Solved papers for JEE Main & Advanced JEE Main Paper (Held On 10 April 2016)

done JEE Main Paper (Held On 10 April 2016) Total Questions - 30

• question_answer1) A bottle has an opening of radius a and length b. A cork of length b and radius \[\left( a+\Delta a \right)\] where \[\left( \Delta a<          JEE Main Online Paper (Held On 10 April 2016)         
  A)
  \[\left( 2\pi g\mu B\,\,b \right)\Delta a\]                
  done clear
  B)
  \[\left( \pi \mu B\,\,b \right)\Delta a\]                
  done clear
  C)
  \[\left( \pi \mu \,B\,\,b \right)a\]                               
  done clear
  D)
  \[\left( 4\pi \mu \,B\,\,b \right)\Delta a\]                
  done clear
  View Answer play_arrow

• question_answer2) Consider an electromagnetic wave propagating in vacuum. Choose the correct statement :   JEE Main Online Paper (Held On 10 April 2016)
  A)
  For an electromagnetic wave propagating in +y direction the electric field is \[\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( x,t \right)\hat{z}\]and the magnetic field is \[\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{z}}\left( x,t \right)\hat{y}\]                
  done clear
  B)
  For an electromagnetic wave propagating in +y direction the electric field is \[\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( x,t \right)\hat{y}\]and he magnetic field is\[\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{yz}}\left( x,t \right)\hat{z}\]                
  done clear
  C)
  For an electromagnetic wave propagating in +x direction the electric field is \[\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( y,z,t \right)\left( \hat{y}+\hat{z} \right)\]and the magnetic field is\[\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{yz}}\left( y,z,t \right)\left( \hat{y}+\hat{z} \right)\]                
  done clear
  D)
  For an electromagnetic wave propagating in +x direction the electric field is \[\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( x,t \right)\left( \hat{y}-\hat{z} \right)\]and eh magnetic field is \[B=\frac{1}{\sqrt{2}}{{B}_{yz}}\left( x,t \right)\left( \hat{y}+\hat{z} \right)\]                
  done clear
  View Answer play_arrow

• question_answer3) A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 divisions when \[R=2400\,\,\Omega \].Deflection becomes 20 divisions when resistance taken form resistance box is\[4900\,\,\,\Omega \]. Then we can conclude:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  Resistance required on R.B. For a deflection of 10 divisions is \[9800\,\,\,\Omega \].                
  done clear
  B)
  Full scale deflection current is 2 mA.                
  done clear
  C)
  Current sensitivity of galvanometer is \[20\mu A/\] division.                
  done clear
  D)
  Resistance of galvanometer is \[200\,\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer4) A carnot freezer takes heat from water at \[^{o}C\] inside it and rejects it to the room at a temperature of\[{{27}^{o}}C\]. The latent heat of ice is\[336\times {{10}^{3}}J\,k{{g}^{-1}}\]. If 5 kg of water at \[{{0}^{o}}C\]is converted into ice at \[{{0}^{o}}C\]by the freezer, then the energy consumed by the freezer is close to:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[1.68\times {{10}^{6}}J\]                                               
  done clear
  B)
  \[1.71\times {{10}^{7}}J\]                
  done clear
  C)
  \[1.51\times {{10}^{5}}J\]                                               
  done clear
  D)
  1\[1.67\times {{10}^{5}}J\]
  done clear
  View Answer play_arrow

• question_answer5) A realistic graph depicting the variation of the reciprocal of input resistance in an input characteristics measurement in a common emitter transistor configuration is :   JEE Main Online Paper (Held On 10 April 2016)
  A)
                 
  done clear
  B)
  
  done clear
  C)
                           
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer6) A particle of mass m is acted upon by a force F given by the empirical law \[F=\frac{R}{{{t}^{2}}}V(t)\].If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :   JEE Main Online Paper (Held On 10 April 2016)
  A)
  log v(t) against t                  
  done clear
  B)
  v(t) against\[{{t}^{2}}\]                
  done clear
  C)
  log v(t) against\[\frac{1}{{{t}^{2}}}\]                          
  done clear
  D)
  log v(t) against\[\frac{1}{t}\]                
  done clear
  View Answer play_arrow

• question_answer7) A fighter plane of length 20m, wing span (distance from tip of one wing to the tip of the other wing) of 15m and height 5m is flying towards east over Delhi. Its speed is \[240\,m{{s}^{-1}}\]The earth's magnetic field over Delhi is \[5\times {{10}^{-5}}\]T with the declination angle \[\sim {{0}^{o}}\] and dip of \[\theta \]such that sin\[\theta =\frac{2}{3}\].If the voltage developed is \[{{V}_{B}}\] between the lower and upper side of the plane and \[{{V}_{w}}\]. between the tips the wings then\[{{V}_{B}}\] and VW are closed to:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[{{V}_{B}}=40mV,{{V}_{w}}=135mV\] with left side of pilot at higher voltage.
  done clear
  B)
  \[{{V}_{B}}=40mV,{{V}_{w}}=135mV\] with right side of pilot at high voltage.
  done clear
  C)
  \[{{V}_{B}}=45mV,{{V}_{w}}=120mV\] with left side of pilot at higher voltage.
  done clear
  D)
  \[{{V}_{B}}=45mV,{{V}_{w}}=120mV\]with right side of  pilot at higher voltage.
  done clear
  View Answer play_arrow

• question_answer8) To get an output of 1 from the circuit shown in figure the input must be :   JEE Main Online Paper (Held On 10 April 2016)
  A)
  =1, b =1, c = 0                       
  done clear
  B)
  a = 1, b =0, c = 0                
  done clear
  C)
  a =0, b = 0, c = 1                   
  done clear
  D)
  a =1, b =0, c = 1
  done clear
  View Answer play_arrow

• question_answer9) To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  Four         
  done clear
  B)
  Two
  done clear
  C)
  Three                                      
  done clear
  D)
  Five
  done clear
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• question_answer10) An astronaut of mass m is working on a satellite orbiting the earth at a distance h. from the earth's surface. The radius of the earth is R, while its mass is M. The gravitational pull FG on the astronaut is:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[{{F}_{G}}\frac{G{{M}_{m}}}{{{\left( R+h \right)}^{2}}}\]
  done clear
  B)
               zero since astronaut feels weightless
  done clear
  C)
  \[\frac{G{{M}_{m}}}{{{\left( R+h \right)}^{2}}}<{{F}_{G}}<\frac{G{{M}_{m}}}{{{R}^{2}}}\]
  done clear
  D)
  \[0<{{F}_{G}}<\frac{G{{M}_{m}}}{{{R}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer11) In the figure shown/ ABC is a uniform wire. If centre of mass wire lies vertically below point A, then\[\frac{BC}{AB}\]   JEE Main Online Paper (Held On 10 April 2016)
  A)
  1.85                                                          
  done clear
  B)
  1.5                
  done clear
  C)
  3                                                                
  done clear
  D)
  1.37                
  done clear
  View Answer play_arrow

• question_answer12) A neutron moving with a speed 'v' makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  10.2 eV                                   
  done clear
  B)
  12.1 eV                
  done clear
  C)
  20.4 eV                   
  done clear
  D)
  16.8 eV
  done clear
  View Answer play_arrow

• question_answer13) Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to : (Take the radius of the drum to be 1.25m and its axle to be horizontal):     JEE Main Online Paper (Held On 10 April 2016)
  A)
  1.3                                            
  done clear
  B)
  0.4
  done clear
  C)
  27.0                                          
  done clear
  D)
  8.0
  done clear
  View Answer play_arrow

• question_answer14) A photoelectric surface is illuminated successively by monochromatic light of wavelengths \[\]and\[\frac{}{3}\]. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 time that in the first case, the work function of the surface is :   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[\frac{3hc}{}\]                                    
  done clear
  B)
  \[\frac{hc}{}\]
  done clear
  C)
  \[\frac{hc}{3}\]                                    
  done clear
  D)
  \[\frac{hc}{2}\]
  done clear
  View Answer play_arrow

• question_answer15) A,B,C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C in (BD) holds ture .Then which of the combination is not a meaningful quantity?   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[{{A}^{2}}-{{B}^{2}}{{C}^{2}}\]                    
  done clear
  B)
  \[\frac{A}{B}-C\]
  done clear
  C)
  \[\frac{C}{BD}-\frac{A{{D}^{2}}}{C}\]                         
  done clear
  D)
  \[\frac{(A-C)}{D}\]
  done clear
  View Answer play_arrow

• question_answer16) A thin 1m long rod has a radius of 5 mm. A force of \[50\,\,\pi kN\]is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false?   JEE Main Online Paper (Held On 10 April 2016)
  A)
  The maximum value of Y that can be determined is \[{{10}^{14}}N/{{m}^{2}}\]
  done clear
  B)
  \[\frac{\Delta Y}{Y}\]?gets minimum contribution from the uncertainty in the length.
  done clear
  C)
  The figure of merit is the larges for the length of the rod.
  done clear
  D)
  \[\frac{\Delta Y}{Y}\]gets its maximum contribution from the uncertainty in strain.
  done clear
  View Answer play_arrow

• question_answer17) Figure shows a network of capacitors where the number indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be \[1\mu F\]is:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[\frac{33}{23}\mu F\]                                     
  done clear
  B)
  \[\frac{31}{23}\mu F\]                
  done clear
  C)
  \[\frac{32}{23}\mu F\]     
  done clear
  D)
  \[\frac{34}{23}\mu F\]
  done clear
  View Answer play_arrow

• question_answer18) Which of the following shown the correct relationship between the pressure 'P' and density 'P' of an ideal gas at constant temperature?   JEE Main Online Paper (Held On 10 April 2016)
  A)
             
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer19) A hemispherical glass body of radius 10cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  20 cm below flat surface
  done clear
  B)
  30 cm below flat surface                
  done clear
  C)
  16 cm below flat surface                
  done clear
  D)
  14 cm below flat surface
  done clear
  View Answer play_arrow

• question_answer20) In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rest son top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer longer stays in contact with the piston, is closed to :   JEE Main Online Paper (Held On 10 April 2016)
  A)
  0.7 Hz                      
  done clear
  B)
  1.2 Hz
  done clear
  C)
  1.9 Hz
  done clear
  D)
  0.1 Hz
  done clear
  View Answer play_arrow

• question_answer21) Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30cm. The wavelength of light 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year \[=9.46\times {{10}^{15}}\]m) of the order of:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[{{10}^{8}}km\]                 
  done clear
  B)
  \[{{10}^{6}}km\]
  done clear
  C)
  \[{{10}^{11}}km\]                               
  done clear
  D)
  \[{{10}^{10}}km\]
  done clear
  View Answer play_arrow

• question_answer22) A conducting metal circular -wire loop of radius r is placed perpendicular to a magnetic field which varies with time as \[B={{B}_{0e}}^{-t/\tau }\], where B0 and \[\tau \]are constants, at t = 0 . If the resistance of the loop is R then the heat generated in the loop after a long time \[(t-\infty )\] is:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}R}{\tau }\]                     
  done clear
  B)
  \[\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}}{2\tau R}\]
  done clear
  C)
  \[\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}}{\tau R}\]                     
  done clear
  D)
  \[\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}}{2\tau R}\]
  done clear
  View Answer play_arrow

• question_answer23) A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by \[{{n}^{2}}R\,{{t}^{2}}\]where n is a constant. The power delivered to the particle by the force acting on it, is:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[M\,\,n\,{{R}^{2}}\,{{t}^{2}}\]                    
  done clear
  B)
  \[\frac{1}{2}M{{n}^{2}}{{R}^{2}}{{t}^{2}}\]
  done clear
  C)
  \[M\,{{n}^{2}}{{R}^{2}}t\]                              
  done clear
  D)
  \[M\,n\,{{R}^{2}}\,t\]
  done clear
  View Answer play_arrow

• question_answer24) The ratio (R) of output resistance \[{{r}_{0}}\], and the input resistance \[{{r}_{1}}\]in measurements of input and out put characteristics of a transistor is typically in the range:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[R\sim 0.1-0.01\]              
  done clear
  B)
  \[R\sim 0.1-1.0\]
  done clear
  C)
  \[R\sim {{10}^{2}}-{{10}^{^{3}}}\]               
  done clear
  D)
  \[R\sim 1-{{10}^{{}}}\]
  done clear
  View Answer play_arrow

• question_answer25) A modulated signal \[{{C}_{m}}\,\,(t)\]has the form \[{{C}_{m}}\,\,(t)=30\,\sin \,300\pi t+10\,(\cos \,200\pi t-\cos 400\pi t)\].The carrier frequency fc, the modulating frequency (message frequency) \[{{f}_{\omega }}\], and the modulation index \[\mu \]are respectively given by :   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[{{f}_{c}}=200\,Hz\,;\,{{f}_{\omega }}=30Hz\,;\,\mu =\frac{1}{2}\]                
  done clear
  B)
  \[{{f}_{c}}=150\,Hz\,;\,{{f}_{\omega }}=50Hz\,;\,\mu =\frac{2}{3}\]
  done clear
  C)
  \[{{f}_{c}}=200\,Hz\,;\,{{f}_{\omega }}=50Hz\,;\,\mu =\frac{1}{2}\]                
  done clear
  D)
  \[{{f}_{c}}=150\,Hz\,;\,{{f}_{\omega }}=30Hz\,;\,\mu =\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer26) The resistance of an electrical toaster has a temperature dependence given by \[R\,\,(T)={{R}_{0}}[1+\alpha (T-{{T}_{0}}]\]in its range of operation. At \[{{T}_{0}}=300\,K,\,R=100\Omega \]. And at\[T=500\,K,\,R=120\Omega \]. The toaster is connected to a voltage source at 200 V and its temperature is raised at a constant rate form300 to 500 K in 30s. The total work done in raising the temperature is:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[400\,In\frac{1.5}{1.3}J\]                               
  done clear
  B)
   300 J
  done clear
  C)
  \[200\,In\frac{2}{3}J\]                      
  done clear
  D)
  \[400\,In\frac{5}{6}J\]
  done clear
  View Answer play_arrow

• question_answer27) Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed 'v' in a uniform magnetic field B going into the plane of the paper (see figure) . If charge densities \[{{\sigma }^{1}}\]and \[{{\sigma }^{2}}\] are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)   JEE Main Online Paper (Held On 10 April 2016)
  A)
               \[{{\sigma }_{1}}=\frac{-{{\varepsilon }_{0}}vB}{2},\,{{\sigma }_{2}}=\frac{-2{{\varepsilon }_{0}}vB}{2}\]
  done clear
  B)
               \[{{\sigma }_{1}}={{\sigma }_{2}}={{\varepsilon }_{0}}vB\]              
  done clear
  C)
  \[{{\sigma }_{1}}=\frac{{{\varepsilon }_{0}}vB}{2},\,{{\sigma }_{2}}=\frac{-{{\varepsilon }_{0}}vB}{2}\]
  done clear
  D)
               \[{{\sigma }_{1}}={{\varepsilon }_{0}}vB,\,{{\sigma }_{2}}=-{{\varepsilon }_{0}}vB\]
  done clear
  View Answer play_arrow

• question_answer28) Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is :
  A)
  12000 J                                    
  done clear
  B)
  12000 J                
  done clear
  C)
  4500 J                      
  done clear
  D)
  9300 J
  done clear
  View Answer play_arrow

• question_answer29) A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beat per second. If the velocity of sound in air is340 m/s, the frequency of horn of the toy car is close to:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  340 Hz                     
  done clear
  B)
  170 Hz
  done clear
  C)
  510 Hz                     
  done clear
  D)
  680 Hz
  done clear
  View Answer play_arrow

• question_answer30) Within a spherical charge distribution of charge density\[\rho (r)\], N equipotential surfaces of potential\[{{V}_{0}},\,{{V}_{0}}+\Delta V,{{V}_{0}}+2\Delta v\], ???..\[{{V}_{0}}+N\Delta V(\Delta V<0)\]are drawn and have increasing radii \[{{r}_{0}},{{r}_{1}}{{r}_{2}},.......{{r}_{N}}\],respectively. If the difference in the radii of the surface is constant for all values of \[{{V}_{0}}\] and \[\Delta V\] then:   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[\rho (r)\alpha r\]                                            
  done clear
  B)
  \[\rho (r)\alpha \frac{1}{{{r}^{2}}}\]                
  done clear
  C)
  \[\rho (r)\alpha \frac{1}{r}\]                          
  done clear
  D)
  \[\rho (r)\]= constant
  done clear
  View Answer play_arrow