Solved papers for JEE Main & Advanced AIEEE Solved Paper-2003

done AIEEE Solved Paper-2003 Total Questions - 224

• question_answer1) A particle of mass M and charge Q moving with velocity v describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circle is     AIEEE  Solved  Paper-2003
  A)
  \[\left( \frac{M{{v}^{2}}}{R} \right)2\pi R\]
  done clear
  B)
                        zero      
  done clear
  C)
  BQ \[2\pi R\]        
  done clear
  D)
                        BQv \[2\pi R\]
  done clear
  View Answer play_arrow

• question_answer2) A particle of charge \[-16\times {{10}^{-18}}C\] moving with velocity \[10m{{s}^{-1}}\] along the x-axis enters a region where a magnetic field of induction B is along the y-axis and an electric field of magnitude \[{{10}^{4}}\] V/m is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is     AIEEE  Solved  Paper-2003
  A)
  \[{{10}^{3}}\] Wb / \[{{m}^{2}}\]     
  done clear
  B)
        \[{{10}^{5}}\] Wb/\[{{m}^{2}}\]                
  done clear
  C)
  \[{{10}^{16}}\] Wb/\[{{m}^{2}}\]      
  done clear
  D)
        \[{{10}^{-3}}\] Wb/\[{{m}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer3) A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now, it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T', the ratio T'/T is     AIEEE  Solved  Paper-2003
  A)
  \[\frac{1}{2\sqrt{2}}\]        
  done clear
  B)
                        \[\frac{1}{2}\]                   
  done clear
  C)
  2                                             
  done clear
  D)
  \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer4) A magnetic needle lying parallel to a magnetic field requires W unit of work to turn it through \[{{60}^{o}}\]. The torque needed to maintain the needle in this position will be     AIEEE  Solved  Paper-2003
  A)
  \[\sqrt{3}\] W
  done clear
  B)
                        W           
  done clear
  C)
        \[(\sqrt{3}/2)\]W                            
  done clear
  D)
  2 W
  done clear
  View Answer play_arrow

• question_answer5) The magnetic lines of force inside a bar magnet     AIEEE  Solved  Paper-2003
  A)
  are from north-pole to south-pole of the magnet
  done clear
  B)
  do not exist
  done clear
  C)
  depend upon the area of cross-section of the bar magnet
  done clear
  D)
  are from south-pole to north-pole of the magnet
  done clear
  View Answer play_arrow

• question_answer6) Curie temperature is the temperature above which     AIEEE  Solved  Paper-2003
  A)
  a ferromagnetic material becomes paramagnetic
  done clear
  B)
  a paramagnetic material becomes  diamagnetic
  done clear
  C)
  a ferromagnetic material becomes diamagnetic
  done clear
  D)
  a paramagnetic material becomes ferromagnetic
  done clear
  View Answer play_arrow

• question_answer7) A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of \[5\,m/{{s}^{2}}\], the reading of the spring balance will be     AIEEE  Solved  Paper-2003
  A)
  24 N  
  done clear
  B)
                                        74 N      
  done clear
  C)
        15 N                      
  done clear
  D)
  49 N
  done clear
  View Answer play_arrow

• question_answer8) The length of a wire of a potentiometer is 100 cm and the emf of its stand and cell is. E volt. It is employed to measure the emf of a battery whose internal resistance is \[0.5\,\,\Omega \]. If the balance point is obtained at \[1=30\] cm from the positive end, the emf of the battery is           AIEEE  Solved  Paper-2003
  A)
  \[\frac{30\,E}{100.5}\]         
  done clear
  B)
                        \[\frac{30\,E}{100-05}\]
  done clear
  C)
  \[\frac{30\,(E-0.5i)}{100}\], where \[i\] is the current in the potentiometer wire
  done clear
  D)
  \[\frac{30\,E}{100}\]
  done clear
  View Answer play_arrow

• question_answer9) A strip of copper and another of germanium are cooled from room temperature to 80 K. The resistance of   AIEEE  Solved  Paper-2003
  A)
  each of these decreases
  done clear
  B)
  copper strip increases and that of germanium decreases
  done clear
  C)
  copper strip decreases and that of germanium increases
  done clear
  D)
  each of the above increases
  done clear
  View Answer play_arrow

• question_answer10) Consider telecommunication through optical fibres. Which of the following statements is not true?     AIEEE  Solved  Paper-2003
  A)
  Optical fibres can be of graded refractive index
  done clear
  B)
  Optical fibres are subjected to electro- magnetic interference from outside
  done clear
  C)
  Optical fibres have extremely low transmission loss
  done clear
  D)
  Optical fibres may have homogeneous core with a suitable cladding
  done clear
  View Answer play_arrow

• question_answer11) The thermo-emf of a thermocouple is \[25\mu V{{/}^{o}}C\] at room temperature. A galvanometer of \[40\,\Omega \]. resistance, capable of detecting current as low as \[{{10}^{-5}}\] A, is   connected with the thermocouple. The smallest temperature difference that can be detected by this system is     AIEEE  Solved  Paper-2003
  A)
  \[{{16}^{o}}C\]         
  done clear
  B)
                        \[{{12}^{o}}C\]                 
  done clear
  C)
        \[{{8}^{o}}C\]                                   
  done clear
  D)
  \[{{20}^{o}}C\] 
  done clear
  View Answer play_arrow

• question_answer12) The negative Zn-pole of Daniell cell, sending a constant current through a circuit, decreases in mass by \[0.13\]g in 30 min. If the electrochemical equivalent of Zn and Cu are \[32.5\] and \[31.5\] respectively, the increase in the mass of the positive Cu-pole in this time is     AIEEE  Solved  Paper-2003
  A)
  \[0.180\] g      
  done clear
  B)
                        \[0.141\] g
  done clear
  C)
  \[0.126\]g           
  done clear
  D)
                        \[0.242\] g
  done clear
  View Answer play_arrow

• question_answer13) Dimensions of \[\frac{1}{{{\mu }_{0}}\,{{\varepsilon }_{0}}}\], where symbols have their usual meaning, are     AIEEE  Solved  Paper-2003
  A)
  \[[{{L}^{-1}}T]\]    
  done clear
  B)
                                        \[[{{L}^{2}}{{T}^{2}}]\]                  
  done clear
  C)
        \[[{{L}^{2}}{{T}^{-2}}]\]        
  done clear
  D)
                         \[[L{{T}^{-1}}]\]  
  done clear
  View Answer play_arrow

• question_answer14) A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then, the relation between the moment of inertia \[{{I}_{X}}\] and \[{{I}_{Y}}\] is
  A)
  \[{{l}_{Y}}=32\,{{l}_{X}}\]                             
  done clear
  B)
  \[{{l}_{Y}}=16\,{{l}_{X}}\]                             
  done clear
  C)
  \[{{l}_{Y}}=\,{{l}_{X}}\]                 
  done clear
  D)
  \[{{l}_{Y}}=\,64{{l}_{X}}\]
  done clear
  View Answer play_arrow

• question_answer15) The time period of a satellite of earth is 5 h. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become     AIEEE  Solved  Paper-2003
  A)
  10 h       
  done clear
  B)
        80 h       
  done clear
  C)
        40 h       
  done clear
  D)
        20 h
  done clear
  View Answer play_arrow

• question_answer16) A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is     AIEEE  Solved  Paper-2003
  A)
  \[\frac{L}{4}\]                   
  done clear
  B)
        2L                           
  done clear
  C)
  4L                           
  done clear
  D)
  \[\frac{L}{2}\]
  done clear
  View Answer play_arrow

• question_answer17) Which of the following radiations has the least wavelength?     AIEEE  Solved  Paper-2003
  A)
  \[\gamma \]-rays            
  done clear
  B)
  \[\beta \]-rays                                 
  done clear
  C)
  \[\alpha \]-rays                                
  done clear
  D)
  \[X\]-rays
  done clear
  View Answer play_arrow

• question_answer18) When \[{{U}^{238}}\] nucleus originally at rest, decays by emitting an alpha particle having a speed u, the recoil speed of the residual nucleus is     AIEEE  Solved  Paper-2003
  A)
  \[\frac{4\,u}{238}\]                                        
  done clear
  B)
  \[-\frac{4\,u}{238}\]                      
  done clear
  C)
  \[\frac{4\,u}{234}\]        
  done clear
  D)
        \[-\frac{4\,u}{238}\]
  done clear
  View Answer play_arrow

• question_answer19) Two spherical bodies of mass M and 5 M and radii R and 2 R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
  A)
  \[2.5\] R                              
  done clear
  B)
  \[4.5\] R                              
  done clear
  C)
  \[7.5\] R                              
  done clear
  D)
  \[1.5\] R
  done clear
  View Answer play_arrow

• question_answer20) The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the     AIEEE  Solved  Paper-2003
  A)
  crystal structure
  done clear
  B)
  variation of the number of charge carriers with temperature
  done clear
  C)
  type of bonding
  done clear
  D)
  variation of scattering mechanism with temperature
  done clear
  View Answer play_arrow

• question_answer21) A car moving with a speed of 50 km/h, can be stopped by brakes after atleast 6 m. If the same car is moving at a speed of 100 km/h, the minimum stopping distance is     AIEEE  Solved  Paper-2003
  A)
  12m      
  done clear
  B)
        18m      
  done clear
  C)
        24m      
  done clear
  D)
        6m
  done clear
  View Answer play_arrow

• question_answer22) A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of \[{{30}^{o}}\] with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground?              \[[g=10\,m/{{s}^{2}},\sin {{30}^{o}}=1/2,\cos {{30}^{o}}=\sqrt{3}/2]\]
  A)
  \[5.20\] m
  done clear
  B)
                        \[4.33\] m                          
  done clear
  C)
  \[2.60\] m                          
  done clear
  D)
  \[8.66\] m
  done clear
  View Answer play_arrow

• question_answer23) An ammeter reads upto 1 A. Its internal resistance is \[0.81\,\,\Omega \]. To increase the range to 10 A, the value of the required shunt is     AIEEE  Solved  Paper-2003
  A)
  \[0.03\,\,\Omega \]
  done clear
  B)
                        \[0.3\,\,\Omega \]                         
  done clear
  C)
        \[0.9\,\,\Omega \]                         
  done clear
  D)
  \[0.09\,\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer24) The physical quantities not having same dimensions are     AIEEE  Solved  Paper-2003
  A)
  torque and work
  done clear
  B)
  momentum and Planck's constant
  done clear
  C)
  stress and Young's modulus
  done clear
  D)
  speed and \[{{({{\mu }_{0}}-{{\varepsilon }_{0}})}^{-1/2}}\]
  done clear
  View Answer play_arrow

• question_answer25) Three forces start acting C simultaneously   on a particle   moving   with velocity v. These forces are    represented in magnitude and direction by the three sides of a \[\Delta ABC\] (as shown). The particle will now move with velocity                  AIEEE  Solved  Paper-2003
  A)
  less than v
  done clear
  B)
   greater than v  
  done clear
  C)
  \[\left| v \right|\] in the direction of largest force BC
  done clear
  D)
   v remain unchanged
  done clear
  View Answer play_arrow

• question_answer26) Resultant force is zero, as three forces acting on the particle can be represented in magnitude and direction by three sides of a triangle in same order. Hence, by Newton's 2nd law \[\left( F=m\frac{d\,\,v}{dt} \right)\], particle velocity (v) will be same. (\[\because \] if F = 0, v = constant) If the electric flux entering and leaving an enclosed surface respectively is \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\], the electric charge inside the surface will be     AIEEE  Solved  Paper-2003
  A)
  \[({{\phi }_{2}}-{{\phi }_{1}}){{\varepsilon }_{0}}\]        
  done clear
  B)
  \[({{\phi }_{1}}+{{\phi }_{2}})/{{\varepsilon }_{0}}\]                        
  done clear
  C)
  \[({{\phi }_{2}}-{{\phi }_{1}})/{{\varepsilon }_{0}}\]       
  done clear
  D)
        \[({{\phi }_{1}}+{{\phi }_{2}}){{\varepsilon }_{0}}\]
  done clear
  View Answer play_arrow

• question_answer27) A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is \[0.2\]. The weight of the block is                  AIEEE  Solved  Paper-2003
  A)
          20 N      
  done clear
  B)
        50 N                      
  done clear
  C)
        100 N                    
  done clear
  D)
        2 N
  done clear
  View Answer play_arrow

• question_answer28) A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10s. Then, the coefficient of friction is     AIEEE  Solved  Paper-2003
  A)
  \[0.02\]                               
  done clear
  B)
  \[0.03\]                               
  done clear
  C)
        \[0.06\]               
  done clear
  D)
  \[0.01\]
  done clear
  View Answer play_arrow

• question_answer29) Consider the following two statements A. Linear momentum of a system of particles is zero. B. Kinetic energy of a system of particles is zero. Then,     AIEEE  Solved  Paper-2003
  A)
  A does not imply B and B does not imply A
  done clear
  B)
  A implies B but B does not imply A
  done clear
  C)
  A does not imply B but B implies A
  done clear
  D)
  A implies B and B implies A
  done clear
  View Answer play_arrow

• question_answer30) Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon     AIEEE  Solved  Paper-2003
  A)
  the rates at which currents are changing in the two coils
  done clear
  B)
  relative position and orientation of the two coils
  done clear
  C)
  time for which current is flown
  done clear
  D)
  the currents in the two coils
  done clear
  View Answer play_arrow

• question_answer31) . A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is     AIEEE  Solved  Paper-2003
  A)
  \[\frac{P\,m}{M+m}\]                  
  done clear
  B)
  \[\frac{P\,m}{M-m}\]                   
  done clear
  C)
  P                            
  done clear
  D)
  \[\frac{P\,M}{M+m}\]
  done clear
  View Answer play_arrow

• question_answer32) A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then, the true statement about the scale reading is     AIEEE  Solved  Paper-2003
  A)
  both the scales read M kg each
  done clear
  B)
  the scale of the lower one reads M kg and of the upper one zero
  done clear
  C)
  the reading of the two scales can be anything but the sum of the readings will be M kg
  done clear
  D)
  both the scales read M/2 kg
  done clear
  View Answer play_arrow

• question_answer33) A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then, the elastic energy stored in the wire is     AIEEE  Solved  Paper-2003
  A)
  \[0.2\] J                               
  done clear
  B)
  10 J                        
  done clear
  C)
  20 J                                        
  done clear
  D)
  \[0.1\]J
  done clear
  View Answer play_arrow

• question_answer34) The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of \[{{45}^{o}}\] with the vertical, the escape velocity will be     AIEEE  Solved  Paper-2003
  A)
  \[11\sqrt{2}\] km/s        
  done clear
  B)
  22 km/s                               
  done clear
  C)
  11 km/s               
  done clear
  D)
        \[11\sqrt{2}\] m/s 
  done clear
  View Answer play_arrow

• question_answer35) A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes \[5T/3\], then the ratio of \[\frac{m}{M}\] is     AIEEE  Solved  Paper-2003
  A)
  \[\frac{3}{5}\]                                   
  done clear
  B)
        \[\frac{25}{9}\]                                
  done clear
  C)
  \[\frac{16}{9}\]                
  done clear
  D)
        \[\frac{5}{3}\]
  done clear
  View Answer play_arrow

• question_answer36) "Heat cannot be itself flow from a body at lower temperature to a body at higher temperature"  is  a  statement  or consequence of     AIEEE  Solved  Paper-2003
  A)
  second law of thermodynamics
  done clear
  B)
  conservation of momentum
  done clear
  C)
  conservation of mass
  done clear
  D)
  first law of thermodynamics
  done clear
  View Answer play_arrow

• question_answer37) Two particles A and B of equal masses are suspended from two massless springs of spring constants \[{{k}_{1}}\] and \[{{k}_{2}}\], respectively. If the   maximum   velocities,   during oscillations are equal, the ratio of amplitudes of A and B is     AIEEE  Solved  Paper-2003
  A)
  \[\sqrt{{{k}_{1}}/{{k}_{2}}}\]         
  done clear
  B)
                        \[{{k}_{1}}/{{k}_{2}}\]                   
  done clear
  C)
  \[\sqrt{{{k}_{2}}/{{k}_{1}}}\]                      
  done clear
  D)
  \[{{k}_{2}}/{{k}_{1}}\] \[\]
  done clear
  View Answer play_arrow

• question_answer38) The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is     AIEEE  Solved  Paper-2003
  A)
  \[11%\]                               
  done clear
  B)
  \[21%\]                               
  done clear
  C)
        \[42%\]                               
  done clear
  D)
        \[10.5%\]
  done clear
  View Answer play_arrow

• question_answer39) The displacement y of a wave travelling in the x-direction is given by \[y={{10}^{-4}}\sin \left( 600\,t-2x+\frac{\pi }{3} \right)\] metre where, \[x\] is expressed in metres and t in seconds. The speed of the wave motion, in \[m{{s}^{-1}}\] is     AIEEE  Solved  Paper-2003
  A)
  300     
  done clear
  B)
        600        
  done clear
  C)
        1200                      
  done clear
  D)
        200
  done clear
  View Answer play_arrow

• question_answer40) When the current changes from \[+2\] A to \[-2\] A in \[0.05\] s, an emf of 8 V is induced in a coil. The coefficient of self-induction of the coil is     AIEEE  Solved  Paper-2003
  A)
  \[0.2\] H              
  done clear
  B)
        \[0.4\] H                              
  done clear
  C)
  \[0.8\] H                              
  done clear
  D)
  \[0.1\] H
  done clear
  View Answer play_arrow

• question_answer41) In an oscillating LC circuit, the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is     AIEEE  Solved  Paper-2003
  A)
  \[Q/2\]                
  done clear
  B)
        \[Q/\sqrt{3}\]                   
  done clear
  C)
  \[Q/\sqrt{2}\]
  done clear
  D)
  Q
  done clear
  View Answer play_arrow

• question_answer42) The core of any transformer is laminated so as to     AIEEE  Solved  Paper-2003
  A)
  reduce the energy loss due to eddy currents
  done clear
  B)
  make it light weight
  done clear
  C)
  make it robust and strong
  done clear
  D)
  increase the secondary voltage
  done clear
  View Answer play_arrow

• question_answer43) Let F be the force acting on a particle having position vector r and \[\tau \] be the torque of this force about the origin. Then,     AIEEE  Solved  Paper-2003
  A)
  \[r\,.\,\tau =0\] and \[F\,.\,\,\tau \ne 0\]            
  done clear
  B)
  \[r\,.\,\,\tau \ne 0\] and \[F\,.\,\,\tau =0\]
  done clear
  C)
  \[r\,.\,\,\tau \ne 0\] and \[F\,.\,\,\tau \ne 0\]
  done clear
  D)
  \[r\,.\,\,\tau =0\] and \[F\,.\,\,\tau =0\]
  done clear
  View Answer play_arrow

• question_answer44) A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is     AIEEE  Solved  Paper-2003
  A)
  \[0.4\,ln\,2\]         
  done clear
  B)
        \[0.2\,\ln \,2\]                  
  done clear
  C)
        \[0.1\,\ln \,2\]                  
  done clear
  D)
        \[0.8\,\ln \,2\]
  done clear
  View Answer play_arrow

• question_answer45) A nucleus with \[Z=92\] emits the following in a sequence: \[\alpha ,\alpha ,{{\beta }^{-}},{{\beta }^{-}},\alpha ,\alpha ,\alpha ,\alpha ;{{\beta }^{-}},{{\beta }^{-}},\alpha ,{{\beta }^{+}},{{\beta }^{+}},\alpha \]. The Z of the resulting nucleus is     AIEEE  Solved  Paper-2003
  A)
  76          
  done clear
  B)
        78       
  done clear
  C)
        82          
  done clear
  D)
        74
  done clear
  View Answer play_arrow

• question_answer46) Which of the following cannot be emitted by radioactive substances during their decay?     AIEEE  Solved  Paper-2003
  A)
   Protons              
  done clear
  B)
  Neutrinos                           
  done clear
  C)
  Helium nuclei     
  done clear
  D)
        Electrons
  done clear
  View Answer play_arrow

• question_answer47) A 3 V battery with negligible internal resistance is connected in a circuit as shown in the figure. The current I, in the circuit will be                    AIEEE  Solved  Paper-2003
  A)
  1 A                         
  done clear
  B)
  \[1.5\] A  
  done clear
  C)
                        2 A                         
  done clear
  D)
  1 A
  done clear
  View Answer play_arrow

• question_answer48) A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor     AIEEE  Solved  Paper-2003
  A)
  decreases                          
  done clear
  B)
  remains unchanged
  done clear
  C)
  becomes infinite
  done clear
  D)
  Increases
  done clear
  View Answer play_arrow

• question_answer49) The displacement of a particle varies according to the relation \[x=4\,(\cos \pi \,t+\sin \pi t)\]. The amplitude of the particle is     AIEEE  Solved  Paper-2003
  A)
  \[-4\]    
  done clear
  B)
                        4                             
  done clear
  C)
  \[4\sqrt{2}\]
  done clear
  D)
  8
  done clear
  View Answer play_arrow

• question_answer50) A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point P at a distance R/2 from the centre of the shell is     AIEEE  Solved  Paper-2003
  A)
  \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}\]       
  done clear
  B)
                        \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}-\frac{2q}{4\pi {{\varepsilon }_{0}}R}\]     
  done clear
  C)
  \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}+\frac{q}{4\pi {{\varepsilon }_{0}}R}\] 
  done clear
  D)
        \[\frac{(q+Q)}{4\pi {{\varepsilon }_{0}}R}\frac{2}{R}\]
  done clear
  View Answer play_arrow

• question_answer51) The work done in placing a charge of \[8\times {{10}^{-18}}C\] on a condenser of capacity \[100\mu F\] is     AIEEE  Solved  Paper-2003
  A)
  \[16\times {{10}^{-32}}\] J          
  done clear
  B)
  \[3.1\times {{10}^{-26}}\] J                         
  done clear
  C)
  \[4\times {{10}^{-10}}\] J       
  done clear
  D)
        \[32\times {{10}^{-32}}\] J
  done clear
  View Answer play_arrow

• question_answer52) The coordinates of a moving particle at any time t are given by \[x=\alpha {{t}^{3}}\] and \[y=\beta {{t}^{3}}\]. The speed of the particle at time t is given by     AIEEE  Solved  Paper-2003
  A)
  \[3t\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]  
  done clear
  B)
        \[3{{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
  done clear
  C)
        \[{{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]      
  done clear
  D)
        \[\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer53) During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio, \[{{C}_{p}}/{{C}_{V}}\] for the gas is     AIEEE  Solved  Paper-2003
  A)
  4/3     
  done clear
  B)
                        2                             
  done clear
  C)
        5/3        
  done clear
  D)
        3/2
  done clear
  View Answer play_arrow

• question_answer54) Which of the following parameters does not characterise the thermodynamic state of matter?     AIEEE  Solved  Paper-2003
  A)
  Temperature
  done clear
  B)
                        Pressure                             
  done clear
  C)
  Work           
  done clear
  D)
  Volume
  done clear
  View Answer play_arrow

• question_answer55) A Carnot engine takes \[3\times {{10}^{6}}\] cal of heat from a reservoir at \[{{627}^{o}}C\] and gives it to a sink at \[{{27}^{o}}C\]. The work done by the engine is     AIEEE  Solved  Paper-2003
  A)
  \[42\times {{10}^{6}}\]J     
  done clear
  B)
                        \[8.4\times {{10}^{6}}\]J              
  done clear
  C)
  \[16.8\times {{10}^{6}}\] J     
  done clear
  D)
                        Zero
  done clear
  View Answer play_arrow

• question_answer56) A spring of spring constant \[5\times {{10}^{3}}\,N/m\] is stretched initially by 5 cm from the unstretched position. Then, the work required to stretch it further by another 5 cm is     AIEEE  Solved  Paper-2003
  A)
  \[12.50\]N-m   
  done clear
  B)
        \[18.75\]N-m    
  done clear
  C)
                        \[25.00\] N-m        
  done clear
  D)
        \[6.25\] N-m
  done clear
  View Answer play_arrow

• question_answer57) A metal wire of linear mass density of \[9.8\] g/m is stretched with a tension of 10 kg-wt between two rigid supports 1 m apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n of the alternating source is     AIEEE  Solved  Paper-2003
  A)
  50 Hz    
  done clear
  B)
        100 Hz                  
  done clear
  C)
  200 Hz                  
  done clear
  D)
  25 Hz
  done clear
  View Answer play_arrow

• question_answer58) A tuning fork of known frequency 256 Hz makes 5 beats/s with the vibrating string of a piano. The beat frequency decreases to 2 beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was     AIEEE  Solved  Paper-2003
  A)
  (256 + 2) Hz       
  done clear
  B)
        (256 - 2) Hz                         
  done clear
  C)
  (256 - 5) Hz       
  done clear
  D)
        (256 + 5) Hz
  done clear
  View Answer play_arrow

• question_answer59) A body executes simple harmonic motion. The potential energy (PE), the kinetic energy (KE) and total energy (TE) are measured as function of displacement \[x\]. Which of the following statements is true?     AIEEE  Solved  Paper-2003
  A)
  KE is maximum when \[x=0\]
  done clear
  B)
  TE is zero when \[x=0\]
  done clear
  C)
  KE is maximum when \[x\] is maximum
  done clear
  D)
  PE is maximum when \[x=0\]
  done clear
  View Answer play_arrow

• question_answer60) In the nuclear fusion reaction,                 \[_{1}^{2}H+_{1}^{3}H\to _{2}^{4}He+n\] given that the repulsive potential energy between the two nuclei is \[7.7\times {{10}^{-14}}\] J the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant \[k=1.38\times {{10}^{-23}}J/K\]]     AIEEE  Solved  Paper-2003
  A)
                          \[{{10}^{7}}\] K  
  done clear
  B)
                        \[{{10}^{5}}\] K                                
  done clear
  C)
  \[{{10}^{3}}\] K                                
  done clear
  D)
  \[{{10}^{9}}\] K
  done clear
  View Answer play_arrow

• question_answer61) Which of the following atoms has the lowest ionisation potential?     AIEEE  Solved  Paper-2003
  A)
  \[_{7}^{14}N\]  
  done clear
  B)
                                        \[_{55}^{133}Cs\]           
  done clear
  C)
        \[_{18}^{40}Ar\]                              
  done clear
  D)
        \[_{8}^{16}O\]
  done clear
  View Answer play_arrow

• question_answer62) The wavelengths involved in the spectrum of deuterium \[\left( _{1}^{2}D \right)\] are slightly different from that of hydrogen spectrum, because     AIEEE  Solved  Paper-2003
  A)
  sizes of the two nuclei are different
  done clear
  B)
  nuclear forces are different in the two cases
  done clear
  C)
  masses of the two nuclei are different
  done clear
  D)
  attraction between the electron and the nucleus is different in the two cases
  done clear
  View Answer play_arrow

• question_answer63) In the middle of the depletion layer of reverse biased p-n junction, the     AIEEE  Solved  Paper-2003
  A)
  electric field is zero        
  done clear
  B)
  potential is maximum
  done clear
  C)
  electric field is maximum
  done clear
  D)
  potential is zero
  done clear
  View Answer play_arrow

• question_answer64) If the binding energy of the electron in a hydrogen atom is \[13.6\] eV, the energy required to remove the electron from the first excited state of \[L{{i}^{2+}}\] is     AIEEE  Solved  Paper-2003
  A)
  \[30.6\] eV
  done clear
  B)
  \[13.6\] eV                         
  done clear
  C)
  \[3.4\] eV                           
  done clear
  D)
  \[122.4\] eV
  done clear
  View Answer play_arrow

• question_answer65) A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to     AIEEE  Solved  Paper-2003
  A)
  \[{{t}^{3/4}}\]                                   
  done clear
  B)
        \[{{t}^{3/2}}\]   
  done clear
  C)
        \[{{t}^{1/4}}\]                   
  done clear
  D)
        \[{{t}^{1/2}}\]
  done clear
  View Answer play_arrow

• question_answer66) A rocket with a lift-off mass \[3.5\times {{10}^{4}}\] kg is blasted   upwards   with   an   initial acceleration of \[10\,m/{{s}^{2}}\] . Then, the initial thrust of the blast is     AIEEE  Solved  Paper-2003
  A)
  \[3.5\times {{10}^{5}}\] N   
  done clear
  B)
        \[7.0\times {{10}^{5}}\] N                           
  done clear
  C)
  \[14.0\times {{10}^{5}}\] N      
  done clear
  D)
        \[1.75\times {{10}^{5}}\] N
  done clear
  View Answer play_arrow

• question_answer67) To demonstrate the phenomenon of interference, we require two sources which emit radiations of     AIEEE  Solved  Paper-2003
  A)
  nearly the same frequency
  done clear
  B)
  the same frequency
  done clear
  C)
  different wavelength
  done clear
  D)
  the same frequency and having a definite phase relationship
  done clear
  View Answer play_arrow

• question_answer68) Three charges \[-{{q}_{1}},+{{q}_{2}}\] and \[-{{q}_{3}}\] are placed as shown in the figure. The x-component of the force on \[-{{q}_{1}}\] is proportional to                  AIEEE  Solved  Paper-2003
  A)
  \[\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta \]     
  done clear
  B)
        \[\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta \]
  done clear
  C)
                        \[\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta \]      
  done clear
  D)
        \[\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta \]
  done clear
  View Answer play_arrow

• question_answer69) A 220 V, 1000 W bulb is connected across a 110 V mains supply. The power consumed will be     AIEEE  Solved  Paper-2003
  A)
  750 W                   
  done clear
  B)
        500 W                   
  done clear
  C)
  250 W           
  done clear
  D)
  1000 W
  done clear
  View Answer play_arrow

• question_answer70) The image formed by an objective of a compound microscope is     AIEEE  Solved  Paper-2003
  A)
  virtual and diminished
  done clear
  B)
  real and diminished
  done clear
  C)
  real and enlarged
  done clear
  D)
  virtual and enlarged
  done clear
  View Answer play_arrow

• question_answer71) The earth radiates in the infrared region of the spectrum. The spectrum is correctly given by     AIEEE  Solved  Paper-2003
  A)
  Rayleigh Jeans law
  done clear
  B)
  Planck's law of radiation
  done clear
  C)
  Stefan's law of radiation
  done clear
  D)
  Wien's law
  done clear
  View Answer play_arrow

• question_answer72) To get three images of a single object, one should have two plane mirrors at an angle of     AIEEE  Solved  Paper-2003
  A)
  \[{{60}^{o}}\]                                    
  done clear
  B)
  \[{{90}^{o}}\]                                    
  done clear
  C)
  \[{{120}^{o}}\]                                 
  done clear
  D)
  \[{{30}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer73) According to Newton's law of cooling, the rate of cooling of a body is proportional to \[{{(\Delta \theta )}^{n}}\], where \[\Delta \theta \] is the difference of the temperature of the body and the surroundings and n is equal to     AIEEE  Solved  Paper-2003
  A)
  2            
  done clear
  B)
                        3                                             
  done clear
  C)
  4                                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer74) The length of a given cylindrical wire is increased by \[100%\]. Due to the consequent decrease in diameter, the change in the resistance of the wire will be     AIEEE  Solved  Paper-2003
  A)
                                          \[200%\]          
  done clear
  B)
                        \[100%\]                             
  done clear
  C)
  \[50%\]                               
  done clear
  D)
  \[300%\] 
  done clear
  View Answer play_arrow

• question_answer75) In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inner-orbit jumps of the electron for Bohr orbits in an atom of hydrogen?     AIEEE  Solved  Paper-2003
  A)
  \[3\to 2\] 
  done clear
  B)
                        \[5\to 2\]
  done clear
  C)
  \[4\to 1\]                            
  done clear
  D)
  \[2\to 5\]
  done clear
  View Answer play_arrow

• question_answer76) The de-Broglie wavelength of a tennis ball of mass 60g moving with a velocity of 10 m/s is approximately (Planck's constant, \[h=6.63\times {{10}^{-34}}\] Js)     AIEEE  Solved  Paper-2003
  A)
  \[{{10}^{-33}}\] m
  done clear
  B)
                        \[{{10}^{-31}}\] m                           
  done clear
  C)
   \[{{10}^{-16}}\]m          
  done clear
  D)
         \[{{10}^{-25}}\] m
  done clear
  View Answer play_arrow

• question_answer77) The orbital angular momentum for an electron revolving in an orbit is given by \[\sqrt{l(l+1)}\frac{h}{2\pi }\]. This momentum for an s-electron will be given by
  A)
  \[+\frac{1}{2}.\,\frac{h}{2\pi }\]           
  done clear
  B)
        zero      
  done clear
  C)
  \[\,\frac{h}{2\pi }\]                        
  done clear
  D)
        \[\sqrt{2}\,.\,\frac{h}{2\pi }\]
  done clear
  View Answer play_arrow

• question_answer78) How many unit cells are present in a cube shaped ideal crystal of \[NaCl\] of mass \[1.00\]g? [At. masses Na \[=23,\,\,Cl=35.5\]]     AIEEE  Solved  Paper-2003
  A)
  \[2.57\times {{10}^{21}}\]     
  done clear
  B)
  \[5.14\times {{10}^{21}}\]                           
  done clear
  C)
  \[1.28\times {{10}^{21}}\]                           
  done clear
  D)
  \[1.71\times {{10}^{21}}\]
  done clear
  View Answer play_arrow

• question_answer79) Glass is a     AIEEE  Solved  Paper-2003
  A)
                                          micro-crystalline solid   
  done clear
  B)
  super-cooled liquid
  done clear
  C)
  gel                         
  done clear
  D)
  polymeric mixture
  done clear
  View Answer play_arrow

• question_answer80) Which one of the following statements is correct?     AIEEE  Solved  Paper-2003
  A)
  Manganese salts give a violet borax bead test in the reducing flame
  done clear
  B)
  From a mixed precipitate of \[AgCl\] and \[Agl,\] ammonia solution dissolves only \[AgCl\]
  done clear
  C)
  Ferric ions give a deep green precipitate on adding potassium ferrocyanide solution
  done clear
  D)
  On boiling a solution having \[{{K}^{+}},C{{a}^{2+}}\] and \[HCO_{3}^{-}\] ions we get a precipitate \[{{K}_{2}}Ca{{(C{{O}_{3}})}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer81) According to the periodic law of elements, the variation in properties of elements is related to their     AIEEE  Solved  Paper-2003
  A)
  atomic masses
  done clear
  B)
        nuclear masses
  done clear
  C)
  atomic numbers              
  done clear
  D)
  nuclear neutron-proton number ratio
  done clear
  View Answer play_arrow

• question_answer82) Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that graphite     AIEEE  Solved  Paper-2003
  A)
  is a non-crystalline substance
  done clear
  B)
  is an allotropic form of diamond
  done clear
  C)
  has molecules of variable molecular masses like polymers
  done clear
  D)
  has carbon atoms arranged in large plates of rings of strongly bound carbon atoms with weak interplate bonds
  done clear
  View Answer play_arrow

• question_answer83) The IUPAC name of \[C{{H}_{2}}COCH{{(C{{H}_{3}})}_{2}}\] is     AIEEE  Solved  Paper-2003
  A)
  isopropylmethyl ketone
  done clear
  B)
  2-methyl-S-butanone
  done clear
  C)
  4-methyli-sopropyl ketone
  done clear
  D)
  3-methyl-2-butanone
  done clear
  View Answer play_arrow

• question_answer84) When \[C{{H}_{2}}=CH-COOH\] is reduced with \[LiAl{{H}_{4}}\], the compound obtained will be     AIEEE  Solved  Paper-2003
  A)
  \[C{{H}_{3}}-C{{H}_{2}}-COOH\]
  done clear
  B)
        \[C{{H}_{2}}=CH-C{{H}_{2}}OH\]
  done clear
  C)
  \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}OH\]
  done clear
  D)
  \[C{{H}_{3}}-C{{H}_{2}}-CHO\]
  done clear
  View Answer play_arrow

• question_answer85) According to the kinetic theory of gases, in an ideal gas, between two successive collisions a gas molecule travels      AIEEE  Solved  Paper-2003
  A)
  in a circular path
  done clear
  B)
  in a wavy path
  done clear
  C)
  in a straight line path
  done clear
  D)
  with an accelerated velocity
  done clear
  View Answer play_arrow

• question_answer86) Which of the following group of transition metals is called coinage metals?     AIEEE  Solved  Paper-2003
  A)
  Cu, Ag, Au        
  done clear
  B)
        Ru, Rh, Pd                          
  done clear
  C)
  Fe, Co, Ni         
  done clear
  D)
        Os, Ir, Pt
  done clear
  View Answer play_arrow

• question_answer87) The general formula \[{{C}_{n}}{{H}_{2n}}{{O}_{2}}\] could be for open chain     AIEEE  Solved  Paper-2003
  A)
  diketones           
  done clear
  B)
        carboxylic-acids
  done clear
  C)
                        diols                      
  done clear
  D)
        dialdehydes
  done clear
  View Answer play_arrow

• question_answer88) An ether is more volatile than an alcohol having the same molecular formula. This is due to     AIEEE  Solved  Paper-2003
  A)
  dipolar character of ethers
  done clear
  B)
  alcohols having resonance structures
  done clear
  C)
  inter-molecular hydrogen bonding in ethers
  done clear
  D)
  inter-molecular hydrogen bonding in alcohols
  done clear
  View Answer play_arrow

• question_answer89) Among the following four structures I to IV \[{{C}_{2}}{{H}_{5}}-\overset{\begin{smallmatrix}  C{{H}_{3}} \\  || \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{3}}{{H}_{7}}C{{H}_{3}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-\overset{\begin{smallmatrix}  C{{H}_{3}} \\  || \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{2}}{{H}_{5}}\]                                 (I)                           (II)              \[H-\overset{\begin{smallmatrix}  H \\  | \end{smallmatrix}}{\mathop{{{\underset{\begin{smallmatrix}  | \\  H \end{smallmatrix}}{\mathop{C}}\,}^{\oplus }}}}\,\]                         \[{{C}_{2}}{{H}_{5}}-\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{2}}{{H}_{5}}\]                   (III)                                       (IV) it is true that     AIEEE  Solved  Paper-2003
  A)
  all four are chiral compounds
  done clear
  B)
  only I and II are chiral compounds
  done clear
  C)
  only III is a chiral compound
  done clear
  D)
  only II and IV are chiral compounds
  done clear
  View Answer play_arrow

• question_answer90) Which one of the following processes will produce hard water?     AIEEE  Solved  Paper-2003
  A)
  Saturation of water with \[CaC{{O}_{3}}\]
  done clear
  B)
  Saturation of water with \[MgC{{O}_{3}}\]
  done clear
  C)
  Saturation of water with \[CaS{{O}_{4}}\]
  done clear
  D)
  Addition of \[N{{a}_{2}}S{{O}_{4}}\] to water
  done clear
  View Answer play_arrow

• question_answer91) Which one of the following compounds has the smallest bond angle in its molecule?     AIEEE  Solved  Paper-2003
  A)
  \[S{{O}_{2}}\]                                   
  done clear
  B)
  \[O{{H}_{2}}\]                  
  done clear
  C)
  \[S{{H}_{2}}\]                                   
  done clear
  D)
  \[N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer92) Which one of the following pairs of molecules will have permanent dipole moments for both members?     AIEEE  Solved  Paper-2003
  A)
                                          \[Si{{F}_{4}}\] and \[N{{O}_{2}}\]   
  done clear
  B)
        \[N{{O}_{2}}\] and \[C{{O}_{2}}\]
  done clear
  C)
        \[N{{O}_{2}}\] and \[{{O}_{3}}\]      
  done clear
  D)
        \[Si{{F}_{4}}\] and \[C{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer93) Which one of the following group represents a collection of isoelectronic species? (At. no. Cs-55. Br-35)     AIEEE  Solved  Paper-2003
  A)
                          \[N{{a}^{+}},C{{a}^{2+}},M{{g}^{2+}}\]
  done clear
  B)
        \[{{N}^{3-}},{{F}^{-}},N{{a}^{+}}\]
  done clear
  C)
        Be, \[A{{l}^{3+}},C{{l}^{-}}\]      
  done clear
  D)
        \[C{{a}^{2+}},C{{s}^{+}},Br\]
  done clear
  View Answer play_arrow

• question_answer94) In the anion \[HCO{{O}^{-}}\] the two carbon-oxygen bonds are found to be of equal length. What is the reason for it?     AIEEE  Solved  Paper-2003
  A)
  Electronic orbits of carbon atom are hybridized
  done clear
  B)
  The \[c=0\] bond is weaker than the C?O bond
  done clear
  C)
  The anion \[HCO{{O}^{-}}\] has two resonating structures
  done clear
  D)
  The anion is obtained by the removal of a proton from the acid molecule
  done clear
  View Answer play_arrow

• question_answer95) The pair of species having identical shapes for molecules of both species is     AIEEE  Solved  Paper-2003
  A)
                                          \[C{{F}_{4}},S{{F}_{4}}\]         
  done clear
  B)
                        \[Xe{{F}_{2}},C{{O}_{2}}\]                           
  done clear
  C)
        \[B{{r}_{3}},PC{{l}_{3}}\]        
  done clear
  D)
                        \[P{{F}_{5}},l{{F}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer96) The atomic numbers of vanadium (V), chromium (Cr), manganese (Mn) and iron (Fe) are respectively 23, 24, 25 and 26. Which one of these may be expected to have the highest second ionisation enthalpy?     AIEEE  Solved  Paper-2003
  A)
                          V                            
  done clear
  B)
  Cr                           
  done clear
  C)
  Mn                        
  done clear
  D)
  Fe
  done clear
  View Answer play_arrow

• question_answer97) Consider the reaction equilibrium,              \[2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g);\]                                                 \[\Delta {{H}^{o}}=-198\,k\,J\] On the basis of Le Chatelier's principle, the condition favourable for the forward reaction is     AIEEE  Solved  Paper-2003
  A)
  lowering of temperature as well as pressure
  done clear
  B)
  increasing temperature as well as pressure
  done clear
  C)
  lowering the temperature and increasing the pressure
  done clear
  D)
  any value of temperature and pressure
  done clear
  View Answer play_arrow

• question_answer98) What volume of hydrogen gas, at 273K and 1 atm pressure will be consumed in obtaining \[21.6\] g of elemental boron (atomic mass \[=10.8\]) from the reduction of boron trichloride by hydrogen?     AIEEE  Solved  Paper-2003
  A)
                                          \[89.6\] L                            
  done clear
  B)
        \[67.2\] L                            
  done clear
  C)
  \[44.8\] L                            
  done clear
  D)
  \[22.4\] L
  done clear
  View Answer play_arrow

• question_answer99) For the reaction equilibrium,                 \[{{N}_{2}}{{O}_{4}}(g)\overset{{}}{leftrightarrows}2NO(g)\] the concentrations of \[{{N}_{2}}{{O}_{4}}\] and \[N{{O}_{2}}\] at equilibrium    are   \[4.8\times {{10}^{-2}}\] and \[1.2\times {{10}^{-2}}mol\,{{L}^{-1}}\] respectively. The value of \[{{K}_{c}}\] for the reaction is     AIEEE  Solved  Paper-2003
  A)
                          \[3.3\times {{10}^{2}}mol\,{{L}^{-1}}\]  
  done clear
  B)
        \[3\times {{10}^{-1}}mol\,{{L}^{-1}}\]
  done clear
  C)
        \[3\times {{10}^{-3}}mol\,{{L}^{-1}}\]   
  done clear
  D)
        \[3\times {{10}^{3}}mol\,{{L}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer100) The solubility in water of a sparingly soluble salt \[A{{B}_{2}}\] is \[1.0\times {{10}^{-5}}mol\,{{L}^{-1}}\] Its solubility product number will be     AIEEE  Solved  Paper-2003
  A)
                          \[4\times {{10}^{-15}}\]                               
  done clear
  B)
  \[4\times {{10}^{-10}}\]                               
  done clear
  C)
  \[1\times {{10}^{-15}}\]               
  done clear
  D)
        \[1\times {{10}^{-10}}\]
  done clear
  View Answer play_arrow

• question_answer101) When during electrolysis of a solution of \[AgN{{O}_{3}}\], 9650 coulombs of charge pass through the electroplating bath, the mass of silver deposited on the cathode will be     AIEEE  Solved  Paper-2003
  A)
                          \[1.08\] g                            
  done clear
  B)
  \[10.8\] g                            
  done clear
  C)
  \[21.6\] g                            
  done clear
  D)
  108 g
  done clear
  View Answer play_arrow

• question_answer102) For the redox reaction, \[Zn(s)+C{{u}^{2+}}(0.1M)\xrightarrow{{}}Z{{n}^{2+}}(1M)+Cu(s)\]taking place in a cell, \[E_{cell}^{o}\] is \[1.10\] volt. \[{{E}_{cell}}\] for the cell will be \[\left( 2.303\frac{RT}{F}=0.0591 \right)\]     AIEEE  Solved  Paper-2003
  A)
                          \[2.14\] V                           
  done clear
  B)
  \[1.80\] V                           
  done clear
  C)
  \[1.07\] V                           
  done clear
  D)
  \[0.82\] V
  done clear
  View Answer play_arrow

• question_answer103) In a \[0.2\] molal aqueous solution of a weak acid HX, the degree of ionisation is \[0.3\]. Taking \[{{K}_{f}}\] for water as \[1.85\], the freezing point of the solution will be nearest to     AIEEE  Solved  Paper-2003
  A)
                          \[-{{0.480}^{o}}C\]       
  done clear
  B)
        \[-{{0.360}^{o}}C\]                         
  done clear
  C)
  \[-{{0.260}^{o}}C\]        
  done clear
  D)
        \[+\,{{0.480}^{o}}C\]
  done clear
  View Answer play_arrow

• question_answer104) The rate law for a reaction between the substances A and B is given by rate \[=k\,{{[A]}^{n}}{{[B]}^{m}}\]. On doubling   the concentration of A and halving the concentration of B, the ratio of the new rate to the earlier rate of the reaction will be as   AIEEE  Solved  Paper-2003
  A)
  \[\frac{1}{{{2}^{m+n}}}\]                             
  done clear
  B)
  (m + n)                                
  done clear
  C)
  (n - m)                 
  done clear
  D)
  \[{{2}^{(n-m)}}\]
  done clear
  View Answer play_arrow

• question_answer105) 25 mL of a solution of barium hydroxide on titration with \[0.1\] molar solution of hydrochloric acid gave a titre value of 35 mL. The molarity of barium hydroxide solution was     AIEEE  Solved  Paper-2003
  A)
                          \[0.07\]                               
  done clear
  B)
  \[0.14\]                               
  done clear
  C)
  \[0.28\]                               
  done clear
  D)
  \[0.35\]
  done clear
  View Answer play_arrow

• question_answer106) The correct relationship between free energy change in a reaction and the corresponding equilibrium constant \[{{K}_{c}}\] is     AIEEE  Solved  Paper-2003
  A)
                          \[\Delta G=RT\,\ln \,{{K}_{c}}\] 
  done clear
  B)
        \[-\Delta G=RT\,\ln \,{{K}_{c}}\]
  done clear
  C)
        \[\Delta {{G}^{o}}=RT\,\ln \,{{K}_{c}}\]
  done clear
  D)
        \[-\Delta {{G}^{o}}=RT\,\ln \,{{K}_{c}}\]
  done clear
  View Answer play_arrow

• question_answer107) If at 298K the bond energies of \[C-H,C-C,\,C=C\] and \[H-H\] bonds are respectively 414, 347, 615 and 435 kJ \[mo{{l}^{-1}}\], the value of enthalpy change for the reaction \[{{H}_{2}}C=C{{H}_{2}}(g)+{{H}_{2}}(g)\xrightarrow{\,}\,{{H}_{3}}C-C{{H}_{3}}(g)\] at 298K will be     AIEEE  Solved  Paper-2003
  A)
                                          \[+250\] kJ        
  done clear
  B)
        \[-250\] kJ                          
  done clear
  C)
        \[+125\] kJ        
  done clear
  D)
        \[-125\] kJ
  done clear
  View Answer play_arrow

• question_answer108) The enthalpy change for reaction does not depend upon the     AIEEE  Solved  Paper-2003
  A)
  physical state of reactants and products
  done clear
  B)
  use of different reactants for the same product
  done clear
  C)
  nature of intermediate reaction steps
  done clear
  D)
  difference in initial or final temperatures of involved substances
  done clear
  View Answer play_arrow

• question_answer109) A pressure cooker reduces cooking time for food because     AIEEE  Solved  Paper-2003
  A)
  heat is more evenly distributed in the cooking space
  done clear
  B)
  boiling point of water involved in cooking is increased
  done clear
  C)
  the higher pressure inside the cooker crushes the food material
  done clear
  D)
  cooking involves chemical changes helped by a rise in temperature
  done clear
  View Answer play_arrow

• question_answer110) If liquids A and B form an ideal solution, the     AIEEE  Solved  Paper-2003
  A)
  enthalpy of mixing is zero
  done clear
  B)
  entropy of mixing is zero
  done clear
  C)
  free energy of mixing is zero
  done clear
  D)
  free energy as well as the entropy of mixing are each zero
  done clear
  View Answer play_arrow

• question_answer111) For the reaction system                 \[2NO(g)+{{O}_{2}}(g)\xrightarrow{{}}2N{{O}_{2}}(g)\]   volume is suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to \[{{O}_{2}}\] and second order with respect to NO; the rate of reaction will     AIEEE  Solved  Paper-2003
  A)
  diminish to one-fourth of its initial value
  done clear
  B)
  diminish to one-eighth of its initial value
  done clear
  C)
  increase to eight times of its initial value
  done clear
  D)
  increase to four times of its initial value
  done clear
  View Answer play_arrow

• question_answer112) For a cell reaction involving a two-electron change, the standard emf of the cell is found to be \[0.295\] V at \[{{25}^{o}}C\]. The equilibrium constant of the reaction at \[{{25}^{o}}C\] will be     AIEEE  Solved  Paper-2003
  A)
  \[1\times {{10}^{-10}}\]               
  done clear
  B)
        \[29.5\times {{10}^{-2}}\]                            
  done clear
  C)
  10                                          
  done clear
  D)
  \[1\times {{10}^{10}}\]
  done clear
  View Answer play_arrow

• question_answer113) In an irreversible process taking place at constant T and p and in which only pressure-volume work is being done, the change in Gibbs free energy (dG) and change in entropy (dS), satisfy the criteria     AIEEE  Solved  Paper-2003
  A)
  \[{{(dS)}_{V,E}}<0,{{(dG)}_{T,P}}<0\]    
  done clear
  B)
  \[{{(dS)}_{V,E}}>0,{{(dG)}_{T,P}}<0\]
  done clear
  C)
  \[{{(dS)}_{V,E}}=0,{{(dG)}_{T,P}}=0\]
  done clear
  D)
  \[{{(dS)}_{V,E}}=0,{{(dG)}_{T,P}}>0\]
  done clear
  View Answer play_arrow

• question_answer114) Which one of the following characteristics is not correct for physical adsorption?     AIEEE  Solved  Paper-2003
  A)
  Adsorption on solids is reversible
  done clear
  B)
  Adsorption increases with increase in temperature
  done clear
  C)
  Adsorption is spontaneous
  done clear
  D)
  Both enthalpy and entropy of adsorption are negative
  done clear
  View Answer play_arrow

• question_answer115) In the respect of the equation \[k=A{{e}^{-{{E}_{\alpha }}/RT}}\] in chemical kinetics, which one of the following statements is correct?     AIEEE  Solved  Paper-2003
  A)
  k is equilibrium constant
  done clear
  B)
  A is adsorption factor
  done clear
  C)
  \[{{E}_{a}}\] is energy of activation
  done clear
  D)
  R is Rydberg constant
  done clear
  View Answer play_arrow

• question_answer116) Standard reduction electrode potentials of three metals A, B and C are \[+1.5\] V, \[-3.0\] V and \[-1.2\] V respectively. The reducing power of these metals are     AIEEE  Solved  Paper-2003
  A)
  \[B>C>A\]       
  done clear
  B)
        \[A>B>C\]                          
  done clear
  C)
  \[C>B>A\]      
  done clear
  D)
                        \[A>C>B\]
  done clear
  View Answer play_arrow

• question_answer117) Which one of the following substances has the highest proton affinity?   AIEEE  Solved  Paper-2003
  A)
  \[{{H}_{2}}O\]                                  
  done clear
  B)
               \[{{H}_{2}}S\]
  done clear
  C)
  \[N{{H}_{3}}\]                  
  done clear
  D)
        \[P{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer118) Which one of the following is an amphoteric oxide?     AIEEE  Solved  Paper-2003
  A)
                          \[ZnO\]                               
  done clear
  B)
  \[N{{a}_{2}}O\]                                
  done clear
  C)
  \[S{{O}_{2}}\]                   
  done clear
  D)
  \[{{B}_{2}}{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer119) A red solid is insoluble in water. However, it becomes soluble if some KI is added to water. Heating the red solid in a test tube results in liberation of some violet coloured fumes and droplets of a metal appear on the cooler parts of the test tube. The red solid is     AIEEE  Solved  Paper-2003
  A)
                          \[{{(N{{H}_{4}})}_{2}}C{{r}_{2}}{{O}_{7}}\]     
  done clear
  B)
        \[Hg{{l}_{2}}\]                  
  done clear
  C)
  \[HgO\]                               
  done clear
  D)
  \[P{{b}_{3}}{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer120) Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The explanation for it is that     AIEEE  Solved  Paper-2003
  A)
  concentrated hydrochloric acid emits strongly smelling HCI gas all the time
  done clear
  B)
  oxygen in air reacts with the emitted HCI gas to form a cloud of chlorine gas 
  done clear
  C)
  strong affinity of HCI gas for moisture in air results in forming of droplets of liquid solution which appears like a cloudy smoke
  done clear
  D)
  due to strong affinity for water, concentrated hydrochloric acid pulls moisture of air towards itself. This moisture forms droplets of water and hence the cloud
  done clear
  View Answer play_arrow

• question_answer121) The substance used in Holmes signals of the ship is a mixture of     AIEEE  Solved  Paper-2003
  A)
  \[Ca{{C}_{2}}+C{{a}_{3}}{{P}_{2}}\]
  done clear
  B)
                                        \[C{{a}_{3}}{{(P{{O}_{4}})}_{2}}+P{{b}_{3}}{{O}_{4}}\]
  done clear
  C)
  \[{{H}_{3}}P{{O}_{4}}\,+CaC{{l}_{2}}\]   
  done clear
  D)
  \[N{{H}_{3}}+HOCl\]
  done clear
  View Answer play_arrow

• question_answer122) The number of d-electrons retained in \[F{{e}^{2+}}\] (At. no. \[Fe=26\]) ions is     AIEEE  Solved  Paper-2003
  A)
                                          3                             
  done clear
  B)
        4                             
  done clear
  C)
  5                                             
  done clear
  D)
  6
  done clear
  View Answer play_arrow

• question_answer123) What would happen when a solution of potassium chromate is treated with an excess of dilute nitric acid?     AIEEE  Solved  Paper-2003
  A)
  \[C{{r}^{3+}}\] and \[C{{r}_{2}}O_{7}^{2-}\] are formed
  done clear
  B)
  \[C{{r}_{2}}O_{7}^{2-}\] and \[{{H}_{2}}O\] are formed
  done clear
  C)
  \[CrO_{4}^{2-}\] is reduced to \[+3\] state of Cr
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer124) In the coordination compound, \[{{K}_{4}}[Ni{{(CN)}_{4}}]\], the oxidation state of nickel is     AIEEE  Solved  Paper-2003
  A)
  \[-1\]   
  done clear
  B)
                                        0         
  done clear
  C)
        \[+1\]                                   
  done clear
  D)
        \[+2\]   
  done clear
  View Answer play_arrow

• question_answer125) Ammonia forms the complex ion \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] with copper ions in the alkaline solutions but not in acidic solutions. What is the reason for it?     AIEEE  Solved  Paper-2003
  A)
  In acidic solutions hydration protects copper ions
  done clear
  B)
  In acidic solutions protons coordinate with ammonia molecules forming \[NH_{4}^{+}\] ions and \[N{{H}_{3}}\] molecules are not available
  done clear
  C)
  In alkaline solutions insoluble \[Cu{{(OH)}_{2}}\] is precipitated which is soluble in excess of any alkali
  done clear
  D)
  Copper hydroxide is an amphoteric substance
  done clear
  View Answer play_arrow

• question_answer126) One mole of the complex compound \[Co{{(N{{H}_{3}})}_{5}}C{{l}_{3}}\], gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with two moles of \[AgN{{O}_{3}}\] solution to yield two moles of \[AgCl\] (s). The structure of the complex is     AIEEE  Solved  Paper-2003
  A)
  \[[Co{{(N{{H}_{3}})}_{5}}Cl]C{{l}_{2}}\] 
  done clear
  B)
  \[[Co{{(N{{H}_{3}})}_{3}}C{{l}_{2}}].2N{{H}_{3}}\]
  done clear
  C)
  \[[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl.\,N{{H}_{3}}\]
  done clear
  D)
  \[[Co{{(N{{H}_{3}})}_{4}}Cl]C{{l}_{2}}.N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer127) The radius of \[L{{a}^{3+}}\] (atomic number of \[La=57\]) is \[1.06\overset{o}{\mathop{A}}\,\]. Which one of the following given values will be closest to the radius of \[L{{u}^{3+}}\] (atomic number of \[Lu=71\])?     AIEEE  Solved  Paper-2003      
  A)
  \[1.60\,\overset{o}{\mathop{A}}\,\]     
  done clear
  B)
        \[1.40\,\overset{o}{\mathop{A}}\,\]     
  done clear
  C)
  \[1.06\,\overset{o}{\mathop{A}}\,\]                     
  done clear
  D)
  \[0.85\,\overset{o}{\mathop{A}}\,\]
  done clear
  View Answer play_arrow

• question_answer128) The radionuclide \[_{90}^{234}Th\] undergoes two successive \[\beta \] -decays followed by one \[\alpha \] -decay. The atomic number and the mass number respectively of the resulting radionuclide are     AIEEE  Solved  Paper-2003  
  A)
                          92 and 234    
  done clear
  B)
        94 and 230                          
  done clear
  C)
   90 and 230       
  done clear
  D)
        92 and 230
  done clear
  View Answer play_arrow

• question_answer129) the half-life of a radioactive isotope is 3 h. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 h would be     AIEEE  Solved  Paper-2003
  A)
                          \[4.0\] g              
  done clear
  B)
        \[8.0\] g                              
  done clear
  C)
  \[12.0\] g                            
  done clear
  D)
  \[16.0\] g   
  done clear
  View Answer play_arrow

• question_answer130) Several blocks of magnesium are fixed to the bottom of a ship to     AIEEE  Solved  Paper-2003
  A)
  keep away the sharks  
  done clear
  B)
  make the ship lighter
  done clear
  C)
  prevent action of water and salt
  done clear
  D)
  prevent puncturing by under-sea rocks
  done clear
  View Answer play_arrow

• question_answer131) In curing cement plasters water is sprinkled from time to time. This helps in     AIEEE  Solved  Paper-2003
  A)
  keeping it cool
  done clear
  B)
  developing interlocking needle-like crystals of hydrated silicates
  done clear
  C)
  hydrating sand and gravel mixed with cement
  done clear
  D)
  converting sand into silicic acid
  done clear
  View Answer play_arrow

• question_answer132) Which one of the following statements is not true?       AIEEE  Solved  Paper-2003
  A)
  The conjugate base of \[{{H}_{2}}PO_{4}^{-}\] is \[HPO_{4}^{2-}\]
  done clear
  B)
  \[pH+pOH=14\] for all aqueous solutions
  done clear
  C)
  The pH of \[1\times {{10}^{-8}}M\]HCl is 8
  done clear
  D)
  96,500 coulombs of electricity when passed through a \[CuS{{O}_{4}}\] solution deposit 1g equivalent of copper at the cathode 
  done clear
  View Answer play_arrow

• question_answer133) The correct order of increasing basic nature for the bases \[N{{H}_{3}},C{{H}_{3}}N{{H}_{2}}\] and \[{{(C{{H}_{3}})}_{2}}NH\]is      AIEEE  Solved  Paper-2003
  A)
  \[C{{H}_{3}}N{{H}_{2}}<N{{H}_{3}}<{{(C{{H}_{3}})}_{2}}NH\]
  done clear
  B)
  \[{{(C{{H}_{3}})}_{2}}NH<N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}\]
  done clear
  C)
  \[N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\]
  done clear
  D)
  \[C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH<N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer134) Butene-1 may be converted to butane by reaction with     AIEEE  Solved  Paper-2003
  A)
  \[Zn-HCl\]                          
  done clear
  B)
  \[Sn-HCl\]
  done clear
  C)
  \[Zn-Hg\]
  done clear
  D)
  \[Pd/{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer135) The solubilities of carbonates decrease down the magnesium group due to a decrease in     AIEEE  Solved  Paper-2003
  A)
  lattice energies of solids
  done clear
  B)
  hydration energies of cations
  done clear
  C)
  inter-ionic attraction
  done clear
  D)
  entropy of solution formation
  done clear
  View Answer play_arrow

• question_answer136) During dehydration of alcohols to alkenes by heating with concentrated \[{{H}_{2}}S{{O}_{4}}\] the initiation step is     AIEEE  Solved  Paper-2003
  A)
  protonation of alcohol molecule
  done clear
  B)
  formation of carbocation
  done clear
  C)
  elimination of water       
  done clear
  D)
  formation of an ester         
  done clear
  View Answer play_arrow

• question_answer137)     Which one of the following nitrates will leave behind a metal on strong heating?     AIEEE  Solved  Paper-2003
  A)
  Ferric nitrate                     
  done clear
  B)
  Copper nitrate
  done clear
  C)
        Manganese nitrate        
  done clear
  D)
  Silver nitrate
  done clear
  View Answer play_arrow

• question_answer138) When rain is accompanied by a thunderstorm, the collected rain water will have a pH value     AIEEE  Solved  Paper-2003
  A)
  slightly lower than that of rain water without thunderstorm
  done clear
  B)
  slightly higher than that when the thunderstorm is not there
  done clear
  C)
  uninfluenced by occurrence of thunderstorm
  done clear
  D)
  which depends on the amount of dust in air
  done clear
  View Answer play_arrow

• question_answer139) Complete hydrolysis of cellulose gives     AIEEE  Solved  Paper-2003
  A)
  D-fructose  
  done clear
  B)
                        D-ribose                              
  done clear
  C)
  D-glucose         
  done clear
  D)
        L-glucose
  done clear
  View Answer play_arrow

• question_answer140) For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liquid metal which does not solidify before glass. The metal used can be     AIEEE  Solved  Paper-2003
  A)
  mercury         
  done clear
  B)
                        tin          
  done clear
  C)
  sodium                                
  done clear
  D)
  magnesium
  done clear
  View Answer play_arrow

• question_answer141) The substance not likely to contain \[CaC{{O}_{3}}\] is     AIEEE  Solved  Paper-2003
  A)
  a marble statue               
  done clear
  B)
  calcined gypsum
  done clear
  C)
        sea shells                            
  done clear
  D)
  dolomite
  done clear
  View Answer play_arrow

• question_answer142) The reason for double helical structure of DNA is operation of     AIEEE  Solved  Paper-2003
  A)
  van der Waals' forces
  done clear
  B)
  dipole-dipole interaction
  done clear
  C)
  hydrogen bonding
  done clear
  D)
  electrostatic attractions
  done clear
  View Answer play_arrow

• question_answer143) Bottles containing \[{{C}_{6}}{{H}_{5}}I\] and \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}I\] lost their original labels. They were labelled A and B for testing. A and B were separately taken in a test tube and boiled with \[NaOH\] solution. The end solution in each tube was made acidic with dilute \[HN{{O}_{3}}\] and then some \[AgN{{O}_{3}}\] solution was added. Substance B gave a yellow precipitate. Which one of the following statements is true for this experiment?     AIEEE  Solved  Paper-2003
  A)
  A was \[{{C}_{6}}{{H}_{5}}l\]      
  done clear
  B)
        A was \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}l\]
  done clear
  C)
    B was \[{{C}_{6}}{{H}_{5}}l\]      
  done clear
  D)
  Addition of \[HN{{O}_{3}}\] was unnecessary
  done clear
  View Answer play_arrow

• question_answer144) Ethyl isocyanide on hydrolysis in acidic medium generates     AIEEE  Solved  Paper-2003
  A)
  ethylamine salt and methanoic acid
  done clear
  B)
  propanoic acid and ammonium salt
  done clear
  C)
  ethanoic acid and ammonium salt
  done clear
  D)
  methylamine salt and ethanoic acid
  done clear
  View Answer play_arrow

• question_answer145) The internal energy change when a system goes from state A to B is 40 kJ/mol. If the system goes from A to B by a reversible path and returns to state A by an irreversible path, what would be the net change in internal energy?     AIEEE  Solved  Paper-2003
  A)
  40 kJ                                     
  done clear
  B)
  > 40 kJ                  
  done clear
  C)
  < 40 kJ                                  
  done clear
  D)
  zero
  done clear
  View Answer play_arrow

• question_answer146) The reaction of chloroform with alcoholic KOH and p-toluidine form     AIEEE  Solved  Paper-2003
  A)
  
  done clear
  B)
  
  done clear
  C)
   
  done clear
  D)
      
  done clear
  View Answer play_arrow

• question_answer147) Nylon threads are made of
  A)
  polyvinyl polymer
  done clear
  B)
  polyester polymer
  done clear
  C)
  polyamide polymer
  done clear
  D)
  polyethylene polymer
  done clear
  View Answer play_arrow

• question_answer148) On mixing a certain alkane with chlorine and irradiating it with Ultraviolet light, it forms only one monochloroalkane. This alkane could be     AIEEE  Solved  Paper-2003
  A)
  propane              
  done clear
  B)
        pentane                              
  done clear
  C)
  isopentane                        
  done clear
  D)
  neopentane
  done clear
  View Answer play_arrow

• question_answer149) Which of the following could act as a propellant for rockets?      AIEEE  Solved  Paper-2003
  A)
  Liquid hydrogen + liquid nitrogen
  done clear
  B)
  Liquid oxygen + liquid argon
  done clear
  C)
  Liquid hydrogen + liquid oxygen
  done clear
  D)
   Liquid nitrogen + liquid oxygen    
  done clear
  View Answer play_arrow

• question_answer150)              A function \[f\] from the set of natural numbers to integers defined by             \[f(n)=\left\{ \begin{align}   & \frac{n-1}{n},\text{ }when\text{ }n\text{ }is\text{ }odd \\  & \frac{-n}{2},\,\,when\text{ }n\text{ }is\text{ }even \\ \end{align} \right.\]  is     AIEEE  Solved  Paper-2003
  A)
  one-one but not onto
  done clear
  B)
  onto but not one-one
  done clear
  C)
  one-one and onto both
  done clear
  D)
  neither one-one nor onto
  done clear
  View Answer play_arrow

• question_answer151) Let \[{{z}_{1}}\] and \[{{z}_{2}}\] be two roots of the equation \[{{z}_{2}}+az+b=0,\,\,z\] being complex. Further, assume that the origin, \[{{z}_{1}}\] and \[{{z}_{2}}\] form an equilateral triangle. Then,     AIEEE  Solved  Paper-2003
  A)
                                          \[{{a}^{2}}=b\]                                 
  done clear
  B)
  \[{{a}^{2}}=2b\]               
  done clear
  C)
                        \[{{a}^{2}}=3b\]           
  done clear
  D)
                        \[{{a}^{2}}=4b\]
  done clear
  View Answer play_arrow

• question_answer152) If z and \[\omega \] are two non-zero complex numbers  such  that  \[\left| z\,\omega  \right|=1\] and arg (z) - arg \[(\omega )=\frac{\pi }{2}\], then \[\overline{z}\omega \] is equal to     AIEEE  Solved  Paper-2003    
  A)
                          1                             
  done clear
  B)
  -1           
  done clear
  C)
  \[i\]                                       
  done clear
  D)
  \[-i\]
  done clear
  View Answer play_arrow

• question_answer153) If \[{{\left( \frac{1+i}{1-i} \right)}^{x}}=1\] , then             AIEEE  Solved  Paper-2003   
  A)
  \[x=4\,n\], where n is any positive integer
  done clear
  B)
  \[x=2\,n\], where n is any positive integer
  done clear
  C)
  \[x=4\,n+1\], where n is any positive integer
  done clear
  D)
  \[x=2\,n+1\], where n is any positive integer
  done clear
  View Answer play_arrow

• question_answer154) If \[\left| \begin{matrix}    a & {{a}^{2}} & 1+{{a}^{3}}  \\  b & {{b}^{2}} & 1+{{b}^{3}}  \\   c & {{c}^{2}} & 1+{{c}^{3}}  \\ \end{matrix} \right|=0\] and vectors \[(1,\,\,a,\,\,{{a}^{2}})\], \[(1,\,\,a,\,\,{{a}^{2}})\] and \[(1,\,\,c,\,\,{{c}^{2}})\] are non-coplanar, then the product abc equals     AIEEE  Solved  Paper-2003
  A)
  2                             
  done clear
  B)
  -1                           
  done clear
  C)
  1                             
  done clear
  D)
  0
  done clear
  View Answer play_arrow

• question_answer155) If the system of linear equations                 \[x+2\] ay \[+\,az=0\]                 \[x+3\] by \[+\,bz=0\] and        \[x+4\] cy \[+cz=0\] has a non-zero solution, then a, b, c     AIEEE  Solved  Paper-2003
  A)
                          are in AP                             
  done clear
  B)
  are in GP                             
  done clear
  C)
  are in HP                             
  done clear
  D)
  satisfy a+2b+3c=0
  done clear
  View Answer play_arrow

• question_answer156) If the sum of the roots of the quadratic equation \[a{{x}^{2}}+bx+c=0\] is equal to the sum of the squares f their reciprocals, then \[\frac{a}{c},\frac{b}{a}\], and \[\frac{c}{b}\] are in     AIEEE  Solved  Paper-2003
  A)
  arithmetic progression                 
  done clear
  B)
  geometric progression
  done clear
  C)
  harmonic progression
  done clear
  D)
  arithmetico-geometric progression
  done clear
  View Answer play_arrow

• question_answer157) The number of the real solutions of the equation \[{{x}^{2}}-3\left| x \right|+2=0\] is
  A)
  2                             
  done clear
  B)
  4             
  done clear
  C)
  1                             
  done clear
  D)
  3
  done clear
  View Answer play_arrow

• question_answer158) The value of a for which one root of the quadratic equation             \[({{a}^{2}}-5a+3)\,{{x}^{2}}+(3a-1)\,x+2=0\] is twice as large as the other, is     AIEEE  Solved  Paper-2003
  A)
  2/3                        
  done clear
  B)
        -2/3       
  done clear
  C)
        1/3                        
  done clear
  D)
        -1/3
  done clear
  View Answer play_arrow

• question_answer159) If \[A=\left| \begin{matrix}    a & b  \\ b & a  \\ \end{matrix} \right|\] and \[{{A}^{2}}=\left| \begin{matrix} \alpha  & \beta   \\ \beta  & \alpha   \\ \end{matrix} \right|\],  then     AIEEE  Solved  Paper-2003
  A)
  \[\alpha ={{a}^{2}}+{{b}^{2}},\,\beta =ab\]
  done clear
  B)
        \[\alpha ={{a}^{2}}+{{b}^{2}},\,\beta =2ab\]
  done clear
  C)
  \[\alpha ={{a}^{2}}+{{b}^{2}},\,\beta ={{a}^{2}}-{{b}^{2}}\]
  done clear
  D)
  \[\alpha =2ab,\,\,\beta ={{a}^{2}}+{{b}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer160) A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is     AIEEE  Solved  Paper-2003
  A)
  140        
  done clear
  B)
        196        
  done clear
  C)
        280        
  done clear
  D)
        346
  done clear
  View Answer play_arrow

• question_answer161) The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by     AIEEE  Solved  Paper-2003
  A)
                                          \[6!\,\,\times 5!\]                           
  done clear
  B)
        30          
  done clear
  C)
        \[5!\,\,\times 4!\]                           
  done clear
  D)
        \[7!\,\,\times 5!\]
  done clear
  View Answer play_arrow

• question_answer162) If \[1,\,\omega ,\,{{\omega }^{2}}\]are the cube roots of unity, then                 \[\Delta =\left| \begin{matrix}    1 & {{\omega }^{n}} & {{\omega }^{2n}}  \\    {{\omega }^{n}} & {{\omega }^{2n}} & 1  \\    {{\omega }^{2n}} & 1 & {{\omega }^{n}}  \\ \end{matrix} \right|\] is equal to     AIEEE  Solved  Paper-2003
  A)
                          0                             
  done clear
  B)
  1                             
  done clear
  C)
  \[\omega \]                       
  done clear
  D)
        \[{{\omega }^{2}}\]
  done clear
  View Answer play_arrow

• question_answer163) If \[^{n}{{C}_{r}}\] denotes the number of combinations of n things taken r at a time, then the expression \[^{n}{{C}_{r+1}}{{+}^{n}}{{C}_{r-1}}+2{{\times }^{n}}{{C}_{r}}\] equals     AIEEE  Solved  Paper-2003
  A)
                          \[^{n+2}{{C}_{r}}\]                         
  done clear
  B)
  \[^{n+2}{{C}_{r+1}}\]                    
  done clear
  C)
  \[^{n+1}{{C}_{r}}\]                                         
  done clear
  D)
  \[^{n+1}{{C}_{r+1}}\]
  done clear
  View Answer play_arrow

• question_answer164) The number of integral terms in the expansion of \[{{(\sqrt{3}+\sqrt[8]{5})}^{256}}\] is     AIEEE  Solved  Paper-2003
  A)
                                          32          
  done clear
  B)
        33          
  done clear
  C)
        34          
  done clear
  D)
        35
  done clear
  View Answer play_arrow

• question_answer165) If \[x\] is positive, the first negative term in the expansion of \[{{(1+x)}^{27/5}}\] is     AIEEE  Solved  Paper-2003
  A)
                          7th term 
  done clear
  B)
                        5th term                             
  done clear
  C)
  8th term            
  done clear
  D)
        6th term
  done clear
  View Answer play_arrow

• question_answer166) The     sum     of     the     series \[\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\]... upto \[\infty \] is equal to     AIEEE  Solved  Paper-2003
  A)
                          \[2\,\,{{\log }_{e}}2\]
  done clear
  B)
                        \[{{\log }_{e}}\,\,2-1\]                  
  done clear
  C)
        \[{{\log }_{e}}\,\,2\]                      
  done clear
  D)
        \[{{\log }_{e}}\,\,\left( \frac{4}{e} \right)\]
  done clear
  View Answer play_arrow

• question_answer167) Let \[f(x)\] be a polynomial function of second degree. If \[f(1)=f(-1)\] and a, b, c are in AP, then \[f'\,(a),\,\,f'(b)\] and \[f'(c)\] are in     AIEEE  Solved  Paper-2003
  A)
  AP                         
  done clear
  B)
  GP
  done clear
  C)
  HP
  done clear
  D)
  arithmetico-geometric progression
  done clear
  View Answer play_arrow

• question_answer168) If \[{{x}_{1}},{{x}_{2}},{{x}_{3}}\] and \[{{y}_{1}},{{y}_{2}},{{y}_{3}}\] are both in GP with the same common ratio, then the points \[({{x}_{1}},{{y}_{1}}),\,({{x}_{2}},{{y}_{2}})\] and \[({{x}_{3}},{{y}_{3}})\]      AIEEE  Solved  Paper-2003
  A)
  lie on a straight                
  done clear
  B)
  line lie on an ellipse
  done clear
  C)
  lie on a circle
  done clear
  D)
  are vertices of a triangle
  done clear
  View Answer play_arrow

• question_answer169) The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is     AIEEE  Solved  Paper-2003
  A)
                                          \[a\cot \,\left( \frac{\pi }{v} \right)\]
  done clear
  B)
        \[\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\]                    
  done clear
  C)
  \[a\cot \,\left( \frac{\pi }{2n} \right)\]
  done clear
  D)
  \[\frac{a}{4}\cot \left( \frac{\pi }{2n} \right)\]
  done clear
  View Answer play_arrow

• question_answer170) If a \[\Delta ABC\],                 \[a{{\cos }^{2}}\left( \frac{C}{2} \right)+c{{\cos }^{2}}\left( \frac{A}{2} \right)=\frac{3b}{2}\] then the sides a, b and c     AIEEE  Solved  Paper-2003
  A)
                                          are in AP         
  done clear
  B)
                        are in GP             
  done clear
  C)
                        are in HP         
  done clear
  D)
                        satisfy a + b = c
  done clear
  View Answer play_arrow

• question_answer171) In \[\Delta ABC\], medians AD and BE are drawn. If AD = 4, \[\angle DAB=\frac{\pi }{6}\] and \[\angle ABE=\frac{\pi }{3}\], then the area of the \[\Delta ABC\] is     AIEEE  Solved  Paper-2003
  A)
                          8/3                        
  done clear
  B)
        16/3                      
  done clear
  C)
        32/3                      
  done clear
  D)
        64/3
  done clear
  View Answer play_arrow

• question_answer172) The trigonometric equation \[{{\sin }^{-1}}x=2{{\sin }^{-1}}a\], has a solution for     AIEEE  Solved  Paper-2003
  A)
                          \[-\frac{1}{\sqrt{2}}<a<\frac{1}{\sqrt{2}}\]          
  done clear
  B)
  all real values of a                           
  done clear
  C)
  \[\left| a \right|<\frac{1}{2}\]                   
  done clear
  D)
        \[\left| a \right|\ge \frac{1}{\sqrt{2}}\]
  done clear
  View Answer play_arrow

• question_answer173) The upper 3/4th portion of a vertical pole subtends an angle \[{{\tan }^{-1}}3/5\] at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is     AIEEE  Solved  Paper-2003
  A)
                                          20m      
  done clear
  B)
                        40m      
  done clear
  C)
        60m      
  done clear
  D)
        80 m
  done clear
  View Answer play_arrow

• question_answer174) The real number \[x\] when added to its inverse gives the minimum sum at \[x\] equals to     AIEEE  Solved  Paper-2003
  A)
                          2         
  done clear
  B)
                        1             
  done clear
  C)
        -1                           
  done clear
  D)
  -2
  done clear
  View Answer play_arrow

• question_answer175) If \[f:R\to R\] satisfies\[f(x+y)=f(x)+f(y)\], for all \[x,y\in R\] and \[f(1)=7\], then \[\sum\limits_{r=1}^{n}{f(r)}\] is     AIEEE  Solved  Paper-2003
  A)
                          \[\frac{7n}{2}\]                
  done clear
  B)
                        \[\frac{7(n+1)}{2}\]                        
  done clear
  C)
  \[7n\,(n+1)\]                    
  done clear
  D)
  \[\frac{7n\,(n+1)}{2}\]
  done clear
  View Answer play_arrow

• question_answer176) If \[f(x)={{x}^{n}}\], then the value of \[f(1)-\frac{f'(1)}{1!}+\frac{f''(1)}{2!}-\frac{f'''(1)}{3!}+...+\frac{{{(-1)}^{n}}{{f}^{n}}(1)}{n!}\]     AIEEE  Solved  Paper-2003
  A)
                          \[{{2}^{n}}\]      
  done clear
  B)
                        \[{{2}^{n-1}}\]                                  
  done clear
  C)
  0                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer177) Domain of definition of the function \[f(x)=\frac{3}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x)\], is     AIEEE  Solved  Paper-2003
  A)
                                          (1, 2)        
  done clear
  B)
                        \[(-1,0)\cup (1,2)\]
  done clear
  C)
  \[(1,2)\cup (2,\infty )\] 
  done clear
  D)
        \[(-1,0)\cup (1,2,)\cup (2,\infty )\]
  done clear
  View Answer play_arrow

• question_answer178) \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\left[ 1-\tan \left( \frac{x}{2} \right) \right][1-\sin x]}{\left[ 1+\tan \left( \frac{x}{2} \right) \right]{{[x-2x]}^{3}}}\]  is     AIEEE  Solved  Paper-2003
  A)
                                          \[\frac{1}{8}\]                                   
  done clear
  B)
        0                             
  done clear
  C)
  \[\frac{1}{32}\]                                
  done clear
  D)
        \[\infty \]  
  done clear
  View Answer play_arrow

• question_answer179) If \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\log \,(3+x)-\log \,(3-x)}{x}=k\] then value of k is     AIEEE  Solved  Paper-2003
  A)
                          0                             
  done clear
  B)
  -1/3       
  done clear
  C)
        2/3        
  done clear
  D)
        -2/3
  done clear
  View Answer play_arrow

• question_answer180) Let f(a) = g(a) = k and their nth derivatives \[{{f}^{n}}(a),\,{{g}^{n}}(a)\] exist and are not equal for some n. Further, if \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)\,g(x)-i(a)-g(a)f(x)+g(a)}{g(x)-f(x)}=4\], then the value of k is equal to     AIEEE  Solved  Paper-2003
  A)
  4             
  done clear
  B)
        2                             
  done clear
  C)
  1                             
  done clear
  D)
  0
  done clear
  View Answer play_arrow

• question_answer181) The function \[f(x)=\log \,(x+\sqrt{\,{{x}^{2}}+1})\], is     AIEEE  Solved  Paper-2003
  A)
  an even function
  done clear
  B)
  an odd function
  done clear
  C)
  a periodic function
  done clear
  D)
  neither an even nor an odd function
  done clear
  View Answer play_arrow

• question_answer182) If \[f(x)=\left\{ \begin{matrix}    x{{e}^{-\left[ \frac{1}{\left| x \right|}+\frac{1}{x} \right]}} & ,x\ne 0  \\    0 & ,x=0  \\ \end{matrix} \right.\] , then f(x) is     AIEEE  Solved  Paper-2003
  A)
  continuous as well as differentiable for all x
  done clear
  B)
  continuous for all x but not differentiable at \[x=0\]
  done clear
  C)
  neither differentiable nor continuous at \[x=0\]
  done clear
  D)
  discontinuous everywhere
  done clear
  View Answer play_arrow

• question_answer183) If the function \[f(x)=2{{x}^{3}}-9a{{x}^{2}}+12{{a}^{2}}x+1\], where a > 0, attains its maximum and minimum at p and q respectively such that \[{{p}^{2}}=q\], then a equals     AIEEE  Solved  Paper-2003
  A)
                                          3             
  done clear
  B)
        1             
  done clear
  C)
        2             
  done clear
  D)
        1/2
  done clear
  View Answer play_arrow

• question_answer184) If \[f(y)={{e}^{y}},g(y)=y;y>0\] and\[F(t)=\int_{0}^{t}{f(t-y)\,g(y)\,dy}\], then      AIEEE  Solved  Paper-2003
  A)
  \[F(t)=1-{{e}^{-t}}(1+t)\]
  done clear
  B)
        \[F(t)\,={{e}^{t}}\,-(1+t)\]
  done clear
  C)
        \[F(t)=t{{e}^{-t}}\]        
  done clear
  D)
  \[F(t)=t{{e}^{-t}}\]
  done clear
  View Answer play_arrow

• question_answer185) If \[f(a+b-x)=f(x)\], then \[\int_{a}^{b}{x\,f(x)\,dx}\] is equal to     AIEEE  Solved  Paper-2003
  A)
  \[\frac{a+b}{2}\int_{a}^{b}{f(b-x)\,dx}\]
  done clear
  B)
        \[\frac{a+b}{2}\int_{a}^{b}{f(x)\,dx}\]
  done clear
  C)
  \[\frac{b-a}{2}\int_{a}^{b}{f(x)\,dx}\]
  done clear
  D)
        \[\frac{a+b}{2}\int_{a}^{b}{f(a+b+x)\,dx}\]
  done clear
  View Answer play_arrow

• question_answer186) The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\int_{0}^{{{x}^{2}}}{{{\sec }^{2}}t\,dt}}{x\sin x}\] is     AIEEE  Solved  Paper-2003
  A)
  3                             
  done clear
  B)
  2             
  done clear
  C)
  1                             
  done clear
  D)
  -1
  done clear
  View Answer play_arrow

• question_answer187) The    value    of    the    integral \[I=\int_{0}^{1}{x{{(1-x)}^{n}}dx}\] is     AIEEE  Solved  Paper-2003
  A)
          \[\frac{1}{n+1}\] 
  done clear
  B)
                                        \[\frac{1}{n+2}\]                             
  done clear
  C)
  \[\frac{1}{n+1}-\frac{1}{n+2}\] 
  done clear
  D)
        \[\frac{1}{n+1}+\frac{1}{n+2}\]
  done clear
  View Answer play_arrow

• question_answer188) \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{1+{{2}^{4}}+{{3}^{4}}+....+{{n}^{4}}}{{{n}^{5}}}\]                                                                             \[-\underset{x\to \infty }{\mathop{\lim }}\,\frac{1+{{2}^{3}}+{{3}^{3}}+....+{{n}^{3}}}{{{n}^{5}}}\] is
  A)
           1/30                     
  done clear
  B)
  0                             
  done clear
  C)
  1/4        
  done clear
  D)
        1/5
  done clear
  View Answer play_arrow

• question_answer189) Let \[\frac{d}{dx}F(x)=\left( \frac{{{e}^{\sin x}}}{x} \right),x>0\]. If \[\int_{1}^{4}{\,\,\,\frac{3}{x}{{e}^{\sin {{x}^{3}}}}dx=F(k)-F(1)}\]. then one of the possible value of k, is     AIEEE  Solved  Paper-2003
  A)
  15          
  done clear
  B)
        16          
  done clear
  C)
        63          
  done clear
  D)
        64
  done clear
  View Answer play_arrow

• question_answer190) The area of the region bounded by the curves \[y=\left| x-1 \right|\] and \[y=3-\left| x \right|\] is     AIEEE  Solved  Paper-2003
  A)
                                          2 sq units        
  done clear
  B)
                        3 sq units                            
  done clear
  C)
        4 sq units        
  done clear
  D)
                        6 sq units
  done clear
  View Answer play_arrow

• question_answer191) Let \[f(x)\] be a function satisfying \[f'(x)=f(x)\] with \[f(0)=1\] and \[g(x)\] be a function that satisfies \[f(x)+g(x)={{x}^{2}}\]. Then, the value of the integral \[\int_{0}^{1}{f(x)\,g(x)\,dx}\], is     AIEEE  Solved  Paper-2003
  A)
                          \[e-\frac{{{e}^{2}}}{2}-\frac{5}{2}\]                        
  done clear
  B)
  \[e+\frac{{{e}^{2}}}{2}-\frac{3}{2}\]                       
  done clear
  C)
  \[-\frac{{{e}^{2}}}{2}-\frac{3}{2}\]                           
  done clear
  D)
  \[e+\frac{{{e}^{2}}}{2}+\frac{5}{2}\]
  done clear
  View Answer play_arrow

• question_answer192) The degree and order of the differential equation of the family of all parabolas whose axis is X-axis, are respectively     AIEEE  Solved  Paper-2003
  A)
                                          2, 1        
  done clear
  B)
        1, 2        
  done clear
  C)
        3, 2        
  done clear
  D)
        2, 3
  done clear
  View Answer play_arrow

• question_answer193) The solution of the differential equation \[(1+{{y}^{2}})+(x-{{e}^{{{\tan }^{-1}}}}y)\frac{dy}{dx}=0\], is     AIEEE  Solved  Paper-2003
  A)
  \[(x-2)=k{{e}^{-{{\tan }^{-1}}y}}\]           
  done clear
  B)
  \[2\,x\,{{e}^{-{{\tan }^{-1}}y}}={{e}^{2\,{{\tan }^{-1}}y}}+k\]
  done clear
  C)
  \[x{{e}^{{{\tan }^{-1}}}}={{\tan }^{-1}}\,y+k\]
  done clear
  D)
  \[x{{e}^{2\,\,{{\tan }^{-1}}y}}={{e}^{{{\tan }^{-1}}y}}+k\]
  done clear
  View Answer play_arrow

• question_answer194) If the equation of the locus of a point equidistant from the points \[({{a}_{1}}-{{b}_{1}})\] and \[({{a}_{2}}-{{b}_{2}})\] is \[({{a}_{1}}-{{a}_{2}})x+({{b}_{1}}-{{b}_{2}})\,y+c=0\], then the value of 'c' is     AIEEE  Solved  Paper-2003
  A)
  \[\frac{1}{2}(a_{2}^{2}+b_{2}^{2}-a_{1}^{2}-b_{1}^{2})\]             
  done clear
  B)
  \[a_{1}^{2}-a_{2}^{2}+b_{1}^{2}-b_{2}^{2}\]     
  done clear
  C)
  \[\frac{1}{2}\,\,(a_{1}^{2}+a_{2}^{2}+b_{1}^{2}+b_{2}^{2})\]
  done clear
  D)
        \[\sqrt{a_{1}^{2}+b_{1}^{2}-a_{2}^{2}-b_{2}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer195) Locus of centroid of the triangle whose vertices are (b sin t, - b cost) and (1, 0), where t is a parameter, is     AIEEE  Solved  Paper-2003
  A)
  \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]
  done clear
  B)
  \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]
  done clear
  C)
  \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]
  done clear
  D)
  \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer196) If   the   pair   of   straight   lines \[{{x}^{2}}-2pxy-{{y}^{2}}=0\]and \[{{x}^{2}}-2qxy-{{y}^{2}}=0\] be such that each pair bisects the angle between the other pair, then     AIEEE  Solved  Paper-2003
  A)
  \[p=q\]                                
  done clear
  B)
        \[p=-q\]                              
  done clear
  C)
        \[pq=1\]                             
  done clear
  D)
  \[pq=-1\]
  done clear
  View Answer play_arrow

• question_answer197) A square of side a lies above the X-axis and has one vertex at the origin. The side passing through the origin makes an angle \[\left( 0<\alpha <\frac{\pi }{4} \right)\] with the positive direction of X-axis. The equation of its diagonal not passing through the origin is     AIEEE  Solved  Paper-2003
  A)
  \[y(\cos \alpha -\sin \alpha )-x(\sin \alpha -\cos \alpha )=a\]
  done clear
  B)
  \[y(\cos \alpha +\sin \alpha )+x(\sin \alpha -\cos \alpha )=a\]
  done clear
  C)
  \[y(\cos \alpha +\sin \alpha )+x(\sin \alpha +\cos \alpha )=a\]
  done clear
  D)
  \[y(\cos \alpha +\sin \alpha )+x(\cos \alpha -\sin \alpha )=a\]
  done clear
  View Answer play_arrow

• question_answer198) If the two circles \[{{(x-1)}^{2}}+{{(y-3)}^{2}}={{r}^{2}}\] and \[{{x}^{2}}+{{y}^{2}}-8x+2y+8=0\] intersect in two distinct points, then     AIEEE  Solved  Paper-2003
  A)
  \[2<r<8\]                            
  done clear
  B)
  \[r<2\]                 
  done clear
  C)
        \[r=2\]                 
  done clear
  D)
        \[r>2\]
  done clear
  View Answer play_arrow

• question_answer199) The lines \[2x-3y=5\] and \[3x-4y=7\] are diameters of a circle having area as 154 sq units. Then, the equation of the circle is     AIEEE  Solved  Paper-2003
  A)
  \[{{x}^{2}}+{{y}^{2}}+2x-2y=62\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}+2x-2y=47\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}-2x+2y=47\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}-2x+2y=62\]
  done clear
  View Answer play_arrow

• question_answer200) The normal at the point \[(bt_{1}^{2},b{{t}_{1}})\] on a parabola meets the parabola again in the point\[(bt_{2}^{2},2b{{t}_{2}})\], then     AIEEE  Solved  Paper-2003
  A)
  \[{{t}_{2}}=-{{t}_{1}}-\frac{2}{{{t}_{1}}}\]     
  done clear
  B)
        \[{{t}_{2}}=-{{t}_{1}}+\frac{2}{{{t}_{1}}}\]                            
  done clear
  C)
  \[{{t}_{2}}={{t}_{1}}-\frac{2}{{{t}_{1}}}\]      
  done clear
  D)
        \[{{t}_{2}}={{t}_{1}}+\frac{2}{{{t}_{1}}}\]
  done clear
  View Answer play_arrow

• question_answer201) The foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and the hyperbola \[\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25}\] coincide. Then, the value of \[{{b}^{2}}\] is     AIEEE  Solved  Paper-2003
  A)
  1                             
  done clear
  B)
  5                             
  done clear
  C)
  7                             
  done clear
  D)
  9
  done clear
  View Answer play_arrow

• question_answer202) A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 3), B(2, 1, 3) and C(-1, 1, 2). Then, the angle between the faces OAB and ABC will be     AIEEE  Solved  Paper-2003
  A)
  \[{{\cos }^{-1}}\left( \frac{19}{35} \right)\]       
  done clear
  B)
        \[{{\cos }^{-1}}\left( \frac{17}{31} \right)\]                          
  done clear
  C)
  \[{{30}^{o}}\]                                    
  done clear
  D)
  \[{{90}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer203) The radius of the circle in which the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2x-2y-4z-19=0\] is cut by the plane \[x+2y+2z+7=0\], is     AIEEE  Solved  Paper-2003
  A)
                          1                             
  done clear
  B)
  2                             
  done clear
  C)
  3                             
  done clear
  D)
  4
  done clear
  View Answer play_arrow

• question_answer204) The lines \[\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}\] and \[\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}\] are coplanar, if     AIEEE  Solved  Paper-2003
  A)
                                          k = 0 or - 1      
  done clear
  B)
                        k = 1 or ? 1                         
  done clear
  C)
  k = 0 or -3      
  done clear
  D)
                        k = 3 or -3
  done clear
  View Answer play_arrow

• question_answer205) The two lines \[x=ay\,+b,\,\,z=cy+d\] and\[x=a'\,y+b',\,z=c'\,y+d'\] will be perpendicular, if and only if     AIEEE  Solved  Paper-2003
  A)
  \[aa'+bb'+cc'+1=0\]
  done clear
  B)
        \[aa'+bb'+cc'=0\]
  done clear
  C)
  \[(a+a')\,(b+b')+(c+c')=0\]
  done clear
  D)
  \[aa'+cc'+1=0\]   
  done clear
  View Answer play_arrow

• question_answer206) The shortest distance from the plane \[12x+4y+3z=327\] to the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+4x-2y-6z=155\] is     AIEEE  Solved  Paper-2003
  A)
  26          
  done clear
  B)
        \[11\frac{4}{13}\]                            
  done clear
  C)
        13      
  done clear
  D)
        39
  done clear
  View Answer play_arrow

• question_answer207) Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b?, c from the origin, then     AIEEE  Solved  Paper-2003
  A)
  \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}+\frac{1}{a{{'}^{2}}}+\frac{1}{{{b}^{'2}}}+\frac{1}{c{{'}^{2}}}=0\]
  done clear
  B)
   \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}-\frac{1}{{{c}^{2}}}+\frac{1}{a{{'}^{2}}}+\frac{1}{{{b}^{'2}}}-\frac{1}{c{{'}^{2}}}=0\]
  done clear
  C)
   \[\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}-\frac{1}{{{c}^{2}}}+\frac{1}{a{{'}^{2}}}-\frac{1}{{{b}^{'2}}}-\frac{1}{c{{'}^{2}}}=0\]
  done clear
  D)
   \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}-\frac{1}{a{{'}^{2}}}-\frac{1}{{{b}^{'2}}}-\frac{1}{c{{'}^{2}}}=0\]
  done clear
  View Answer play_arrow

• question_answer208) a, b, c   are three vectors, such that \[a+b+c=0,\,\,\left| a \right|=1,\,\,\left| b \right|=2,\,\,\left| c \right|=3\], then \[a\,.\,b+b\,.\,\,c+c\,.\,\,a\] is equal to     AIEEE  Solved  Paper-2003
  A)
                          0                             
  done clear
  B)
  -7                           
  done clear
  C)
  7                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer209) If u, v and w are three non-coplanar vectors, then (u + v - w) . [(u - v) \[\times \] (v - w)] equals     AIEEE  Solved  Paper-2003
  A)
                          0                                             
  done clear
  B)
  \[u\,.\,v\times w\]         
  done clear
  C)
  \[u\,.\,w\times v\]            
  done clear
  D)
        \[3u\,.\,v\times w\]
  done clear
  View Answer play_arrow

• question_answer210) Consider points A, B, C and D with position vectors  \[7\hat{i}-4\hat{j}+7\hat{k}\], \[\hat{i}-6\hat{j}+10\hat{k}\], \[-\hat{i}-3\hat{j}+4\,\hat{k}\]and \[5\,\hat{i}-\hat{j}+5\,\hat{k}\], respectively. Then, ABCD is a     AIEEE  Solved  Paper-2003
  A)
                                          square                 
  done clear
  B)
        rhombus
  done clear
  C)
  rectangle            
  done clear
  D)
  parallelogram but not a rhombus None of the given option is correct.
  done clear
  View Answer play_arrow

• question_answer211) The vectors \[AB=3\hat{i}+4\hat{k}\] and \[AC=5\,\hat{i}-2\,\hat{j}+4\,\hat{k}\] are the sides of a \[\Delta ABC\]. The length of the median through A is     AIEEE  Solved  Paper-2003
  A)
                                          \[\sqrt{18}\]                      
  done clear
  B)
        \[\sqrt{72}\]                      
  done clear
  C)
        \[\sqrt{33}\]      
  done clear
  D)
        \[\sqrt{288}\]
  done clear
  View Answer play_arrow

• question_answer212) A particle acted on by constant forces \[4\,\hat{i}+\hat{j}-3\,\hat{k}\] and \[3\,\hat{i}+\hat{j}-\,\hat{k}\] is displaced from the point \[\hat{i}+2\hat{j}+3\,\hat{k}\] to the point \[5\,\hat{i}+4\,\hat{j}+\,\hat{k}\]. The total work done by the forces is     AIEEE  Solved  Paper-2003
  A)
                                          20 units           
  done clear
  B)
                        30 units                               
  done clear
  C)
  40 units     
  done clear
  D)
        50 units
  done clear
  View Answer play_arrow

• question_answer213) Let \[u=\hat{i}+\hat{j},\,v=\hat{i}-\hat{j}\] and \[w=\hat{i}+2\,\hat{j}+3\,\,\hat{k}\]. If \[\hat{n}\] is a unit vector such that \[u\,.\,\,\hat{n}=0\] and \[v\,.\,\,\hat{n}=0\], then \[\left| w\,.\,\,\hat{n} \right|\] is equal to     AIEEE  Solved  Paper-2003
  A)
  0                             
  done clear
  B)
  1                             
  done clear
  C)
  2                             
  done clear
  D)
  3
  done clear
  View Answer play_arrow

• question_answer214) The median of a set of 9 distinct observations is 205. If each of the largest 4 observations of the set is increased by 2, then the median of the new set     AIEEE  Solved  Paper-2003
  A)
  is increased by 2
  done clear
  B)
  is decreased by 2
  done clear
  C)
  is two times the original median
  done clear
  D)
  remains the same as that of the original set
  done clear
  View Answer play_arrow

• question_answer215) In an experiment with 15 observations on x, the following results were available \[\sum {{x}^{2}}=2830,\,\,\sum x=170\]. One observation that was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance is     AIEEE  Solved  Paper-2003
  A)
  78.00             
  done clear
  B)
        188.66                  
  done clear
  C)
        177.33            
  done clear
  D)
                        8.33
  done clear
  View Answer play_arrow

• question_answer216) Five horses are in a race. Mr A selects two of the horses at random and bets on them. The probability that Mr A selected the winning horse, is     AIEEE  Solved  Paper-2003
  A)
  \[\frac{4}{5}\]                                   
  done clear
  B)
        \[\frac{3}{5}\]                                   
  done clear
  C)
        \[\frac{1}{5}\]                                                   
  done clear
  D)
  \[\frac{2}{5}\]
  done clear
  View Answer play_arrow

• question_answer217) Events A, B, C are mutually exclusive 3x +1 events   such that \[P(A)=\frac{3x+1}{3},\,P(B)=\frac{1-x}{4}\] and \[P(C)=\frac{1-2x}{2}\]. The set of possible values of x are in the interval     AIEEE  Solved  Paper-2003
  A)
                          \[\left[ \frac{1}{3},\frac{1}{2} \right]\]   
  done clear
  B)
  \[\left[ \frac{1}{3},\frac{2}{3} \right]\]                   
  done clear
  C)
  \[\left[ \frac{1}{3},\frac{13}{3} \right]\]                
  done clear
  D)
  \[\left[ 0,1 \right]\]
  done clear
  View Answer play_arrow

• question_answer218) The mean and variance of a random variable  X  having a binomial distribution are 4 and 2 respectively, then \[P(X=1)\] is     AIEEE  Solved  Paper-2003
  A)
                                          \[\frac{1}{32}\]                
  done clear
  B)
        \[\frac{1}{16}\]                                
  done clear
  C)
        \[\frac{1}{8}\]                                   
  done clear
  D)
        \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer219) The resultant of forces P and Q is R. If Q is doubled, then R is doubled. If the direction of Q is reversed, then R is again doubled, then? \[{{P}^{2}}:{{Q}^{2}}:{{R}^{2}}\] is     AIEEE  Solved  Paper-2003
  A)
                                          3 : 1 : 1                 
  done clear
  B)
        2 : 3 : 2                 
  done clear
  C)
        1 : 2 : 3                 
  done clear
  D)
        2 : 3 : 1
  done clear
  View Answer play_arrow

• question_answer220) Let \[{{R}_{1}}\] and \[{{R}_{2}}\] respectively be the maximum ranges up and down an inclined plane and R be the maximum range on the horizontal plane. Then. \[{{R}_{1}},R,{{R}_{2}}\] are in     AIEEE  Solved  Paper-2003
  A)
                          AGP                                      
  done clear
  B)
  AP                                         
  done clear
  C)
  GP                                         
  done clear
  D)
  HP
  done clear
  View Answer play_arrow

• question_answer221) A couple is of moment G and the force forming the couple is P. If P is turned through a right angle, the moment of the couple thus formed is H. If instead, the forces P is turned through an angle a, then the moment of couple becomes     AIEEE  Solved  Paper-2003
  A)
                          \[G\sin \alpha -H\cos \alpha \]                 
  done clear
  B)
  \[H\cos \alpha +G\sin \alpha \]
  done clear
  C)
        \[G\cos \alpha +H\sin \alpha \]
  done clear
  D)
        \[H\sin \alpha -G\cos \alpha \]
  done clear
  View Answer play_arrow

• question_answer222) Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uniform acceleration f. Let \[\alpha \] be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time     AIEEE  Solved  Paper-2003
  A)
                          \[\frac{u\sin \alpha }{f}\]                            
  done clear
  B)
  \[\frac{f\cos \alpha }{u}\]                           
  done clear
  C)
  \[u\sin \alpha \]                              
  done clear
  D)
  \[\frac{u\cos \alpha }{f}\]
  done clear
  View Answer play_arrow

• question_answer223) Two stones are projected from the top of a cliff h metres high, with the same speed u, so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle \[\theta \] to the horizontal, then tan \[\theta \] equals       AIEEE  Solved  Paper-2003
  A)
                                          \[\sqrt{\frac{2u}{gh}}\]                
  done clear
  B)
        \[2g\,\sqrt{\frac{u}{h}}\]                             
  done clear
  C)
  \[2h\,\sqrt{\frac{u}{g}}\]                             
  done clear
  D)
  \[u\,\sqrt{\frac{2}{gh}}\]
  done clear
  View Answer play_arrow

• question_answer224) A body travels a distance s in t seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration f and in the second part with constant retardation r. The value of t is given by     AIEEE  Solved  Paper-2003
  A)
                          \[2s\left( \frac{1}{f}+\frac{1}{r} \right)\]                              
  done clear
  B)
  \[\frac{2s}{\frac{1}{f}+\frac{1}{r}}\]                        
  done clear
  C)
  \[\sqrt{2s\,(f+r)}\]      
  done clear
  D)
        \[\sqrt{2s\,\left( \frac{1}{f}+\frac{1}{r} \right)}\]
  done clear
  View Answer play_arrow