Solved papers for JEE Main & Advanced AIEEE Solved Paper-2013

done AIEEE Solved Paper-2013 Total Questions - 30

• question_answer1) A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged n a liquid  of density \[\sigma \] at equilibrium position. The extension\[{{x}_{0}}\]of the spring when it is in equilibrium is: (Here, k is spring constant)   AIEEE Solevd Paper-2013    
  A)
  \[\frac{Mg}{k}\]                              
  done clear
  B)
  \[\frac{Mg}{k}\left( 1-\frac{LA\sigma }{M} \right)\]
  done clear
  C)
  \[\frac{Mg}{k}\left( 1-\frac{LA\sigma }{2M} \right)\]      
  done clear
  D)
  \[\frac{Mg}{k}\left( 1+\frac{LA\sigma }{M} \right)\]
  done clear
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• question_answer2) A metallic rod of length\[\ell \] is tied to a string of length\[2\ell \]and made to rotate with angular speed\[\omega \]on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. induced across the ends of the rod is:     AIEEE Solevd Paper-2013
  A)
  \[\frac{2B\omega {{\ell }^{2}}}{2}\]                        
  done clear
  B)
  \[\frac{3B\omega {{\ell }^{2}}}{2}\]
  done clear
  C)
  \[\frac{4B\omega {{\ell }^{2}}}{2}\]        
  done clear
  D)
  \[\frac{5B\omega {{\ell }^{2}}}{2}\]
  done clear
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• question_answer3) This question has statement I and Statement II. Of the four choice given after the statements, choose the one that best describes the two statements. Statement - I: A Point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as \[f\left( \frac{1}{2}m{{v}^{2}} \right)\]then\[f=\left( \frac{m}{M+m} \right)\] Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.     AIEEE Solevd Paper-2013
  A)
  Statement - I is true, Statement - II is true, statement - II is a correct explanation of Statement - I
  done clear
  B)
  Statement - I is true, Statement - II is true, statement - II is not a correct explanation of Statement - I
  done clear
  C)
  Statement - I is true, Statement - II is false
  done clear
  D)
  Statement - I is false, Statement - II is true
  done clear
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• question_answer4) Let\[[{{\varepsilon }_{0}}]\]denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = Time and A = electric current, then:     AIEEE Solevd Paper-2013
  A)
  \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{2}}A]\]
  done clear
  B)
  \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]\]
  done clear
  C)
  \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{2}}{{T}^{-1}}{{A}^{-2}}]\]
  done clear
  D)
  \[[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{2}}{{T}^{-1}}A]\]  
  done clear
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• question_answer5) A Projectile is given an initial velocity of\[(\hat{i}+2\hat{j})m/s\]+ where\[\hat{i}\]is along the ground and \[\hat{j}\]is along the vertical. If\[g=10\text{ }m/{{s}^{2}},\]the equation of its trajectory is :     AIEEE Solevd Paper-2013
  A)
  \[y=x-5{{x}^{2}}\]
  done clear
  B)
  \[y=2x-5{{x}^{2}}\]
  done clear
  C)
  \[4y=2x-5{{x}^{2}}\]
  done clear
  D)
  \[4y=2x-25{{x}^{2}}\]
  done clear
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• question_answer6) The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to \[\alpha \] times its original magnitude, where α equals:     AIEEE Solevd Paper-2013
  A)
  0.7                                         
  done clear
  B)
  0.81       
  done clear
  C)
         0.729    
  done clear
  D)
         0.6
  done clear
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• question_answer7) Two capacitors\[{{C}_{1}}\]and\[{{C}_{2}}\]are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then:     AIEEE Solevd Paper-2013
  A)
  \[5{{C}_{1}}=3{{C}_{2}}\]                             
  done clear
  B)
  \[3{{C}_{1}}=5{{C}_{2}}\]             
  done clear
  C)
         \[3{{C}_{1}}+5{{C}_{2}}=0\]
  done clear
  D)
         \[9{{C}_{1}}=4{{C}_{2}}\]
  done clear
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• question_answer8) A sonometer wire of length 1.5 m is made of steel. The tension in it produce an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are \[7.7\times {{10}^{3}}kg/{{m}^{3}}\] and \[2.2\times {{10}^{11}}\] \[N/{{m}^{2}}\]respectively?     AIEEE Solevd Paper-2013
  A)
  188.5 Hz                              
  done clear
  B)
  178.2 Hz              
  done clear
  C)
         200.5 Hz              
  done clear
  D)
         770 Hz
  done clear
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• question_answer9) A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is:     AIEEE Solevd Paper-2013
  A)
  \[9.1\times {{10}^{-11}}weber\]              
  done clear
  B)
  \[6\times {{10}^{-11}}weber\]
  done clear
  C)
                         \[3.3\times {{10}^{-11}}weber\]              
  done clear
  D)
  \[6.6\times {{10}^{-9}}weber\]
  done clear
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• question_answer10) Diameter of a plano - convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is\[2\times {{10}^{8}}m/s,\] the focal length of the lens is:     AIEEE Solevd Paper-2013
  A)
  15 cm                   
  done clear
  B)
  20 cm   
  done clear
  C)
         30 cm   
  done clear
  D)
         10 cm
  done clear
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• question_answer11) What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?     AIEEE Solevd Paper-2013
  A)
  \[\frac{5GmM}{6R}\]                    
  done clear
  B)
  \[\frac{2GmM}{3R}\]    
  done clear
  C)
         \[\frac{GmM}{2R}\]       
  done clear
  D)
         \[\frac{GmM}{3R}\]  
  done clear
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• question_answer12) A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.     AIEEE Solevd Paper-2013
  A)
  10.62 MHz                          
  done clear
  B)
  10.62 kHz            
  done clear
  C)
         5.31 MHz
  done clear
  D)
                        5.31 kHz
  done clear
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• question_answer13) A beam of unpolarised light of intensity\[{{I}_{0}}\]is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of\[45{}^\circ \] relative to that of A. The intensity of the emergent light is:     AIEEE Solevd Paper-2013
  A)
  \[{{I}_{0}}\]                                                       
  done clear
  B)
  \[{{I}_{0}}/2\]
  done clear
  C)
  \[{{I}_{0}}/4\]   
  done clear
  D)
         \[{{I}_{0}}/8\]
  done clear
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• question_answer14) The supply voltage to a room is 120 V. The resistance of the lead wires is\[6\Omega .\] A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb?     AIEEE Solevd Paper-2013
  A)
  zero Volt             
  done clear
  B)
         2.9 Volt                
  done clear
  C)
         13.3 Volt             
  done clear
  D)
         10.04 Volt
  done clear
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• question_answer15) The above \[p-v\] diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is:     AIEEE Solevd Paper-2013
  A)
  \[{{p}_{0}}{{v}_{0}}\]     
  done clear
  B)
         \[\left( \frac{13}{2} \right){{p}_{0}}{{v}_{0}}\]    
  done clear
  C)
         \[\left( \frac{11}{2} \right){{p}_{0}}{{v}_{0}}\]    
  done clear
  D)
         \[4{{p}_{0}}{{v}_{0}}\]
  done clear
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• question_answer16) A hoop of radius r and mass m rotating with an angular velocity \[{{\omega }_{0}}\] is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?     AIEEE Solevd Paper-2013
  A)
  \[\frac{r{{\omega }_{0}}}{4}\]   
  done clear
  B)
         \[\frac{r{{\omega }_{0}}}{3}\]   
  done clear
  C)
         \[\frac{r{{\omega }_{0}}}{2}\]   
  done clear
  D)
         \[r{{\omega }_{0}}\]
  done clear
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• question_answer17) An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is \[{{V}_{0}}\] and its pressure is\[{{P}_{0}}\]. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:     AIEEE Solevd Paper-2013
  A)
  \[\frac{1}{2\pi }\frac{{{A}_{\gamma }}{{P}_{0}}}{{{V}_{0}}M}\]                  
  done clear
  B)
  \[\frac{1}{2\pi }\frac{{{V}_{0}}M{{P}_{0}}}{{{A}^{2}}\gamma }\]
  done clear
  C)
         \[\frac{1}{2\pi }\sqrt{\frac{{{A}^{2}}\gamma {{P}_{0}}}{M{{V}_{0}}}}\]
  done clear
  D)
         \[\frac{1}{2\pi }\sqrt{\frac{M{{V}_{0}}}{{{A}_{\gamma }}{{P}_{0}}}}\]
  done clear
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• question_answer18) If a piece of metal is heated to temperature\[\theta \] and then allowed to cool in a room which is at temperature\[{{\theta }_{0}},\]the graph between the temperature T of the metal and time t will be closed to:     AIEEE Solevd Paper-2013
  A)
                
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
        
  done clear
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• question_answer19) This question has statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two statements. Statement − I: Higher the range, greater is the resistance of ammeter. Statement − II: To increase the range of ammeter, additional shunt needs to be used across it.     AIEEE Solevd Paper-2013
  A)
  Statement - I is true, Statements - II is true, Statement - II is the correct explanation of Statements ? I
  done clear
  B)
  Statement - I is true, Statement - II is true, Statement - II is not the correct explanation of Statement - I.
  done clear
  C)
  Statement - I is true, Statement - II is false.
  done clear
  D)
  Statement - I is false, Statement - II is true.
  done clear
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• question_answer20) In an LCR circuit as shown below both switches are open initially. Now switch\[{{S}_{1}}\]is closed,\[{{S}_{2}}\]kept open. (q is charge on the capacitor and\[\tau =RC\]is Capacitive time constant). Which of the following statement is correct?     AIEEE Solevd Paper-2013
  A)
  Work done by the battery is half of the energy dissipated in the resistor
  done clear
  B)
  \[At\text{ }t=\tau ,\text{ }q=CV/2\]
  done clear
  C)
  \[~At\text{ }t=2\tau ,\text{ }q=CV(1-{{e}^{-2}})\]
  done clear
  D)
  \[At\text{ }t=\frac{\tau }{2},q=CV(1-{{e}^{-1}})\]
  done clear
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• question_answer21) Two coherent point sources\[{{S}_{1}}\]and\[{{S}_{2}}\]are separated by a small distance 'd' as shown. The fringes obtained on the screen will be:     AIEEE Solevd Paper-2013
  A)
  points
  done clear
  B)
  straight lines
  done clear
  C)
  semi−circles
  done clear
  D)
  concentric circles
  done clear
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• question_answer22) The magnetic field in a travelling electromagnetic wave has a peak value of 20 \[nT\]. The peak value of electric field strength is:     AIEEE Solevd Paper-2013
  A)
  \[\frac{3V}{m}\]                                              
  done clear
  B)
  \[\frac{6V}{m}\]                              
  done clear
  C)
  \[\frac{9V}{m}\]                              
  done clear
  D)
         \[\frac{12V}{m}\]
  done clear
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• question_answer23) The anode voltage of a photocell is kept fixed. The wavelength \[\lambda \] of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows:     AIEEE Solevd Paper-2013
  A)
                
  done clear
  B)
   
  done clear
  C)
    
  done clear
  D)
          
  done clear
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• question_answer24) The I − V characteristic of an LED is:     AIEEE Solevd Paper-2013
  A)
      
  done clear
  B)
              
  done clear
  C)
             
  done clear
  D)
  
  done clear
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• question_answer25) Assume that a drop of liquid evaporates by decrease in its surface energy. So that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is\[\rho \]and L is its latent heat of vaporization.     AIEEE Solevd Paper-2013
  A)
  \[\frac{\rho L}{T}\]                         
  done clear
  B)
         \[\sqrt{\frac{T}{\rho L}}\]            
  done clear
  C)
         \[\frac{T}{\rho L}\]                         
  done clear
  D)
         \[\frac{2T}{\rho L}\]
  done clear
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• question_answer26) In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number \[(n-1).\]If \[n>>1,\]the frequency of radiation emitted is proportional to:     AIEEE Solevd Paper-2013
  A)
  \[\frac{1}{n}\]  
  done clear
  B)
                         \[\frac{1}{{{n}^{2}}}\]                   
  done clear
  C)
         \[\frac{1}{{{n}^{3/2}}}\]               
  done clear
  D)
         \[\frac{1}{{{n}^{3}}}\]
  done clear
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• question_answer27) The graph between angle of deviation \[(\delta )\] and angle of incidence (i) for a triangular prism is represented by:     AIEEE Solevd Paper-2013
  A)
    
  done clear
  B)
   
  done clear
  C)
  
  done clear
  D)
        
  done clear
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• question_answer28) Two charges, each equal to q, are kept at \[x=-a\] and\[x=a\] on the x−axis. A particle of mass m and charge\[{{q}_{0}}=\frac{q}{2}\] is placed at the origin. If charge\[{{q}_{0}}\]is given a small displacement\[(y<<a)\] along the y−axis, the net force acting on the particle is proportional to:     AIEEE Solevd Paper-2013
  A)
  y             
  done clear
  B)
                         − y                         
  done clear
  C)
  \[\frac{1}{y}\]                   
  done clear
  D)
         \[-\frac{1}{y}\]
  done clear
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• question_answer29) Two short bar magnets of length 1 cm each have magnetic moments 1.20\[A{{m}^{2}}\]and 1.00\[A{{m}^{2}}\]respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid - point O of the line joining their centre is close to (Horizontal component of earth′s magnetic induction is\[3.6\times {{10}^{-5}}Wb/{{m}^{2}}\])     AIEEE Solevd Paper-2013
  A)
  \[3.6\times {{10}^{-5}}Wb/{{m}^{2}}\]
  done clear
  B)
  \[2.56\times {{10}^{-4}}Wb/{{m}^{2}}\]
  done clear
  C)
  \[3.50\times {{10}^{-4}}Wb/{{m}^{2}}\]
  done clear
  D)
  \[5.80\times {{10}^{-4}}Wb/{{m}^{2}}\]
  done clear
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• question_answer30) A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is:     AIEEE Solevd Paper-2013
  A)
  \[\frac{Q}{8\pi {{\varepsilon }_{0}}L}\]  
  done clear
  B)
         \[\frac{3Q}{4\pi {{\varepsilon }_{0}}L}\]
  done clear
  C)
         \[\frac{Q}{4\pi {{\varepsilon }_{0}}L\ell n2}\]     
  done clear
  D)
         \[\frac{Q\ell n2}{4\pi {{\varepsilon }_{0}}L}\]
  done clear
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