Solved papers for JEE Main & Advanced AIEEE Solved Paper-2006

done AIEEE Solved Paper-2006 Total Questions - 150

• question_answer1) The Kirchhoff's first law\[(\Sigma i=0)\]and second law\[(\Sigma iR=\Sigma E)\], where the symbols have their usual meanings, are respectively based on       AIEEE  Solved  Paper-2006
  A)
  Conservation of charge, conservation of momentum
  done clear
  B)
  Conservation of energy, conservation of charge
  done clear
  C)
  Conservation of momentum, conservation of charge
  done clear
  D)
  Conservation of charge, conservation of energy
  done clear
  View Answer play_arrow

• question_answer2) Needles\[{{N}_{1}},{{N}_{2}}\]and\[{{N}_{3}}\]are made of a ferromagnetic, a paramagnetic and a diamagnetic substance, respectively. A magnet when brought close to them will     AIEEE  Solved  Paper-2006  
  A)
  Attract\[{{N}_{1}}\]and\[{{N}_{2}}\]strongly but repel\[{{N}_{3}}\]
  done clear
  B)
  Attract\[{{N}_{1}}\]strongly, \[{{N}_{2}}\]weakly and repel\[{{N}_{3}}\] weakly
  done clear
  C)
  Attract\[{{N}_{1}}\]strongly, but repel\[{{N}_{2}}\]and\[{{N}_{3}}\]weakly
  done clear
  D)
  attract all three of them
  done clear
  View Answer play_arrow

• question_answer3) A material B has twice the specific resistance of A. A circular wire made of B has twice the diameter of a wire made of Then, for the two wires to have the same resistance, the ratio \[{{l}_{B}}/{{l}_{A}}\] respective lengths must be     AIEEE  Solved  Paper-2006
  A)
  1             
  done clear
  B)
                         \[\frac{1}{2}\]                   
  done clear
  C)
         \[\frac{1}{4}\]                   
  done clear
  D)
         2
  done clear
  View Answer play_arrow

• question_answer4) In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a     AIEEE  Solved  Paper-2006
  A)
  helix                     
  done clear
  B)
         straight line                       
  done clear
  C)
  ellipse                  
  done clear
  D)
         circle
  done clear
  View Answer play_arrow

• question_answer5) An electric dipole is placed at an angle of \[30{}^\circ \]to a non-uniform electric field. The dipole will experience     AIEEE  Solved  Paper-2006
  A)
  a translational force only in the direction of the field
  done clear
  B)
  a translational force only in a direction normal to the direction of the field
  done clear
  C)
  a torque as well as a translational force
  done clear
  D)
  a torque only
  done clear
  View Answer play_arrow

• question_answer6) A particle located at\[x=0\]at time\[t=0\], starts moving along the positive x-direction with a velocity v that varies as \[v=\alpha \sqrt{x}\]. The displacement of the particle varies with time as     AIEEE  Solved  Paper-2006
  A)
  \[{{t}^{2}}\]    
  done clear
  B)
                         \[t\]     
  done clear
  C)
         \[{{t}^{1/2}}\]                   
  done clear
  D)
         \[{{t}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer7) A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is\[4\text{ }m{{s}^{-1}}\]. The kinetic energy of the other mass is     AIEEE  Solved  Paper-2006
  A)
  144 J     
  done clear
  B)
                         288 J                     
  done clear
  C)
         192 J                     
  done clear
  D)
         96 J
  done clear
  View Answer play_arrow

• question_answer8) A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed\[v\text{ }m{{s}^{-1}}\]. The velocity of sound in air is \[300\,m{{s}^{-1}}\]. If the person can hear frequencies up to a maximum of 10000 Hz, the maximum value of v up to which he can hear the whistle is     AIEEE  Solved  Paper-2006
  A)
  \[15\sqrt{2}m{{s}^{-1}}\]       
  done clear
  B)
         \[15/\sqrt{2}m{{s}^{-1}}\]           
  done clear
  C)
         \[15m{{s}^{-1}}\]            
  done clear
  D)
         \[30\,m{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer9) A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of \[45{}^\circ \]with the initial vertical direction is     AIEEE  Solved  Paper-2006
  A)
  \[Mg(\sqrt{2}+1)\]         
  done clear
  B)
  \[Mg\sqrt{2}\] 
  done clear
  C)
         \[\frac{Mg}{\sqrt{2}}\]                 
  done clear
  D)
         \[Mg(\sqrt{2}-1)\]
  done clear
  View Answer play_arrow

• question_answer10) A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time the particle goes up is     AIEEE  Solved  Paper-2006
  A)
  \[-0.5J\]              
  done clear
  B)
         \[-1.25\,J\]         
  done clear
  C)
         1.25 J                    
  done clear
  D)
         0.5 J
  done clear
  View Answer play_arrow

• question_answer11) The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is       AIEEE  Solved  Paper-2006
  A)
  0.01s                     
  done clear
  B)
         10s                        
  done clear
  C)
         0.1s                       
  done clear
  D)
         100s
  done clear
  View Answer play_arrow

• question_answer12) Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy?       AIEEE  Solved  Paper-2006
  A)
  \[\frac{1}{6}s\]      
  done clear
  B)
                         \[\frac{1}{4}s\]                 
  done clear
  C)
         \[\frac{1}{3}s\]                 
  done clear
  D)
         \[\frac{1}{12}s\]
  done clear
  View Answer play_arrow

• question_answer13) Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on earth, at a distance r from the sun.
  A)
  \[4\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}\]        
  done clear
  B)
  \[\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}\]
  done clear
  C)
         \[r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/4\pi {{r}^{2}}\]
  done clear
  D)
         \[{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}\] where, \[{{r}_{0}}\] is the radius of the earth and a is Stefan's constant.
  done clear
  View Answer play_arrow

• question_answer14) Which of the following units denote the dimensions\[[M{{L}^{2}}/{{Q}^{2}}],\]where 0 denotes the electric charge?       AIEEE  Solved  Paper-2006
  A)
  \[Wb/{{m}^{2}}\]          
  done clear
  B)
         henry (H)            
  done clear
  C)
         \[H/{{m}^{2}}\]           
  done clear
  D)
         Weber (Wb)
  done clear
  View Answer play_arrow

• question_answer15) A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes up to 2 m height further, find the magnitude of the force. Consider\[g=10\text{ }m/{{s}^{2}}\].     AIEEE  Solved  Paper-2006
  A)
  4N             
  done clear
  B)
                         16N                       
  done clear
  C)
         20N                       
  done clear
  D)
         22N
  done clear
  View Answer play_arrow

• question_answer16) A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is     AIEEE  Solved  Paper-2006
  A)
  105 Hz         
  done clear
  B)
         1.05 Hz 
  done clear
  C)
         1050 Hz          
  done clear
  D)
         10.5 Hz
  done clear
  View Answer play_arrow

• question_answer17) Consider a two particle system with particles having masses\[{{m}_{1}}\]and\[{{m}_{2}}\]. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?     AIEEE  Solved  Paper-2006
  A)
  \[\frac{{{m}_{2}}}{{{m}_{1}}}d\]
  done clear
  B)
                         \[\frac{{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}d\]         
  done clear
  C)
         \[\frac{{{m}_{1}}}{{{m}_{2}}}d\]               
  done clear
  D)
         \[d\]
  done clear
  View Answer play_arrow

• question_answer18) A player caught a cricket ball of mass 150 g moving at a rate of 20 m/s. If the catching process is completed in 0.1 s, the force of the blow exerted by the ball on the hand of the player is equal to     AIEEE  Solved  Paper-2006
  A)
  150N                                     
  done clear
  B)
  3N                                         
  done clear
  C)
  30N                       
  done clear
  D)
         300N
  done clear
  View Answer play_arrow

• question_answer19) In a common-base mode of a transistor, the collector current is 5.488 mA for an emitter current of 5.60 mA. The value of the base current amplification factor (P) will be     AIEEE  Solved  Paper-2006
  A)
  49             
  done clear
  B)
                         50                          
  done clear
  C)
         51                          
  done clear
  D)
         48
  done clear
  View Answer play_arrow

• question_answer20) A thermocouple is made of two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is kept cold, then an electric current will     AIEEE  Solved  Paper-2006
  A)
  flow from Antimony to Bismuth at the hot junction
  done clear
  B)
  flow from Bismuth to Antimony at the cold junction
  done clear
  C)
  not flow through the thermocouple
  done clear
  D)
  flow from Antimony to Bismuth at the cold junction
  done clear
  View Answer play_arrow

• question_answer21) The threshold frequency for a metallic surface corresponds to an energy of 6.2 eV and the stopping potential for a radiation incident on this surface is 5V. The incident radiation lies in     AIEEE  Solved  Paper-2006
  A)
  ultraviolet region
  done clear
  B)
  infrared region
  done clear
  C)
  visible region
  done clear
  D)
  X-ray region
  done clear
  View Answer play_arrow

• question_answer22) An alpha nucleus of energy \[\frac{1}{2}m{{v}^{2}}\]bombards a heavy nuclear target of charge \[Ze\]. Then, the distance of closest approach for the alpha nucleus will be proportional to     AIEEE  Solved  Paper-2006
  A)
  \[{{v}^{2}}\]                      
  done clear
  B)
         \[1/m\]
  done clear
  C)
         \[1/{{v}^{4}}\]                  
  done clear
  D)
         \[1/Ze\]
  done clear
  View Answer play_arrow

• question_answer23) The time taken by a photoelectron to come out after the photon strikes is approximately     AIEEE  Solved  Paper-2006
  A)
  \[{{10}^{-4}}s\]
  done clear
  B)
                         \[{{10}^{-10}}s\]              
  done clear
  C)
         \[{{10}^{-16}}s\]              
  done clear
  D)
         \[{{10}^{-1}}s\]
  done clear
  View Answer play_arrow

• question_answer24) When\[_{3}L{{i}^{7}}\]nuclei are bombarded by protons and the resultant nuclei are\[_{4}B{{e}^{8}},\] the emitted particles will be     AIEEE  Solved  Paper-2006
  A)
  alpha particles  
  done clear
  B)
        beta particles
  done clear
  C)
                         gamma photons
  done clear
  D)
         neutrons
  done clear
  View Answer play_arrow

• question_answer25) The current I drawn from the 5 V source will be   AIEEE  Solved  Paper-2006
  A)
  0.33 A  
  done clear
  B)
                         0.5 A     
  done clear
  C)
         0.67 A                   
  done clear
  D)
  0.17 A
  done clear
  View Answer play_arrow

• question_answer26) The energy spectrum of \[\beta \]-particles [number N(E) as a function of \[\beta \]-energy E] emitted from a radioactive source is     AIEEE  Solved  Paper-2006
  A)
     
  done clear
  B)
  
  done clear
  C)
        
  done clear
  D)
        
  done clear
  View Answer play_arrow

• question_answer27) In a series resonant LCR circuit, .the voltage across R is 100 V and\[R=1k\,\Omega \]. With\[C=2\mu F\]. The resonant frequency\[\omega \] is 200 rad/s. At resonance, the voltage across L is     AIEEE  Solved  Paper-2006
  A)
  \[2.5\times {{10}^{-2}}V\]                           
  done clear
  B)
  \[40\,V\]             
  done clear
  C)
          \[250\,V\]         
  done clear
  D)
         \[4\times {{10}^{-3}}\,V\]
  done clear
  View Answer play_arrow

• question_answer28) The resistance of a bulb filament is\[100\text{ }\Omega \].at a temperature of\[100{}^\circ C\]. If its temperature coefficient of resistance is\[0.005/{}^\circ C,\]its resistance will become\[200\,\Omega \]. at a temperature of     AIEEE  Solved  Paper-2006
  A)
  \[300{}^\circ C\]              
  done clear
  B)
         \[400{}^\circ C\]              
  done clear
  C)
         \[500{}^\circ C\]              
  done clear
  D)
         \[200{}^\circ C\]
  done clear
  View Answer play_arrow

• question_answer29) Two insulating plates are both uniformly charged in such a way that the potential difference between them is\[{{V}_{2}}-{{V}_{1}}=20\,V\] (i.e., plate 2 is at a higher potential). The plates are separated by\[d=0.1\text{ }m\]and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2? \[(e=1.6\times {{10}^{-19}}C,{{m}_{0}}=9.11\times {{10}^{-31}}kg)\]   AIEEE  Solved  Paper-2006
  A)
  \[2.65\times {{10}^{6}}\text{ }m/s\]  
  done clear
  B)
         \[7.02\times {{10}^{12}}\text{ }m/s\]    
  done clear
  C)
  \[1.87\times {{10}^{6}}m/s\]                     
  done clear
  D)
  \[32\times {{10}^{-19}}m/s\]
  done clear
  View Answer play_arrow

• question_answer30) In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency \[\omega \] in a magnetic field B. The maximum value of emf generated in the coil is     AIEEE  Solved  Paper-2006
  A)
  \[NABR\,\omega \]        
  done clear
  B)
         \[NAB\]               
  done clear
  C)
          \[NABR\]           
  done clear
  D)
         \[NAB\,\omega \]
  done clear
  View Answer play_arrow

• question_answer31) A solid which is not transparent to visible light and whose conductivity increases with temperature is formed by     AIEEE  Solved  Paper-2006
  A)
  ionic bonding
  done clear
  B)
  covalent bonding
  done clear
  C)
  van der Waals' bonding
  done clear
  D)
  metallic bonding
  done clear
  View Answer play_arrow

• question_answer32) The refractive index of glass is 1.520 for red light and 1.525 for bin l light. Let\[{{D}_{1}}\]and\[{{D}_{2}}\]be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then,     AIEEE  Solved  Paper-2006
  A)
  \[{{D}_{1}}<{{D}_{2}}\]
  done clear
  B)
  \[{{D}_{1}}={{D}_{2}}\]
  done clear
  C)
  \[{{D}_{1}}\]can be less than or greater than\[{{D}_{2}}\] depending upon. The angle of prism
  done clear
  D)
  \[{{D}_{1}}>{{D}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer33) If the ratio of the concentration of electrons to that of holes in a semiconductor is\[\frac{7}{5}\]and the ratio of currents is \[\frac{7}{4}\], then what is the ratio of their drift velocities?     AIEEE  Solved  Paper-2006
  A)
  \[\frac{5}{8}\]                   
  done clear
  B)
         \[\frac{4}{5}\]                   
  done clear
  C)
         \[\frac{5}{4}\]                  
  done clear
  D)
         \[\frac{4}{7}\]
  done clear
  View Answer play_arrow

• question_answer34) In a Wheatstone?s bridge, three resistances P, Q and R are connected in the three arms and the fourth arm is formed by two resistances\[{{S}_{1}}\]and\[{{S}_{2}}\]connected in parallel. The condition for the bridge to be balanced will be     AIEEE  Solved  Paper-2006
  A)
  \[\frac{P}{Q}=\frac{2R}{{{S}_{1}}+{{S}_{2}}}\]                    
  done clear
  B)
  \[\frac{P}{Q}=\frac{R({{S}_{1}}+{{S}_{2}})}{{{S}_{1}}{{S}_{2}}}\]
  done clear
  C)
         \[\frac{P}{Q}=\frac{R({{S}_{1}}+{{S}_{2}})}{2{{S}_{1}}{{S}_{2}}}\]
  done clear
  D)
         \[\frac{P}{Q}=\frac{R}{{{S}_{1}}+{{S}_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer35) The flux linked with a coil at any instant t is given by \[\phi =10{{t}^{2}}-50t+250\] The induced emf at\[t=3\text{ }s\]is     AIEEE  Solved  Paper-2006
  A)
  \[-190V\]       
  done clear
  B)
         \[-10V\]              
  done clear
  C)
         \[10V\]                
  done clear
  D)
         \[190V\]
  done clear
  View Answer play_arrow

• question_answer36) A long solenoid has 200 turns/cm and carries a current i. The magnetic field at its centre is \[6.28\,\times {{10}^{-2}}\,Wb/{{m}^{2}}\]. Another long solenoid has 100 turns/cm and it carries a current\[i/3\]. The value of the magnetic field at its centre is     AIEEE  Solved  Paper-2006
  A)
  \[1.05\times {{10}^{-2}}Wb/{{m}^{2}}\]                
  done clear
  B)
  \[1.05\times {{10}^{-5}}Wb/{{m}^{2}}\]
  done clear
  C)
  \[1.05\times {{10}^{-3}}Wb/{{m}^{2}}\]
  done clear
  D)
  \[1.05\times {{10}^{-4}}Wb/{{m}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer37) The circuit has two oppositely connected ideal diodes in parallel. What is the current flowing in the circuit?     AIEEE  Solved  Paper-2006
  A)
  1.71 A              
  done clear
  B)
         2.00 A   
  done clear
  C)
         2.31 A              
  done clear
  D)
         1.33A
  done clear
  View Answer play_arrow

• question_answer38) In the following, which one of the diodes is reverse biased?     AIEEE  Solved  Paper-2006
  A)
  
  done clear
  B)
                     
  done clear
  C)
                 
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer39) 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  Solved  Paper-2006
  A)
  
  done clear
  B)
               
  done clear
  C)
        
  done clear
  D)
        
  done clear
  View Answer play_arrow

• question_answer40) If the binding energy per nucleon in\[_{3}^{7}Li\]and\[_{2}^{4}He\]nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction \[P+_{3}^{7}Li\to 2_{2}^{4}He\] energy of proton must be     AIEEE  Solved  Paper-2006
  A)
  28.24 MeV     
  done clear
  B)
         17.28 MeV         
  done clear
  C)
         1.46 MeV
  done clear
  D)
  39.2 MeV
  done clear
  View Answer play_arrow

• question_answer41) An electric bulb is rated\[220\text{ }V-100\text{ }W\]The power consumed by it when operated on 110 V will be     AIEEE  Solved  Paper-2006
  A)
  75 W                     
  done clear
  B)
  40 W     
  done clear
  C)
         25 W     
  done clear
  D)
         50 W
  done clear
  View Answer play_arrow

• question_answer42) The 'rad' is the correct unit used to report the measurement of     AIEEE  Solved  Paper-2006
  A)
  the ability of a beam of gamma ray photons to produce ions in a target
  done clear
  B)
  the energy delivered by radiation to a target
  done clear
  C)
  the biological effect of radiation
  done clear
  D)
  the rate of decay of a radioactive source
  done clear
  View Answer play_arrow

• question_answer43) A coin is placed on a horizontal platform which   undergoes   vertical   simple harmonic motion of angular frequency\[\omega \]. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time     AIEEE  Solved  Paper-2006
  A)
  at the mean position of the platform
  done clear
  B)
  for an amplitude of \[g/{{\omega }^{2}}\]
  done clear
  C)
  for an amplitude of\[{{g}^{2}}/{{\omega }^{2}}\]
  done clear
  D)
  at the highest position of the platform
  done clear
  View Answer play_arrow

• question_answer44) Four point masses, each of value m, are placed at the corners of a square ABCD of side \[l\]. The moment of inertia of this system about an axis passing through A and parallel to BD is     AIEEE  Solved  Paper-2006
  A)
  \[2m{{l}^{2}}\]                 
  done clear
  B)
  \[\sqrt{3}\,m{{l}^{2}}\]
  done clear
  C)
                         \[3\,m{{l}^{2}}\]              
  done clear
  D)
         \[\,m{{l}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer45) A force of \[-F\hat{k}\] acts on O, the origin of the coordinate system. The torque about the point \[(1,-1)\]is     AIEEE  Solved  Paper-2006
  A)
  \[F(\hat{i}-\hat{j})\]        
  done clear
  B)
         \[-F(\hat{i}+\hat{j})\]   
  done clear
  C)
         \[F(\hat{i}+\hat{j})\]         
  done clear
  D)
         \[-F(\hat{i}-\hat{j})\]
  done clear
  View Answer play_arrow

• question_answer46) The potential energy of a 1 kg particle free to move along the x-axis is given by \[V(x)=\left( \frac{{{x}^{4}}}{4}-\frac{{{x}^{2}}}{2} \right)J\] The total mechanical energy of the particle is 2 J. Then, the maximum speed (in m/s) is     AIEEE  Solved  Paper-2006
  A)
  \[3/\sqrt{2}\]    
  done clear
  B)
         \[\sqrt{2}\]        
  done clear
  C)
         \[1/\sqrt{2}\]   
  done clear
  D)
         2
  done clear
  View Answer play_arrow

• question_answer47) A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity\[\omega \]. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity\[\omega '\]is equal to     AIEEE  Solved  Paper-2006
  A)
  \[\frac{\omega (m+2M)}{m}\]  
  done clear
  B)
         \[\frac{\omega (m-2M)}{(m-2M)}\]
  done clear
  C)
  \[\frac{\omega m}{(m+M)}\]    
  done clear
  D)
         \[\frac{\omega m}{(m+2M)}\]
  done clear
  View Answer play_arrow

• question_answer48) A wire elongates by\[l\,mm\] when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm)     AIEEE  Solved  Paper-2006
  A)
  \[l\]                       
  done clear
  B)
         \[2l\]                    
  done clear
  C)
  zero                      
  done clear
  D)
         \[l/2\]
  done clear
  View Answer play_arrow

• question_answer49) An inductor\[(L=100mH)\], a resistor\[(R=100\,\Omega )\] and a battery\[(E=100\,V)\]are initially connected in series as shown in the figure. After a long time, the battery is disconnected after short circuiting the points A and B. The current in the circuit 1 ms after the short circuit is   AIEEE  Solved  Paper-2006
  A)
  \[1/e\,A\]                          
  done clear
  B)
  \[e\text{ }A\]                   
  done clear
  C)
                         \[0.1A\]               
  done clear
  D)
         \[1\,A\]
  done clear
  View Answer play_arrow

• question_answer50) Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire, the in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B is     AIEEE  Solved  Paper-2006
  A)
  4 : 1          
  done clear
  B)
                         1 : 2                       
  done clear
  C)
         2 : 1                       
  done clear
  D)
         1 : 4
  done clear
  View Answer play_arrow

• question_answer51) Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature \[{{T}_{0}},\] while box B contains one mole of helium at temperature (7/3)\[{{T}_{0}}\]. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases,\[{{T}_{f}}\]in terms of\[{{T}_{0}}\]is     AIEEE  Solved  Paper-2006
  A)
  \[{{T}_{f}}=\frac{3}{7}{{T}_{0}}\]                              
  done clear
  B)
  \[{{T}_{f}}=\frac{7}{3}{{T}_{0}}\]              
  done clear
  C)
         \[{{T}_{f}}=\frac{3}{2}{{T}_{0}}\]              
  done clear
  D)
         \[{{T}_{f}}=\frac{5}{2}{{T}_{0}}\]
  done clear
  View Answer play_arrow

• question_answer52) The work of 146 kJ is performed in order to compress one kilo mole of a gas adiabatically and in this process, the temperature of the gas increases   by\[7{}^\circ C\].   The   gas   is \[(R=8.3\,J\,mo{{l}^{-1}}{{K}^{-1}})\]     AIEEE  Solved  Paper-2006
  A)
  diatomic
  done clear
  B)
  triatomic
  done clear
  C)
  a mixture of monatomic and diatomic
  done clear
  D)
  monatomic
  done clear
  View Answer play_arrow

• question_answer53) If the lattice constant of this semiconductor is decreased, then which of the following is correct?     AIEEE  Solved  Paper-2006
  A)
  All \[{{E}_{c}},{{E}_{g}},{{E}_{v}}\] increase
  done clear
  B)
  \[{{E}_{c}}\]and\[rms\]increase, but\[{{E}_{g}}\]decreases
  done clear
  C)
  \[{{E}_{c}}\]and \[{{E}_{v}}\]decrease, but\[{{E}_{g}}\]increases
  done clear
  D)
  All \[{{E}_{c}},\,{{E}_{g}},\,{{E}_{v}}\] decrease
  done clear
  View Answer play_arrow

• question_answer54) The \[rms\] value of the electric field of the light coming from the sun is 720 N/C. The average total energy density of the electromagnetic wave is     AIEEE  Solved  Paper-2006
  A)
  \[4.58\times {{10}^{-6}}J/{{m}^{3}}\]   
  done clear
  B)
         \[6.37\times {{10}^{-9}}J/{{m}^{3}}\]
  done clear
  C)
         \[81.35\times {{10}^{-12}}J/{{m}^{3}}\]
  done clear
  D)
  \[3.3\times {{10}^{-3}}J/{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer55) If the terminal speed of a sphere of gold (density\[=19.5\text{ }kg/{{m}^{3}}\]) is 0.2 m/s in a viscous liquid (density\[=1.5\text{ }kg/{{m}^{3}}\]), find the terminal speed of a sphere of silver (density =10.5\[kg/{{m}^{3}}\]) of the same size in the same liquid.     AIEEE  Solved  Paper-2006
  A)
  0.4 m/s        
  done clear
  B)
        0.133 m/s           
  done clear
  C)
         0.1 m/s          
  done clear
  D)
         0.2 m/s
  done clear
  View Answer play_arrow

• question_answer56) \[HBr\]reacts with\[C{{H}_{2}}=CHOC{{H}_{3}}\]under anhydrous   conditions   at   room temperature to give     AIEEE  Solved  Paper-2006
  A)
  \[C{{H}_{3}}CHO\]and\[C{{H}_{3}}Br\]
  done clear
  B)
  \[BrC{{H}_{2}}CHO\]and\[C{{H}_{3}}OH\]
  done clear
  C)
  \[BrC{{H}_{2}}C{{H}_{2}}OC{{H}_{3}}\]
  done clear
  D)
  \[{{H}_{3}}CCHBrOC{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer57) The IUPAC name of the compound shown below is     AIEEE  Solved  Paper-2006
  A)
  2-bromo-6-chlorocyclohex-1-ene
  done clear
  B)
  6-bromo-2-chlorocyclohexene
  done clear
  C)
  3-bromo-1-chlorocyclohexene
  done clear
  D)
  1-bromo-3-chlorocyclohexene
  done clear
  View Answer play_arrow

• question_answer58) The increasing order of the rate of\[HCN\] addition to compounds I-IV is (A)\[HCHO\]                      (B)\[C{{H}_{3}}COC{{H}_{3}}\] (C)\[PhCOC{{H}_{3}}\]                   (D)\[PhCOPh\]     AIEEE  Solved  Paper-2006
  A)
  \[I<II<III<IV\]                   
  done clear
  B)
  \[IV<II<III<I\]
  done clear
  C)
         \[IV<III<II<I\]
  done clear
  D)
  \[III<IV<II<I\]
  done clear
  View Answer play_arrow

• question_answer59) How many moles of magnesium phosphate, \[M{{g}_{3}}{{(P{{O}_{4}})}_{2}}\]will contain 0.25 mole of oxygen atoms?     AIEEE  Solved  Paper-2006
  A)
  0.02                       
  done clear
  B)
         \[3.125\times {{10}^{-2}}\]         
  done clear
  C)
         \[1.25\times {{10}^{-2}}\]      
  done clear
  D)
         \[2.5\times {{10}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer60) According to Bohr's theory, the angular momentum of an electron in 5th orbit is
  A)
  \[25\frac{h}{\pi }\]
  done clear
  B)
                         \[1.0\frac{h}{\pi }\]        
  done clear
  C)
         \[10\frac{h}{\pi }\]         
  done clear
  D)
         \[2.5\frac{h}{\pi }\]
  done clear
  View Answer play_arrow

• question_answer61) Which of the following molecules/ions does not contain unpaired electrons?     AIEEE  Solved  Paper-2006
  A)
  \[O_{2}^{2-}\]                  
  done clear
  B)
         \[{{B}_{2}}\]                      
  done clear
  C)
  \[N_{2}^{+}\]                   
  done clear
  D)
         \[{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer62) Total volume of atoms present in a face-centre cubic unit cell of a metal is (r is atomic radius)     AIEEE  Solved  Paper-2006
  A)
  \[\frac{20}{3}\pi {{r}^{3}}\]         
  done clear
  B)
         \[\frac{24}{3}\pi {{r}^{3}}\]         
  done clear
  C)
         \[\frac{12}{3}\pi {{r}^{3}}\]         
  done clear
  D)
         \[\frac{16}{3}\pi {{r}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer63) A reaction was found to be second order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will     AIEEE  Solved  Paper-2006
  A)
  remain unchanged
  done clear
  B)
  triple
  done clear
  C)
  increases by a factor of 4
  done clear
  D)
  double
  done clear
  View Answer play_arrow

• question_answer64) Which of the following chemical reactions depicts the oxidizing behavior of\[{{H}_{2}}S{{O}_{4}}\]?     AIEEE  Solved  Paper-2006
  A)
  \[2HI+{{H}_{2}}S{{O}_{4}}\to {{I}_{2}}+S{{O}_{2}}+{{H}_{2}}O\]
  done clear
  B)
  \[Ca{{(OH)}_{2}}+{{H}_{2}}S{{O}_{4}}\to CaS{{O}_{4}}+2{{H}_{2}}O\]
  done clear
  C)
  \[NaCl+{{H}_{2}}S{{O}_{4}}\to NaHS{{O}_{4}}+HCl\]
  done clear
  D)
  \[2PC{{l}_{5}}+{{H}_{2}}S{{O}_{4}}\to 2POC{{l}_{3}}+2HCl+S{{O}_{2}}C{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer65) The IUPAC name for the complex \[[CO(N{{O}_{2}}){{(N{{H}_{3}})}_{5}}]C{{l}_{2}}\]is     AIEEE  Solved  Paper-2006
  A)
  nitrito-N-pentaaminecobalt (III) chloride
  done clear
  B)
  nitrito-N-pentaaminecobalt (II) chloride
  done clear
  C)
  pentaamine nitrito-N-cobalt (II) chloride
  done clear
  D)
  pentaamine nitrito-N-cobalt (III) chloride
  done clear
  View Answer play_arrow

• question_answer66) The term anomers of glucose refers to     AIEEE  Solved  Paper-2006
  A)
  isomers of glucose that differ in configurations at carbons one and four (C-1 and C-4)
  done clear
  B)
  a mixture of (D)-glucose and (L)-glucose
  done clear
  C)
  enantiomers of glucose
  done clear
  D)
  isomers of glucose that differ in configuration at carbon one (C-1)
  done clear
  View Answer play_arrow

• question_answer67) In the transformation of\[_{92}^{238}U\]to\[_{92}^{234}U\], if one emission is an \[\alpha \]-particle, what should be the other emission (s)?     AIEEE  Solved  Paper-2006
  A)
  Two \[{{\beta }^{-}}\]
  done clear
  B)
  Two \[{{\beta }^{-}}\]and one \[{{\beta }^{+}}\]
  done clear
  C)
  One \[{{\beta }^{-}}\] and one\[\gamma \]
  done clear
  D)
  One \[{{\beta }^{+}}\] and one \[{{\beta }^{-}}\]
  done clear
  View Answer play_arrow

• question_answer68) Phenyl magnesium bromide reacts with methanol to give     AIEEE  Solved  Paper-2006
  A)
  a mixture of anisol and\[Mg(OH)Br\]
  done clear
  B)
  a mixture of benzene and\[Mg(OMe)Br\]
  done clear
  C)
  a mixture of toluene and\[Mg(OH)Br\]
  done clear
  D)
  a mixture of phenol and\[Mg(Me)Br\]
  done clear
  View Answer play_arrow

• question_answer69) \[C{{H}_{3}}Br+N{{u}^{-}}\to C{{H}_{3}}-Nu+B{{r}^{-}}\] The decreasing order of the rate of the above reaction with nucleophiles \[(N{{u}^{-}})A\] to IV is \[[N{{u}^{-}}=(A)\,Ph{{O}^{-}},\,(B)\,Ac{{O}^{-}},\,(C)\,H{{O}^{-}},\,(D)\,C{{H}_{3}}{{O}^{-}}]\]     AIEEE  Solved  Paper-2006
  A)
  \[D>C>A<B\]
  done clear
  B)
  \[D>C>B>A\]
  done clear
  C)
                         \[A>B>C>D\]
  done clear
  D)
         \[B>D>C>A\]
  done clear
  View Answer play_arrow

• question_answer70) The pyrimidine bases present in DNA are     AIEEE  Solved  Paper-2006
  A)
  cytosine and adenine
  done clear
  B)
  cytosine and guanine
  done clear
  C)
  cytosine and thymine
  done clear
  D)
  cytosine and uracil
  done clear
  View Answer play_arrow

• question_answer71) Among the following the one that gives positive iodoform test upon reaction with 12 and\[NaOH\]is     AIEEE  Solved  Paper-2006
  A)
  \[C{{H}_{3}}C{{H}_{2}}CH(OH)C{{H}_{2}}C{{H}_{3}}\]
  done clear
  B)
  \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}C{{H}_{2}}OH\]
  done clear
  C)
  
  done clear
  D)
  \[PhCHOHC{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer72) The increasing order of stability of the following free radicals is     AIEEE  Solved  Paper-2006
  A)
  \[{{(C{{H}_{3}})}_{2}}\overset{\bullet }{\mathop{C}}\,H<{{(C{{H}_{3}})}_{3}}\overset{\bullet }{\mathop{C}}\,<{{({{C}_{6}}{{H}_{5}})}_{2}}\overset{\bullet }{\mathop{C}}\,H\] \[<{{({{C}_{6}}{{H}_{5}})}_{3}}\overset{\bullet }{\mathop{C}}\,\]                
  done clear
  B)
  \[{{({{C}_{6}}{{H}_{5}})}_{3}}\overset{\bullet }{\mathop{C}}\,<{{({{C}_{6}}{{H}_{5}})}_{2}}\overset{\bullet }{\mathop{C}}\,H<{{(C{{H}_{3}})}_{3}}\overset{\bullet }{\mathop{C}}\,\]                                                               \[<{{(C{{H}_{3}})}_{2}}\overset{\bullet }{\mathop{C}}\,H\]                
  done clear
  C)
   \[{{({{C}_{6}}{{H}_{5}})}_{2}}\overset{\bullet }{\mathop{C}}\,H<{{({{C}_{6}}{{H}_{5}})}_{3}}\overset{\bullet }{\mathop{C}}\,<{{(C{{H}_{3}})}_{3}}\overset{\bullet }{\mathop{C}}\,\]                                                               \[<{{(C{{H}_{3}})}_{2}}\overset{\bullet }{\mathop{C}}\,H\]                
  done clear
  D)
   \[{{(C{{H}_{3}})}_{2}}\overset{\bullet }{\mathop{C}}\,H<{{(C{{H}_{3}})}_{3}}\overset{\bullet }{\mathop{C}}\,<{{({{C}_{6}}{{H}_{5}})}_{3}}\overset{\bullet }{\mathop{C}}\,\]                                                           \[<{{({{C}_{6}}{{H}_{5}})}_{2}}\overset{\bullet }{\mathop{C}}\,H\]
  done clear
  View Answer play_arrow

• question_answer73) Uncertainty in the position of an electron (mass\[=9.1\times {{10}^{-31}}kg\]) moving with a velocity\[300\text{ }m{{s}^{-1}},\] accurate upon 0.001% will be\[(h=6.63\times {{10}^{-34}}Js)\])     AIEEE  Solved  Paper-2006
  A)
  \[19.2\times {{10}^{-2}}m\]    
  done clear
  B)
         \[5.76\,\times {{10}^{-2}}\,m\]
  done clear
  C)
                         \[1.92\times {{10}^{-2}}m\]     
  done clear
  D)
         \[3.84\times {{10}^{-2}}m\]
  done clear
  View Answer play_arrow

• question_answer74) Phosphorus pentachloride dissociates as follows, in a closed reaction vessel, \[PC{{l}_{5}}(g)PC{{l}_{3}}(g)+C{{l}_{2}}(g)\] If total pressure at equilibrium of the reaction mixture is p and degree of dissociation of \[PC{{l}_{5}}\] is\[x\], the partial pressure of\[PC{{l}_{3}}\]will be     AIEEE  Solved  Paper-2006
  A)
   \[\left( \frac{x}{x+1} \right)P\]                
  done clear
  B)
   \[\left( \frac{2x}{1-x} \right)P\]               
  done clear
  C)
          \[\left( \frac{x}{x-1} \right)P\] 
  done clear
  D)
         \[\left( \frac{x}{1-x} \right)P\]
  done clear
  View Answer play_arrow

• question_answer75) The standard enthalpy of formation \[(\Delta H_{f}^{o})\] at 298 K for methane,\[C{{H}_{4}}(g),\]is \[-74.8\text{ }kJ\text{ }mo{{l}^{-1}}\] The additional information required to determine the average energy for\[CH\] bond formation would be     AIEEE  Solved  Paper-2006
  A)
   the dissociation energy of Hg and enthalpy of sublimation of carbon
  done clear
  B)
   latent heat of vaporisation of methane
  done clear
  C)
   the first four ionisation energies of carbon and electron gain enthalpy of hydrogen
  done clear
  D)
   the dissociation energy of hydrogen molecule,\[{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer76) Among the following mixtures, dipole-dipole as the major interaction, is present in     AIEEE  Solved  Paper-2006
  A)
   benzene and ethanol
  done clear
  B)
   acetonitrile and acetone
  done clear
  C)
  \[KCl\]and water
  done clear
  D)
  benzene and carbon tetrachloride
  done clear
  View Answer play_arrow

• question_answer77) Fluorobenzene\[({{C}_{6}}{{H}_{5}}F)\]can be synthesized in the laboratory     AIEEE  Solved  Paper-2006
  A)
  by heating phenol with HF and KF
  done clear
  B)
  from aniline by diazotisation followed by heating the diazonium salt with \[HB{{F}_{4}}\]
  done clear
  C)
   by direct fluorination of benzene with \[{{F}_{2}}\] gas
  done clear
  D)
   by reacting bromobenzene with NaF solution
  done clear
  View Answer play_arrow

• question_answer78) A metal, M forms chlorides in its +2 and +4 oxidation states. Which of the following statements about these chlorides is correct?     AIEEE  Solved  Paper-2006
  A)
  \[MC{{l}_{2}}\] is more volatile than\[MC{{l}_{4}}\]
  done clear
  B)
  \[MC{{l}_{2}}\]is more soluble in anhydrous ethanol than\[MC{{l}_{4}}\]
  done clear
  C)
  \[MC{{l}_{2}}\]is more ionic than\[MC{{l}_{4}}\]
  done clear
  D)
  \[MC{{l}_{2}}\]is more easily hydrolysed than\[MC{{l}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer79) Which of the following statement is true?     AIEEE  Solved  Paper-2006
  A)
  \[{{H}_{2}}P{{O}_{3}}\]is a stronger acid than\[{{H}_{2}}S{{O}_{3}}\]
  done clear
  B)
  In aqueous medium HF is a stronger acid than\[HCl\]
  done clear
  C)
  \[HCl{{O}_{4}}\]is a weaker acid than\[HCl{{O}_{3}}\]
  done clear
  D)
  \[HN{{O}_{3}}\]is a stronger acid than \[HN{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer80) The molar conductivities \[\hat{\ }_{NaOAc}^{o}\]and \[\hat{\ }_{HCl}^{o}\]at infinite dilution in water at\[25{}^\circ C\]are 91.0 and \[426.2\text{ }S\text{ }c{{m}^{2}}/mol\]respectively. To calculate \[\hat{\ }_{HOAc'}^{o}\]the additional value required is     AIEEE  Solved  Paper-2006
  A)
  \[\hat{\ }_{{{H}_{2}}O}^{o}\]                     
  done clear
  B)
         \[\hat{\ }_{KCl}^{o}\]                    
  done clear
  C)
         \[\hat{\ }_{NaOH}^{o}\]              
  done clear
  D)
         \[\hat{\ }_{NaCl}^{o}\]
  done clear
  View Answer play_arrow

• question_answer81) Which one of the following sets of ions represents a collection of isoelectronic species?     AIEEE  Solved  Paper-2006
  A)
  \[{{K}^{+}},C{{l}^{-}},C{{a}^{2+}},S{{c}^{3+}}\]
  done clear
  B)
  \[B{{a}^{2+}},S{{r}^{2+}},{{K}^{+}},{{S}^{2-}}\]
  done clear
  C)
  \[{{N}^{3-}},{{O}^{2-}},{{F}^{-}},{{S}^{2-}}\]
  done clear
  D)
  \[L{{i}^{+}},N{{a}^{+}},M{{g}^{2+}},C{{a}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer82) The correct order of increasing acid strength of the compounds (I) \[C{{H}_{3}}C{{O}_{2}}H\]                    (II) \[MeOC{{H}_{2}}C{{O}_{2}}H\] (III) \[C{{F}_{3}}C{{O}_{2}}H\]                  (IV)   AIEEE  Solved  Paper-2006
  A)
  II < IV < I < III    
  done clear
  B)
  IV < I < III < II     
  done clear
  C)
  IV < I < II < III    
  done clear
  D)
  I < IV < III < II
  done clear
  View Answer play_arrow

• question_answer83) In which of the following molecules/ions, all the bonds are not equal?     AIEEE  Solved  Paper-2006
  A)
  \[S{{F}_{4}}\]  
  done clear
  B)
                         \[Si{{F}_{4}}\]  
  done clear
  C)
         \[Xe{{F}_{4}}\]                 
  done clear
  D)
         \[B{{F}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer84) What products are expected from the disproportionation reaction of hypochlorous acid?     AIEEE  Solved  Paper-2006
  A)
  \[HCl{{O}_{3}}\]and \[C{{l}_{2}}O\]         
  done clear
  B)
  \[HCl{{O}_{2}}\]and\[HCl{{O}_{4}}\]       
  done clear
  C)
  \[HCl\]and\[C{{l}_{2}}O\]            
  done clear
  D)
  \[HCl\]and\[HCl{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer85) Nickel\[(Z=28)\]combines with a uninegative monodentate ligand\[{{X}^{-}}\]to form a paramagnetic complex\[{{[Ni{{X}_{4}}]}^{2-}}\]. The number of unpaired electron (s) in the nickel and geometry of this complex ion are, respectively     AIEEE  Solved  Paper-2006
  A)
  one, tetrahedral
  done clear
  B)
         two, tetrahedral
  done clear
  C)
         one, square planar         
  done clear
  D)
  two, square planar
  done clear
  View Answer play_arrow

• question_answer86) In\[Fe{{(CO)}_{5}},\]the\[FeC\]bond possesses     AIEEE  Solved  Paper-2006
  A)
  \[\pi -\]character only
  done clear
  B)
  both\[\sigma \]and\[\pi \]characters
  done clear
  C)
  ionic character only
  done clear
  D)
  \[\sigma -\]character only
  done clear
  View Answer play_arrow

• question_answer87) The increasing order of the first ionization enthalpies of the elements B, P, S and p (lowest first) is     AIEEE  Solved  Paper-2006
  A)
  \[F<S<P<B\]      
  done clear
  B)
  \[P<S<B<F\]
  done clear
  C)
         \[B<P<S<F\]   
  done clear
  D)
        \[B<S<P<F\]
  done clear
  View Answer play_arrow

• question_answer88) An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If\[{{T}_{i}}\]is the initial temperature and\[{{T}_{f}}\]is the final temperature, which of the following statements is correct?     AIEEE  Solved  Paper-2006
  A)
  \[{{({{T}_{f}})}_{irrev}}>{{({{T}_{f}})}_{rev}}\]
  done clear
  B)
  \[{{T}_{f}}>{{T}_{i}}\]for reversible process but\[{{T}_{f}}={{T}_{i}}\]for irreversible process
  done clear
  C)
  \[{{({{T}_{f}})}_{rev}}={{({{T}_{i}})}_{irrev}}\]
  done clear
  D)
  \[{{T}_{f}}={{T}_{i}}\]for both reversible and irreversible processes
  done clear
  View Answer play_arrow

• question_answer89) In Langmuir's model of adsorption of a gas on a solid surface     AIEEE  Solved  Paper-2006
  A)
  the rate of dissociation of adsorbed molecules from the surface does not depend on the surface covered
  done clear
  B)
  the adsorption at a single site on the surface may involve multiple molecules at the same time
  done clear
  C)
  the mass of gas striking a given area of surface is proportional to the pressure of the gas
  done clear
  D)
  the mass of gas striking a given area of surface is independent of the pressure of the gas
  done clear
  View Answer play_arrow

• question_answer90) Rate of a reaction can be expressed by Arrhenius equation as \[k=A{{e}^{-E/RT}}\] In this equation, E represents     AIEEE  Solved  Paper-2006
  A)
  the energy above which all the. Colliding molecules will react
  done clear
  B)
  the energy below which colliding molecules will not react
  done clear
  C)
  the total energy of the reacting molecules at a temperature, T
  done clear
  D)
  the fraction of molecules with energy greater than the activation energy of the reaction
  done clear
  View Answer play_arrow

• question_answer91) The structure of the major product formed in the following reaction is     AIEEE  Solved  Paper-2006
  A)
  
  done clear
  B)
                    
  done clear
  C)
        
  done clear
  D)
        
  done clear
  View Answer play_arrow

• question_answer92) Reaction of trans-2-phenyl-1- bromocyclopentane on reaction with alcoholic \[KOH\]produces     AIEEE  Solved  Paper-2006
  A)
  4-phenylcyclopentene
  done clear
  B)
  2-phenylcyclopentene
  done clear
  C)
  1-phenylcyclopentene
  done clear
  D)
  3-phenylcyclopentene
  done clear
  View Answer play_arrow

• question_answer93) Increasing order of stability among the three main conformations (i.e.. Eclipse, Ami, Gauche) of 2-fluoroethanol is     AIEEE  Solved  Paper-2006
  A)
  Eclipse, Gauche, Anti
  done clear
  B)
  Gauche, Eclipse, Anti
  done clear
  C)
  Eclipse, Anti, Gauche
  done clear
  D)
  Anti, Gauche, Eclipse
  done clear
  View Answer play_arrow

• question_answer94) The structure of the compound that gives a tribromo derivative on treatment with bromine water is     AIEEE  Solved  Paper-2006
  A)
                         
  done clear
  B)
             
  done clear
  C)
               
  done clear
  D)
          
  done clear
  View Answer play_arrow

• question_answer95) The decreasing values of bond angles from\[N{{H}_{3}}(107{}^\circ )\]to\[Sb{{H}_{3}}(91{}^\circ )\]down group-15 of the periodic table is due to     AIEEE  Solved  Paper-2006
  A)
  increasing\[bp-bp\]repulsion
  done clear
  B)
  increasing p-orbital character in\[s{{p}^{3}}\]
  done clear
  C)
  decreasing \[lp-bp\] repulsion
  done clear
  D)
  decreasing electronegativity
  done clear
  View Answer play_arrow

• question_answer96)  The alkene formed as a major product in the above elimination reaction is     AIEEE  Solved  Paper-2006
  A)
                             
  done clear
  B)
  \[C{{H}_{2}}=C{{H}_{2}}\]            
  done clear
  C)
               
  done clear
  D)
        
  done clear
  View Answer play_arrow

• question_answer97) The 'spin-only' magnetic moment [in units of Bohr magneton,\[({{\mu }_{\beta }})]\]of\[N{{i}^{2+}}\]in aqueous solution would be (Atomic number of\[Ni=28\])     AIEEE  Solved  Paper-2006
  A)
  2.84       
  done clear
  B)
         4.90       
  done clear
  C)
         0                             
  done clear
  D)
         1.73
  done clear
  View Answer play_arrow

• question_answer98) The equilibrium constant for the reaction \[S{{O}_{3}}(g)S{{O}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\] is\[{{K}_{c}}=4.9\times {{10}^{-2}}\]. The value of\[{{K}_{c}}\]for the reaction \[2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g)\]will be     AIEEE  Solved  Paper-2006
  A)
  416  
  done clear
  B)
                                         \[2.40\times {{10}^{-3}}\]            
  done clear
  C)
         \[9.8\times {{10}^{-2}}\]              
  done clear
  D)
  \[4.9\times {{10}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer99) Following statements regarding the periodic trends of chemical reactivity of the alkali metals and the halogens are given. Which of these statements gives the correct picture?     AIEEE  Solved  Paper-2006
  A)
  The reactivity decreases in the alkali metals but increases in the halogens with increase in atomic number down the group
  done clear
  B)
  In both the alkali metals and the halogens, the chemical reactivity decreases with increase in atomic number down the group
  done clear
  C)
  Chemical reactivity increases with increase in atomic number down the group in both the alkali metals and halogens
  done clear
  D)
  In alkali metals, the reactivity increases but in the halogens it decreases with increase in atomic number down the group
  done clear
  View Answer play_arrow

• question_answer100) Given the data at\[25{}^\circ C,\] \[Ag+{{I}^{-}}\xrightarrow{{}}AgI+{{e}^{-}};\]                     \[E{}^\circ =0.152\text{ }V\] \[Ag\xrightarrow{{}}A{{g}^{+}}+{{e}^{-}};\]                     \[E{}^\circ =-0.800\text{ }V\] What is the value of\[\log \text{ }{{K}_{sp}}\]for\[AgI\]? \[\left( 2.303\frac{RT}{F}=0.059\,V \right)\]     AIEEE  Solved  Paper-2006
  A)
  \[\text{ }8.12\]                 
  done clear
  B)
         \[+\text{ }8.612\]            
  done clear
  C)
         \[-37.83\]                           
  done clear
  D)
  \[-16.13\]
  done clear
  View Answer play_arrow

• question_answer101) The following mechanism has been proposed for the reaction of\[NO\]with\[B{{r}_{2}}\]to form\[NOBr\]. \[NO(g)+B{{r}_{2}}(g)NOB{{r}_{2}}(g)\] \[NOB{{r}_{2}}(g)+NO(g)\xrightarrow{{}}2NOBr(g)\] If the second step is the rate determining step, the order of the reaction with respect to\[NO(g)\]is     AIEEE  Solved  Paper-2006
  A)
  1       
  done clear
  B)
                         0             
  done clear
  C)
         3             
  done clear
  D)
         2
  done clear
  View Answer play_arrow

• question_answer102) Lanthanoid contraction is caused due to     AIEEE  Solved  Paper-2006
  A)
  the appreciable shielding on outer electrons by\[4f\]electrons from the nuclear charge
  done clear
  B)
  the appreciable shielding on outer electrons by\[5d\]electrons from the nuclear charge
  done clear
  C)
  the same effective nuclear charge from\[Ce\]to\[Lu\]
  done clear
  D)
  the imperfect shielding on outer electrons by\[4f\]electrons from the nuclear charge
  done clear
  View Answer play_arrow

• question_answer103) Resistance of a conductivity cell filled with a solution of an electrolyte of concentration 0.1 M is\[100\text{ }\Omega \]. The conductivity of this solution is\[1.29\text{ }S\text{ }{{m}^{-1}}\].Resistance of the same cell when filled with 0.2 M of the same solution is\[520\,\Omega \]The molar conductivity of 0.02 M solution of the electrolyte will be     AIEEE  Solved  Paper-2006
  A)
  \[124\times {{10}^{-4}}S\,{{m}^{2}}\text{ }mo{{l}^{-1}}\]
  done clear
  B)
  \[1240\times {{10}^{-4}}S\,{{m}^{2}}mo{{l}^{-1}}\]
  done clear
  C)
  \[1.24\times {{10}^{-4}}S\,{{m}^{2}}mo{{l}^{-1}}\]
  done clear
  D)
  \[12.4\times {{10}^{-4}}S\,{{m}^{2}}mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer104) The ionic mobility of alkali metal ions in aqueous solution is maximum for     AIEEE  Solved  Paper-2006
  A)
  \[{{K}^{+}}\]                      
  done clear
  B)
         \[R{{b}^{+}}\]   
  done clear
  C)
         \[L{{i}^{+}}\]                     
  done clear
  D)
         \[N{{a}^{+}}\]
  done clear
  View Answer play_arrow

• question_answer105) Density of a 2.05 M solution of acetic acid in water is\[1.02\text{ }g/mL\]. The molality of the solution is     AIEEE  Solved  Paper-2006
  A)
  \[1.14\text{ }mol\text{ }k{{g}^{-1}}\]     
  done clear
  B)
  \[3.28\text{ }mol\text{ }k{{g}^{-1}}\]
  done clear
  C)
         \[2.28\text{ }mol\text{ }k{{g}^{-1}}\]                     
  done clear
  D)
  \[0.44\text{ }mol\text{ }k{{g}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer106) The enthalpy changes for the following processes are listed below \[C{{l}_{2}}(g)=2Cl(g)\]  \[242.3\text{ }kJ\text{ }mo{{l}^{-1}}\] \[{{I}_{2}}(g)=2I(g),\]                     \[151.0\text{ }kJ\text{ }mo{{l}^{-1}}\] \[ICl(g)=I(g)+Cl(g),\]       \[211.3\text{ }kJ\text{ }mo{{l}^{-1}}\] \[{{I}_{2}}(s)={{I}_{2}}(g),\]         \[62.76\text{ }kJ\text{ }mo{{l}^{-1}}\] Given that the standard states for iodine and chlorine are\[{{I}_{2}}(s)\]and\[C{{l}_{2}}(g)\], the standard enthalpy of formation of \[ICl\,(g)\] is     AIEEE  Solved  Paper-2006
  A)
  \[-\text{ }14.6\text{ }kJ\text{ }mo{{l}^{-1}}\]     
  done clear
  B)
  \[-\text{ }16.8\text{ }kJ\text{ }mo{{l}^{-1}}\]
  done clear
  C)
          \[+\text{ }16.8\text{ }kJ\text{ }mo{{l}^{-1}}\]
  done clear
  D)
         \[+\text{ }244.8\text{ }kJ\text{ }mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer107) How many EDTA (ethylenediaminetetra acetic acid) molecules are required to make an octahedral complex with a \[C{{a}^{2+}}\] ion ?     AIEEE  Solved  Paper-2006
  A)
  six                          
  done clear
  B)
         three    
  done clear
  C)
         one                       
  done clear
  D)
         two
  done clear
  View Answer play_arrow

• question_answer108)  The electrophile involved in the above reaction is     AIEEE  Solved  Paper-2006
  A)
  dichloromethyl cation\[(\overset{\oplus }{\mathop{CH}}\,C{{l}_{2}})\]
  done clear
  B)
  dichlorocarbene\[(:CC{{l}_{2}})\]
  done clear
  C)
  trichloromethyl anion\[(\overset{-}{\mathop{C}}\,C{{l}_{3}})\]
  done clear
  D)
  forrnyl cation\[(\overset{\oplus }{\mathop{C}}\,HO)\]
  done clear
  View Answer play_arrow

• question_answer109) 18 g of glucose\[({{C}_{6}}{{H}_{12}}{{O}_{6}})\]is added to 178.2 g of water. The vapour pressure of water for this aqueous solution at\[100{}^\circ C\]is     AIEEE  Solved  Paper-2006
  A)
  759.00 torr         
  done clear
  B)
  7.60 torr              
  done clear
  C)
         76.00 torr           
  done clear
  D)
         752.40 torr
  done clear
  View Answer play_arrow

• question_answer110) \[(\Delta H-\Delta U)\]for the formation of carbon monoxide (CO) from its elements at 298 K is\[(R=8.314J{{K}^{-1}}mo{{l}^{-1}})\]     AIEEE  Solved  Paper-2006
  A)
  \[-1238.78\text{ }J\text{ }mo{{l}^{-1}}\]               
  done clear
  B)
  \[1238.78\text{ }J\text{ }mo{{l}^{-1}}\]
  done clear
  C)
        \[-\text{ }2477.57\text{ }J\text{ }mo{{l}^{-1}}\]                 
  done clear
  D)
  \[2477.57\text{ }J\text{ }mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer111) If the roots of the quadratic equation \[{{x}^{2}}+px+q=0\]are tan\[30{}^\circ \]and tan\[15{}^\circ \] respectively, then the value of\[2+q-p\]is     AIEEE  Solved  Paper-2006
  A)
  3                             
  done clear
  B)
         0                             
  done clear
  C)
         1                             
  done clear
  D)
         2
  done clear
  View Answer play_arrow

• question_answer112) The    value    of    the    integral\[\int_{3}^{6}{\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}}}dx\]is     AIEEE  Solved  Paper-2006
  A)
  \[\frac{3}{2}\]                   
  done clear
  B)
         2                             
  done clear
  C)
         1                             
  done clear
  D)
         \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer113) Let W denotes the words in the English dictionary. Define the relation R by \[R=\{(x,y)\in W\times W|\] the words\[x\]and y have atleast one letter in common}. Then, R is     AIEEE  Solved  Paper-2006
  A)
  reflexive, symmetric and not transitive
  done clear
  B)
  reflexive, symmetric and transitive
  done clear
  C)
  reflexive, not symmetric and transitive
  done clear
  D)
  not reflexive, symmetric and transitive
  done clear
  View Answer play_arrow

• question_answer114) The number of values of\[x\]in the interval \[[0,3\pi ]\]satisfying the equation \[2\text{ }si{{n}^{2}}x+5\text{ }sin\text{ }x-3=0\]is     AIEEE  Solved  Paper-2006
  A)
  6                             
  done clear
  B)
         1                             
  done clear
  C)
         2                             
  done clear
  D)
         4
  done clear
  View Answer play_arrow

• question_answer115) If A and B are square matrices of size\[n\times n\]such that\[{{A}^{2}}-{{B}^{2}}=(A-B)(A+B),\]then which of the following will be always true?     AIEEE  Solved  Paper-2006
  A)
  \[AB=BA\]
  done clear
  B)
  Either of A or B is a zero matrix
  done clear
  C)
  Either of A or B is an identity matrix
  done clear
  D)
  \[A=B\]
  done clear
  View Answer play_arrow

• question_answer116) The value of\[\sum\limits_{k=1}^{10}{\left( \sin \frac{2k\pi }{11}+i\cos \frac{2k\pi }{11} \right)}\]is     AIEEE  Solved  Paper-2006
  A)
  1             
  done clear
  B)
         -1           
  done clear
  C)
         \[-i\]                     
  done clear
  D)
         \[i\]
  done clear
  View Answer play_arrow

• question_answer117) If \[(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c}),\] where \[\vec{a},\,\vec{b}\] and \[\vec{c}\] are any three vectors such that \[\vec{a}.\vec{b}\ne 0,\vec{b}.\vec{c}\ne 0,\] then \[\vec{a}\] and \[\vec{c}\] are     AIEEE  Solved  Paper-2006
  A)
  inclined at an angle of\[\frac{\pi }{6}\]between them b
  done clear
  B)
  perpendicular    
  done clear
  C)
        parallel
  done clear
  D)
  inclined at an angle of\[\frac{\pi }{3}\]between them
  done clear
  View Answer play_arrow

• question_answer118) All the values of m for which both roots of the equation \[{{x}^{2}}-2mx+{{m}^{2}}-1=0\]are greater than -2 but less than 4 lie in the interval     AIEEE  Solved  Paper-2006
  A)
  \[m>3\]                               
  done clear
  B)
  \[-1<m<3\]        
  done clear
  C)
         \[1<m<4\]          
  done clear
  D)
  \[-2<m<0\]
  done clear
  View Answer play_arrow

• question_answer119) ABC is a triangle, right singled at A. The resultant of the forces acting along \[\overrightarrow{AB},\,\overrightarrow{AC}\] with magnitudes\[\frac{1}{AB}\]and\[\frac{1}{AC}\]respectively is the force along \[\overrightarrow{AD},\] where D is the foot of the perpendicular from A to BC. The magnitude of the resultant is     AIEEE  Solved  Paper-2006
  A)
  \[\frac{(AB)(AC)}{AB+AC}\]       
  done clear
  B)
         \[\frac{1}{AB}+\frac{1}{AC}\]    
  done clear
  C)
         \[\frac{1}{AD}\]                               
  done clear
  D)
         \[\frac{A{{B}^{2}}+A{{C}^{2}}}{(A{{B}^{2}}){{(AC)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer120) Suppose, a population A has 100 observations 101, 102,..., 200 and another population B has 100 observations 151, 152, .... 250. If\[{{V}_{A}}\]and\[{{V}_{B}}\]represent the variances of the two populations respectively, then\[\frac{{{V}_{A}}}{{{V}_{B}}}\]is     AIEEE  Solved  Paper-2006
  A)
  \[\frac{9}{4}\]                   
  done clear
  B)
         \[\frac{4}{9}\]                   
  done clear
  C)
         \[\frac{2}{3}\]                   
  done clear
  D)
         1
  done clear
  View Answer play_arrow

• question_answer121) \[\int_{-3\pi /2}^{-\pi /2}{[{{(x+\pi )}^{3}}+{{\cos }^{2}}(x+3\pi )]}dx\]is equal to     AIEEE  Solved  Paper-2006
  A)
  \[\left( \frac{{{\pi }^{4}}}{32} \right)+\left( \frac{\pi }{2} \right)\]                              
  done clear
  B)
  \[\frac{\pi }{2}\]                              
  done clear
  C)
         \[\left( \frac{\pi }{4} \right)-1\] 
  done clear
  D)
         \[\frac{{{\pi }^{4}}}{32}\]
  done clear
  View Answer play_arrow

• question_answer122) In an ellipse, the distances between its foci is 6 and minor axis is 8. Then. Its eccentricity is     AIEEE  Solved  Paper-2006
  A)
  \[\frac{1}{2}\]               
  done clear
  B)
                         \[\frac{4}{5}\]                                   
  done clear
  C)
  \[\frac{1}{\sqrt{5}}\]                     
  done clear
  D)
         \[\frac{3}{5}\]
  done clear
  View Answer play_arrow

• question_answer123) The locus of the vertices of the family of parabolas\[y=\frac{{{a}^{3}}{{x}^{2}}}{3}+\frac{{{a}^{2}}x}{2}-2a\]is     AIEEE  Solved  Paper-2006
  A)
  \[xy=\frac{3}{4}\]           
  done clear
  B)
         \[xy=\frac{35}{16}\]       
  done clear
  C)
         \[xy=\frac{64}{105}\]    
  done clear
  D)
         \[xy=\frac{105}{64}\]
  done clear
  View Answer play_arrow

• question_answer124) A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is     AIEEE  Solved  Paper-2006
  A)
  \[3x-4y+7=0\]                   
  done clear
  B)
  \[4x+3y=24\]    
  done clear
  C)
         \[3x+4y=25\]      
  done clear
  D)
         \[x+y=7\]
  done clear
  View Answer play_arrow

• question_answer125) The value of a, for which the points A, B, C with position vectors\[2\hat{i}-\hat{j}+\hat{k},\hat{i}-3\hat{j}-5\hat{k}\]and \[a\hat{i}-3\hat{j}+\hat{k}\] respectively are the vertices of a right angled triangle with \[C=\frac{\pi }{2}\]are     AIEEE  Solved  Paper-2006
  A)
  -2 and -1         
  done clear
  B)
         -2 and 1               
  done clear
  C)
                         2 and -1          
  done clear
  D)
         2 and 1
  done clear
  View Answer play_arrow

• question_answer126) \[\int_{0}^{\pi }{x\,f\,(\sin \,x)\,dx}\] is equal to     AIEEE  Solved  Paper-2006
  A)
  \[\pi \int_{0}^{\pi }{f(\sin x)}dx\]
  done clear
  B)
         \[\frac{\pi }{2}\int_{0}^{\pi /2}{f(\sin x)}dx\]     
  done clear
  C)
  \[\pi \int_{0}^{\pi /2}{f(\cos x)}dx\]
  done clear
  D)
         \[\pi \int_{0}^{\pi /2}{f(\cos x)}dx\]
  done clear
  View Answer play_arrow

• question_answer127) The two lines\[x=ay+b,z=cy+d\]and\[x=a'y+b',z=c'y+d'\]are perpendicular to each other, if     AIEEE  Solved  Paper-2006
  A)
  \[aa'+cc'=1\]     
  done clear
  B)
         \[\frac{a}{a'}\,+\frac{c}{c'}\,=-1\]            
  done clear
  C)
         \[\frac{a}{a'}\,+\frac{c}{c'}\,=1\]              
  done clear
  D)
         \[aa'+cc'=-1\]
  done clear
  View Answer play_arrow

• question_answer128) At an election, a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for atleast one candidate, then the number of ways in which he can vote, is     AIEEE  Solved  Paper-2006
  A)
  6210          
  done clear
  B)
                         385                        
  done clear
  C)
         1110                      
  done clear
  D)
         5040
  done clear
  View Answer play_arrow

• question_answer129) If the expansion in powers of\[x\]of the function \[\frac{1}{(1-ax)(1-bx)}\]is\[{{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+{{a}_{2}}{{x}^{3}}+....,\]then\[{{a}_{n}}\]is     AIEEE  Solved  Paper-2006
  A)
  \[\frac{{{a}^{n}}-{{b}^{n}}}{b-a}\]           
  done clear
  B)
         \[\frac{{{a}^{n+1}}-{{b}^{n+1}}}{b-a}\] 
  done clear
  C)
         \[\frac{{{b}^{n+1}}-{{a}^{n+1}}}{b-a}\] 
  done clear
  D)
         \[\frac{{{b}^{n}}-{{a}^{n}}}{b-a}\]
  done clear
  View Answer play_arrow

• question_answer130) For  natural   numbers   m,   n,  if \[{{(1-y)}^{m}}{{(1+y)}^{n}}=1+{{a}_{1}}y+{{a}_{2}}{{y}^{2}}+.....\]and\[{{a}_{1}}={{a}_{2}}=10,\]then (m, n) is     AIEEE  Solved  Paper-2006
  A)
  (35, 20)         
  done clear
  B)
         (45, 35)
  done clear
  C)
         (35, 45)            
  done clear
  D)
         (20, 45)
  done clear
  View Answer play_arrow

• question_answer131) A particle has two velocities of equal magnitude inclined to each other at an angle \[\theta \]. If one of them is halved, the angle between the- other and the original resultant velocity is bisected by the new resultant. Then, 0 is     AIEEE  Solved  Paper-2006
  A)
  \[120{}^\circ \]                                 
  done clear
  B)
  \[45{}^\circ \]                   
  done clear
  C)
         \[60{}^\circ \]                   
  done clear
  D)
         \[90{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer132) At a telephone enquiry system, the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 min time intervals. The probability that there is atmost one phone call during a 10 min time period, is     AIEEE  Solved  Paper-2006
  A)
  \[\frac{5}{6}\]           
  done clear
  B)
                         \[\frac{6}{55}\]
  done clear
  C)
  \[\frac{6}{{{e}^{5}}}\]                   
  done clear
  D)
         \[\frac{6}{{{5}^{e}}}\]
  done clear
  View Answer play_arrow

• question_answer133) A body falling .from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4 s prior to passing through P. If \[g=10m/{{s}^{2}},\]then the height above the point P from where the body began to fall is                    AIEEE  Solved  Paper-2006
  A)
  900m
  done clear
  B)
                                         320 m   
  done clear
  C)
         680 m                   
  done clear
  D)
         720 m      
  done clear
  View Answer play_arrow

• question_answer134) The set of points, where \[f(x)=\frac{x}{1+|x|}\]is differentiable, is     AIEEE  Solved  Paper-2006
  A)
  \[(-\infty ,-1)\cup (-1,\infty )\]  
  done clear
  B)
  \[(-\infty ,\infty )\]         
  done clear
  C)
         \[(0,\infty )\]    
  done clear
  D)
         \[(-\infty ,0\cup (0,\infty )\]
  done clear
  View Answer play_arrow

• question_answer135) Let\[A=\left[ \begin{matrix}    1 & 2  \\    3 & 4  \\ \end{matrix} \right]\]and\[B=\left[ \begin{matrix}    a & 0  \\    0 & b  \\ \end{matrix} \right],a,b,\in N\]. Then,     AIEEE  Solved  Paper-2006
  A)
  there exist more than one but finite number of B's such that\[AB=BA\]
  done clear
  B)
  there exists exactly one B such that\[AB=BA\]
  done clear
  C)
  there exist infinitely many 8's such that\[AB=BA\]
  done clear
  D)
  there cannot exist any B such that\[AB=BA\]
  done clear
  View Answer play_arrow

• question_answer136) Let \[{{a}_{1}},{{a}_{2}},{{a}_{3}},....\] be terms of an AP. If \[\frac{{{a}_{1}}+{{a}_{2}}+.....+{{a}_{p}}}{{{a}_{1}}+{{a}_{2}}+....{{a}_{q}}}=\frac{{{p}^{2}}}{{{q}^{2}}},\] \[p\ne q,\]then\[\frac{{{a}_{6}}}{{{a}_{21}}}\]equals     AIEEE  Solved  Paper-2006
  A)
  \[\frac{7}{2}\]                   
  done clear
  B)
         \[\frac{2}{7}\]                   
  done clear
  C)
  \[\frac{11}{41}\]                              
  done clear
  D)
         \[\frac{41}{11}\]
  done clear
  View Answer play_arrow

• question_answer137) The function\[f(x)=\frac{x}{2}+\frac{2}{x}\]has a local minimum at     AIEEE  Solved  Paper-2006
  A)
  \[x=-2\]               
  done clear
  B)
  \[x=0\]
  done clear
  C)
         \[x=1\]                
  done clear
  D)
         \[x=2\]
  done clear
  View Answer play_arrow

• question_answer138) Angle between the tangents to the curve\[y={{x}^{2}}-5x+6\]at the points (2, 0) and (3, 0) is     AIEEE  Solved  Paper-2006
  A)
  \[\pi /2\]             
  done clear
  B)
         \[\pi /6\]             
  done clear
  C)
         \[\pi /4\]                 
  done clear
  D)
         \[\pi /3\]
  done clear
  View Answer play_arrow

• question_answer139) If \[x\]is real, the maximum value of\[\frac{3{{x}^{2}}+9x+17}{3{{x}^{2}}+9x+7}\]is     AIEEE  Solved  Paper-2006
  A)
  41   
  done clear
  B)
                                         1                             
  done clear
  C)
         17/7              
  done clear
  D)
                         1/4
  done clear
  View Answer play_arrow

• question_answer140) A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length\[x\]. The maximum area enclosed by the park is     AIEEE  Solved  Paper-2006
  A)
  \[\sqrt{\frac{{{x}^{3}}}{8}}\]                      
  done clear
  B)
  \[\frac{1}{2}{{x}^{2}}\] 
  done clear
  C)
         \[\pi {{x}^{2}}\]                
  done clear
  D)
         \[\frac{3}{2}{{x}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer141) If\[(a,\text{ }{{a}^{2}})\]falls inside the angle made by the lines \[y=\frac{x}{2},\text{ }x>0\]and\[y=3x,\text{ }x>0,\]then a belongs to       AIEEE  Solved  Paper-2006
  A)
  \[(3,\infty )\]    
  done clear
  B)
         \[\left( \frac{1}{2},3 \right)\]     
  done clear
  C)
         \[\left( -3,-\frac{1}{2} \right)\]  
  done clear
  D)
         \[\left( 0,\frac{1}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer142) If\[{{x}^{m}}{{y}^{n}}={{(x+y)}^{m+n}},\]then\[\frac{dy}{dx}\]is       AIEEE  Solved  Paper-2006
  A)
  \[\frac{x+y}{xy}\]
  done clear
  B)
                         \[xy\]                                   
  done clear
  C)
  \[\frac{x}{y}\]                   
  done clear
  D)
         \[\frac{y}{x}\]
  done clear
  View Answer play_arrow

• question_answer143) If the lines\[3x-4y-7=0\]and\[2x-3y-5=0\]are two diameters of a circle of area\[49\,\pi \,sq\]units, the equation of the circle is       AIEEE  Solved  Paper-2006
  A)
  \[{{x}^{2}}+{{y}^{2}}+2x-2y-62=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}-2x+2y-62=0\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}-2x+2y-47=0\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}+2x-2y-47=0\]
  done clear
  View Answer play_arrow

• question_answer144) The image of the point (-1, 3, 4) in the plane \[x-2y=0\]is       AIEEE  Solved  Paper-2006
  A)
  (15, 11, 4)         
  done clear
  B)
  \[\left( -\frac{17}{3},-\frac{19}{3},1 \right)\]       
  done clear
  C)
   (8, 4, 4)          
  done clear
  D)
         \[\left( -\frac{17}{3},-\frac{19}{3},4 \right)\]
  done clear
  View Answer play_arrow

• question_answer145) The differential equation whose solution is \[A{{x}^{2}}+B{{y}^{2}}=1,\]where A and B are arbitrary constants, is of       AIEEE  Solved  Paper-2006
  A)
  first order and second degree
  done clear
  B)
  first order and first degree
  done clear
  C)
  second order and first degree
  done clear
  D)
  second order and second degree
  done clear
  View Answer play_arrow

• question_answer146) The value of \[\int_{I}^{a}{[x]\,f'\,(x)\,dx,\,\,a>1,}\] where\[[x]\] denotes  the  greatest  integer  not exceeding \[x,\]is       AIEEE  Solved  Paper-2006
  A)
  \[[a]f(a)-\{f(1)+f(2)+....+f([a])\}\]
  done clear
  B)
  \[[a]f([a])-\{f(1)+f(2)+....+f(a)\}\]
  done clear
  C)
  \[af([a])-\{f(1)+f(2)+....+f(a)\}\]
  done clear
  D)
  \[af(a)-\{f(1)+f(2)+....+f([a])\}\]
  done clear
  View Answer play_arrow

• question_answer147) Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid-points of the chords of the circle C 'that subtend an angle of\[\frac{2\pi }{3}\]at its centre, is       AIEEE  Solved  Paper-2006
  A)
  \[{{x}^{2}}+{{y}^{2}}=1\]             
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}=\frac{27}{4}\]
  done clear
  C)
                         \[{{x}^{2}}+{{y}^{2}}=\frac{9}{4}\]           
  done clear
  D)
         \[{{x}^{2}}+{{y}^{2}}=\frac{3}{2}\]
  done clear
  View Answer play_arrow

• question_answer148) If\[{{a}_{1}},{{a}_{2}},....{{a}_{n}}\]are in HP, then the expression\[{{a}_{1}}{{a}_{2}}+{{a}_{2}}{{a}_{3}}+,....+{{a}_{n-1}}{{a}_{n}}\]is equal to       AIEEE  Solved  Paper-2006
  A)
  \[(n-1)({{a}_{1}}-{{a}_{n}})\]
  done clear
  B)
         \[n{{a}_{1}}{{a}_{n}}\]  
  done clear
  C)
         \[(n-1){{a}_{1}}{{a}_{n}}\]           
  done clear
  D)
         \[n({{a}_{1}}-{{a}_{n}})\]
  done clear
  View Answer play_arrow

• question_answer149) If\[{{z}^{2}}+z+1=0,\]where z is complex number, then the value of \[{{\left( z+\frac{1}{z} \right)}^{2}}+{{\left( {{z}^{2}}+\frac{1}{{{z}^{2}}} \right)}^{2}}+{{\left( {{z}^{3}}+\frac{1}{{{z}^{3}}} \right)}^{2}}\] \[+......+{{\left( {{z}^{6}}+\frac{1}{{{z}^{6}}} \right)}^{2}}\]is       AIEEE  Solved  Paper-2006
  A)
  54                          
  done clear
  B)
  6                             
  done clear
  C)
         12          
  done clear
  D)
         18
  done clear
  View Answer play_arrow

• question_answer150) If\[0<x<\pi \]and \[\cos x+\sin x=\frac{1}{2},\]then \[tan\text{ }x\]is       AIEEE  Solved  Paper-2006
  A)
  \[\frac{(4-\sqrt{7})}{3}\]
  done clear
  B)
                         \[-\frac{(4+\sqrt{7})}{3}\]           
  done clear
  C)
         \[\frac{(1+\sqrt{7})}{4}\]             
  done clear
  D)
         \[\frac{(1-\sqrt{7})}{4}\]
  done clear
  View Answer play_arrow