Solved papers for JEE Main & Advanced AIEEE Solved Paper-2007

done AIEEE Solved Paper-2007 Total Questions - 40

• question_answer1) The displacement of an object attached to a spring and executing simple harmonic motion is given by\[2x+3y+z=1\]\[x+3y+2z=2\] metre. The time at which the maximum speed first occurs is       AIEEE  Solved  Paper-2007
  A)
   0.5 s                                     
  done clear
  B)
   0.75 s   
  done clear
  C)
          0.125s                 
  done clear
  D)
          0.25s
  done clear
  View Answer play_arrow

• question_answer2) In an AC circuit, the voltage applied is\[cos\text{ }\alpha \] \[1/\sqrt{3}\]The resulting current in the circuit is\[1/\sqrt{2}\]. The power consumption in the circuit is given by       AIEEE  Solved  Paper-2007  
  A)
  \[P=\frac{{{E}_{0}}{{l}_{0}}}{\sqrt{2}}\]            
  done clear
  B)
          P = zero              
  done clear
  C)
         \[P=\frac{{{E}_{0}}{{l}_{0}}}{2}\]            
  done clear
  D)
          \[P=\sqrt{2}\,{{E}_{0}}{{l}_{0}}\]
  done clear
  View Answer play_arrow

• question_answer3) An electric charge\[{{y}^{2}}={{x}^{2}}-2xy\frac{dy}{dx}\]is placed at the origin (0, 0) of X-Y coordinate system. Two points A and B are situated at\[{{p}^{2}}+{{q}^{2}}=1,\]and (2, 0) respectively. The potential difference between the points A and B will be       AIEEE  Solved  Paper-2007
  A)
   9V                                         
  done clear
  B)
   zero                     
  done clear
  C)
          2V                         
  done clear
  D)
          4.5V
  done clear
  View Answer play_arrow

• question_answer4) A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery, will be       AIEEE  Solved  Paper-2007
  A)
   1
  done clear
  B)
                                          2                            
  done clear
  C)
          \[(p+q)\]                           
  done clear
  D)
          \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer5) An ideal coil of 10 H is connected in series with a resistance of \[\frac{1}{\sqrt{2}}\] and a battery of 5 V. After 2 s, the connection is made, the current flowing (in ampere) in the circuit is       AIEEE  Solved  Paper-2007
  A)
   \[\sqrt{2}\]           
  done clear
  B)
          e                           
  done clear
  C)
          \[{{e}^{-1}}\]          
  done clear
  D)
  \[30{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer6) A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at\[2a/\sqrt{3}\]and\[2a\sqrt{3}\]is       AIEEE  Solved  Paper-2007
  A)
   \[a/\sqrt{3}\]                                   
  done clear
  B)
   4            
  done clear
  C)
          1            
  done clear
  D)
          \[a\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer7) A current\[^{20}{{C}_{0}}{{-}^{20}}{{C}_{1}}{{+}^{20}}{{C}_{2}}{{-}^{20}}{{C}_{3}}+....{{+}^{20}}{{C}_{10}}\]flows along the length of an infinitely long, straight, thin walled pipe. Then,       AIEEE  Solved  Paper-2007
  A)
   The magnetic field is zero only on the axis of the pipe
  done clear
  B)
   The magnetic field is different at different points inside the pipe
  done clear
  C)
   The magnetic field at any point inside the pipe is zero
  done clear
  D)
   The magnetic field at all points inside the pipe is the same, but not zero
  done clear
  View Answer play_arrow

• question_answer8) If\[{{-}^{20}}{{C}_{10}}\]is the mass of an oxygen isotope\[\frac{1}{2}{{\,}^{20}}{{C}_{10}}\]and\[^{20}{{C}_{10}}\]are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is       AIEEE  Solved  Paper-2007
  A)
   \[P(x,\text{ }y)\]  
  done clear
  B)
          \[|~z+4|\le 3,\]
  done clear
  C)
   \[|~z+1|\]          
  done clear
  D)
   \[D=\left| \begin{matrix}    1 & 1 & 1  \\    1 & 1+x & 1  \\    1 & 1 & 1+y  \\ \end{matrix} \right|\]
  done clear
  View Answer play_arrow

• question_answer9) In gamma ray emission from a nucleus       AIEEE  Solved  Paper-2007
  A)
   Both the neutron number and the proton number change
  done clear
  B)
   There is no change in the proton number and the neutron number
  done clear
  C)
   Only the neutron number changes
  done clear
  D)
   Only the proton number changes
  done clear
  View Answer play_arrow

• question_answer10) If in a\[x\ne 0\]junction diode, a square input signal of 10 V is applied as shown Then, the output signal across \[{{R}_{L}}\] will be     AIEEE  Solved  Paper-2007
  A)
   
  done clear
  B)
          
  done clear
  C)
               
  done clear
  D)
          
  done clear
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• question_answer11) Photon of frequency v has a momentum associated with it. If c is the velocity of light, the momentum is       AIEEE  Solved  Paper-2007
  A)
   v/c                        
  done clear
  B)
          \[y\ne 0\]          
  done clear
  C)
          \[x\]    
  done clear
  D)
          \[x\]
  done clear
  View Answer play_arrow

• question_answer12) The velocity of a particle is\[x\]If its position is\[x\]at\[\frac{{{x}^{2}}}{{{\cos }^{2}}\alpha }-\frac{{{y}^{2}}}{{{\sin }^{2}}\alpha }=1,\]then its displacement after unit time\[\frac{\pi }{4}\]is       AIEEE  Solved  Paper-2007
  A)
  \[{{v}_{0}}+2g+3f\]    
  done clear
  B)
          \[{{v}_{0}}+g/2+f/3\]
  done clear
  C)
          \[{{v}_{0}}+g+f\]
  done clear
  D)
   \[{{v}_{0}}+g/2+f\]
  done clear
  View Answer play_arrow

• question_answer13) For the given uniform square lamina ABCD, whose centre is O     AIEEE  Solved  Paper-2007
  A)
   \[\sqrt{2}\,{{l}_{AC}}={{l}_{EF}}\]
  done clear
  B)
   \[{{l}_{AD}}=4{{l}_{EF}}\]
  done clear
  C)
          \[{{l}_{AC}}={{l}_{EF}}\]              
  done clear
  D)
          \[{{l}_{AC}}=\sqrt{2}\,{{l}_{EF}}\]
  done clear
  View Answer play_arrow

• question_answer14) A point mass oscillates along the x-axis according to the law\[{{\log }_{3}}e\].If the acceleration of the particle is written as \[{{\log }_{e}}3\]then       AIEEE  Solved  Paper-2007
  A)
   \[f(x)={{\tan }^{-1}}(\sin x+\cos x)\]
  done clear
  B)
     \[(\pi /4,\pi /2)\]
  done clear
  C)
   \[(-\pi /2,\pi /4)\]
  done clear
  D)
   \[(0,\pi /2)\]
  done clear
  View Answer play_arrow

• question_answer15) Charges are placed on the vertices of a square as shown. Let \[\vec{E}\] be the electric field and V be the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then       AIEEE  Solved  Paper-2007
  A)
   E remains unchanged, V changes
  done clear
  B)
   both E and V change
  done clear
  C)
  E and V remain unchanged
  done clear
  D)
   E changes, V remains unchanged
  done clear
  View Answer play_arrow

• question_answer16) The half-life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially, they have the same number of atoms. Then,       AIEEE  Solved  Paper-2007
  A)
   X will decay faster than Y
  done clear
  B)
   Y will decay faster than X
  done clear
  C)
   Y and X have same decay rate initially
  done clear
  D)
   X and Y decay at same rate always
  done clear
  View Answer play_arrow

• question_answer17) A Carnot engine, having an efficiency of \[\eta =1/10\] as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is       AIEEE  Solved  Paper-2007
  A)
   99 J       
  done clear
  B)
          90 J       
  done clear
  C)
          1 J                         
  done clear
  D)
          100 J
  done clear
  View Answer play_arrow

• question_answer18) Carbon, silicon and germanium have four valence electrons each. At room temperature, which one of the following statements is most appropriate?
  A)
   The number of free conduction electrons is significant in C but small in Si and\[A=\left[ \begin{matrix}    5 & 5\alpha  & \alpha   \\    0 & \alpha  & 5\alpha   \\    0 & 0 & 5  \\ \end{matrix} \right]\]
  done clear
  B)
   The number of free conduction electrons is negligibly small in all the three
  done clear
  C)
   The number of free electrons for conduction is significant in all the three
  done clear
  D)
   The number of free electrons for conduction is significant only in\[|{{A}^{2}}|=25,\]and\[{{5}^{2}}\]but small in C
  done clear
  View Answer play_arrow

• question_answer19) A charged particle with charge g enters a region of constant, uniform and mutually orthogonal fields \[\vec{E}\] and \[\vec{B}\] with a velocity v perpendicular to both \[\vec{E}\] and \[\vec{B}\] and comes out without any change in magnitude or direction of v. Then,       AIEEE  Solved  Paper-2007
  A)
   \[\vec{v}=\vec{E}\times \vec{B}/{{B}^{2}}\]
  done clear
  B)
   \[\vec{v}=\vec{B}\times \vec{E}/{{B}^{2}}\]
  done clear
  C)
   \[\vec{v}=\vec{E}\times \vec{B}/{{E}^{2}}\]    
  done clear
  D)
          \[\vec{v}=\vec{B}\times \vec{E}/{{E}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer20) The potential at a point x (measured in\[{{e}^{-\frac{1}{2}}}\]due to some charges situated on the x-axis is given by\[{{e}^{+\frac{1}{2}}}\]volt. The electric field E at \[x=4\,\mu m\] is given by       AIEEE  Solved  Paper-2007
  A)
   \[{{\tan }^{-1}}\frac{b}{ac}\]and in the -ve\[45{}^\circ \]direction
  done clear
  B)
   \[{{\tan }^{-1}}\frac{bc}{a(c-a)}\]and in the +ve\[{{\tan }^{-1}}\frac{bc}{a}\]direction
  done clear
  C)
   \[{{y}^{2}}=8x\]and in the -ve\[y=x+2\]direction
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x-12y-2\text{ }z+20=0,\]and in the +ve\[a=\hat{i}+\hat{j}+\hat{k},b=\hat{i}-\hat{j}+2\hat{k}\]direction
  done clear
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• question_answer21) Which of the following transitions in hydrogen atoms emit photons of highest frequency?       AIEEE  Solved  Paper-2007
  A)
   n = 2 to n = 6   
  done clear
  B)
          n = 6 to n = 2
  done clear
  C)
                          n = 2 to n = 1    
  done clear
  D)
          n = 1 to n = 2
  done clear
  View Answer play_arrow

• question_answer22) A block of mass m is connected to another block of mass M by a spring (massless) of spring constant k. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and' the spring is unstretehed. Then, a constant force F starts acting on the block of mass M to pull it; Find the force on the block of mass m.     AIEEE  Solved  Paper-2007
  A)
   \[c=x\hat{i}+(x-2)\hat{j}-\hat{k}\]                         
  done clear
  B)
   \[x\]                    
  done clear
  C)
   \[R=(3,3\sqrt{3})\]        
  done clear
  D)
          \[\angle PQR\]
  done clear
  View Answer play_arrow

• question_answer23) Two lenses of power -15D and +5D are in contact with each other. The focal length of the combination is:       AIEEE  Solved  Paper-2007
  A)
   \[\sqrt{3}x+y=0\]           
  done clear
  B)
          \[x+\frac{\sqrt{3}}{2}y=0\]        
  done clear
  C)
          \[\frac{\sqrt{3}}{2}x+y=0\]        
  done clear
  D)
          \[x+\sqrt{3}y=0\]
  done clear
  View Answer play_arrow

• question_answer24) One end of a thermally insulated rod is kept at a temperature\[m{{y}^{2}}+(1-{{m}^{2}})xy-m{{x}^{2}}=0\]and the other at\[xy=0,\]. The rod is composed of two sections of lengths\[-\frac{1}{2}\]and\[-2\] and thermal conductivities \[{{K}_{1}}\] and \[{{K}_{2}}\] respectively. The temperature at the interface of the two sections is       AIEEE  Solved  Paper-2007
  A)
   \[f(x)=\int_{1}^{x}{\frac{\log \,t}{1+t}}dt\]
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[f:R\to R\]
  done clear
  D)
   \[f(x)=\]
  done clear
  View Answer play_arrow

• question_answer25) A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of       AIEEE  Solved  Paper-2007
  A)
   1000                                     
  done clear
  B)
   10000  
  done clear
  C)
                          10                         
  done clear
  D)
          100
  done clear
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• question_answer26) If\[min\{x+1,|~x|+1\}\]and\[f\{x\}\ge 1\]denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then       AIEEE  Solved  Paper-2007
  A)
   \[x\in R\]
  done clear
  B)
          \[f(x)\]
  done clear
  C)
          \[x=1\]
  done clear
  D)
          \[f(x)\]
  done clear
  View Answer play_arrow

• question_answer27) A charged particle moves through a magnetic field perpendicular to its direction. Then,       AIEEE  Solved  Paper-2007
  A)
   the momentum changes but the kinetic energy is constant
  done clear
  B)
   both momentum and kinetic energy of the particle are not constant
  done clear
  C)
   both momentum and kinetic energy of the particle are constant
  done clear
  D)
   kinetic energy changes but the momentum is constant
  done clear
  View Answer play_arrow

• question_answer28) Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current\[f(x)\]and COD carries a current\[x=0\]. The magnetic field on a point lying at a distance d from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by       AIEEE  Solved  Paper-2007
  A)
   \[\frac{{{\mu }_{0}}}{2\pi }\,{{\left( \frac{({{l}_{1}}+{{l}_{2}})}{d} \right)}^{1/2}}\]
  done clear
  B)
          \[\frac{{{\mu }_{0}}}{2\pi d}\,{{(l_{1}^{2}+l_{2}^{2})}^{1/2}}\]
  done clear
  C)
                          \[\frac{{{\mu }_{0}}}{2\pi d}\,(l_{1}^{{}}+l_{2}^{{}})\]
  done clear
  D)
                          \[\frac{{{\mu }_{0}}}{2\pi d}\,(l_{1}^{2}+l_{2}^{2})\]
  done clear
  View Answer play_arrow

• question_answer29) The resistance of a wire is\[\int_{\sqrt{2}}^{x}{\frac{dt}{t\sqrt{{{t}^{2}}-1}}}=\pi /2\] at\[\pi \]and \[\sqrt{3}/2\],at\[2\sqrt{2}\] The resistance of the wire at \[\int{\frac{dx}{\cos x+\sqrt{3}\sin x}}\] will be       AIEEE  Solved  Paper-2007
  A)
   \[\frac{1}{2}\log \tan \left( \frac{x}{2}+\frac{\pi }{12} \right)+C\]                             
  done clear
  B)
          \[\frac{1}{2}\log \tan \left( \frac{x}{2}-\frac{\pi }{12} \right)+C\]                              
  done clear
  C)
   \[\log \tan \left( \frac{x}{2}+\frac{\pi }{12} \right)+C\]                  
  done clear
  D)
          \[\log \tan \left( \frac{x}{2}-\frac{\pi }{12} \right)+C\]
  done clear
  View Answer play_arrow

• question_answer30) A parallel plate ' condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is       AIEEE  Solved  Paper-2007
  A)
   \[{{y}^{2}}=x\]
  done clear
  B)
          \[y=|\text{ }x|\]
  done clear
  C)
          \[\frac{2}{3}\]  
  done clear
  D)
          zero
  done clear
  View Answer play_arrow

• question_answer31) If\[\frac{1}{6}\]arid\[\frac{1}{3}\]are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio \[{{x}^{2}}+ax+1=0\]to be       AIEEE  Solved  Paper-2007
  A)
   1            
  done clear
  B)
                          zero     
  done clear
  C)
          \[\sqrt{5},\]      
  done clear
  D)
          \[(-3,\infty )\]
  done clear
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• question_answer32) A circular disc of radius R is removed from a bigger circular disc of radius 2R, such that the circumference of the discs coincide. The centre of mass of the new disc is\[(3,\infty )\]from the centre of the bigger disc. The value of \[\alpha \] is       AIEEE  Solved  Paper-2007
  A)
   \[(-\infty ,-3)\]    
  done clear
  B)
                          \[x=(2\times {{10}^{-2}})\cos \pi t\]                      
  done clear
  C)
   \[a=2\times {{10}^{-2}}m=2cm\]             
  done clear
  D)
          \[t=0,\]
  done clear
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• question_answer33) A round uniform body of radius R, mass M and moment of inertia\[x=2\text{ }cm\]rolls down (without slipping) an inclined plane making an angle \[\theta \] with the horizontal. Then, its acceleration is       AIEEE  Solved  Paper-2007
  A)
   \[\frac{g\sin \theta }{1+l/M{{R}^{2}}}\]
  done clear
  B)
          \[\frac{g\sin \theta }{1+M{{R}^{2}}/l}\]
  done clear
  C)
          \[\frac{g\sin \theta }{1-l/M{{R}^{2}}}\]
  done clear
  D)
          \[\frac{g\sin \theta }{1-M{{R}^{2}}/l}\]
  done clear
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• question_answer34) Angular momentum of the particle rotating with a central force is constant due to       AIEEE  Solved  Paper-2007
  A)
   constant force
  done clear
  B)
          constant linear momentum
  done clear
  C)
          zero torque
  done clear
  D)
          constant torque
  done clear
  View Answer play_arrow

• question_answer35) A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by       AIEEE  Solved  Paper-2007
  A)
   9.34cm                                
  done clear
  B)
          2.5cm                  
  done clear
  C)
          11.0cm                                
  done clear
  D)
          8.5cm
  done clear
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• question_answer36) A particle is projected at\[T=2s\]to the horizontal with a kinetic energy K. The kinetic energy at the highest point is       AIEEE  Solved  Paper-2007
  A)
   K                                           
  done clear
  B)
          zero                     
  done clear
  C)
          K/4                       
  done clear
  D)
          K/2
  done clear
  View Answer play_arrow

• question_answer37) In a Young's double-slit experiment, the intensity at a point where the path difference is\[=\frac{T}{4}=\frac{2}{4}=0.5s\] (\[\pi /2\]being the wavelength of the light used), is\[{{v}_{a}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{({{10}^{-3}})}{OA}\]. If\[=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{({{10}^{-3}})}{\sqrt{{{(\sqrt{2})}^{2}}+{{(\sqrt{2})}^{2}}}}\]denotes the maximum intensity, \[{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{({{10}^{-3}})}{OB}\]is equal to       AIEEE  Solved  Paper-2007
  A)
   \[=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{({{10}^{-3}})}{2}\]                     
  done clear
  B)
          \[{{V}_{A}}-{{V}_{B}}=0\]                           
  done clear
  C)
          \[=\frac{\frac{1}{2}qV}{qV}=\frac{1}{2}\]                            
  done clear
  D)
          \[I={{I}_{0}}(1-{{e}^{-t/\tau }})\]
  done clear
  View Answer play_arrow

• question_answer38) Two springs, of force constants\[{{I}_{0}}=\frac{E}{R}=\frac{5}{5}=1\,A\]and\[\tau =\frac{L}{R}=\frac{10}{5}=2\,s\]are connected to a mass m as shown. The frequency of oscillation of the mass is \[f\]. If both\[(\therefore -t/\tau =\frac{-2}{2}=-1)\]and\[J=\frac{i}{\pi {{a}^{2}}}\]are made four times their original values, the frequency of. oscillation becomes       AIEEE  Solved  Paper-2007
  A)
   \[\oint{B.dl}={{\mu }_{0}}.{{i}_{enclosed}}\]    
  done clear
  B)
                                          \[\oint{B.dl}={{\mu }_{0}}.{{i}_{enclosed}}\]                                     
  done clear
  C)
          \[x=2\times {{10}^{-2}}\]                                            
  done clear
  D)
          \[cos\text{ }\pi t\]
  done clear
  View Answer play_arrow

• question_answer39) When a system is taken from state\[E={{E}_{0}}\]to state f along the path \[iaf,\] it is found that\[sin\text{ }\omega t\] and\[I={{I}_{0}}\sin \left( \omega t-\frac{\pi }{2} \right)\]. Along the path ibf, \[p=\frac{{{E}_{0}}{{I}_{0}}}{\sqrt{2}}\]cal. W along the path \[ibf\] is       AIEEE  Solved  Paper-2007
  A)
   6 cal                                     
  done clear
  B)
          16 cal                   
  done clear
  C)
          66 cal                                   
  done clear
  D)
          14 cal
  done clear
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• question_answer40) A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is       AIEEE  Solved  Paper-2007
  A)
   \[p=\frac{{{E}_{0}}{{I}_{0}}}{2}\] 
  done clear
  B)
                          \[P=\sqrt{2}{{E}_{0}}{{I}_{0}}\]                
  done clear
  C)
          \[{{10}^{-3}}\mu C\]                     
  done clear
  D)
          \[(\sqrt{2},\sqrt{2})\]
  done clear
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