Solved papers for JEE Main & Advanced JEE Main Paper (Held On 11 April 2015)

done JEE Main Paper (Held On 11 April 2015) Total Questions - 30

• question_answer1) If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum \[{{\mu }_{0}}\]can be expressed in units of: JEE Main Online Paper (Held On 11 April 2015)
  A)
  \[\left( \frac{hc}{m{{e}^{2}}} \right)\]
  done clear
  B)
  \[\left( \frac{h}{m{{e}^{2}}} \right)\]
  done clear
  C)
  \[\left( \frac{h}{c{{e}^{2}}} \right)\]
  done clear
  D)
  \[\left( \frac{m{{c}^{2}}}{h{{e}^{2}}} \right)\]
  done clear
  View Answer play_arrow

• question_answer2) A vector \[\vec{A}\] is rotated by a small angle\[\Delta \theta \]radians \[(\Delta \theta <<1)\] to get a new vector \[\vec{B}.\] In that case\[|\vec{B}-\vec{A}|\]is: [JEE Main Online Paper (Held On 11 April 2015)]          
  A)
   0
  done clear
  B)
  \[|\vec{A}|\left( 1-\frac{{{\Delta }_{\theta }}2}{2} \right)\]
  done clear
  C)
  \[|\vec{A}|\Delta \theta \]
  done clear
  D)
  \[|\vec{B}|\Delta \theta -|\vec{A}|\]
  done clear
  View Answer play_arrow

• question_answer3) A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length \[L(L>>r)\] and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed v, the average force experienced by each support after a long time is (assume all collisions are elastic) : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{m{{\upsilon }^{2}}}{L-nr}\]
  done clear
  B)
  \[\frac{m{{\upsilon }^{2}}}{L-2nr}\]
  done clear
  C)
  \[\frac{m{{\upsilon }^{2}}}{2(L-nr)}\]
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer4) A particle is moving in a circle of radius r under the action of a force \[F=\alpha {{r}^{2}}\]which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy=0 for r=0): [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\alpha {{r}^{3}}\]
  done clear
  B)
  \[\frac{1}{2}\alpha {{r}^{3}}\]
  done clear
  C)
  \[\frac{4}{3}\alpha {{r}^{3}}\]
  done clear
  D)
  \[\frac{5}{6}\alpha {{r}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer5) A uniform thin rod AB of length L has linear mass density \[\mu (x)=a+\frac{bx}{L},\]where x is measured from A. If the CM of the rod lies at a distance of \[\left( \frac{7}{12}L \right)\]from A, then a and b are related as : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   a = b
  done clear
  B)
   a = 2b
  done clear
  C)
   2a = b
  done clear
  D)
   3a = 2b
  done clear
  View Answer play_arrow

• question_answer6) A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of radius 0.6 m. The height of the table from the ground is 0.8 m. If the angular speed of the particle is 12 rad \[{{\text{s}}^{\text{-1}}}\text{,}\]the magnitude of its angular momentum about a point on the ground right under the centre of the circle is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\text{8}\text{.64}\,\text{kg}\,{{\text{m}}^{\text{2}}}{{\text{s}}^{\text{-1}}}\]
  done clear
  B)
  \[\text{11}\text{.52}\,\text{kg}\,{{\text{m}}^{\text{2}}}{{\text{s}}^{\text{-1}}}\]
  done clear
  C)
  \[\text{14}\text{.4}\,\text{kg}\,{{\text{m}}^{\text{2}}}{{\text{s}}^{\text{-1}}}\]
  done clear
  D)
  \[\text{20}\text{.16}\,\text{kg}\,{{\text{m}}^{\text{2}}}{{\text{s}}^{\text{-1}}}\]
  done clear
  View Answer play_arrow

• question_answer7) Which of the following most closely depicts the correct variation of the gravitation potential V(r) due to a large planet of radius R and uniform mass density? (figures are not drawn to scale) [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer8) A cylindrical block of wood (density \[=650\,kg\,{{m}^{-3}}\]), of base area \[30\text{ }c{{m}^{2}}\]and height 54 cm, floats in a liquid of density \[900\text{ }kg{{m}^{-}}^{3}.\]The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   65 cm
  done clear
  B)
   52 cm
  done clear
  C)
   39 cm
  done clear
  D)
   26 cm
  done clear
  View Answer play_arrow

• question_answer9) A beaker contains a fluid of density\[\rho \,kg/{{m}^{3}},\] specific heat \[S\text{ }J/kg{}^\circ C\]and viscosity t| . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area \[(\overset{\bullet }{\mathop{Q}}\,/A)\]by convection when beaker is put on a hot plate, a student proposes that it should depend on \[\eta ,\left( \frac{S\Delta \theta }{h} \right)\]and\[\left( \frac{1}{\rho g} \right)\]when \[\Delta \theta \] (in \[{}^\circ C\] ) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for \[(\overset{\bullet }{\mathop{Q}}\,/A)\]is: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\eta \frac{S\Delta \theta }{h}\]
  done clear
  B)
  \[\eta \left( \frac{S\Delta \theta }{h} \right)\left( \frac{1}{\rho g} \right)\]
  done clear
  C)
  \[\frac{S\Delta \theta }{\eta h}\]
  done clear
  D)
  \[\left( \frac{S\Delta \theta }{\eta h} \right)\left( \frac{1}{\rho g} \right)\]
  done clear
  View Answer play_arrow

• question_answer10) An experiment takes 10 minutes to raise the temperature of water in a container from \[0{}^\circ C\] to \[100{}^\circ C\] and another 55 minutes to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of water to be \[1\text{ }cal/g\text{ }{}^\circ C\], the heat of vapourization according to this experiment will come out to be: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   530 cal/g
  done clear
  B)
   540 cal/g
  done clear
  C)
   550 cal/g
  done clear
  D)
   560 cal/g
  done clear
  View Answer play_arrow

• question_answer11) Using equipartition of energy, the specific heat \[(in\text{ }J\text{ }k{{g}^{-1}}{{K}^{-}}^{1})\] of aluminium at room temperature can be estimated to be (atomic weight of aluminium = 27) [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   25
  done clear
  B)
   410
  done clear
  C)
   925
  done clear
  D)
   1850
  done clear
  View Answer play_arrow

• question_answer12) A pendulum with time period of 1s is losing energy due to damping. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in\[{{s}^{-1}}\]) is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{1}{30}\ln 3\]
  done clear
  B)
  \[\frac{1}{15}\ln 3\]
  done clear
  C)
   2
  done clear
  D)
  \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer13) A source of sound emits sound waves at frequency \[{{f}_{0}}.\]It is moving towards an observer with fixed speed \[{{\upsilon }_{s}}({{\upsilon }_{s}}<\upsilon ,\] where \[\upsilon \] is the speed of sound in air). If the observer were to move towards the source with speed \[{{\upsilon }_{0}},\] one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as \[{{\upsilon }_{0}}\]is changed. The variation of f with \[{{\upsilon }_{0}}\]is given correctly by: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   graph A with slope \[=\frac{{{f}_{0}}}{(\upsilon -{{\upsilon }_{s}})}\]
  done clear
  B)
     graph A with slope\[=\frac{{{f}_{0}}}{(\upsilon +{{\upsilon }_{s}})}\]
  done clear
  C)
     graph B with slope \[=\frac{{{f}_{0}}}{(\upsilon -{{\upsilon }_{s}})}\]
  done clear
  D)
     graph B with slope\[=\frac{{{f}_{0}}}{(\upsilon +{{\upsilon }_{s}})}\]
  done clear
  View Answer play_arrow

• question_answer14) A wire, of length L(=20 cm), is bent into a semi-circular arc. If the two equal halves, of the arc, were each to be uniformly charged with charges \[\pm Q.[|Q|={{10}^{3}}{{\varepsilon }_{0}}\]Coulomb where \[{{\varepsilon }_{0}}\]is the permittivity (in SI units) of free space] the net electric field at the centre 0 of the semi-circular arc would be : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[(50\times {{10}^{3}}N/C)\hat{J}\]
  done clear
  B)
  \[(25\times {{10}^{3}}N/C)\hat{i}\]
  done clear
  C)
  \[(25\times {{10}^{3}}N/C)\hat{j}\]
  done clear
  D)
  \[(50\times {{10}^{3}}N/C)\hat{i}\]
  done clear
  View Answer play_arrow

• question_answer15) An electric field \[\overset{\to }{\mathop{E}}\,=\left( 25\,\hat{i}+30\hat{j} \right)N{{C}^{-1}}\] exists in a region of space. If the potential at the origin is taken to be zero then the potential at x = 2 m, y = 2 m is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   -130J
  done clear
  B)
   -12.0J
  done clear
  C)
   -140J
  done clear
  D)
   -110J
  done clear
  View Answer play_arrow

• question_answer16) In figure is shown a system of four capacitors connected across a 10 V battery. Charge that will flow from switch S when it is closed is: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[5\mu C\] from b to a
  done clear
  B)
  \[20\mu C\] from a to b
  done clear
  C)
  \[5\mu C\] from a to b
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer17) In the electric network shown, when no current flows through the \[4\Omega \]resistor in the arm EB, the potential difference between the points A and D will be: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   3V
  done clear
  B)
   4V
  done clear
  C)
   5V
  done clear
  D)
   6V
  done clear
  View Answer play_arrow

• question_answer18) The value of the resistor, \[{{R}_{S}},\]needed in the dc voltage regulator circuit shown here, equals : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[({{V}_{i}}-{{V}_{L}})/n\,{{I}_{L}}\]
  done clear
  B)
  \[({{V}_{i}}+{{V}_{L}})/n\,{{I}_{L}}\]
  done clear
  C)
  \[({{V}_{i}}-{{V}_{L}})/(n+1)\,{{I}_{L}}\]
  done clear
  D)
  \[({{V}_{i}}+{{V}_{L}})/(n+1)\,{{I}_{L}}\]
  done clear
  View Answer play_arrow

• question_answer19) Two long straight parallel wires, carrying (adjustable) currents \[\,{{I}_{1}}\]and \[\,{{I}_{2}},\] are kept at a distance d apart. If the force 'F' between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of 'F', on the product \[\,{{I}_{1}}\,{{I}_{2}},\]would be : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer20) A wire carrying current I is tied between points P and Q and is in the shape of a circular arch of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, shown by xxx) in the vicinity of the wire. If the wire subtends an angle \[2{{\theta }_{0}}\] at the centre of the circle (of which it forms an arch) then the tension in the wire is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   \[IBR\]
  done clear
  B)
  \[\frac{IBR}{\sin {{\theta }_{0}}}\]
  done clear
  C)
  \[\frac{IBR}{2\sin {{\theta }_{0}}}\]
  done clear
  D)
  \[\frac{IBR{{\theta }_{0}}}{\sin {{\theta }_{0}}}\]
  done clear
  View Answer play_arrow

• question_answer21) A short bar magnet is placed in the magnetic meridian of the earth with north pole pointing north. Neutral points are found at a distance of 30 cm from the magnet on the East - West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in \[A{{m}^{2}}\]is close to : (Given \[\frac{{{\mu }_{0}}}{4\pi }={{10}^{-7}}\] in SI units and \[{{B}_{H}}=\]Horizontal component of earth's magnetic field \[=3.6\times {{10}^{-}}^{5}\] Tesla.) [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   9.7
  done clear
  B)
   4.9
  done clear
  C)
   19.4
  done clear
  D)
   14.6
  done clear
  View Answer play_arrow

• question_answer22) For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C', when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C', must have been connected in : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   series with C and has a magnitude\[\frac{1-{{\omega }^{2}}LC}{{{\omega }^{2}}L}.\]
  done clear
  B)
   series with C and has a magnitude\[\frac{C}{({{\omega }^{2}}LC-1)}.\]
  done clear
  C)
   parallel with C and has a magnitude\[\frac{C}{({{\omega }^{2}}LC-1)}.\]
  done clear
  D)
    parallel with C and has a magnitude\[\frac{1-{{\omega }^{2}}LC}{{{\omega }^{2}}L}.\]
  done clear
  View Answer play_arrow

• question_answer23) For plane electromagnetic waves propagating in the z direction, which one of the following combination gives the correct possible direction for \[\overset{\to }{\mathop{E}}\,\]and \[\overset{\to }{\mathop{B}}\,\]field respectively? [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\left( \hat{i}+2\hat{j} \right)\]and\[\left( 2\hat{i}-\hat{j} \right)\]
  done clear
  B)
  \[\left( -2\hat{i}-3\hat{j} \right)\]and\[\left( 3\hat{i}-2\hat{j} \right)\]
  done clear
  C)
  \[\left( 2\hat{i}+3\hat{j} \right)\]and\[\left( \hat{i}+2\hat{j} \right)\]
  done clear
  D)
  \[\left( 3\hat{i}+4\hat{j} \right)\]and\[\left( 4\hat{i}-3\hat{j} \right)\]
  done clear
  View Answer play_arrow

• question_answer24) A thin convex lens of focal length T is put on a plane mirror as shown in the figure. When an object is kept at a distance 'a' from the lens - mirror combination, its image is formed at a distance\[\frac{a}{3}\]in front of the combination. The value of 'a' is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   f
  done clear
  B)
   2f
  done clear
  C)
   3f
  done clear
  D)
   \[\frac{3}{2}f\]
  done clear
  View Answer play_arrow

• question_answer25) In a Young's double slit experiment with light of wavelength\[\lambda \]the separation of slits is d and distance of screen is D such that \[D>>d>>\lambda .\]If the Fringe width is \[\beta ,\] the distance from point of maximum intensity to the point where intensity falls to half of maximum intensity on either side is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{\beta }{2}\]
  done clear
  B)
  \[\frac{\beta }{4}\]
  done clear
  C)
  \[\frac{\beta }{3}\]
  done clear
  D)
  \[\frac{\beta }{6}\]
  done clear
  View Answer play_arrow

• question_answer26) Unpolarized light of intensity in is incident on surface of a block of glass at Brewster's angle. In that case, which one of the following statements is true? [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   transmitted light is partially polarized with intensity \[{{I}_{0}}/2.\]
  done clear
  B)
    transmitted light is completely polarized with intensity less than \[{{I}_{0}}/2.\]
  done clear
  C)
     reflected light is completely polarized with intensity less than \[{{I}_{0}}/2.\]
  done clear
  D)
     reflected light is partially polarized with intensity \[{{I}_{0}}/2.\]
  done clear
  View Answer play_arrow

• question_answer27) The de - Broglie wavelength associated with the electron in the n = 4 level is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   two times the de-Broglie wavelength of the electron in the ground state
  done clear
  B)
    four times the de-Broglie wavelength of the electron in the ground state
  done clear
  C)
     half of the de-Broglie wavelength of the electron in the ground state
  done clear
  D)
     1/4th of the de-Broglie wavelength of the electron in the ground state 
  done clear
  View Answer play_arrow

• question_answer28) Let \[{{N}_{\beta }}\] be the number of \[\beta \] particles emitted by 1 gram of \[N{{a}^{24}}\] radioactive nuclei (half-life = 15 hrs) in 7.5 hours, \[{{N}_{\beta }}\] is close to (Avogadro number \[=6.023\times {{10}^{23}}/g.\]mole) : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[6.2\times {{10}^{21}}\]
  done clear
  B)
  \[7.5\times {{10}^{21}}\]
  done clear
  C)
  \[1.25\times {{10}^{22}}\]
  done clear
  D)
  \[1.75\times {{10}^{22}}\]
  done clear
  View Answer play_arrow

• question_answer29) A 2V battery is connected across AB as shown in the figure. The value of the current supplied by the battery when in one case battery's positive terminal is connected to A and in other case when positive terminal of battery is connected to B will respectively be : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   0.2 A and 0.1 A
  done clear
  B)
   0.4 A and 0.2 A
  done clear
  C)
   0.1 A and 0.2 A
  done clear
  D)
   0.2 A and 0.4 A
  done clear
  View Answer play_arrow

• question_answer30) The AC voltage across a resistance can be measured using a : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   potentiometer
  done clear
  B)
   moving coil galvanometer
  done clear
  C)
   moving magnet galvanometer
  done clear
  D)
   hot wire voltmeter
  done clear
  View Answer play_arrow