Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

done Jamia Millia Islamia Solved Paper-2013 Total Questions - 170

• question_answer1) The change in the gravitational potential energy when a body of mass m is raised to a height\[nR\]above the surface of the earth is (where R is the radius of the earth)
  A)
   \[\left( \frac{n}{n+1} \right)mgR\]                         
  done clear
  B)
   \[\left( \frac{n}{n-1} \right)mgR\]
  done clear
  C)
   \[nmgR\]                           
  done clear
  D)
   \[\left( \frac{mgR}{n} \right)\]
  done clear
  View Answer play_arrow

• question_answer2)     To break a wire of 1 m length, minimum 40 kg weight is required, then the wire of the same material of double and 6 m length will required breaking weight
  A)
   80 kg wt             
  done clear
  B)
   240 kg wt
  done clear
  C)
   200 kg wt           
  done clear
  D)
   160 kg wt
  done clear
  View Answer play_arrow

• question_answer3)     Mercury boils at\[367{}^\circ C\]. However, mercury thermometers are made such that they can measure temperature upto\[500{}^\circ C\]. This is done by
  A)
   maintaing vacuum above mercury column in the stem of the thermometer
  done clear
  B)
   filling nitrogen gas at high pressure above the mercury column
  done clear
  C)
   filling oxygen gas at high pressure above the mercury column
  done clear
  D)
   filling nitrogen gas at low pressure above the mercury column
  done clear
  View Answer play_arrow

• question_answer4)     A gas under goes a change of state during which 100 J of heat is supplied to it and it does 20 J work. The system is brought back to its original state through a process during which 20 J of heat is released by the gas. The work done by the gas in the second process is
  A)
   60 J                       
  done clear
  B)
   40 J
  done clear
  C)
   80 J                       
  done clear
  D)
   20 J
  done clear
  View Answer play_arrow

• question_answer5)     Air is filled at\[60{}^\circ C\]in a vessel of open mouth. The vessel is heated to a temperature T, so that \[1/4\]th part of air escape. Assuming the volume of the vessel remaining constant, the value of T is
  A)
   \[80{}^\circ C\]                
  done clear
  B)
   \[444{}^\circ C\]
  done clear
  C)
   \[333{}^\circ C\]                             
  done clear
  D)
   \[171{}^\circ C\]
  done clear
  View Answer play_arrow

• question_answer6)     The displacement-time graph of a particles executing SHM is as shown in the figure The corresponding force-time graph of the particle is
  A)
                
  done clear
  B)
   
  done clear
  C)
              
  done clear
  D)
   
  done clear
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• question_answer7)     The maximum particle velocity in a wave motion is half the wave velocity, then the amplitude of the wave is equal to
  A)
   \[\frac{\lambda }{4\pi }\]                                           
  done clear
  B)
   \[\frac{2\lambda }{\pi }\]
  done clear
  C)
   \[\frac{\lambda }{2\pi }\]                                           
  done clear
  D)
   \[\lambda \]
  done clear
  View Answer play_arrow

• question_answer8)     The work done in carrying a charge q once round a circle of radius a with a charge Q at its centre is
  A)
   \[\frac{qQ}{4\pi {{\varepsilon }_{0}}a}\]                              
  done clear
  B)
   \[\frac{qQ}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}\]
  done clear
  C)
   \[\frac{q}{4\pi {{\varepsilon }_{0}}a}\]                 
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer9)     On increasing the temperature of a conductor, its resistance increase because the
  A)
   relaxation time increases
  done clear
  B)
   mass of electron increases
  done clear
  C)
   electron density decreases
  done clear
  D)
   relaxation time decreases
  done clear
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• question_answer10)     How much heat is produced by 1500 W heater in 7 min?
  A)
   1.5kcal                
  done clear
  B)
   15kcal
  done clear
  C)
   150kcal               
  done clear
  D)
   1500kcal
  done clear
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• question_answer11)     Two particles A and B of masses\[{{m}_{A}}\]and\[{{m}_{B}}\] respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The spead of the particles are\[{{\upsilon }_{A}}\]and\[{{\upsilon }_{B}}\]respectively and the trajectories are as shown in the figure. Then,
  A)
   \[{{m}_{A}}{{v}_{A}}<{{m}_{B}}{{v}_{B}}\]         
  done clear
  B)
   \[{{m}_{A}}{{v}_{A}}>{{m}_{B}}{{v}_{B}}\]
  done clear
  C)
   \[{{m}_{A}}<{{m}_{B}}\,and\,{{v}_{A}}<{{v}_{B}}\]        
  done clear
  D)
  \[{{m}_{A}}={{m}_{B}}\,and\,{{v}_{A}}={{v}_{B}}\]
  done clear
  View Answer play_arrow

• question_answer12)     A proton travelling at\[23{}^\circ C\]w.r.t. the direction of a magnetic field of strength 2.6 mT experiences a magnetic force of\[6.5\times {{10}^{-17}}N\]. What is the speed of the proton?
  A)
   \[2\times {{10}^{5}}\text{ }m/s\]            
  done clear
  B)
   \[4\times {{10}^{5}}\text{ }m/s\]
  done clear
  C)
   \[6\times {{10}^{5}}\text{ }m/s\]            
  done clear
  D)
   \[6\times {{10}^{-5}}\text{ }m/s\]
  done clear
  View Answer play_arrow

• question_answer13)     The magnetic moment produced in a substance of 1 g is\[6\times {{10}^{-7}}A{{m}^{2}}\]. If its density is \[5g/c{{m}^{2}},\] then the intensity of magnetisation in A/m will be
  A)
   \[8.3\times {{10}^{6}}\]               
  done clear
  B)
   3.0
  done clear
  C)
   \[1.2\times {{10}^{-7}}\]             
  done clear
  D)
   \[3\times {{10}^{-6}}\]
  done clear
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• question_answer14)     The angle which the total magnetic field of earth makes with the surfaces of the earth is called
  A)
   declination                        
  done clear
  B)
   magnetic meridian
  done clear
  C)
   geographic meridian     
  done clear
  D)
   inclination
  done clear
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• question_answer15)     When the current changes from\[+2A\] to\[-2A\] in 0.05 s, an emf of 8 V is induced in a coil. The coefficient of self induction of the coil is
  A)
   0.2 H                                    
  done clear
  B)
   0.4 H  
  done clear
  C)
   0.8 H                    
  done clear
  D)
   0.1 H
  done clear
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• question_answer16)     A force of 49 N is just able to move a block of wood weighing 10 kg on a rough horizontal surface. Its coefficient of friction is
  A)
   1                            
  done clear
  B)
   0.7
  done clear
  C)
   0.5                        
  done clear
  D)
   zero
  done clear
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• question_answer17)     A smooth block is released at rest on a\[45{}^\circ \]incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
  A)
   \[{{\mu }_{k}}=1-\frac{1}{{{n}^{2}}}\]                   
  done clear
  B)
   \[{{\mu }_{k}}=\sqrt{1-\frac{1}{{{n}^{2}}}}\]
  done clear
  C)
   \[{{\mu }_{s}}=1-\frac{1}{{{n}^{2}}}\]                   
  done clear
  D)
   \[{{\mu }_{s}}=\sqrt{1-\frac{1}{{{n}^{2}}}}\]
  done clear
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• question_answer18)     For a moving particle (mass m, velocity\[\upsilon \]) having a momentum P, which one of the following correctly describes the kinetic energy of the particle?
  A)
   \[\frac{{{p}^{2}}}{2m}\]                                              
  done clear
  B)
   \[\frac{p}{2m}\]
  done clear
  C)
   \[\frac{{{v}^{2}}}{2m}\]                                               
  done clear
  D)
   \[\frac{v}{2m}\]
  done clear
  View Answer play_arrow

• question_answer19)     300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. Taking \[g=10m{{s}^{-2}}\]work done against friction is
  A)
   200 J                    
  done clear
  B)
   100J
  done clear
  C)
   zero                     
  done clear
  D)
   1000J
  done clear
  View Answer play_arrow

• question_answer20)     The work done by a force\[F=(-6{{x}^{3}})iN,\]in displacing a particle from\[x=4\text{ }m\]to \[x=-2m\] is
  A)
   360 J                                    
  done clear
  B)
   240 J
  done clear
  C)
   \[-240J\]           
  done clear
  D)
   \[-360J\]
  done clear
  View Answer play_arrow

• question_answer21)     A system consisting of two masses connected by a massless rod lies along the\[x-\]axis. A 0.4 kg mass is at a distance\[x=2\text{ }m\] while a 0.6 kg mass is at a distance\[x=7\text{ }m\]. The. \[x-\] coordinate of the centre of mass is
  A)
   5 m                       
  done clear
  B)
   3.5 m
  done clear
  C)
   4.5 m                   
  done clear
  D)
   4 m
  done clear
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• question_answer22)     If linear density of a rod of length 3 m varies as \[\lambda =2+x,\]then the position of the centre of gravity of the rod is
  A)
   \[\frac{7}{3}m\]                                              
  done clear
  B)
   \[\frac{12}{7}m\]
  done clear
  C)
   \[\frac{10}{7}m\]                           
  done clear
  D)
   \[\frac{9}{7}m\]
  done clear
  View Answer play_arrow

• question_answer23)     Escape velocity at surface of earth is \[11.2km{{s}^{-1}},\]escape velocity from a planet whose mass is the same as that of earth and radius 1/4 that of earth is
  A)
   \[2.8\text{ }km{{s}^{-1}}\]                         
  done clear
  B)
   \[15.6km{{s}^{-1}}\]
  done clear
  C)
   \[22.4\text{ }km{{s}^{-1}}\]                       
  done clear
  D)
   \[44.8\text{ }km{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer24)     Two satellites A and B go around a planet P in circular orbits having radius 4R and\[R\] respectively. If the speed of satellite A is\[3\upsilon ,\] then the speed of satellite B will be
  A)
   6v                                         
  done clear
  B)
   9V
  done clear
  C)
   3v                                         
  done clear
  D)
   None of these
  done clear
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• question_answer25)     A sphere of radius 3 cm is subjected to a pressure of 100 atm. Its volume decreases by 0.3 cc. What will be its bulk modulus?
  A)
   \[4\text{ }\pi \times {{10}^{5}}\text{ }atm\]                      
  done clear
  B)
   \[\text{3}\times 4\pi \times {{10}^{3}}\text{ }atm\]
  done clear
  C)
   \[4\text{ }\pi \times {{10}^{6}}\text{ }atm\]      
  done clear
  D)
   \[4\pi \times {{10}^{8}}\text{ }atm\]
  done clear
  View Answer play_arrow

• question_answer26)     A body subjected to strain several times will not obey Hookes law due to
  A)
   yield point                         
  done clear
  B)
   permanent state
  done clear
  C)
   elastic fatigue                  
  done clear
  D)
   breaking stress
  done clear
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• question_answer27)     The area of cross-section of a wire of length 1.1 m is\[1m{{m}^{2}}\]. It is leaded with 1 kg of Youngs    modulus    of   copper   is\[1.1\times {{10}^{11}}N{{m}^{-2}},\]then the increase in length will be (if\[g=10m{{s}^{-2}}\])
  A)
   0.01 mm             
  done clear
  B)
   0.075 mm
  done clear
  C)
   0.1 mm               
  done clear
  D)
   0.15mm
  done clear
  View Answer play_arrow

• question_answer28)     Water flows along a horizontal pipe whose cross-section is not constant. The pressure is 1 cm of Hg where the velocity is\[35\text{ }cm{{s}^{-1}}\]. At a point where the velocity is\[65\text{ }cm{{s}^{-1}},\]the pressure will be
  A)
   0.89 cm of Hg                   
  done clear
  B)
   8.9 cm of Hg
  done clear
  C)
   0.5 cm of Hg                     
  done clear
  D)
   1 cm of Hg
  done clear
  View Answer play_arrow

• question_answer29)     The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are\[{{\upsilon }_{2}}\] respectively. If A is the cross-sectional area of the wing and p is the density of air. Then the upward life is
  A)
   \[\frac{1}{2}\rho A({{v}_{1}}-{{v}_{2}})\]             
  done clear
  B)
   \[\frac{1}{2}\rho A({{v}_{1}}+{{v}_{2}})\]
  done clear
  C)
   \[\frac{1}{2}\rho A(v_{1}^{2}-v_{2}^{2})\]          
  done clear
  D)
   \[\frac{1}{2}\rho A(v_{1}^{2}+v_{2}^{2})\]
  done clear
  View Answer play_arrow

• question_answer30)     If two soap bubbles of different radii are connected by a tube, then
  A)
   air flows from the bigger bubble to the smaller bubble till the sizes become equal
  done clear
  B)
   air flows from bigger bubble to the smaller bubble till the sizes are interchanged
  done clear
  C)
   air flows from the smaller bubble to the bigger
  done clear
  D)
   there is no flow of air
  done clear
  View Answer play_arrow

• question_answer31)     At which temperature the Fahrenheit and Celsius scale give equal readings?
  A)
   \[40{}^\circ \]                 
  done clear
  B)
   \[37{}^\circ \]
  done clear
  C)
   \[-40{}^\circ \]                 
  done clear
  D)
   \[80{}^\circ \]
  done clear
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• question_answer32)     When the temperature of a rod increases from t to\[t+\Delta t,\]its moment of inertia increases from \[I\]to\[I+\Delta I\].If\[\alpha \]be the coefficient of linear expansion of the rod, then the value of\[\frac{\Delta I}{I}\]is
  A)
   \[2\alpha \,\Delta t\]                    
  done clear
  B)
   \[\alpha \,\Delta t\]
  done clear
  C)
   \[\frac{\alpha \,\Delta t}{2}\]                   
  done clear
  D)
   \[\frac{\,\Delta t}{\alpha }\]
  done clear
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• question_answer33)     Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities K and 2K respectively. The equivalent thermal conductivity of the slab is
  A)
   3 K                        
  done clear
  B)
   \[\frac{4}{3}K\]   
  done clear
  C)
   \[\frac{2}{3}K\]                                               
  done clear
  D)
   \[\sqrt{2}K\]
  done clear
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• question_answer34)     A body cools from\[50{}^\circ C\]to\[49.9{}^\circ C\]in 5 s. How long will it take to cool from\[40{}^\circ C\]to\[39.9{}^\circ C\]? [Assume   the   temperature   of the surroundings to be\[30{}^\circ C\]and Newtons law of cooling to be valid]
  A)
   2.5s                      
  done clear
  B)
   5s  
  done clear
  C)
   20s                       
  done clear
  D)
   10s
  done clear
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• question_answer35)     A ball is released from the top of a tower of height h m. It takes t s to reach the ground what is the position of the ball in T/3 s?
  A)
   \[\frac{h}{9}m\]from the ground
  done clear
  B)
   \[\frac{7h}{9}m\]from the ground
  done clear
  C)
   \[\frac{8h}{9}m\]from the ground
  done clear
  D)
   \[\frac{17h}{9}m\]from the ground
  done clear
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• question_answer36) A source of sound and an observer are approaching each other with the same speed, which is equal to \[\frac{1}{10}\]th times the speed of sound. The apparent relative change in the frequency of the source is
  A)
   22.2 % increase               
  done clear
  B)
   22.2% decrease
  done clear
  C)
   18.2% decrease              
  done clear
  D)
   18.2% increase
  done clear
  View Answer play_arrow

• question_answer37) The maximum power dissipated in an external resistance R, when connected to a cell of emf \[E\]and internal resistance r is will
  A)
   \[\frac{{{E}^{2}}}{r}\]                                   
  done clear
  B)
   \[\frac{{{E}^{2}}}{2r}\] 
  done clear
  C)
   \[\frac{{{E}^{2}}}{3r}\]                                 
  done clear
  D)
   \[\frac{{{E}^{2}}}{4r}\]
  done clear
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• question_answer38) A charge q coulomb makes\[n\]revalution in 1 s in a circular orbit of radius r. The magnetic field at the centre of the orbit in N/Am is
  A)
   \[\left( \frac{2\pi m}{q}\times {{10}^{-7}} \right)\]         
  done clear
  B)
   \[\left( \frac{2\pi q}{q} \right)\times {{10}^{-7}}\]
  done clear
  C)
   \[\left( \frac{2\pi q}{nr} \right)\times {{10}^{-7}}\]         
  done clear
  D)
   \[\left( \frac{2\pi nq}{r} \right)\times {{10}^{-7}}\]
  done clear
  View Answer play_arrow

• question_answer39) The time period of a freely suspended bar magnet in a field in 2 s. It is cut into two equal parts along its axis, then the time period is
  A)
   \[4s\]                                  
  done clear
  B)
   0.5s
  done clear
  C)
   \[2s\]                                  
  done clear
  D)
   0.25 s
  done clear
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• question_answer40) The velocities of light in two different mediums are\[2\times {{10}^{8}}\text{ }m/s\]and \[2.5\times {{10}^{8}}m/s\]respectively. The critical angle for these medium is
  A)
   \[{{\sin }^{-1}}\left( \frac{1}{5} \right)\]                               
  done clear
  B)
   \[{{\sin }^{-1}}\left( \frac{4}{5} \right)\]
  done clear
  C)
   \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]                               
  done clear
  D)
   \[{{\sin }^{-1}}\left( \frac{1}{4} \right)\]
  done clear
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• question_answer41) Cathode ray of velocity\[{{10}^{6}}m/s\]describe an approximate circular path of radius 1 m in an electric field 300 V/cm. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be
  A)
   2400 V/cm                         
  done clear
  B)
   600 V/cm
  done clear
  C)
   1200 V/cm                         
  done clear
  D)
   12000 V/cm
  done clear
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• question_answer42) When an electron jumps from the orbit \[n=2\] to\[n=4,\]then the wavelength of the radiations observed will be (R is Rydbergs constant)
  A)
   \[\frac{16}{3R}\]                                             
  done clear
  B)
   \[\frac{16}{5R}\]
  done clear
  C)
   \[\frac{5R}{16}\]                                             
  done clear
  D)
   \[\frac{3R}{16}\]
  done clear
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• question_answer43) In the figure shown below
  A)
   In both Fig. I and Fig. II, the diodes are forward biased
  done clear
  B)
   In both Fig. I and Fig. II, the diodes are reverse biased
  done clear
  C)
   In Fig. I, the diode is forward biased and in Fig. II, the diode is reverse biased
  done clear
  D)
   In Fig. I, the diode is reverse biased and in Fig. II, the diode is forward biased
  done clear
  View Answer play_arrow

• question_answer44) The electromagnetic radiation has an energy of 13.2 KeV. Then the radiation belongs to the region of
  A)
   visible light                        
  done clear
  B)
   ultraviolet
  done clear
  C)
   infrared                              
  done clear
  D)
   X-ray
  done clear
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• question_answer45) A proton is moving in a uniform magnetic field B is a circular path of radius a in a direction perpendicular to z-axis along which field B exists. Calculate the angular momentum, if the radius is a and charge on proton is e
  A)
   \[\frac{Be}{{{a}^{2}}}\]                                
  done clear
  B)
   \[e{{B}^{2}}a\]
  done clear
  C)
   \[{{a}^{2}}eB\]                
  done clear
  D)
   \[aeB\]
  done clear
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• question_answer46) An electric motor operates on a 50 V supply and a current of 12 A. If the efficiency of the motor is 30%, what is the resistance of the winding of the motor?
  A)
   \[6\,\Omega \]                               
  done clear
  B)
   \[4\,\Omega \]
  done clear
  C)
   \[2.9\,\Omega \]                            
  done clear
  D)
   \[3.2\,\Omega \]
  done clear
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• question_answer47) Beats are produced by two waves given by\[{{y}_{1}}=a\sin 200\pi t\]and\[{{y}_{2}}=a\sin 208\pi t\]. The number of beats heard per second is
  A)
   zero                     
  done clear
  B)
   one
  done clear
  C)
   four                     
  done clear
  D)
   eight
  done clear
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• question_answer48) A wheel having moment of inertia\[2\text{ }kg-{{m}^{2}}\] about its vertical axis, rotates at the rate of 60 rpm about the axis. The torque Which can stop the wheels rotation in one minute would be
  A)
   \[\frac{2\pi }{15}Nm\]                 
  done clear
  B)
   \[\frac{\pi }{12}Nm\]
  done clear
  C)
   \[\frac{\pi }{15}Nm\]                    
  done clear
  D)
   \[\frac{\pi }{10}Nm\]
  done clear
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• question_answer49) The power of pump, which can pump 200 kg of water to a height of 50 m in 10 s, will be
  A)
   \[10\times {{10}^{3}}W\]            
  done clear
  B)
   \[20\times {{10}^{3}}W\]
  done clear
  C)
   \[4\times {{10}^{3}}W\]              
  done clear
  D)
   \[6\times {{10}^{3}}W\]
  done clear
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• question_answer50) The coefficient of restitute e, for a perfectly elastic collision is
  A)
   0                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   1                            
  done clear
  D)
   \[\infty \]
  done clear
  View Answer play_arrow

• question_answer51) An elastic with kinetic energy 5eV is incident on a H-atom in its ground state. The collision
  A)
   must be elastic
  done clear
  B)
   may be partially elastic
  done clear
  C)
   may be completely elastic
  done clear
  D)
   may be completely inelastic
  done clear
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• question_answer52) Circular disc of mass 2 kg and radius 1 m is rotating about an axis perpendicular to its plane and passing through its centre of mass with a rotational kinetic energy of 8 J. The angular momentum in (j s) is
  A)
   8                            
  done clear
  B)
   4
  done clear
  C)
   2                            
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer53) If T is reverberation time of a auditorium of volume y, then
  A)
   \[T\propto {{V}^{2}}\]                 
  done clear
  B)
   \[T\propto V\]
  done clear
  C)
   \[T\propto \frac{1}{V}\]                              
  done clear
  D)
   \[T\propto \frac{1}{{{V}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer54) The electric potential at the surface of an atomic nucleus\[(z=50)\]of radius\[9\times {{10}^{-15}}m\] is
  A)
   80V                                      
  done clear
  B)
   \[8\times {{10}^{6}}V\]
  done clear
  C)
   9V                                         
  done clear
  D)
   \[9\times {{10}^{5}}V\]
  done clear
  View Answer play_arrow

• question_answer55) The potential energy of a charged parallel plate capacitor is\[{{U}_{0}}\]. If a slab of dielectric constant k is inserted between the plates, then the new potential energy will be
  A)
   \[\frac{{{v}_{0}}}{k}\]                                   
  done clear
  B)
   \[{{v}_{0}}{{k}^{2}}\]
  done clear
  C)
   \[\frac{{{v}_{0}}}{{{k}^{2}}}\]                                    
  done clear
  D)
   \[v_{0}^{2}\]
  done clear
  View Answer play_arrow

• question_answer56) A chemical reaction was carried out at 300 K and 280 K. The rate constants were found to be\[{{k}_{1}}\]and\[{{k}_{2}}\]respectively. Then
  A)
   \[{{k}_{2}}=0.25{{k}_{1}}\]                         
  done clear
  B)
   \[{{k}_{2}}=0.5{{k}_{1}}\]
  done clear
  C)
   \[{{k}_{2}}=2{{k}_{1}}\]                               
  done clear
  D)
   \[{{k}_{2}}=4{{k}_{1}}\]
  done clear
  View Answer play_arrow

• question_answer57) 10 g of a radioactive isotope is reduced to 1.25 s in 12 yr. Therefore, half-life period of the isotope is
  A)
   3yr                                        
  done clear
  B)
   4yr
  done clear
  C)
   8yr                                        
  done clear
  D)
   24yr
  done clear
  View Answer play_arrow

• question_answer58) In physisorption, adsorbent does not show specificity for any particular gas because
  A)
   gases involved behave like ideal gases
  done clear
  B)
   enthalpy of adsorption is low
  done clear
  C)
   it is a reversible process
  done clear
  D)
   involved van der Waals forces are universal
  done clear
  View Answer play_arrow

• question_answer59) Lyophobic sol can be protected by
  A)
   by addition of lyophilic sol
  done clear
  B)
   by addition of an electrolyte
  done clear
  C)
   by addition of oppositely charged sol
  done clear
  D)
   by boiling
  done clear
  View Answer play_arrow

• question_answer60) The main reactions occurring in blast furnace during extraction of iron from haematite are
  A)
   \[F{{e}_{2}}{{O}_{3}}+3CO\xrightarrow[{}]{{}}2Fe+3C{{O}_{2}}\]
  done clear
  B)
   \[FeO+Si{{O}_{2}}\xrightarrow[{}]{{}}FeSi{{O}_{3}}\]
  done clear
  C)
   \[F{{e}_{2}}{{O}_{3}}+3C\xrightarrow[{}]{{}}2Fe+3CO\]
  done clear
  D)
   \[CaO+Si{{O}_{2}}\xrightarrow[{}]{{}}CaSi{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer61) Electrolytic refining is used to purify which of the following metals?
  A)
   Cu and Zn          
  done clear
  B)
   Ge and Si
  done clear
  C)
   Zr and Ti             
  done clear
  D)
   Zn and Hg
  done clear
  View Answer play_arrow

• question_answer62) The following acids have been arranged in order of decreasing acid strength. Identify the correct order\[HOCI(I),HOBr(II)\]and\[HOI(III)\]
  A)
   \[I>III>II\]                         
  done clear
  B)
   \[II>I>III\]
  done clear
  C)
   \[III>II>I\]                         
  done clear
  D)
   \[I>II>III\]
  done clear
  View Answer play_arrow

• question_answer63) The correct formula of salt formed by the neutralisation of hypo-phosphorus acid with \[NaOH\]is
  A)
   \[Na{{H}_{2}}P{{O}_{2}}\]          
  done clear
  B)
  \[N{{a}_{2}}HP{{O}_{2}}\]
  done clear
  C)
   \[N{{a}_{3}}P{{O}_{2}}\]             
  done clear
  D)
   \[N{{a}_{3}}P{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer64) Which one of the following alkaline earth metal sulphates has hydration enthalpy higher than the lattice enthalpy?
  A)
   \[BeS{{O}_{4}}\]             
  done clear
  B)
   \[CaS{{O}_{4}}\]
  done clear
  C)
   \[BaS{{O}_{4}}\]             
  done clear
  D)
   \[SrS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer65) In the preparation of amorphous silicon, HF acid is used to remove
  A)
   \[Mg\]                                
  done clear
  B)
   \[Si{{O}_{2}}\]
  done clear
  C)
   \[Si\]                  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer66) Cartisone is a molecular substance containing 21 atoms of carbon per molecule. The mass percentage of carbon in cortisone is 69.98%. Its molar mass is
  A)
   176.5                   
  done clear
  B)
   252.2
  done clear
  C)
   287.6                   
  done clear
  D)
   360.1
  done clear
  View Answer play_arrow

• question_answer67) Octet rule is not followed in
  A)
   \[NaCl,MgC{{l}_{2}},MgO\]
  done clear
  B)
   \[PC{{l}_{3}},N{{H}_{3}},{{H}_{2}}O\]
  done clear
  C)
   \[{{N}_{2}}{{O}_{4}},CC{{l}_{4}},{{N}_{2}}{{O}_{5}}\]
  done clear
  D)
   \[B{{F}_{3}},BeC{{l}_{2}}\]and \[N{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer68) A molecule of the type\[A{{X}_{5}}\]has square pyramidal geometry. Hence, number of lone pairs on A is
  A)
   1                            
  done clear
  B)
   2
  done clear
  C)
   3                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer69) Compound X is highly volatile and insoluble in water. Bonding in X is
  A)
   ionic 
  done clear
  B)
                          covalent
  done clear
  C)
   polar covalent                 
  done clear
  D)
   coordinate
  done clear
  View Answer play_arrow

• question_answer70) The correct order of increasing ionic character is
  A)
   \[BeC{{l}_{2}}<MgC{{l}_{2}}<CaC{{l}_{2}}<BaC{{l}_{2}}\]
  done clear
  B)
   \[BeC{{l}_{2}}<CaC{{l}_{2}}<MgC{{l}_{2}}<BaC{{l}_{2}}\]
  done clear
  C)
   \[MgC{{l}_{2}}<CaC{{l}_{2}}<BeC{{l}_{2}}<BaC{{l}_{2}}\]
  done clear
  D)
   \[BaC{{l}_{2}}<CaC{{l}_{2}}<MgC{{l}_{2}}<BeC{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer71) Which of the following changes requires a reducing agent?
  A)
   \[CrO_{4}^{2-}\xrightarrow[{}]{{}}C{{r}_{2}}O_{7}^{2-}\]
  done clear
  B)
   \[BrO_{3}^{-}\xrightarrow[{}]{{}}Br{{O}^{-}}\]
  done clear
  C)
   \[{{H}_{3}}As{{O}_{3}}\xrightarrow[{}]{{}}HAsO_{4}^{2-}\]
  done clear
  D)
   \[Al{{(OH)}_{3}}\xrightarrow{{}}Al(OH)_{4}^{-}\]
  done clear
  View Answer play_arrow

• question_answer72) Aluminium-25 decays by emitting a positron. The species immediately produced has
  A)
   \[12p.13n.13{{e}^{-}}\]                
  done clear
  B)
   \[13p,\text{ }12n,\text{ }13{{e}^{-}}\]
  done clear
  C)
   \[12p,13n,12{{e}^{-}}\]                
  done clear
  D)
   \[14p,\text{ }11n,14{{e}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer73) At a given condition, 1 mole of\[{{O}_{2}}\]occupies volume 30 L. What is volume occupied by 1 equivalent of\[{{O}_{2}}\]?
  A)
   2.5 L                     
  done clear
  B)
   5.0 L
  done clear
  C)
   7.5 L                     
  done clear
  D)
   10L
  done clear
  View Answer play_arrow

• question_answer74) \[{{H}_{2}}{{O}_{2}}\xrightarrow[{}]{{}}{{H}_{2}}O+{{O}_{2}};\]This represents
  A)
   oxidation of\[{{N}_{2}}{{O}_{2}}\]
  done clear
  B)
   reduction of\[{{N}_{2}}{{O}_{2}}\]
  done clear
  C)
   disproportionation of\[{{H}_{2}}{{O}_{2}}\]
  done clear
  D)
   acidic nature of\[{{N}_{2}}{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer75) Which is not true statement about\[FeO\]?
  A)
   It is non-stoichiometric and is metal deficient
  done clear
  B)
   It is a basic oxide
  done clear
  C)
   Its aqueous solution changes to\[Fe{{(OH)}_{3}}\]and then to\[F{{e}_{2}}{{O}_{3}}.{{({{H}_{2}}O)}_{n}}\]by atmospheric oxygen
  done clear
  D)
   It gives red colour with KCNS
  done clear
  View Answer play_arrow

• question_answer76) Spin only magnetic moment of the compound \[Hg[Co{{(SCN)}_{4}}]\]is
  A)
   \[\sqrt{3}BM\]                
  done clear
  B)
   \[\sqrt{8}BM\]
  done clear
  C)
   \[\sqrt{15}BM\]                              
  done clear
  D)
   \[\sqrt{24}BM\]
  done clear
  View Answer play_arrow

• question_answer77) Lead poisoning in the body can be removed by
  A)
   EDTA in the form of calcium dihydrogen salt
  done clear
  B)
   cis-platin
  done clear
  C)
   Zeisses salt
  done clear
  D)
   DMG
  done clear
  View Answer play_arrow

• question_answer78) Which of the following, cations is not paramagnetic?
  A)
   \[S{{C}^{3+}}(aq)\]                        
  done clear
  B)
   \[T{{i}^{3+}}(aq)\]
  done clear
  C)
   \[{{V}^{3+}}(aq)\]                          
  done clear
  D)
   \[C{{r}^{3+}}(aq)\]
  done clear
  View Answer play_arrow

• question_answer79) The. free   energy  change  for  the decomposition reaction,\[\frac{2}{3}A{{l}_{2}}{{O}_{3}}\xrightarrow[{}]{{}}\frac{4}{3}Al+{{O}_{2}}\]is\[\Delta G=+960\,kJ\] (\[F=96500\text{ }C\,mo{{l}^{-1}}\]) The minimum potential difference required to reduce \[A{{l}_{2}}{{O}_{3}}\]at\[500{}^\circ C\]will be
  A)
   1.345V                
  done clear
  B)
   1.724V
  done clear
  C)
   2.146V                
  done clear
  D)
   2.487V
  done clear
  View Answer play_arrow

• question_answer80) An increase in equivalent conductance of a strong electrolyte with dilution is mainly due to
  A)
   increase in number of ions
  done clear
  B)
   increase in ionic mobility of ions
  done clear
  C)
   100% ionisation of electrolyte at normal dilution
  done clear
  D)
   increase in both i.e., number of ions and ionic mobility of ions
  done clear
  View Answer play_arrow

• question_answer81) Calculate the resulting molarity of the solution that is obtained by adding 5 g of\[NaOH\]to 250 mL of\[\frac{M}{4}\]\[NaOH\]solution (density =1.05 g \[c{{m}^{-3}}\]). The density of the resulting solution is 1.08 g\[c{{m}^{-3}}\].
  A)
   0.41 M               
  done clear
  B)
   0.56 M
  done clear
  C)
   0.63 M               
  done clear
  D)
   0.76 M
  done clear
  View Answer play_arrow

• question_answer82) One component of a solution follows Raoults law over the entire range\[0\le {{x}_{1}}\le 1\].The second component must follow Raoults law in the range when\[{{x}_{2}}\]is
  A)
   close to zero                    
  done clear
  B)
   close to 1
  done clear
  C)
   \[0\le {{x}_{2}}\le 0.5\]                
  done clear
  D)
   \[0\le {{x}_{2}}\le 1\]
  done clear
  View Answer play_arrow

• question_answer83) The   intermetallic   compound\[LiAg\]crystallises in cubic lattice in which both lithium and silver have coordination number of eight. The crystal class is
  A)
   simple cubic                     
  done clear
  B)
   body centred cubic
  done clear
  C)
   face centred cubic         
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer84) For a cubic crsytal, the face diagonal is\[3.50\text{ }\overset{o}{\mathop{\text{A}}}\,\] The face length is
  A)
   \[\text{2}\text{.475 }\overset{o}{\mathop{\text{A}}}\,\]                           
  done clear
  B)
   \[\text{1}\text{.326 }\overset{o}{\mathop{\text{A}}}\,\]
  done clear
  C)
   \[\text{1}\text{.218 }\overset{o}{\mathop{\text{A}}}\,\]                           
  done clear
  D)
   \[\text{1}\text{.078 }\overset{o}{\mathop{\text{A}}}\,\]
  done clear
  View Answer play_arrow

• question_answer85) Which one of the following alcohols will yield the corresponding alkyl chloride on reaction with  cone. \[HCl\] at  room temperature?
  A)
   \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\]  
  done clear
  B)
  \[C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\mathop{CHOH}}\,\]
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\mathop{CHC{{H}_{2}}OH}}\,\]
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-OH\]
  done clear
  View Answer play_arrow

• question_answer86) Arrange the following compounds in increasing order of rate of reaction towards nucleophilic substitution
  A)
   I < II < III                             
  done clear
  B)
   III < II < I
  done clear
  C)
   I < III < II                             
  done clear
  D)
   III < I < II
  done clear
  View Answer play_arrow

• question_answer87) In the addition of\[HBr\]to propene in the absence of peroxides, the first step involves the addition of
  A)
   \[{{H}^{\bullet }}\]                                        
  done clear
  B)
   \[B{{r}^{\bullet }}\]
  done clear
  C)
   \[{{H}^{+}}\]                   
  done clear
  D)
   \[B{{r}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer88) Salol is
  A)
             
  done clear
  B)
   
  done clear
  C)
     
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer89) Sulphonation of phenol at low temperature gives
  A)
   2-phenol sulphonic acid, a major product
  done clear
  B)
   4-phenol sulphonic add, a major product -
  done clear
  C)
   Both (a) and (b)
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer90) Which of the following B group vitamins can be stored in our body?
  A)
   Vitamin \[{{B}_{1}}\]                    
  done clear
  B)
   Vitamin\[{{B}_{2}}\]
  done clear
  C)
   Vitamin \[{{B}_{6}}\]                    
  done clear
  D)
   Vitamin \[{{B}_{12}}\]
  done clear
  View Answer play_arrow

• question_answer91) Sucrose is a
  A)
   monosaccharide, reducing sugar
  done clear
  B)
   disaccharide, reducing sugar
  done clear
  C)
   monosaccharide, non-reducing sugar
  done clear
  D)
   disaccharide, non-reducing sugar
  done clear
  View Answer play_arrow

• question_answer92) Which one of the following compounds do not undergo aldol condensation?
  A)
   \[C{{H}_{3}}COC{{H}_{3}}\]                       
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}CHO\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}COC{{H}_{2}}C{{H}_{3}}\]   
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}CHO\]
  done clear
  View Answer play_arrow

• question_answer93) In the reaction\[C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[{}]{SOC{{l}_{2}}}A\xrightarrow[{}]{N{{H}_{3}}(excess)}\]\[B\xrightarrow[{}]{B{{r}_{2}}/KOH}C\]Product C is
  A)
   \[C{{H}_{3}}COC{{H}_{3}}\]                       
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}CHO\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}COC{{H}_{2}}C{{H}_{3}}\]    
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}CHO\]
  done clear
  View Answer play_arrow

• question_answer94) Which one of the following is a anti-depressant drug?
  A)
   Iproniazid                          
  done clear
  B)
   Aspirin
  done clear
  C)
   Morphine                          
  done clear
  D)
   Seldane
  done clear
  View Answer play_arrow

• question_answer95) Arrange the following alkenes in order of increasing reactivity towards anionic polymerisation \[\underset{I}{\mathop{{{H}_{2}}C=CHC{{H}_{3}},}}\,\] \[\underset{II}{\mathop{{{H}_{2}}C=C{{F}_{2}},}}\,\] \[\underset{III}{\mathop{{{H}_{2}}C=CHCN}}\,\]\[\underset{IV}{\mathop{{{H}_{2}}C=CH{{C}_{6}}{{H}_{5}}}}\,\]
  A)
   I < IV < II < III                    
  done clear
  B)
   I < II < III < IV
  done clear
  C)
   III < II < I < IV                    
  done clear
  D)
   IV < III < II < I
  done clear
  View Answer play_arrow

• question_answer96) Number of waves made by a Bohr electron in one complete revolution in its fourth orbit is
  A)
   2                            
  done clear
  B)
   3
  done clear
  C)
   4                            
  done clear
  D)
   \[\infty \]
  done clear
  View Answer play_arrow

• question_answer97)  An electron in H-atom in its ground state absorbs 1.50 times as much as energy as the minimum required for its escape (13.6 eV) from the atom. Thus, KE given to emitted electron is
  A)
   13.6eV                
  done clear
  B)
   20.4 eV
  done clear
  C)
   34.0eV                                
  done clear
  D)
   6.8eV
  done clear
  View Answer play_arrow

• question_answer98) In the following reaction, we start with 2 moles of\[{{N}_{2}}\]and 5 moles of\[{{H}_{2}}\]exerting a total prssure of 7 aim at a given temperature in a closed vessel. When 50% of\[{{N}_{2}}\]s converted into\[N{{H}_{3}},\] partial pressure of\[N{{H}_{3}}\]is \[{{N}_{2}}+3{{H}_{2}}\xrightarrow[{}]{{}}2N{{H}_{3}}\]
  A)
   2.8 atm               
  done clear
  B)
   2atm
  done clear
  C)
   3.2 atm               
  done clear
  D)
   4 atm
  done clear
  View Answer play_arrow

• question_answer99) Average volume available to a molecule in a sample of ideal gas at STP is
  A)
   \[3.72\times {{10}^{-20}}c{{m}^{3}}\]
  done clear
  B)
   \[2.69\times {{10}^{19}}c{{m}^{3}}\]
  done clear
  C)
   \[22400c{{m}^{3}}\]
  done clear
  D)
   \[22400\times 6.02\times {{10}^{23}}c{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer100) At\[90{}^\circ C,\]the following equilibrium is established\[{{H}_{2}}(g)+S(s){{H}_{2}}S(g);\]\[{{K}_{c}}=6.8\times {{10}^{-2}}\] If 0.20 mole hydrogen and 1.0 mole of sulphur are heated to\[90{}^\circ C\]in a 1.0 L vessel, what will be the partial pressure of\[{{H}_{2}}S\]at equilibrium?
  A)
   0.25 atm                             
  done clear
  B)
   0.38 atm
  done clear
  C)
   0.46 atm                             
  done clear
  D)
   0.56 atm
  done clear
  View Answer play_arrow

• question_answer101) In the following reaction,\[A+B+QC+D\]the temperature is increased,  then concentration of the             products will
  A)
   remain constant
  done clear
  B)
   decrease
  done clear
  C)
   increase
  done clear
  D)
   first increase then decrease
  done clear
  View Answer play_arrow

• question_answer102) What is\[\Delta E{}^\circ ,\]when 1.00 mole of liquid water vaporise at\[100{}^\circ C\]? The heat of vaporisation, \[\Delta H_{vap}^{o}\] of water at\[100{}^\circ C\]is\[40.66\text{ }kJmo{{l}^{-1}}\].
  A)
  \[-25.48\text{ }kJmo{{l}^{-1}}\]                
  done clear
  B)
  \[+25.48\text{ }kJ\text{ m}o{{l}^{-1}}\]
  done clear
  C)
  \[-36.73kJmo{{l}^{-1}}\]               
  done clear
  D)
  \[+36.73kJmo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer103) 1 mole of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of\[27{}^\circ C\]. The work done is 3 kJ. The final temperature of the gas is equal to(\[{{C}_{V}}=20\,J\,mo{{l}^{-1}}{{K}^{-1}}\])
  A)
   75K                       
  done clear
  B)
   150K
  done clear
  C)
   225 K                   
  done clear
  D)
   300 K
  done clear
  View Answer play_arrow

• question_answer104) Bond energy of\[N-H,H-H\]and\[N\equiv N\] bonds are\[{{q}_{1}},{{q}_{2}}\]and\[{{q}_{3}};\Delta H\]of\[{{N}_{2}}+3{{H}_{2}}\xrightarrow[{}]{{}}2N{{H}_{3}}\]is
  A)
   \[{{q}_{3}}+3{{q}_{2}}-2{{q}_{1}}\]         
  done clear
  B)
   \[2{{q}_{1}}-{{q}_{3}}-2{{q}_{2}}\]
  done clear
  C)
   \[{{q}_{3}}+3{{q}_{2}}-6{{q}_{1}}\]         
  done clear
  D)
   \[{{q}_{1}}+{{q}_{2}}-{{q}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer105) Enthalpy of neutralization of\[HF(aq)\]\[HF(aq)+O{{H}^{-}}(aq)\xrightarrow[{}]{{}}{{F}^{-}}(aq)+{{H}_{2}}O(l)\]is \[-68.60\,kJ\,mo{{l}^{-1}}\]and enthalpy change for the reaction is\[-55.83\text{ }kJ\,mo{{l}^{-1}}\].\[{{H}^{+}}(aq)+O{{H}^{-}}(aq)\xrightarrow[{}]{{}}{{H}_{2}}O(l)\] Thus, enthalpy change \[(kJ\,mo{{l}^{-1}})\] for the dissociation is\[HF(aq)\xrightarrow[{}]{{}}{{H}^{+}}(aq)+{{F}^{-}}(aq)\]
  A)
   \[-12.77\]                          
  done clear
  B)
   \[+12.77\]
  done clear
  C)
   \[-124.43\]                        
  done clear
  D)
   \[+124.43\]
  done clear
  View Answer play_arrow

• question_answer106) Slaked lime,\[Ca{{(OH)}_{2}}\]is used extensively in sewage treatment. What is the maximum pH that can be established in\[Ca{{(OH)}_{2}}(aq)\]? \[Ca{{(OH)}_{2}}(s)C{{a}^{2+}}(aq)+2O{{H}^{-}}(aq);\]\[{{K}_{sp}}=5.5\times {{10}^{-6}}\]
  A)
   1.66                      
  done clear
  B)
   12.35
  done clear
  C)
   7                            
  done clear
  D)
   14
  done clear
  View Answer play_arrow

• question_answer107) Arrange the following in decreasing order of their basic strength
  A)
   III > I > II                             
  done clear
  B)
   I > III > II
  done clear
  C)
   lI > III > I                             
  done clear
  D)
   III > II > I
  done clear
  View Answer play_arrow

• question_answer108) Which one of the following statements is true?
  A)
   Diastereomers are a pair of isomers related spatially as object and mirror image
  done clear
  B)
   Diastereomers can often be separated by fractional crystallization
  done clear
  C)
   Diastereomers have identical physical and chemical properties
  done clear
  D)
   Diastereomers rotate the plane of polarisation of plane polarised light to an equal but opposite extent
  done clear
  View Answer play_arrow

• question_answer109) Which of the following is not a source of carbene?
  A)
   \[C{{H}_{2}}{{N}_{2}}\]                
  done clear
  B)
   \[{{H}_{2}}C=C=O\]
  done clear
  C)
   \[CHC{{l}_{3}}/KOH\]   
  done clear
  D)
   \[C{{H}_{2}}{{I}_{2}}/Zn\]
  done clear
  View Answer play_arrow

• question_answer110) If the relative reactivity of\[1{}^\circ ,\text{ }2{}^\circ \]and\[3{}^\circ \]hydrogens towards free radical chlorination is \[1:4.5:5.5,\]what would be the percentage of 1-chloro-2-methyl cyclohexane in the free radical chlorination of methyl cyclohexane?
  A)
   25%                      
  done clear
  B)
   33.6%
  done clear
  C)
   60%                      
  done clear
  D)
   75%
  done clear
  View Answer play_arrow

• question_answer111) If the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the next n terms. Then, the ratio of the sum of the first 2n terms to the next 2n terms is
  A)
   \[\frac{1}{5}\]                                  
  done clear
  B)
   \[\frac{2}{3}\]
  done clear
  C)
   \[\frac{3}{4}\]                                  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer112)     If a, b and c are real and\[{{x}^{3}}-3{{b}^{2}}x+2{{c}^{3}}\]is divisible by\[(x-a)\]and\[(x-b),\]then
  A)
   \[a=-b=-c\]      
  done clear
  B)
   \[a=2b=2c\]
  done clear
  C)
   \[4{{b}^{2}}=ac\]            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer113)     If\[{{z}_{1}}\]and\[{{z}_{2}}\]are two complex numbers such that Im\[({{z}_{1}}+{{z}_{2}})=0\]and\[({{z}_{1}}{{z}_{2}})=0,\]then
  A)
  \[{{z}_{1}}=-{{z}_{2}}\]                                 
  done clear
  B)
   \[{{z}_{1}}={{z}_{2}}\]
  done clear
  C)
   \[{{z}_{1}}={{\overline{z}}_{2}}\]            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer114)     In the expansion of\[{{(4-3x)}^{7}},\]when\[x=\frac{2}{3},\] the numerically greatest term is
  A)
   \[{{T}_{4}}\]                    
  done clear
  B)
   \[{{T}_{3}}\]
  done clear
  C)
   \[{{T}_{5}}\]                    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer115)     How many numbers can be formed from the digits 1,2,3 and 4 when the repetition is not allowed?
  A)
   \[^{4}{{P}_{4}}\]                                             
  done clear
  B)
   \[^{4}{{P}_{3}}\]
  done clear
  C)
   \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{2}}\]      
  done clear
  D)
  \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}{{+}^{4}}{{P}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer116)     The value of\[\left| \begin{matrix}    1 & 1 & 1 & 1  \\    1 & 2 & 3 & 4  \\    1 & 3 & 6 & 10  \\    1 & 4 & 10 & 20  \\ \end{matrix} \right|\]is
  A)
   0                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   1                            
  done clear
  D)
   10
  done clear
  View Answer play_arrow

• question_answer117)     If A is a non-singular\[3\times 3\]matrix such that\[A{{A}^{T}}={{A}^{T}}A\]and\[B={{A}^{-1}}{{A}^{T}}\]and\[|B|=1,\] then del\[(B-I)\]is equal to
  A)
   1                                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   0                                            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer118)     The number of vectors of unit length perpendicular to the vectors\[a=i+j\]and \[b=j+k,\]is
  A)
   1                            
  done clear
  B)
   2
  done clear
  C)
   4                            
  done clear
  D)
   Infinite
  done clear
  View Answer play_arrow

• question_answer119)     The image (reflection) of the point\[(1,2,-1)\] in the plane\[r.(3i-5j+4k)=5\]is
  A)
   \[\left( \frac{73}{25},\frac{-6}{5},\frac{39}{25} \right)\]
  done clear
  B)
   \[\left( \frac{73}{25},\frac{6}{5},\frac{39}{25} \right)\]
  done clear
  C)
   \[(-1,-2,1)\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer120)     If four dices are rolled, then the number of possible outcomes in which atleast one dice shows 2 is
  A)
   1296                     
  done clear
  B)
   625
  done clear
  C)
   671                                       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer121)     If\[\tan \theta =\alpha -\frac{1}{4\alpha },\]then\[\sec \theta -\tan \theta \]is equal to
  A)
   \[-2a,\frac{1}{2a}\]                        
  done clear
  B)
   \[-\frac{1}{2a},2a\]
  done clear
  C)
   \[2a\]                                  
  done clear
  D)
   \[\frac{1}{2a},2a\]
  done clear
  View Answer play_arrow

• question_answer122)     The smallest and the largest values of\[{{\tan }^{-1}}\left( \frac{1-x}{1+x} \right),\]where\[0\le x\le 1,\]are
  A)
   \[0,\pi \]                                            
  done clear
  B)
   \[1\]
  done clear
  C)
   \[5\]                                    
  done clear
  D)
   \[10\]
  done clear
  View Answer play_arrow

• question_answer123)     The number of solutions of\[\sum\limits_{r=1}^{5}{\cos rx}=5\]in the interval\[[0,2\pi ]\]is
  A)
   0                            
  done clear
  B)
   1      
  done clear
  C)
   5                            
  done clear
  D)
   10
  done clear
  View Answer play_arrow

• question_answer124)     The angle of elevation of the top of a tower at the top and the foot of a pole 10 m high are\[30{}^\circ \]and\[60{}^\circ ,\]respectively. The height of the tower is
  A)
   15m                                     
  done clear
  B)
   20m
  done clear
  C)
   \[10\sqrt{3}m\]              
  done clear
  D)
   \[25\sqrt{3}m\]
  done clear
  View Answer play_arrow

• question_answer125)     The equation of the straight line which bisects the intercepts made by the axes on the lines \[x+y=2\]and\[2x+3y=6\]is.
  A)
   \[2x=5\]             
  done clear
  B)
   \[y=1\]   
  done clear
  C)
   \[2y=3\]             
  done clear
  D)
   \[x=1\]
  done clear
  View Answer play_arrow

• question_answer126)     The number of circles touching the line \[y-x=0\]and the y-axis is
  A)
   0                            
  done clear
  B)
   1       
  done clear
  C)
   2                            
  done clear
  D)
   Infinite
  done clear
  View Answer play_arrow

• question_answer127)     If the eccentricity of the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}+1}+\frac{{{y}^{2}}}{{{a}^{2}}+2}=1\]be\[\frac{1}{\sqrt{6}},\]then the latusrectum of ellipse is
  A)
   \[\frac{5}{\sqrt{6}}\]                                    
  done clear
  B)
   \[\frac{10}{\sqrt{6}}\]
  done clear
  C)
   \[\frac{8}{\sqrt{6}}\]                    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer128)     The domain of definition of\[f(x)={{\sin }^{-1}}(|x-1|-z)\]is
  A)
   \[[-2,0]\cup [2,4]\]        
  done clear
  B)
   \[(-2,0)\cup (2,4)\]
  done clear
  C)
   \[[-2,0]\cup [1,3]\]        
  done clear
  D)
   \[[-2,0]\cup [1,3]\]
  done clear
  View Answer play_arrow

• question_answer129)     If \[f(x)=\frac{[x]}{|x|},x\ne 0,\]where\[[.]\]denotes the greatest integer function, then\[f(1)\]is equal to
  A)
   \[-1\]                   
  done clear
  B)
   \[\infty \]
  done clear
  C)
   Non-existent                   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer130)     Which one of the following statement is true?
  A)
   If\[\underset{x\to c}{\mathop{\lim }}\,f(x).g(x)\]and\[\underset{x\to c}{\mathop{\lim }}\,f(x),\]then\[\underset{x\to c}{\mathop{\lim }}\,g(x)\]exists
  done clear
  B)
   If\[\underset{x\to c}{\mathop{\lim }}\,f(x).g(x)\]exists, then\[\underset{x\to c}{\mathop{\lim }}\,f(x)\]and \[\underset{x\to c}{\mathop{\lim }}\,f(x)\underset{x\to c}{\mathop{\lim }}\,g(x)\]exists
  done clear
  C)
   If\[\underset{x\to c}{\mathop{\lim }}\,\{f(x)+g(x)\}\]and\[\underset{x\to c}{\mathop{\lim }}\,f(x)\]exists, then \[\underset{x\to c}{\mathop{\lim }}\,g(x)\]exists
  done clear
  D)
   If\[\underset{x\to c}{\mathop{\lim }}\,\{f(x)+g(x)\}\]exists, then\[\underset{x\to c}{\mathop{\lim }}\,f(x)\]and \[\underset{x\to c}{\mathop{\lim }}\,g(x)\]exists
  done clear
  View Answer play_arrow

• question_answer131)     If\[f(x)=\left\{ \begin{matrix}    {{x}^{n}}\sin \left( \frac{1}{{{x}^{2}}} \right), & x\ne 0  \\    0, & x=0  \\ \end{matrix} \right.\]where, \[(n\in I),\] then which one of the following is not true?
  A)
   \[\underset{x\to 0}{\mathop{\lim }}\,f(x)\]exist for\[n>1\]
  done clear
  B)
  \[f\]is continuous at\[x=\text{0}\]for\[n>1\]
  done clear
  C)
  \[f\]is differentiable at\[x=\text{0}\]for\[n>1\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer132)     The maximum value of the function\[f(x)=\frac{{{(1+x)}^{0.6}}}{1+{{x}^{0.6}}}\]in the interval [0, 1] is
  A)
   \[{{2}^{0.4}}\]                                  
  done clear
  B)
   \[{{2}^{-0.4}}\]
  done clear
  C)
   \[1\]                                    
  done clear
  D)
   \[{{2}^{0.6}}\]
  done clear
  View Answer play_arrow

• question_answer133)     \[\int{\frac{\sqrt{x-1}}{x\sqrt{x+1}}}dx\]is equal to
  A)
   \[\log |x-\sqrt{{{x}^{2}}-1}|-{{\tan }^{-1}}x+C\]
  done clear
  B)
   \[\log |x+\sqrt{{{x}^{2}}-1}|-{{\tan }^{-1}}x+C\]
  done clear
  C)
   \[\log |x-\sqrt{{{x}^{2}}-1}|-{{\sec }^{-1}}x+C\]
  done clear
  D)
   \[\log |x+\sqrt{{{x}^{2}}-1}|-{{\sec }^{-1}}x+C\]
  done clear
  View Answer play_arrow

• question_answer134)     If\[\int_{1/2}^{2}{\frac{1}{x}}\cos e{{c}^{101}}\left( x-\frac{1}{x} \right)dx=k,\]then the value of \[k\]is
  A)
   1                            
  done clear
  B)
   \[\frac{1}{2}\]      
  done clear
  C)
   0                            
  done clear
  D)
   \[\frac{1}{101}\]
  done clear
  View Answer play_arrow

• question_answer135)     The order of the differential equation of all tangent lines to the parabola\[y={{x}^{2}}\]is
  A)
   1                            
  done clear
  B)
   2
  done clear
  C)
   3                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer136)     The arithmetic mean of the data given by

  Variate \[(x)\]	0	1	2	3	?	N
  Frequency \[(f)\]	\[^{n}{{C}_{0}}\]	\[^{n}{{C}_{1}}\]	\[^{n}{{C}_{2}}\]	\[^{n}{{C}_{3}}\]	?	\[^{n}{{C}_{n}}\]

  A)
   \[\frac{(n+1)}{2}\]
  done clear
  B)
   \[\frac{n}{2}\]
  done clear
  C)
   \[\frac{{{2}^{n}}}{n}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer137)     If the relation\[R:A\to B,\]where A = {1,2,3, 4} and B = {1,3,5} is defined by \[R=\{(x,y):x<y,x\in A,y\in B\},\],then\[{{R}^{-1}}oR\]is equal to
  A)
   \[\{1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\]
  done clear
  B)
   \[\{(3,1),(5,1),(5,2),(5,3),(5,4)\}\]
  done clear
  C)
   \[\{(3,3),(3,5),(5,3),(5,5)\}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer138)     For an increasing AP\[{{a}_{1}},{{a}_{2}},.....,{{a}_{n}},\]if\[{{a}_{1}}+{{a}_{2}}+{{a}_{3}}=-12\]and\[{{a}_{1}}{{a}_{3}}{{a}_{5}}=80,\]then which of the following does not hold?
  A)
   \[{{a}_{1}}=-10\]            
  done clear
  B)
   \[{{a}_{2}}=-1\]
  done clear
  C)
   \[{{a}_{3}}=-4\]                               
  done clear
  D)
   \[{{a}_{5}}=2\]
  done clear
  View Answer play_arrow

• question_answer139)     The sum of the non-real roots of\[({{x}^{2}}+x-2)({{x}^{2}}+x-3)=12\]is
  A)
   1                                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   \[-6\]                                   
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer140)     If\[{{\log }_{1/2}}\frac{|z{{|}^{2}}+2|z|+4}{2|z{{|}^{2}}+1}<0,\]then the region traced by z is
  A)
   \[|z|<3\]                           
  done clear
  B)
   \[1<|z|<3\]
  done clear
  C)
   \[|z|>1\]                           
  done clear
  D)
   \[|z|<2\]
  done clear
  View Answer play_arrow

• question_answer141)     In the expansion of\[{{(1+x)}^{n}},\]7th and 8th terms are equal, then the value of\[{{\left( \frac{7}{x}+6 \right)}^{2}}\]is
  A)
   \[n\]                                    
  done clear
  B)
   \[{{n}^{2}}\]
  done clear
  C)
   \[{{n}^{3}}\]                     
  done clear
  D)
   \[{{n}^{4}}\]
  done clear
  View Answer play_arrow

• question_answer142)     If n arithmetic means are inserted between two sets of numbers\[a,2b\]and\[2a,b\]where \[a,b\in R\]suppose mth mean between these two sets of numbers is same, then the ratio \[a:b\]equals to
  A)
   \[n-m+1:m\]                    
  done clear
  B)
   \[n-m+1:n\]
  done clear
  C)
   \[m:n-m+1\]                    
  done clear
  D)
   \[n:n-m+1\]
  done clear
  View Answer play_arrow

• question_answer143)     If the roots of the equation\[a{{x}^{2}}+bx+c=0\] are real and distinct, then
  A)
   both roots are greater than \[\frac{-b}{2a}\]
  done clear
  B)
   both roots are less than\[\frac{-b}{2a}\]
  done clear
  C)
   one of the roots exceeds\[\frac{-b}{2a}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer144)     If\[g(x)\]and\[h(x)\]are two polynomials such that the polynomial\[p(x)=g({{x}^{2}})+xh({{x}^{2}})\]is divisible by\[{{x}^{2}}+x+1,\]then
  A)
   \[g(1)=h(1)=0\]               
  done clear
  B)
   \[g(1)=h(1)\ne 0\]
  done clear
  C)
   \[g(1)-h(1)=1\]                
  done clear
  D)
   \[g(1)+h(1)=1\]
  done clear
  View Answer play_arrow

• question_answer145)     The value of \[2.{{C}_{0}}+\frac{{{2}^{2}}}{2}.{{C}_{1}}\]\[+\frac{{{2}^{3}}}{3}.{{C}_{2}}+\frac{{{2}^{4}}}{4}.{{C}_{3}}+....+\frac{{{2}^{11}}}{11}.{{C}_{10}}\]is
  A)
   \[\frac{{{3}^{11}}-1}{11}\]                          
  done clear
  B)
   \[\frac{{{2}^{11}}-1}{11}\]
  done clear
  C)
   \[\frac{{{11}^{3}}-1}{11}\]                          
  done clear
  D)
   \[\frac{{{11}^{2}}-1}{11}\]
  done clear
  View Answer play_arrow

• question_answer146)     In how many ways can mn letters be posted in n letter boxes?
  A)
   \[{{(mn)}^{n}}\]             
  done clear
  B)
   \[{{m}^{mn}}\]
  done clear
  C)
   \[{{n}^{mn}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer147)     If\[a,b\]and c are non-zero real numbers such  that \[\left| \begin{matrix}    bc & ca & ab  \\    ca & ab & bc  \\    ab & bc & ca  \\ \end{matrix} \right|=0,\]then
  A)
   only \[\frac{1}{a}+\frac{1}{b\omega }+\frac{1}{c{{\omega }^{2}}}=0\]
  done clear
  B)
   only \[\frac{1}{a}+\frac{1}{b{{\omega }^{2}}}+\frac{1}{c\omega }=0\]
  done clear
  C)
   \[\frac{1}{a\omega }+\frac{1}{b{{\omega }^{2}}}+\frac{1}{c}=0\]
  done clear
  D)
    All of the above
  done clear
  View Answer play_arrow

• question_answer148)     If\[f(x)=\frac{1+x}{1-x}\]and A is matrix for which\[{{A}^{3}}=0,\]then f is equal to
  A)
   \[I+A+{{A}^{2}}\]                           
  done clear
  B)
   \[I+2A+2{{A}^{2}}\]
  done clear
  C)
   \[I+A+{{A}^{2}}\]                           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer149)     The vectors\[a=3i-2j+2k\]and\[b=-i-2k\]are the adjacent sides of a parallelogram. Then, angle between its diagonals is
  A)
   \[\frac{\pi }{4}\]                                             
  done clear
  B)
   \[\frac{\pi }{3}\]
  done clear
  C)
   \[\frac{\pi }{2}\]                                             
  done clear
  D)
   \[\frac{2\pi }{3}\]
  done clear
  View Answer play_arrow

• question_answer150)     A line passes through the two points \[A(2,-3,-1)\]and\[B(8,-1,2)\]. The coordinates of a point on this line at a distance of 14 units from A are
  A)
   (10, 7, 7)             
  done clear
  B)
   (14, 0, 5)
  done clear
  C)
   (86, 25, 41)                        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer151)     If a dice is rolled 4 times, then the probability of getting a larger number than the previous number each time is
  A)
   \[x+\sqrt{3}y=3\]                           
  done clear
  B)
   \[\sqrt{3}x+y=3\]
  done clear
  C)
   \[x+y=\sqrt{3}\]                             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer152)     The maximum value of \[1+\sin \left( \frac{\pi }{4}+\theta  \right)+2\cos \left( \frac{\pi }{4}-\theta  \right)\]for real values of \[\theta \]is
  A)
   3                                            
  done clear
  B)
   5
  done clear
  C)
   4                                            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer153)     If\[-I<x<0,\]then\[{{\sin }^{-1}}(x)\]equals
  A)
   \[\pi -{{\cos }^{-1}}\{\sqrt{1-{{x}^{2}}}\}\]
  done clear
  B)
   \[{{\tan }^{-1}}\left\{ \frac{x}{\sqrt{1-{{x}^{2}}}} \right\}\]
  done clear
  C)
   \[-{{\cot }^{-1}}\left\{ \frac{\sqrt{1-{{x}^{2}}}}{x} \right\}\]
  done clear
  D)
   \[\cos e{{c}^{-1}}x\]
  done clear
  View Answer play_arrow

• question_answer154)     The arithmetic mean of roots of the equation \[4{{\cos }^{3}}x-4{{\cos }^{2}}x-\cos (315\pi +x)=1\]is
  A)
   \[50\,\pi \]                        
  done clear
  B)
   \[51\,\pi \]
  done clear
  C)
   \[100\,\pi \]                      
  done clear
  D)
   \[315\,\pi \]
  done clear
  View Answer play_arrow

• question_answer155)     ABC is an isosceles triangle in which A is\[(-1,0),\] \[\angle A=\frac{2\pi }{3},\text{ }AB=AC\]and AB is along the \[x-\] axis. If\[BC=4\sqrt{3},\]then the equation of the line BC is
  A)
   \[x+\sqrt{3}y=3\]           
  done clear
  B)
   \[\sqrt{3}x+y=3\]
  done clear
  C)
   \[x+y=\sqrt{3}\]             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer156)     The equation of a circle touching the axes of coordinates and the line\[x\text{ }cos\,\alpha +y\text{ }sin\,\alpha =2\] can be
  A)
   \[{{x}^{2}}+{{y}^{2}}-2gx-2gy={{g}^{2}}=0,\]where\[g=\frac{2}{(\cos \alpha +\sin \alpha +1)}\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}-2gx-2gy+{{g}^{2}}=0,\]where\[g=\frac{2}{(\cos \alpha +\sin \alpha -1)}\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}-2gx+2gy+{{g}^{2}}=0,\]where\[g=\frac{2}{(\cos \alpha -\sin \alpha +1)}\]
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer157)     The equation of the line passing through the centre and bisecting the chord \[7x+y-1=0\] of the ellipse \[{{x}^{2}}+\frac{{{y}^{2}}}{7}=1\]is
  A)
   \[x=y\]               
  done clear
  B)
   \[2x=y\]
  done clear
  C)
   \[x=2y\]            
  done clear
  D)
   \[x+y=0\]
  done clear
  View Answer play_arrow

• question_answer158)     Range of the function \[f(x)=\frac{{{x}^{2}}+x+2}{{{x}^{2}}+x+1},x\in R\]is
  A)
   \[(1,\infty )\]                   
  done clear
  B)
   \[\left( 1,\frac{11}{7} \right)\]
  done clear
  C)
   \[\left( 1,\frac{7}{3} \right)\]                    
  done clear
  D)
   \[\left( 1,\frac{7}{5} \right)\]
  done clear
  View Answer play_arrow

• question_answer159)     If\[f(x)={{\log }_{e}}\{\log x\},\]then\[f(x)\]at\[x=e,\]is
  A)
   \[e\]                                    
  done clear
  B)
   \[-e\]   
  done clear
  C)
   \[{{e}^{2}}\]                     
  done clear
  D)
   \[{{e}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer160)     \[\underset{x\to \pi /2}{\mathop{\lim }}\,\frac{\sin x}{{{\cos }^{-1}}\left[ \frac{1}{4}(3\sin x-\sin 3x) \right]},\]where\[[.]\] denotes greatest integer function, is
  A)
   \[\frac{2}{\pi }\]                                             
  done clear
  B)
   1
  done clear
  C)
   \[\frac{4}{\pi }\]                             
  done clear
  D)
   Does not exist
  done clear
  View Answer play_arrow

• question_answer161)     If\[f(x)\]satisfies the relation\[f\left( \frac{3x-y}{2} \right)=\frac{3f(x)-f(y)}{2},\forall x,y\in R,f(0)=2\]and\[f(0)=1,\]then the value of\[f(2)\]is
  A)
   3
  done clear
  B)
   \[-4\]
  done clear
  C)
   5
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer162)     If\[h(x)={{x}^{m/n}}\]for\[x\in R,\]where\[m,n\]are odd numbers and\[0<m<n,\]then\[y=h(x)\]has
  A)
   no local extremism
  done clear
  B)
   one local maximum
  done clear
  C)
   one local minimum
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer163)     \[\int{\frac{8x+13}{\sqrt{4x+7}}}dx\]is equal to
  A)
   \[\frac{1}{6}(8x+11)\sqrt{4x+7}+C\]
  done clear
  B)
   \[\frac{1}{6}(8x+13)\sqrt{4x+7}+C\]
  done clear
  C)
   \[\frac{1}{6}(8x+9)\sqrt{4x+7}+C\]
  done clear
  D)
   \[\frac{1}{6}(8x+15)\sqrt{4x+7}+C\]
  done clear
  View Answer play_arrow

• question_answer164)     If\[f(x)\]satisfies the condition of Rollers theorem in [1,2], then\[\int_{1}^{2}{f(x)}\,dx\]to is equal to
  A)
   1
  done clear
  B)
   3
  done clear
  C)
   0
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer165)     The degree of the differential equation\[y_{2}^{3/2}-y_{1}^{1/2}-4=0\]is
  A)
   6                                            
  done clear
  B)
   3
  done clear
  C)
   2                                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer166)     Which of the following relation is a function?
  A)
   \[R=\{(x,y):{{x}^{2}}+{{y}^{2}}\le 9\}\]on R
  done clear
  B)
   \[A=\{1,2,3\},B=\{1,2,3,4,5\}\] and \[r=\{(x,\text{ }y):5x+2y\]is a prime number} on A
  done clear
  C)
   \[A=\{1,2,3,4\},B=\{1,2,3,4,5,6,7\}\]and\[R\{(x,y)|y={{x}^{2}}-3x+3\}\]on A
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer167)     The mean weight of 9 items is 15. If one more item is added to the series, the mean becomes 16. The value of 10th item is
  A)
   35                         
  done clear
  B)
   30
  done clear
  C)
   25                         
  done clear
  D)
   20
  done clear
  View Answer play_arrow

• question_answer168)     If\[\alpha \]and\[\beta \]be the roots of the equation\[{{x}^{2}}-ax+b=0\]and\[{{A}_{n}}={{\alpha }^{n}}+{{\beta }^{n}}\]. Then, \[{{A}_{n+1}}-a{{A}_{n}}+b{{A}_{n-1}}\]is equal to
  A)
   \[-a\]                                   
  done clear
  B)
   b
  done clear
  C)
   0                                            
  done clear
  D)
   \[a-b\]
  done clear
  View Answer play_arrow

• question_answer169)     If \[{{z}_{1}}=6+i,{{z}_{2}}=4-3i\] and z be a complex number such that arg\[\left( \frac{z-{{z}_{1}}}{{{z}_{2}}-z} \right)=\frac{\pi }{2},\] then z satisfies
  A)
   \[|z-(5-i)|=5\] 
  done clear
  B)
   \[|z-(5-i)|=\sqrt{5}\]
  done clear
  C)
   \[|z-(5+i)|=5\]
  done clear
  D)
   \[|z-(5+i)|=\sqrt{5}\]
  done clear
  View Answer play_arrow

• question_answer170)     The    value    of    the    expression \[\frac{{{\sin }^{3}}x}{1+\cos x}+\frac{{{\cos }^{3}}x}{1-\sin x}\]is/are
  A)
   \[\sqrt{2}\cos \left( \frac{\pi }{4}-x \right)\]      
  done clear
  B)
   \[\sqrt{2}\cos \left( \frac{\pi }{4}+x \right)\]
  done clear
  C)
   \[\sqrt{2}\sin \left( \frac{\pi }{4}-x \right)\]       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow