D)
  \[2\sin \theta \sqrt{\frac{\pi \lambda gL}{{{\mu }_{0}}\cos \theta }}\]
  done clear
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• question_answer8) In the circuit shown, the current in the \[1\Omega \] resistor is : [JEE Main Solved Paper-2015 ]
  A)
  0.13 A, from Q to P         
  done clear
  B)
  0.13 A, from P to Q
  done clear
  C)
  1.3 A, from P to Q
  done clear
  D)
  0A
  done clear
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• question_answer9) 5 Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can resolve at 500 nm wavelength is [JEE Main Solved Paper-2015 ]
  A)
  \[100\mu m\]                   
  done clear
  B)
  \[300\mu m\]
  done clear
  C)
  \[1\mu m\]                        
  done clear
  D)
  \[30\mu m\]
  done clear
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• question_answer10) An inductor (L = 0.03 H) and a resistor \[(R=0.15k\Omega )\]are connected in series to a battery of 15V EMF in a circuit shown below. The key \[{{K}_{1}}\] has been kept closed for a long time. Then at \[t=0,{{K}_{1}}\]is opened and key \[{{K}_{2}}\] is closed simultaneously. At t = 1ms, the current in the circuit will be : \[\left( {{e}^{5}}\cong 150 \right)\] [JEE Main Solved Paper-2015 ]
  A)
  6.7 mA                 
  done clear
  B)
  0.67 mA
  done clear
  C)
  100 mA                                
  done clear
  D)
  67 mA
  done clear
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• question_answer11) An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to \[{{Q}_{0}}\]and then connected to the L and R as shown below : If a student plots graphs of the square of maximum charge \[\left( Q_{Max}^{2} \right)\]on the capacitor with time (t) for two different values \[{{L}_{1}}\] and \[{{L}_{2}}\] \[\left( {{L}_{1}}>{{L}_{2}} \right)\]of L then which of the following represents this graph correctly ? (plots are schematic and not drawn ot scale) [JEE Main Solved Paper-2015 ]
  A)
                                                 
  done clear
  B)
  
  done clear
  C)
                                                 
  done clear
  D)
  (d)
  done clear
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• question_answer12) In the given circuit, charge \[{{Q}_{2}}\] on the \[2\mu F\] capacitor changes as C is varied from \[1\mu F\] to \[3\mu F.{{Q}_{2}}\] as a function of 'C' is given properly by : (figures are drawn schematically and are not to scale) [JEE Main Solved Paper-2015 ]
  A)
       
  done clear
  B)
  
  done clear
  C)
   
  done clear
  D)
  
  done clear
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• question_answer13) From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is : [JEE Main Solved Paper-2015 ]
  A)
  \[\frac{4M{{R}^{2}}}{9\sqrt{3\pi }}\]      
  done clear
  B)
  \[\frac{4M{{R}^{2}}}{3\sqrt{3\pi }}\]
  done clear
  C)
   \[\frac{M{{R}^{2}}}{32\sqrt{2\pi }}\]                     
  done clear
  D)
  \[\frac{M{{R}^{2}}}{16\sqrt{2\pi }}\]
  done clear
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• question_answer14) The period of oscillation of a simple pendulum is \[T=2\pi \sqrt{\frac{L}{g}}.\]Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of g is : [JEE Main Solved Paper-2015 ]
  A)
  1%                                         
  done clear
  B)
  5%
  done clear
  C)
  2%                                         
  done clear
  D)
  3%
  done clear
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• question_answer15) On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens? principle leads us to conclude that as it travels, the light beam : [JEE Main Solved Paper-2015 ]
  A)
  bends downwards         
  done clear
  B)
  bends upwards
  done clear
  C)
  becomes narrower
  done clear
  D)
  goes horizontally without any deflection
  done clear
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• question_answer16) A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is / are : [JEE Main Solved Paper-2015 ]
  A)
   2005 kHz, 2000 kHz and 1995 kHz
  done clear
  B)
  2000 kHz and 1995 kHz
  done clear
  C)
  2 MHz only
  done clear
  D)
  2005 kHz, and 1995 kHz
  done clear
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• question_answer17) A solid body of constant heat capacity \[1J/{}^\circ C\] is being heated by keeping it in contact with reservoirs in two ways : (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature \[100{}^\circ C\] to final temperature \[200{}^\circ C\]. Entropy change of the body in the two cases respectively is : [JEE Main Solved Paper-2015 ]
  A)
   ln2,2ln2                              
  done clear
  B)
  2ln2,8ln2
  done clear
  C)
  ln2,4ln2                               
  done clear
  D)
  ln2,ln2
  done clear
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• question_answer18) Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume\[u=\frac{U}{V}\propto {{T}^{4}}\]and pressure\[p=\frac{1}{3}\left( \frac{U}{V} \right).\]If the shell now undergoes an adiabatic expansion the relation between T and R is : [JEE Main Solved Paper-2015 ]
  A)
  \[T\propto \frac{1}{R}\]               
  done clear
  B)
  \[T\propto \frac{1}{{{R}^{3}}}\]
  done clear
  C)
  \[T\propto {{e}^{-R}}\]                 
  done clear
  D)
  \[T\propto {{e}^{-3R}}\]
  done clear
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• question_answer19) Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect of the first ? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s2) (The figure are schematic and not drawn to scale) [JEE Main Solved Paper-2015 ]
  A)
                                 
  done clear
  B)
  
  done clear
  C)
                                 
  done clear
  D)
  
  done clear
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• question_answer20) A uniformly charged solid sphere of radius R has potential V0 (measured with respect to \[\infty \] ) on its surface. For this sphere the equipotential surfaces with potentials \[\frac{3{{V}_{0}}}{2},\frac{5{{V}_{0}}}{4},\frac{3{{V}_{0}}}{4}\]and \[\frac{{{V}_{0}}}{4}\]have  radius \[{{R}_{1}},{{R}_{2}},{{R}_{3}}\] and\[{{R}_{4}}\] respectively. Then [JEE Main Solved Paper-2015 ]
  A)
  \[{{R}_{1}}=0\]and\[{{R}_{2}}<\left( {{R}_{4}}-{{R}_{3}} \right)\]
  done clear
  B)
  \[2R<{{R}_{4}}\]
  done clear
  C)
  \[{{R}_{1}}=0\]and\[{{R}_{2}}>\left( {{R}_{4}}-{{R}_{3}} \right)\]
  done clear
  D)
  \[{{R}_{1}}\ne 0\]and\[\left( {{R}_{2}}-{{R}_{1}} \right)>\left( {{R}_{4}}-{{R}_{3}} \right)\]
  done clear
  View Answer play_arrow

• question_answer21) Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is \[\mu ,\] a ray, incident at an angle \[\theta ,\] on the face AB would get transmitted through the face AC of the prism provided. [JEE Main Solved Paper-2015 ]
  A)
  \[\theta >{{\cos }^{-1}}\left[ \mu \sin \left( A+{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right) \right]\]
  done clear
  B)
  \[\theta <{{\cos }^{-1}}\left[ \mu \sin \left( A+{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right) \right]\]
  done clear
  C)
  \[\theta >{{\sin }^{-1}}\left[ \mu \sin \left( A-{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right) \right]\]
  done clear
  D)
  \[\theta <{{\sin }^{-1}}\left[ \mu \sin \left( A-{{\sin }^{-1}}\left( \frac{1}{\mu } \right) \right) \right]\]
  done clear
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• question_answer22) A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12A is placed in different orientations as shown in the figures below : [JEE Main Solved Paper-2015 ]

  A
  B
  C
  D

  If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable eqilibrium?
  A)
  (b) and (d), respectively
  done clear
  B)
  (b) and (c), respectively
  done clear
  C)
   (a) and (b) , respectively
  done clear
  D)
  (a) and (c), respectively
  done clear
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• question_answer23) Two coaxial solenoids of different radii carry current I in the same direction. Let \[{{\vec{F}}_{1}}\]be the magnetic force on the inner soleoid due to the outer one and \[{{\vec{F}}_{2}}\]be the magnetic force on the outer solenoid due to the inner one. Then : [JEE Main Solved Paper-2015 ]
  A)
  \[{{\vec{F}}_{1}}\]is radially inwards and \[{{\vec{F}}_{2}}=0\]
  done clear
  B)
  \[{{\vec{F}}_{1}}\]is radially outwards and \[{{\vec{F}}_{2}}=0\]
  done clear
  C)
   \[{{\vec{F}}_{1}}={{\vec{F}}_{2}}=0\]
  done clear
  D)
  \[{{\vec{F}}_{1}}\]is radially inwards and \[{{\vec{F}}_{2}}\]is radially onwards
  done clear
  View Answer play_arrow

• question_answer24) A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectely inelastic, the percentage loss in the energy during the collision is close to : [JEE Main Solved Paper-2015 ]
  A)
  56 %
  done clear
  B)
  62 %
  done clear
  C)
  44 %                      
  done clear
  D)
  50 %
  done clear
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• question_answer25) Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molcules increases as \[{{V}^{q}},\] where V is the volume of the gas. The value of q is : \[\left( \gamma =\frac{{{C}_{p}}}{{{C}_{v}}} \right)\] [JEE Main Solved Paper-2015 ]
  A)
  \[\frac{\gamma +1}{2}\]              
  done clear
  B)
  \[\frac{\gamma -1}{2}\]
  done clear
  C)
  \[\frac{3\gamma +5}{6}\]                            
  done clear
  D)
  \[\frac{3\gamma -5}{6}\]
  done clear
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• question_answer26) From a solid sphere of mass M and radius R, a spherical portion of radius \[\frac{R}{2}\]is removed, as shown in the figure. Taking gravitional potential V = 0 at \[r=\infty ,\] the potential at the centre of cavity thus formed is: (G = gravitational constant) [JEE Main Solved Paper-2015 ]
  A)
  \[\frac{-2GM}{3R}\]                       
  done clear
  B)
  \[\frac{-2GM}{R}\]
  done clear
  C)
  \[\frac{-GM}{2R}\]                         
  done clear
  D)
  \[\frac{-GM}{R}\]
  done clear
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• question_answer27)  Given in the figure are two blocks A and B of weight 20 N and 100N respectively. There are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is : [JEE Main Solved Paper-2015 ]
  A)
  120 N
  done clear
  B)
  150 N
  done clear
  C)
  100 N                    
  done clear
  D)
  80 N
  done clear
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• question_answer28) D / Physics A long cylinderal shell carries positive surface charge \[\sigma \] in the upper half and negative surface charge \[-\sigma \]in the lower half. The electric field lines around the cylinder will looke like figure given in : (Figures are schematic and not drawn to scale) [JEE Main Solved Paper-2015 ]
  A)
                 
  done clear
  B)
  
  done clear
  C)
                                 
  done clear
  D)
  
  done clear
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• question_answer29) As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom / ion: [JEE Main Solved Paper-2015 ]
  A)
  kinetic energy decrease, potential energy increase but total energy remians same
  done clear
  B)
  kinetic energy and total energy decrease but potential energy increases
  done clear
  C)
  its kinetic energy increases but potential energy and total energy decrease
  done clear
  D)
  kinetic energy, potential energy and total energy decrease
  done clear
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• question_answer30) Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choices given below the list : [JEE Main Solved Paper-2015 ]

  List-I	List-II
  (a) Franck-Hertz Experiment	(i) Particle nature of light
  (b) Photo-electric experiment	(ii) Discrete energy levels of atom
  (c) Davison - Germer Experiment	(iii) Wave nature of electron
  	(iv) Structure of atom

   
  A)
  (A) - (ii) (B) - (i) (C) - (iii)
  done clear
  B)
  (A) - (iv) (B) - (iii) (C) - (ii)
  done clear
  C)
  (A) - (i) (B) - (iv) (C) - (iii)
  done clear
  D)
  (A) - (ii) (B) - (iv) (C) - (iii)
  done clear
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