Solved papers for JEE Main & Advanced JEE Main Solved Paper-2016

done JEE Main Solved Paper-2016 Total Questions - 30

• question_answer1) A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the \[4\mu F\] and \[9\mu F\]capacitors), at a point 30 m from it , would equal: [JEE Main Solved Paper-2016 ]
  A)
   480 N/C                              
  done clear
  B)
  240 N/C
  done clear
  C)
  360 N/C                               
  done clear
  D)
  420 N/C
  done clear
  View Answer play_arrow

• question_answer2) An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears : [JEE Main Solved Paper-2016 ]
  A)
  20 times nearer                
  done clear
  B)
  10 times taller
  done clear
  C)
  10 times nearer               
  done clear
  D)
  20 times taller
  done clear
  View Answer play_arrow

• question_answer3) Hysteresis loops for two magnetic materials A and B are given below : These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use; [JEE Main Solved Paper-2016 ]
  A)
  B for electromagnets and transformers.
  done clear
  B)
  A for electric generators and transformers.
  done clear
  C)
  A for electromagnets and B for electric transformers.
  done clear
  D)
  A for transformers and B for electric generators.
  done clear
  View Answer play_arrow

• question_answer4) Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes , the ratio of decayed numbers of A and B nuclei will be :- [JEE Main Solved Paper-2016 ]
  A)
  5 : 4                                       
  done clear
  B)
  1 : 16
  done clear
  C)
   4 : 1                                      
  done clear
  D)
  1 : 4
  done clear
  View Answer play_arrow

• question_answer5) A particle of mass m is moving along the side of a square of side 'a', with a uniform speed u in the x-y plane as shown in the figure : Which of the following statement is false for the angular momentum \[\vec{L}\] about the origin ? [JEE Main Solved Paper-2016 ]
  A)
  \[\vec{L}=\frac{m\upsilon }{\sqrt{2}}R\hat{k}\]when the particle is moving from D to A
  done clear
  B)
  \[\vec{L}=-\frac{m\upsilon }{\sqrt{2}}R\hat{k}\] when the particle is moving from  to B
  done clear
  C)
   \[\vec{L}=m\upsilon \left[ \frac{R}{\sqrt{2}}-a \right]\hat{k}\]when the particle is moving from C to D
  done clear
  D)
  \[\vec{L}=m\upsilon \left[ \frac{R}{\sqrt{2}}+a \right]\hat{k}\]when the particle is moving from B to C
  done clear
  View Answer play_arrow

• question_answer6) Choose the correct statement : [JEE Main Solved Paper-2016 ]
  A)
  In frequency modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the frequency of the audio signal.
  done clear
  B)
  In amplitude modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal.
  done clear
  C)
  In amplitude modulation the frequency of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal.
  done clear
  D)
  In frequency modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal.
  done clear
  View Answer play_arrow

• question_answer7) In an experiment for determination of refractive index of glass of a prism by \[i-\delta ,\] plot, it was found that a ray incident at angle \[35{}^\circ \], suffers a deviation of \[40{}^\circ \] and that it emerges at angle \[79{}^\circ \]. In that case which of the following is closest to the maximum possible value of the refractive index? [JEE Main Solved Paper-2016 ]
  A)
  1.8                                         
  done clear
  B)
  1.5
  done clear
  C)
  1.6                                         
  done clear
  D)
  1.7
  done clear
  View Answer play_arrow

• question_answer8) 'n' moles of an ideal gas undergoes a process \[A\to B\]as shown in the figure. The maximum temperature of the gas during the process will be : [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{9{{P}_{0}}{{V}_{0}}}{nR}\]                            
  done clear
  B)
  \[\frac{9{{P}_{0}}{{V}_{0}}}{4nR}\]
  done clear
  C)
  \[\frac{3{{P}_{0}}{{V}_{0}}}{2nR}\]                          
  done clear
  D)
  \[\frac{9{{P}_{0}}{{V}_{0}}}{2nR}\]
  done clear
  View Answer play_arrow

• question_answer9) Two identical wires A and B, each of length 'l', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side 'a'. If \[{{B}_{A}}\]and \[{{B}_{B}}\]are the values of magnetic field at the centres of the circle and square respectively, then the ratio \[\frac{{{B}_{A}}}{{{B}_{B}}}\]is: [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{{{\pi }^{2}}}{8\sqrt{2}}\]                                
  done clear
  B)
  \[\frac{{{\pi }^{2}}}{8}\]
  done clear
  C)
  \[\frac{{{\pi }^{2}}}{16\sqrt{2}}\]                             
  done clear
  D)
  \[\frac{{{\pi }^{2}}}{16}\]
  done clear
  View Answer play_arrow

• question_answer10) A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement , it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line ? [JEE Main Solved Paper-2016 ]
  A)
  0.50 mm                              
  done clear
  B)
  0.75 mm
  done clear
  C)
  0.80 mm                              
  done clear
  D)
   0.70 mm
  done clear
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• question_answer11) For a common emitter configuration, if \[\alpha \]and \[\beta \]have their usual meanings, the incorrect relationship between\[\alpha \]and\[\beta \]is [JEE Main Solved Paper-2016 ]
  A)
  \[\alpha =\frac{{{\beta }^{2}}}{1+{{\beta }^{2}}}\]                           
  done clear
  B)
  \[\frac{1}{\alpha }=\frac{1}{\beta }+1\]
  done clear
  C)
  \[\alpha =\frac{\beta }{1-\beta }\]                          
  done clear
  D)
  \[\alpha =\frac{\beta }{1+\beta }\]
  done clear
  View Answer play_arrow

• question_answer12) The box of a pin hole camera, of length L, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength\[\lambda \]the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say \[{{b}_{\min }}\]) when :- [JEE Main Solved Paper-2016 ]
  A)
  \[a=\frac{{{\lambda }^{2}}}{L}\]and\[{{b}_{\min }}=\sqrt{4\lambda L}\]
  done clear
  B)
  \[a=\frac{{{\lambda }^{2}}}{L}\]and\[{{b}_{\min }}=\left( \frac{2{{\lambda }^{2}}}{L} \right)\]
  done clear
  C)
  \[a=\sqrt{\lambda L}\]and\[{{b}_{\min }}=\left( \frac{2{{\lambda }^{2}}}{L} \right)\]
  done clear
  D)
  \[a=\sqrt{\lambda L}\]and\[{{b}_{\min }}=\sqrt{4\lambda L}\]
  done clear
  View Answer play_arrow

• question_answer13) A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies \[\text{3}.\text{8}\times \text{1}0\text{7J}\]of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 \[m{{s}^{}}^{2}\]:- [JEE Main Solved Paper-2016 ]
  A)
  \[\text{12}.\text{89}\times \text{1}{{0}^{\text{3}}}\text{kg}\]  
  done clear
  B)
  \[\text{2}.\text{45}\times \text{1}{{0}^{\text{3}}}\text{kg}\]
  done clear
  C)
  \[\text{6}.\text{45}\times \text{1}{{0}^{\text{3}}}\text{kg}\]    
  done clear
  D)
  \[\text{9}.\text{89}\times \text{1}{{0}^{\text{3}}}\text{kg}\]
  done clear
  View Answer play_arrow

• question_answer14) Arrange the following electromagnetic radiations per quantum in the order of increasing energy :- [JEE Main Solved Paper-2016 ]

  A : Blue light

  B : Yellow light

  C : X-ray

  D : Radio wave

  A)
  B, A, D, C                             
  done clear
  B)
  D, B, A, C
  done clear
  C)
  A, B, D, C                             
  done clear
  D)
  C, A, B, D
  done clear
  View Answer play_arrow

• question_answer15) An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by \[\text{P}{{\text{V}}^{\text{n}}}=\]constant, then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively) :- [JEE Main Solved Paper-2016 ]
  A)
  \[n=\frac{C-{{C}_{v}}}{C-{{C}_{p}}}\]                      
  done clear
  B)
  \[n=\frac{{{C}_{p}}}{{{C}_{v}}}\]
  done clear
  C)
  \[n=\frac{C-{{C}_{p}}}{C-{{C}_{v}}}\]                      
  done clear
  D)
  \[n=\frac{{{C}_{p}}-C}{C-{{C}_{v}}}\]
  done clear
  View Answer play_arrow

• question_answer16) A satellite is reolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R ; h << R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere). [JEE Main Solved Paper-2016 ]
  A)
  \[\sqrt{gR}\left( \sqrt{2}-1 \right)\]        
  done clear
  B)
  \[\sqrt{2gR}\]
  done clear
  C)
  \[\sqrt{gR}\]                     
  done clear
  D)
  \[\sqrt{gR/2}\]
  done clear
  View Answer play_arrow

• question_answer17) A galvanometer having a coil resistance of \[100\Omega \] gives a full scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10A, is :- [JEE Main Solved Paper-2016 ]
  A)
  \[3\Omega \]                                    
  done clear
  B)
  \[0.01\Omega \]
  done clear
  C)
  \[2\Omega \]                                    
  done clear
  D)
  \[0.1\Omega \]
  done clear
  View Answer play_arrow

• question_answer18) Radiation of wavelength \[\lambda ,\]is incident on a photocell. The fastest emitted electron has speed v. If the wavelength of changed to\[\frac{3\lambda }{4},\] the speed of the fastest emitted electron will be :- [JEE Main Solved Paper-2016 ]
  A)
  \[=v{{\left( \frac{3}{5} \right)}^{1/2}}\] 
  done clear
  B)
  \[>v{{\left( \frac{4}{3} \right)}^{1/2}}\]
  done clear
  C)
  \[<v{{\left( \frac{4}{3} \right)}^{1/2}}\]                 
  done clear
  D)
  \[=v{{\left( \frac{4}{3} \right)}^{1/2}}\]
  done clear
  View Answer play_arrow

• question_answer19) If a, b, c, d are inputs to a gate and x is its output, then as per the following time graph, the gate is                   [JEE Main Solved Paper-2016 ]                                                                                                       

  (d)
  (c)
  (b)
  (a)
  (x)

  A)
  NAND                  
  done clear
  B)
  NOT
  done clear
  C)
  AND                      
  done clear
  D)
   OR
  done clear
  View Answer play_arrow

• question_answer20) The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density \[\rho =\frac{A}{r},\]where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is :- [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{2Q}{\pi {{a}^{2}}}\]                                          
  done clear
  B)
  \[\frac{Q}{2\pi {{a}^{2}}}\]
  done clear
  C)
  \[\frac{Q}{2\pi ({{b}^{2}}-{{a}^{2}})}\]                   
  done clear
  D)
  \[\frac{2Q}{\pi ({{a}^{2}}-{{b}^{2}})}\]
  done clear
  View Answer play_arrow

• question_answer21) A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :-
  A)
  \[92\pm 3\text{ }s\]                      
  done clear
  B)
  \[92\pm 2s\]
  done clear
  C)
  \[92\pm 5.0s\]                 
  done clear
  D)
  \[92\pm 1.8\text{ }s\]
  done clear
  View Answer play_arrow

• question_answer22) The temperature dependence of resistances of Cu and un doped Si in the temperature range 300-400K, is best described by :- [JEE Main Solved Paper-2016 ]
  A)
  Linear decrease for Cu, linear decrease for Si.
  done clear
  B)
  Linear increase for Cu, linear increase for Si.
  done clear
  C)
  Linear increase for Cu, exponential increase for Si
  done clear
  D)
  Linear increase for Cu, exponential de crease for Si
  done clear
  View Answer play_arrow

• question_answer23) Identify the semiconductor devices whose characteristics are given below, in the order (a), (b), (c), (d) :-                                                                                                                     [JEE Main Solved Paper-2016 ]
  A)
  Zener diode, Solar cell, Simple diode, Light dependent resistance
  done clear
  B)
  Simple diode, Zener diode, Solar cell, Light dependent resistance
  done clear
  C)
  Zener diode, Simple diode, Light dependent resistance, Solar cell
  done clear
  D)
  Solar cell, Light dependent resistance, Zener diode, Simple diode
  done clear
  View Answer play_arrow

• question_answer24) A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to :- [JEE Main Solved Paper-2016 ]
  A)
  turn left and right alternately.
  done clear
  B)
  turen left.
  done clear
  C)
  turn right.                           
  done clear
  D)
   go straight.
  done clear
  View Answer play_arrow

• question_answer25) A pendulum clock loses 12s a day if the temperature is \[40{}^\circ C\] and gains 4s a day if the temperature is \[20{}^\circ C\]. The temperature at which the clock will show correct time, and the coefficient of linear expansion (a) of the metal of the pendulum shaft are respectively :- [JEE Main Solved Paper-2016 ]
  A)
  \[{{55}^{o}}C;\alpha =1.85\times {{10}^{-2}}{{/}^{o}}C\]
  done clear
  B)
  \[{{25}^{o}}C;\alpha =1.85\times {{10}^{-5}}{{/}^{o}}C\]
  done clear
  C)
  \[{{60}^{o}}C;\alpha =1.85\times {{10}^{-4}}{{/}^{o}}C\]
  done clear
  D)
  \[{{30}^{o}}C;\alpha =1.85\times {{10}^{-3}}{{/}^{o}}C\]
  done clear
  View Answer play_arrow

• question_answer26) A uniform string of length 20m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is :- (take\[\text{g}=\text{1}0\text{m}{{\text{s}}^{\text{2}}}\]) [JEE Main Solved Paper-2016 ]
  A)
  \[\sqrt{2}s\]                                      
  done clear
  B)
  \[2\pi \sqrt{2}s\]
  done clear
  C)
  \[2s\]                                   
  done clear
  D)
  \[2\sqrt{2}s\]
  done clear
  View Answer play_arrow

• question_answer27) A point particle of mass, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals m. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and PR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction m and the distance x(=QR) are, respecitvely close to :- [JEE Main Solved Paper-2016 ]
  A)
  0.29 and 6.5 m  
  done clear
  B)
  0.2 and 6.5 m
  done clear
  C)
  0.2 and 3.5 m    
  done clear
  D)
   0.29 and 3.5 m
  done clear
  View Answer play_arrow

• question_answer28) A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequencty of the air column is now :- [JEE Main Solved Paper-2016 ]
  A)
  f             
  done clear
  B)
  \[\frac{f}{2}\]
  done clear
  C)
  \[\frac{3f}{4}\]                                 
  done clear
  D)
  2f
  done clear
  View Answer play_arrow

• question_answer29) A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance\[\frac{2A}{3}\]from equilibrium position. The new amplitude of the motion is :- [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{7A}{3}\]                
  done clear
  B)
  \[\frac{A}{3}\sqrt{41}\]
  done clear
  C)
   3A                                         
  done clear
  D)
  A 3
  done clear
  View Answer play_arrow

• question_answer30) An arc lamp requires a direct current of 10A at 80V to function. If it is connected to a 220V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :- [JEE Main Solved Paper-2016 ]
  A)
  0.065 H                
  done clear
  B)
  80 H
  done clear
  C)
  0.08 H                   
  done clear
  D)
  0.044 H
  done clear
  View Answer play_arrow