Solved papers for JEE Main & Advanced AIEEE Solved Paper-2009

done AIEEE Solved Paper-2009 Total Questions - 30

• question_answer1) Direction: Q. No. 1 The question contains Statement-I and Statement-II of the four Choices given after the statements, choose the one that best describe the two statements. STATEMENT-1 For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connected point P to point Q. STATEMENT-2 The net work done by a conservative force on an object moving along a closed loop is zero.     AIEEE  Solved  Paper-2009  
  A)
  Statement - 1 is True, Statement - 2 is False.
  done clear
  B)
  Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
  done clear
  C)
  Statement-1 is True, Statement-2 is True; Statement-2 is not the correct explanation for Statement-1.
  done clear
  D)
  Statement - 1 is False, Statement - 2 is true.
  done clear
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• question_answer2) There is a plot of binding energy per nucleon\[{{E}_{b}},\]against the nuclear mass M; A, B, C, D, E, F correspond to different nuclei. Consider four reactions: (i) \[A+B\to C+\varepsilon \] (ii) \[C\to A+B+\varepsilon \] (iii) \[D+E\to F+\varepsilon \] (iv) \[F\to D+E+\varepsilon \] Where \[\varepsilon \] is the energy released? In which reaction is e positive?     AIEEE  Solved  Paper-2009
  A)
  (i) and (iv)
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  B)
  (i) and (iii)           
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  C)
  (ii) and (iv)         
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  D)
  (ii) and (iii).
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• question_answer3) A p-n junction (4) shown in the figure can act as a rectifier. An alternating current source (V) is connected in the circuit. The current (I) in the resistor (R) can be shown by:     AIEEE  Solved  Paper-2009
  A)
   
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  B)
  
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  C)
  
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  D)
   
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• question_answer4) The logic circuit shown below has the input waveforms 'A' and 'B' as shown. Pick out the correct output waveform. Output is:     AIEEE  Solved  Paper-2009
  A)
  
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  B)
   
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  C)
   
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  D)
   
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• question_answer5) If\[x,\text{ v}\]and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?     AIEEE  Solved  Paper-2009
  A)
  \[{{a}^{2}}{{T}^{2}}+4{{\pi }^{2}}{{v}^{2}}\]         
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  B)
  \[aT/x\]               
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  C)
         \[aT+2\pi n\]     
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  D)
         \[aT/v.\]
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• question_answer6) In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of\[45{}^\text{o}\]with the x-axis meets the experimental curve at P. The coordinates of P will be     AIEEE  Solved  Paper-2009
  A)
  (2f, 2f)                 
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  B)
  \[\left( \frac{f}{2},\frac{f}{2} \right)\]    
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  C)
         \[(f,\text{ }f)\] 
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  D)
         \[(4f,\text{ }4f).\]
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• question_answer7)   A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is \[\omega \]. Its centre of mass rises to a maximum height of     AIEEE  Solved  Paper-2009
  A)
  \[\frac{1}{3}\frac{{{\ell }^{2}}{{\omega }^{2}}}{g}\]                         
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  B)
  \[\frac{1}{6}\frac{\ell \omega }{g}\]       
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  C)
         \[\frac{1}{2}\frac{{{\ell }^{2}}{{\omega }^{2}}}{g}\]         
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  D)
         \[\frac{1}{6}\frac{{{\ell }^{2}}{{\omega }^{2}}}{g}\]
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• question_answer8) Let\[p(r)=\frac{Q}{\pi {{R}^{4}}}r\]be the charge density distribution for a solid sphere of radius R and total charge Q. For a point 'p' inside the sphere at distance\[{{r}_{1}}\]from the centre of sphere, the magnitude of electric field is     AIEEE  Solved  Paper-2009
  A)
  0                                             
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  B)
  \[\frac{Q}{4\pi {{\varepsilon }_{0}}r_{1}^{2}}\]  
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  C)
         \[\frac{Qr_{1}^{2}}{4\pi {{\varepsilon }_{0}}{{R}^{4}}}\]
  done clear
  D)
         \[\frac{Qr_{1}^{2}}{3\pi {{\varepsilon }_{0}}{{R}^{4}}}\]
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• question_answer9)   The transition from the state\[n=4\]to\[n=3\]in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:     AIEEE  Solved  Paper-2009
  A)
  \[2\to 1\]                            
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  B)
  \[3\to 2\]            
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  C)
         \[4\to 2\]            
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  D)
          \[5\to 4\]
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• question_answer10) One kg of a diatomic gas is at a pressure of \[8\times {{10}^{4}}N/{{m}^{2}}.\] The density of the gas is\[4\text{ }kg/{{m}^{3}}\]. What is the energy of the gas due to its thermal motion?     AIEEE  Solved  Paper-2009
  A)
  \[3\times {{10}^{4}}J\]                  
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  B)
  \[5\times {{10}^{4}}J\]  
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  C)
         \[6\times {{10}^{4}}J\]  
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  D)
         \[7\times {{10}^{4}}J.\]
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• question_answer11) STATEMENT - 1 The temperature dependence of resistance is usually given as\[R={{R}_{0}}(1+\alpha \,\,\Delta t)\]. The resistance of a wire changes from\[100\,\Omega \]to \[150\,\Omega \] when its temperature is increased from\[27{}^\text{o}C\]to\[227{}^\text{o}C.\] This implies that\[\alpha =2.5\]\[\times {{10}^{3}}/{}^\text{o}C.\] STATEMENT - 2 \[R={{R}_{0}}(1+\alpha \text{ }\Delta t)\]is valid only when the change in the temperature DT is small and\[\Delta R=(R{{R}_{0}})<<{{R}_{0}}.\]     AIEEE  Solved  Paper-2009
  A)
  Statement - 1 is True, Statement - 2 is False.
  done clear
  B)
  Statement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1.
  done clear
  C)
  Statement - 1 is True, Statement - 2 is True; Statement - 2 is not the correct explanation for Statement - 1.
  done clear
  D)
  Statement - 1 is False, Statement - 2 is True.
  done clear
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• question_answer12) Directions Q. Nos. 12 are based on the following paragraph. A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius =b) and DA (radius = a) of the loop are joined by the straight wires AB and CD. A steady current  is flowing in the loop. Angle made by A B and CD at the origin O is 30°. Another straight thin wire with steady current  flowing out of the plane of the paper is kept at the origin.   The magnitude of the magnetic field (B) due to the loop ABCD at the origin (O) is   AIEEE  Solved  Paper-2009  
  A)
  zero
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  B)
  \[\frac{{{\mu }_{0}}I(b-a)}{24ab}\]
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  C)
  \[\frac{{{\mu }_{0}}I}{4\pi }\left[ \frac{b-a}{ab} \right]\]
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  D)
  \[\frac{{{\mu }_{0}}I}{4\pi }\left[ 2(b\_a)+\frac{\pi }{3}(a+b) \right]\]
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• question_answer13) Directions Q. Nos. 13 are based on the following paragraph. A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius =b) and DA (radius = a) of the loop are joined by the straight wires AB and CD. A steady current \[I\] is flowing in the loop. Angle made by A B and CD at the origin O is 30°. Another straight thin wire with steady current \[{{I}_{2}}\] flowing out of the plane of the paper is kept at the origin. Due to the presence of the current \[{{I}_{1}}\] at the origin:     AIEEE  Solved  Paper-2009
  A)
  the forces on AB and DC are zero
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  B)
  the forces on AD and BC are zero
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  C)
  the magnitude of the net force on the loop is given by\[\frac{{{I}_{1}}I}{4\pi }{{\mu }_{0}}\left[ 2(b-a)+\frac{\pi }{3}(a+b) \right]\]
  done clear
  D)
  the magnitude of the net force on the loop is given by\[\frac{{{\mu }_{0}}I{{I}_{1}}}{24ab}(b-a)\]
  done clear
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• question_answer14) A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is:     AIEEE  Solved  Paper-2009
  A)
  393.4 nm                             
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  B)
  885.0 nm             
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  C)
                         442.5 nm                             
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  D)
  776.8 nm.
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• question_answer15) Two points P and Q are maintained at the potentials of 10V and -4V, respectively. The work done in moving 100 electrons from P to Q is     AIEEE  Solved  Paper-2009
  A)
  \[9.60\times {{10}^{17}}J\]         
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  B)
  \[9.60\times {{10}^{17}}J\]
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  C)
         \[2.24\times {{10}^{16}}J\]
  done clear
  D)
         \[2.24\times {{10}^{16}}J.\]
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• question_answer16) The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is:(\[hc=\] \[1240\text{ }eV.nm\])     AIEEE  Solved  Paper-2009
  A)
  \[3.09\text{ }eV\]                           
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  B)
  \[1.41\text{ }eV\]           
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  C)
  \[1.51\text{ }eV\]           
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  D)
         \[1.68\text{ }eV.\]
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• question_answer17) A particle has an initial velocity of\[3\hat{i}+4\hat{j}\]and an acceleration of\[0.4\hat{i}+0.3\hat{j}\]. It speed after 10 s is:     AIEEE  Solved  Paper-2009
  A)
  10 units                               
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  B)
  \[7\sqrt{2}\] units                           
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  C)
  7 units  
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  D)
         8.5 units.
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• question_answer18) A motor cycle starts from rest and accelerates along a straight path at\[2m/{{s}^{2}}.\] At the straight point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest? (Speed of wound\[=330\text{ }m{{s}^{1}}\])     AIEEE  Solved  Paper-2009
  A)
  49 m                     
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  B)
  (2) 98 m               
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  C)
         147 m   
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  D)
         196 m.
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• question_answer19) Consider a rubber ball freely falling from a height\[h=4.9\text{ }m\]onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be:     AIEEE  Solved  Paper-2009
  A)
   
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  B)
   
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  C)
   
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  D)
  
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• question_answer20) A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other tow corners. If the net electrical force on Q is zero, then Q/q equals:     AIEEE  Solved  Paper-2009
  A)
  \[-2\sqrt{2}\]
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  B)
         -1                           
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  C)
         1                             
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  D)
         \[-\frac{1}{\sqrt{2}}\]
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• question_answer21) A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature \[\theta \] along the length\[x\]of the bar from its hot end is best described by which of the following figures?     AIEEE  Solved  Paper-2009
  A)
  
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  B)
  
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  C)
  
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  D)
  
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• question_answer22) A transparent solid cylindrical rod has a refractive index of\[\frac{2}{\sqrt{3}}\].It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle \[\theta \] for which the light ray grazes along the wall of the rod is:   AIEEE  Solved  Paper-2009
  A)
  \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
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  B)
         \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]  
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  C)
         \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]  
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  D)
         \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]
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• question_answer23) Three sound waves of equal amplitudes have frequencies\[(v1),v,(v+1).\]They superpose to give beats. The number of beats produced per second will be     AIEEE  Solved  Paper-2009
  A)
  4
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  B)
                                        3                             
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  C)
         2                             
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  D)
         1.
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• question_answer24) The height at which the acceleration due to gravity becomes\[\frac{g}{9}\](where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is:     AIEEE  Solved  Paper-2009
  A)
  2R                                          
  done clear
  B)
  \[\frac{R}{\sqrt{2}}\]                     
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  C)
         R/2                        
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  D)
         \[\sqrt{2}R\]
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• question_answer25) Two wires are made of the same material and have the same volume. However wire 1 has cross-section area A and wire 2 has cross- sectional area 3A. If the length of wire 1 increases by\[\Delta x\]on applying force F, how much force is needed to stretch wire 2 by the same amount?     AIEEE  Solved  Paper-2009
  A)
  F
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  B)
                                         4F                          
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  C)
         6F                          
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  D)
         9F.
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• question_answer26) In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree \[(=0.5{}^\text{o}),\]then the least count of the instrument is:
  A)
  one minute       
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  B)
         half minute        
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  C)
         one degree       
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  D)
         half degree.
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• question_answer27)  An inductor of inductance\[L=400\text{ }mH\]and resistors of resistances\[{{R}_{1}}=2\text{ }\Omega \]and \[{{R}_{2}}=2\Omega \]are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is:     AIEEE  Solved  Paper-2009
  A)
  \[6\text{ }{{e}^{5t}}V\]
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  B)
  \[\frac{12}{t}{{e}^{-3t}}V\]         
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  C)
  \[6\left( 1-{{e}^{\frac{-t}{0.2}}} \right)V\]
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  D)
  \[12{{e}^{-5t}}V\]
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• question_answer28) Directions Q. Nos. 28 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the p-T diagram. Assuming the gas to be ideal the work done on the gas in taking it from A to B is:     AIEEE  Solved  Paper-2009
  A)
  200 R
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  B)
  300 R    
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  C)
  400 R    
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  D)
  500 R
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• question_answer29) Directions Q. Nos. 29 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the p-T diagram. The work done on the gas is taking it from D to A is   AIEEE  Solved  Paper-2009
  A)
   -414 R
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  B)
  +414 R
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  C)
  -690 R
  done clear
  D)
  +690 R
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• question_answer30) Directions Q. Nos. 30 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the p-T diagram. The net work done on the gas in the cycle ABCDA is     AIEEE  Solved  Paper-2009
  A)
  zero
  done clear
  B)
  276 R    
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  C)
  1076 R  
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  D)
  1904 R
  done clear
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