Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2010

done JCECE Engineering Solved Paper-2010 Total Questions - 150

• question_answer1) At what angle must the two forces \[(x+y)\] and \[(x-y)\]act so that the resultant may be
  A)
  \[{{\cos }^{-1}}\left[ -\frac{{{x}^{2}}+{{y}^{2}}}{2({{x}^{2}}-{{y}^{2}})} \right]\]
  done clear
  B)
  \[{{\cos }^{-1}}\left[ \frac{-2({{x}^{2}}-{{y}^{2}})}{{{x}^{2}}+{{y}^{2}}} \right]\]
  done clear
  C)
  \[{{\cos }^{-1}}\left[ -\frac{({{x}^{2}}+{{y}^{2}})}{({{x}^{2}}-{{y}^{2}})} \right]\]
  done clear
  D)
   \[{{\cos }^{-1}}\left[ -\frac{({{x}^{2}}-{{y}^{2}})}{({{x}^{2}}+{{y}^{2}})} \right]\]
  done clear
  View Answer play_arrow

• question_answer2) A body starts from rest with uniform acceleration. If its velocity after n second is\[v\], then its displacement in the last \[2\,\,s\] is
  A)
  \[\frac{2v(n+1)}{n}\]                     
  done clear
  B)
  \[\frac{v(n+1)}{n}\]
  done clear
  C)
  \[\frac{v(n-1)}{n}\]                        
  done clear
  D)
   \[\frac{2v(n-1)}{n}\]
  done clear
  View Answer play_arrow

• question_answer3) A wheel completes \[2000\] revolutions to cover the \[9.5\,\,km\] distance, then the diameter of the wheel is
  A)
  \[1.5\,\,m\]                       
  done clear
  B)
  \[1.5\,\,cm\]
  done clear
  C)
   \[7.5\,\,cm\]                    
  done clear
  D)
   \[7.5\,\,m\]
  done clear
  View Answer play_arrow

• question_answer4) A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is
  A)
   same everywhere
  done clear
  B)
   lower in front side
  done clear
  C)
   lower in rear side
  done clear
  D)
    lower in upper side
  done clear
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• question_answer5) A block \[A\] weighing \[100\,\,kg\] rests on a block \[B\] and is tied with a horizontal string to the wall at\[C\]. Block \[B\] weighs\[200\,\,kg\]. The coefficient of friction between \[A\] and \[B\] is \[0.25\] and between \[B\] and the surface is\[\frac{1}{3}\]. The horizontal force \[P\] necessary to move the block \[B\] should be\[(g=10\,\,m/{{s}^{2}})\]
  A)
  \[1150\,\,N\]                    
  done clear
  B)
  \[1250\,\,N\]
  done clear
  C)
  \[1300\,\,N\]                    
  done clear
  D)
   \[1420\,\,N\]
  done clear
  View Answer play_arrow

• question_answer6) A boy and a man carry a uniform rod of length\[L\], horizontally in such a way that boy gets \[\frac{1}{4}th\] load. If the boy is at one end of the rod, the distance of the man from the other end is
  A)
  \[\frac{L}{3}\]                                   
  done clear
  B)
  \[\frac{L}{4}\]
  done clear
  C)
  \[\frac{2L}{3}\]                                 
  done clear
  D)
   \[\frac{3L}{4}\]
  done clear
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• question_answer7) Two capillary of lengths \[L\] and \[2L\] and of radii \[R\] and \[2R\] are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary,\[X=\frac{\pi p{{R}^{4}}}{8\eta L})\]
  A)
  \[\frac{8}{9}X\]                                
  done clear
  B)
  \[\frac{9}{8}X\]
  done clear
  C)
   \[\frac{5}{7}X\]                                               
  done clear
  D)
   \[\frac{7}{5}X\]
  done clear
  View Answer play_arrow

• question_answer8) The molecules of a given mass of a gas have a \[\text{rms}\] velocity of \[200\,\,m/s\] at \[{{27}^{o}}C\] and \[1.0\times {{10}^{5}}\,\,N/{{m}^{2}}\]  pressure.  When  the temperature is \[{{127}^{o}}C\] and pressure is \[0.5\times {{10}^{5}}N/{{m}^{2}}\], the \[\text{rms}\] velocity in \[m/s\] will
  A)
  \[\frac{100\sqrt{2}}{3}\]                              
  done clear
  B)
  \[100\sqrt{2}\]
  done clear
  C)
   \[\frac{400}{\sqrt{3}}\]                                
  done clear
  D)
    None of these
  done clear
  View Answer play_arrow

• question_answer9) \[3\,\,A\] of current is flowing in a linear conductor having a length of\[40\,\,cm\]. The conductor is placed in a magnetic field of strength \[500\] gauss and makes an angle of \[{{30}^{o}}\] with direction of the field. It experiences a force of magnitude
  A)
  \[3\times {{10}^{4}}N\]
  done clear
  B)
  \[3\times {{10}^{2}}N\]
  done clear
  C)
  \[3\times {{10}^{-2}}N\]                              
  done clear
  D)
   \[3\times {{10}^{-4}}N\]
  done clear
  View Answer play_arrow

• question_answer10) A \[50\] turn?s Circular coil has a radius of\[3\,\,cm\], it is kept in a magnetic field acting normal to the area of the coil. The magnetic field \[B\] increased from \[0.10\,\,T\] to \[0.35\,\,T\] in \[2\] millisecond. The average induced \[\text{emf}\] in the coil is
  A)
  \[1.77\,\,V\]                      
  done clear
  B)
  \[17.7\,\,V\]
  done clear
  C)
   \[177\,\,V\]                      
  done clear
  D)
   \[0.177\,\,V\]
  done clear
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• question_answer11) In the circuit .shown in figure neglecting source  resistance, the voltmeter and ammeter readings will be respectively
  A)
  \[0\,\,V,\,\,3\,\,A\]
  done clear
  B)
  \[150\,\,V,\,\,3\,\,A\]
  done clear
  C)
  \[150\,\,V,\,\,6\,\,A\]                   
  done clear
  D)
   \[0\,\,V,\,\,8\,\,A\]
  done clear
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• question_answer12) Photon and electron are given energy\[({{10}^{-2}}J)\]. Wavelengths associated with photon and electron are \[{{\lambda }_{ph}}\] and \[{{\lambda }_{el}}\] then, correct statement will be
  A)
  \[{{\lambda }_{ph}}>{{\lambda }_{el}}\]                               
  done clear
  B)
  \[{{\lambda }_{ph}}<{{\lambda }_{el}}\]
  done clear
  C)
  \[{{\lambda }_{ph}}={{\lambda }_{el}}\]                               
  done clear
  D)
   \[\frac{{{\lambda }_{el}}}{{{\lambda }_{ph}}}=c\]
  done clear
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• question_answer13) The wavelength of radiation emitted is\[{{\lambda }_{0}}\]when an electron jumps from the third to the second orbit of hydrogen atom. For the electron jump from the fourth to the second orbit of hydrogen atom, the wavelength of radiation emitted will be
  A)
  \[\frac{16}{25}{{\lambda }_{0}}\]                             
  done clear
  B)
  \[\frac{20}{27}{{\lambda }_{0}}\]
  done clear
  C)
  \[\frac{27}{20}{{\lambda }_{0}}\]                             
  done clear
  D)
  \[\frac{25}{16}{{\lambda }_{0}}\]
  done clear
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• question_answer14) Radius of \[_{2}H{{e}^{4}}\] nucleus is \[3\] fermi. The radius of \[_{82}P{{b}^{206}}\] nucleus will be
  A)
  \[5\]fermi                          
  done clear
  B)
  \[6\]Fermi
  done clear
  C)
  \[11.16\] fermi                 
  done clear
  D)
   \[8\] Fermi
  done clear
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• question_answer15) The contribution in the total current flowing through a semiconductor due to electrons and holes are \[\frac{3}{4}\] and \[\frac{1}{4}\] respectively. If the drift velocity of electrons is \[\frac{5}{2}\] times that of holes at this temperature, then the ratio of concentration of electrons and holes is
  A)
  \[6:5\]                                  
  done clear
  B)
  \[5:6\]
  done clear
  C)
  \[3:2\]                                  
  done clear
  D)
   \[2:3\]
  done clear
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• question_answer16) The attenuation in optical fibre is mainly due to
  A)
   absorption
  done clear
  B)
   scattering
  done clear
  C)
    Neither absorption nor scattering
  done clear
  D)
    Both [a] and [b]
  done clear
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• question_answer17) An astronomical telescope has an angular magnification of magnitude \[5\] for distant objects. The separation between the objective and the eye-piece is \[36\,\,cm\] and the final image is formed at infinity. The focal length \[{{f}_{o}}\] of the objective and the focal length \[{{f}_{e}}\] of the eye-piece are
  A)
  \[{{f}_{o}}=45\,\,cm\]and\[{{f}_{e}}=-9\,\,cm\]
  done clear
  B)
  \[{{f}_{o}}=-7.2\,\,cm\]and\[{{f}_{e}}=5\,\,cm\]
  done clear
  C)
  \[{{f}_{o}}=50\,\,cm\]and\[{{f}_{e}}=10\,\,cm\]
  done clear
  D)
   \[{{f}_{o}}=30\,\,cm\]and\[{{f}_{e}}=6\,\,cm\]
  done clear
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• question_answer18) A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of incident beam. At the first maximum of the diffraction pattern, the phase difference between the rays coming from the edges of the slit is
  A)
  \[0\]                                     
  done clear
  B)
  \[\frac{\pi }{2}\]
  done clear
  C)
  \[\pi \]                                 
  done clear
  D)
   \[2\pi \]
  done clear
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• question_answer19) When the angle of incidence on a material is\[{{60}^{o}}\], the reflected light is completely polarized. The velocity of the refracted ray inside the material is (in\[m{{s}^{-1}})\]
  A)
  \[3\times {{10}^{8}}\]                   
  done clear
  B)
  \[\left[ \frac{3}{\sqrt{2}} \right]\times {{10}^{8}}\]
  done clear
  C)
  \[\sqrt{3}\times {{10}^{8}}\]                      
  done clear
  D)
   \[0.5\times {{10}^{8}}\]
  done clear
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• question_answer20) Which of the following shows greenhouse effect?
  A)
   Ultraviolet rays               
  done clear
  B)
   Infrared rays
  done clear
  C)
    X-rays                
  done clear
  D)
    None of these
  done clear
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• question_answer21) In Rutherford scattering experiment, what will be the correct angle for a scattering for an impact parameter\[b=0\]?
  A)
  \[{{90}^{o}}\]                                    
  done clear
  B)
  \[{{270}^{o}}\]
  done clear
  C)
   \[{{0}^{o}}\]                                     
  done clear
  D)
   \[{{180}^{o}}\]
  done clear
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• question_answer22) A person sees his virtual image by holding a mirror very close to the face. When he moves the mirror away from his face, the image becomes inverted. What type of mirror he is using?
  A)
   Plane mirror                     
  done clear
  B)
   Convex mirror
  done clear
  C)
    Concave mirror              
  done clear
  D)
    None of these
  done clear
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• question_answer23) If a charged spherical conductor of radius \[10\,\,cm\] has potential \[V\] at a point distant \[5\,\,cm\] from its centre, then the potential at a point distant \[15\,\,cm\] from the centre will be
  A)
  \[\frac{1}{3}V\]                                
  done clear
  B)
  \[\frac{2}{3}V\]
  done clear
  C)
  \[\frac{3}{2}V\]                                
  done clear
  D)
   \[3V\]
  done clear
  View Answer play_arrow

• question_answer24) The equation of state of some gases can be expressed as\[\left( p+\frac{a}{{{V}^{2}}} \right)(V-b)=RT\]where, \[p\] is the pressure, \[V\] the volume, \[T\] the absolute temperature and \[a\] and \[b\] are constants. The dimensional formula of \[a\] is
  A)
  \[[M{{L}^{5}}{{T}^{-2}}]\]                            
  done clear
  B)
  \[[{{M}^{-1}}{{L}^{5}}{{T}^{-2}}]\]
  done clear
  C)
  \[[M{{L}^{-1}}{{T}^{-2}}]\]                          
  done clear
  D)
   \[[M{{L}^{-5}}{{T}^{-2}}]\]
  done clear
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• question_answer25) A \[16\,\,kg\] block moving on a frictionless horizontal surface with a velocity of \[4\,\,m/s\] compresses an ideal spring and comes to rest. If the force constant of the spring be \[100\,\,N/m,\] then the spring is compressed by
  A)
  \[1.6\,\,m\]                       
  done clear
  B)
  \[4\,\,m\]
  done clear
  C)
   \[6.1\,\,m\]                      
  done clear
  D)
   \[3.2\,\,m\]
  done clear
  View Answer play_arrow

• question_answer26) A mass of \[6\times {{10}^{24}}kg\] is to be compressed in a sphere in such a way that the escape velocity from the sphere is\[3\times {{10}^{8}}m/s\]. What should be the radius of the sphere?\[(G=6.67\times {{10}^{-11}}N-{{m}^{2}}/k{{g}^{2}})\]
  A)
  \[9\,\,km\]                        
  done clear
  B)
  \[9\,\,m\]
  done clear
  C)
  \[9\,\,cm\]                         
  done clear
  D)
   \[9\,\,mm\]
  done clear
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• question_answer27) A wire of length \[L\] and radius \[r\] fixed at one end and a force \[F\] applied to the other end produces an extension\[l\]. The extension produced in another wire of the same material of length \[2L\] and radius \[2r\] by a force\[2F\], is
  A)
  \[l\]                                       
  done clear
  B)
  \[2l\]
  done clear
  C)
   \[4l\]                                   
  done clear
  D)
   \[\frac{l}{2}\]
  done clear
  View Answer play_arrow

• question_answer28) Two trains are moving towards each other with speeds of \[20\,\,m/s\] and \[15\,\,m/s\] relative to the ground. The first train, sounds a whistle of frequency\[600\,\,Hz\], the frequency of the whistle heard by a passenger in the second train before the train meets is (the speed of sound in air is\[340\,\,m/s)\]
  A)
  \[600\,\,Hz\]                     
  done clear
  B)
  \[585\,\,Hz\]
  done clear
  C)
   \[645\,\,Hz\]                    
  done clear
  D)
  \[666\,\,hz\]
  done clear
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• question_answer29) Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is\[25\]. The intensities of the sources are in the ratio
  A)
  \[25:1\]                               
  done clear
  B)
  \[5:1\]
  done clear
  C)
  \[9:4\]                                  
  done clear
  D)
   \[25:16\]
  done clear
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• question_answer30) A microscope is focussed on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index \[1.5\] is placed over a mark. How should the microscope be moved to get the mark again in focus?
  A)
  \[1\,\,cm\]upward                         
  done clear
  B)
  \[4.5\,\,cm\]downward
  done clear
  C)
   \[1\,\,cm\]downward  
  done clear
  D)
   \[2\,\,cm\]upward
  done clear
  View Answer play_arrow

• question_answer31) A thin lens made of glass of refractive index \[\mu =1.5\] has a focal length equals to \[12\,\,cm\] in air. It is now immersed in water\[\left( \mu =\frac{4}{3} \right)\]. Its new focal length is
  A)
  \[48\,\,cm\]                      
  done clear
  B)
  \[36\,\,cm\]
  done clear
  C)
   \[24\,\,cm\]                     
  done clear
  D)
   \[12\,\,cm\]
  done clear
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• question_answer32) Air is pumped into an automobile tube upto a pressure of \[200\,\,kPa\] in the morning when the air temperature is\[{{22}^{o}}C\]. During the day, temperature rises to \[{{42}^{o}}C\] and the tube expands by\[2%\]. The pressure of the air in the tube  at  this  temperature,  will  be approximately
  A)
  \[212\,\,kPa\]                   
  done clear
  B)
  \[209\,\,kPa\]
  done clear
  C)
  \[206\,\,kPa\]                   
  done clear
  D)
   \[200\,\,kPa\]
  done clear
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• question_answer33) A radioactive material decays by simultaneous emission of two particles with half-lives \[1620\,\,yr\] and \[810\,\,yr\] respectively. The time in year after which one-fourth of the material remains, is
  A)
  \[4860\,\,yr\]                    
  done clear
  B)
  \[3240\,\,yr\]
  done clear
  C)
  \[2340\,\,yr\]                    
  done clear
  D)
   \[1080\,\,yr\]
  done clear
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• question_answer34) A stone dropped from a balloon which is at a height\[h\], reaches the ground after \[t\] second. From the same balloon, if two stones are thrown, one upwards and the other downwards, with the same velocity u and they reach the ground after \[{{t}_{1}}\] and \[{{t}_{2}}\] second respectively, then
  A)
  \[t={{t}_{1}}-{{t}_{2}}\]                
  done clear
  B)
  \[t=\frac{{{t}_{1}}+{{t}_{2}}}{2}\]
  done clear
  C)
   \[t=\sqrt{{{t}_{1}}{{t}_{2}}}\]                    
  done clear
  D)
   \[t=\sqrt{t_{1}^{2}-t_{2}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer35) A shell at rest at the origin explodes into three fragments of masses \[1\,kg,\,\,2\,kg\] and\[m\,\,kg\]. The \[2\,\,kg\]\[\text{and}\]\[1\,\,kg\] pieces fly off with speeds of \[12\,\,m/s\] along x-axis and \[16\,\,m/s\] along y-axis respectively. If the \[m\,\,kg\] piece flies off with a speed of\[40\,\,m/s\], the total mass of the shell must be
  A)
  \[3.7\,\,kg\]                      
  done clear
  B)
  \[4\,\,kg\]
  done clear
  C)
  \[4.5\,\,kg\]                      
  done clear
  D)
   \[5\,\,kg\]
  done clear
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• question_answer36) If a sphere is rolling, then the ratio of its rotational kinetic energy to the total kinetic energy is
  A)
  \[3.7\,\,kg\]                      
  done clear
  B)
  \[4\,\,kg\]
  done clear
  C)
  \[4.5\,\,kg\]                      
  done clear
  D)
   \[5\,\,kg\]
  done clear
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• question_answer37) A body weighs w newton at the surface of the earth. Its weight at a height equals to half the radius of the earth, will be
  A)
  \[\frac{w}{2}\]                                 
  done clear
  B)
  \[\frac{2w}{3}\]
  done clear
  C)
  \[\frac{4w}{9}\]                                               
  done clear
  D)
   \[\frac{8w}{27}\]
  done clear
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• question_answer38) Apart of a long wire carrying a current \[i\] is bent into a circle of radius \[r\] as shown in figure. The net magnetic field at the centre \[O\] of the circular loop is
  A)
  \[\frac{{{\mu }_{0}}I}{4r}\]                                         
  done clear
  B)
  \[\frac{{{\mu }_{0}}I}{2r}\]
  done clear
  C)
  \[\frac{{{\mu }_{0}}I}{2\pi r}(\pi +1)\]                    
  done clear
  D)
  \[\frac{{{\mu }_{0}}I}{2\pi r}(\pi -1)\]
  done clear
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• question_answer39) A \[36\Omega \] galvanometer is shunted by resistance of\[4\Omega \]. The percentage of the total current, which passes through the galvanometer is
  A)
  \[8%\]                                  
  done clear
  B)
  \[9%\]
  done clear
  C)
  \[10%\]                               
  done clear
  D)
   \[91%\]
  done clear
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• question_answer40) A can filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. The time period for a revolution is about
  A)
  \[2\,\,s\]                                             
  done clear
  B)
  \[4\,\,s\]
  done clear
  C)
  \[8\,\,s\]                                             
  done clear
  D)
   \[10\,\,s\]
  done clear
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• question_answer41) The centre of mass of three particles of masses \[1\,\,kg,\,\,2\,\,kg\] and \[3\,\,kg\] is at \[(3,\,\,3,\,\,3)\] with reference to a fixed coordinate system. Where should a fourth particle of mass \[4\,\,kg\] be placed, so that the centre of mass of the system of all particles shifts to a point\[(1,\,\,1,\,\,1)?\]
  A)
  \[(-1,\,\,-1,\,\,-1)\]                        
  done clear
  B)
  \[(-2,\,\,-2,\,\,-2)\]
  done clear
  C)
   \[(2,\,\,2,\,\,2)\]                            
  done clear
  D)
   \[(1,\,\,1,\,\,1)\]
  done clear
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• question_answer42) A pulley fixed to the ceiling carries a string with blocks of masses \[m\] and \[3m\] attached to its ends. The masses of string and pulley are negligible. When the system is released, the acceleration of centre of mass will be
  A)
  \[zero\]                                               
  done clear
  B)
  \[-\frac{g}{4}\]
  done clear
  C)
  \[\frac{g}{2}\]                                   
  done clear
  D)
   \[-\frac{g}{2}\]
  done clear
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• question_answer43) A ray \[PQ\] incident on the refracting face \[BA\] is refracted in the prism \[BAC\] as shown in the figure and emerges from the other refracting face \[AC\] as\[RS\], such that\[AQ=AR\]. If the angle of prism \[A={{60}^{o}}\] and the refractive index of the material of prism is\[\sqrt{3}\], then the angle of deviation of the ray is
  A)
  \[{{60}^{o}}\]                                    
  done clear
  B)
  \[{{45}^{o}}\]
  done clear
  C)
  \[{{30}^{o}}\]                                    
  done clear
  D)
    None of these
  done clear
  View Answer play_arrow

• question_answer44) To get an output 1 from the circuit shown in the figure, the input must be
  A)
  \[A=0,\,\,B=1,\,\,C=0\]
  done clear
  B)
  \[A=1,\,\,B=0,\,\,C=0\]
  done clear
  C)
  \[A=1,\,\,B=0,\,\,C=1\]
  done clear
  D)
   \[A=1,\,\,B=1,\,\,C=0\]
  done clear
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• question_answer45) Minimum number of \[8\mu F\] and \[250\,\,V\] capacitors are used to make a combination of \[16\mu F\] and \[1000\,\,V\] are
  A)
  \[4\]                                     
  done clear
  B)
  \[32\]
  done clear
  C)
  \[8\]                                     
  done clear
  D)
   \[3\]
  done clear
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• question_answer46) Let \[{{E}_{a}}\] be the electric field due to a dipole in its axial plane distant \[l\] and let \[{{E}_{q}}\] be the field in the equatorial plane distant\[l'\], then the relation between \[{{E}_{a}}\] and \[{{E}_{q}}\] will be
  A)
  \[{{E}_{a}}=4{{E}_{q}}\]                
  done clear
  B)
  \[{{E}_{q}}=2{{E}_{a}}\]
  done clear
  C)
  \[{{E}_{a}}=2{{E}_{q}}\]                
  done clear
  D)
   \[{{E}_{q}}=3{{E}_{a}}\]
  done clear
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• question_answer47) The current in the given circuit is-
  A)
  \[0.3\,\,A\]                        
  done clear
  B)
  \[0.4\,\,A\]
  done clear
  C)
  \[0.1\,\,A\]                        
  done clear
  D)
   \[0.2\,\,A\]
  done clear
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• question_answer48) In the circuit shown below what will be the readings of the voltmeter and ammeter? (Total impedance of circuit\[Z=100\Omega )\]
  A)
  \[200\,\,V,\,\,1\,\,A\]                   
  done clear
  B)
  \[800\,\,V,\,\,2\,\,A\]
  done clear
  C)
  \[100\,\,V,\,\,2\,\,A\]                   
  done clear
  D)
   \[220\,\,V,\,\,2.2\,\,A\]
  done clear
  View Answer play_arrow

• question_answer49) A ball of mass \[10\,\,kg\] is moving with a velocity of\[10\,\,m/s\]. It strikes another ball of mass\[5\,\,kg\], which is moving in the same direction with a velocity of\[4\,\,m/s\]. If the collision is elastic, then their velocities after collision will be respectively
  A)
  \[12\,\,m/s,\,\,6\,\,m/s\]           
  done clear
  B)
  \[12\,\,m/s,\,\,25\,\,m/s\]
  done clear
  C)
  \[6\,\,m/s,\,\,12\,\,m/s\]           
  done clear
  D)
   \[8\,\,m/s,\,\,20\,\,m/s\]
  done clear
  View Answer play_arrow

• question_answer50) A hole is made at the bottom of the tank filled with water (density\[1000kg/{{m}^{3}})\]. If the total pressure at the bottom of the tank is \[3\] atmosphere (1 atmosphere\[=105N/{{m}^{2}})\], then the velocity of efflux is
  A)
  \[\sqrt{200}m/s\]                           
  done clear
  B)
  \[\sqrt{400}m/s\]
  done clear
  C)
  \[\sqrt{500}m/s\]                           
  done clear
  D)
   \[\sqrt{800}m/s\]
  done clear
  View Answer play_arrow

• question_answer51) The \[As{{F}_{5}}\] molecule is trigonal bipyramidal. The hybrid orbitals used by the \[As\] atoms, for bonding are
  A)
  \[{{d}_{{{x}^{2}}-{{y}^{2}}}},\,\,{{d}_{{{z}^{2}}}},\,\,s,\,\,{{p}_{x}},\,\,{{p}_{y}}\]
  done clear
  B)
  \[{{d}_{xy}},\,\,s,\,\,{{p}_{x}},\,\,{{p}_{y}},\,\,{{p}_{z}}\]
  done clear
  C)
   \[s,\,\,{{p}_{x}},\,\,{{p}_{y}},\,\,{{p}_{z}},\,\,{{d}_{{{z}^{2}}}}\]
  done clear
  D)
   \[{{d}_{{{x}^{2}}-{{y}^{2}}}},\,\,s,\,\,{{p}_{x}},\,\,{{p}_{y}}\]
  done clear
  View Answer play_arrow

• question_answer52) The low density of ice compared to water is due to
  A)
   induced dipole-induced dipole interactions
  done clear
  B)
   dipole-induced dipole interactions
  done clear
  C)
   hydrogen bonding interactions
  done clear
  D)
    dipole-dipole interactions
  done clear
  View Answer play_arrow

• question_answer53) Inorganic benzene is
  A)
  \[{{B}_{3}}{{H}_{3}}{{N}_{3}}\]                  
  done clear
  B)
  \[B{{H}_{3}}N{{H}_{3}}\]
  done clear
  C)
   \[{{B}_{3}}{{H}_{6}}{{N}_{3}}\]                 
  done clear
  D)
   \[{{H}_{3}}{{B}_{3}}{{N}_{6}}\]
  done clear
  View Answer play_arrow

• question_answer54) Which of the following compounds will show metamerism?
  A)
  \[C{{H}_{3}}-CO-{{C}_{2}}{{H}_{5}}\]      
  done clear
  B)
  \[{{C}_{2}}{{H}_{5}}-S-{{C}_{2}}{{H}_{5}}\]
  done clear
  C)
  \[C{{H}_{3}}-O-C{{H}_{3}}\]        
  done clear
  D)
   \[C{{H}_{3}}-O-{{C}_{2}}{{H}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer55) Benzene on treatment with a mixture of conc. \[HN{{O}_{3}}\] and conc. \[{{H}_{2}}S{{O}_{4}}\]at \[{{100}^{o}}C\] gives
  A)
   nitrobenzene
  done clear
  B)
   \[m-\]dinitrobenzene
  done clear
  C)
   \[p-\]dinitrobenzene
  done clear
  D)
    \[o-\]dinitrobenzene
  done clear
  View Answer play_arrow

• question_answer56) \[0.765\,\,g\] of an acid gives \[0.535\,\,g\] of \[C{{O}_{2}}\] and \[0.138\,\,g\] of. Then, the ratio of the percentage of carbon and hydrogen is
  A)
  \[19:2\]               
  done clear
  B)
  \[18:11\]
  done clear
  C)
   \[20:17\]                            
  done clear
  D)
   \[1:7\]
  done clear
  View Answer play_arrow

• question_answer57) Ziegler-Natta catalyst is
  A)
  \[{{(P{{h}_{3}}P)}_{3}}RhCl\]
  done clear
  B)
  \[K[PtC{{l}_{3}}({{C}_{2}}{{H}_{4}})]\]
  done clear
  C)
   \[[A{{l}_{2}}{{({{C}_{2}}{{H}_{6}})}_{6}}+TiC{{l}_{4}}]\]
  done clear
  D)
   \[[Fe{{({{C}_{2}}{{H}_{5}})}_{2}}]\]
  done clear
  View Answer play_arrow

• question_answer58) \[1\,\,L\] oxygen gas at \[STP\] will weigh
  A)
  \[1.43\,\,g\]                      
  done clear
  B)
   \[2.24\,\,g\]
  done clear
  C)
   \[11.2\,\,g\]                     
  done clear
  D)
   \[22.4\,\,g\]
  done clear
  View Answer play_arrow

• question_answer59) The \[IUPAC\] name of the compound,\[{{C}_{2}}{{H}_{5}}-\underset{\begin{smallmatrix}  || \\  C{{H}_{2}} \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}OH\]is
  A)
   2-ethylprop-2-en-1-ol
  done clear
  B)
   2-hydroxymethylbutan-1-ol
  done clear
  C)
    2-methylenebutan-1-pl
  done clear
  D)
    2-ethyl-3-hydroxyprop-1-ene
  done clear
  View Answer play_arrow

• question_answer60) The chemical name of vitamin \[{{B}_{1}}\] is
  A)
   ascorbic acid    
  done clear
  B)
   riboflavin
  done clear
  C)
    pyridoxine      
  done clear
  D)
    thiamine
  done clear
  View Answer play_arrow

• question_answer61) Glyptal polymer is obtained from glycol by reacting with
  A)
   malonic acid    
  done clear
  B)
   phthalic acid
  done clear
  C)
    maleic acid      
  done clear
  D)
    terephthalic acid
  done clear
  View Answer play_arrow

• question_answer62) Molecular formula of Glauber's salt is
  A)
  \[MgS{{O}_{4}}\cdot 7{{H}_{2}}O\]         
  done clear
  B)
  \[CuS{{O}_{4}}\cdot 5{{H}_{2}}O\]
  done clear
  C)
   \[FeS{{O}_{4}}\cdot 7{{H}_{2}}O\]         
  done clear
  D)
   \[N{{a}_{2}}S{{O}_{4}}\cdot 10{{H}_{2}}O\]
  done clear
  View Answer play_arrow

• question_answer63) The size of colloidal particles is in between
  A)
  \[{{10}^{-7}}-{{10}^{-9}}cm\]     
  done clear
  B)
  \[{{10}^{-9}}-{{10}^{-11}}cm\]
  done clear
  C)
   \[{{10}^{-5}}-{{10}^{-7}}cm\]    
  done clear
  D)
   \[{{10}^{-2}}-{{10}^{-3}}cm\]
  done clear
  View Answer play_arrow

• question_answer64) In the reaction,\[S{{O}_{2}}+2{{H}_{2}}S\xrightarrow{{}}3S+2{{H}_{2}}O\] the substance oxidised is
  A)
  \[{{H}_{2}}S\]                                   
  done clear
  B)
  \[S{{O}_{2}}\]
  done clear
  C)
  \[S\]                                     
  done clear
  D)
   \[{{H}_{2}}O\]
  done clear
  View Answer play_arrow

• question_answer65) The emf of the cell\[Ni|N{{i}^{2+}}(1.0\,\,M)||A{{u}^{3+}}(1.0\,\,M)|Au\]is\[[{{E}^{o}}(N{{i}^{2+}}/Ni)=-0.25\,\,V\]and\[(A{{u}^{3+}}/Au)=+1.5\,\,V]\]
  A)
  \[2.00\,\,V\]                      
  done clear
  B)
  \[1.25\,\,V\]
  done clear
  C)
   \[-1.25\,\,V\]                   
  done clear
  D)
   \[1.75\,\,V\]
  done clear
  View Answer play_arrow

• question_answer66) The heat of neutralisation is highest for the reaction between
  A)
  \[N{{H}_{4}}OH-C{{H}_{3}}COOH\]
  done clear
  B)
  \[HN{{O}_{3}}-N{{H}_{4}}OH\]
  done clear
  C)
   \[NaOH-C{{H}_{3}}COOH\]
  done clear
  D)
   \[HCl-NaOH\]
  done clear
  View Answer play_arrow

• question_answer67) An ideal gas expands in volume from \[1\times {{10}^{-3}}{{m}^{3}}\]to\[1\times {{10}^{-2}}{{m}^{3}}\]at \[300\,\,K\] against a constant pressure of\[1\times {{10}^{5}}N{{m}^{-2}}\]. The work done is
  A)
  \[-900\,\,J\]                       
  done clear
  B)
   \[-900\,\,kJ\]
  done clear
  C)
   \[270\,\,kJ\]                     
  done clear
  D)
   \[900\,\,kJ\]
  done clear
  View Answer play_arrow

• question_answer68) Which one of the following is correct?
  A)
  \[-\Delta G=\Delta H-T\Delta S\]              
  done clear
  B)
  \[\Delta H=\Delta G-T\Delta S\]
  done clear
  C)
   \[\Delta S=\frac{1}{T}[\Delta G-\Delta H]\]        
  done clear
  D)
   \[\Delta S=\frac{1}{T}[\Delta H-\Delta G]\]
  done clear
  View Answer play_arrow

• question_answer69) The electronic configuration of element with atomic number \[24\] is
  A)
  \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}}3{{d}^{4}},\,\,4{{s}^{2}}\]
  done clear
  B)
  \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}}3{{d}^{10}}\]
  done clear
  C)
   \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}}3{{d}^{6}}\]
  done clear
  D)
   \[1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}}3{{d}^{5}},\,\,4{{s}^{1}}\]
  done clear
  View Answer play_arrow

• question_answer70) In van der Waals' equation, of state of the gas law, the constant \['b'\] is a measure of
  A)
   intermolecular repulsions
  done clear
  B)
   intermolecular attraction
  done clear
  C)
    volume occupied by the molecules
  done clear
  D)
    intermolecular collisions per unit volume
  done clear
  View Answer play_arrow

• question_answer71) If the radius of \[{{K}^{+}}\]and\[{{F}^{-}}\] are \[133\,\,pm\] and \[136\,\,pm\] respectively, the distance between \[{{K}^{+}}\]and \[{{F}^{-}}\]in \[KF\] is
  A)
  \[269\,\,pm\]                   
  done clear
  B)
  \[134.5\,\,pm\]
  done clear
  C)
   \[136\,\,pm\]                  
  done clear
  D)
   \[3\,\,pm\]
  done clear
  View Answer play_arrow

• question_answer72) The property of attracting electrons by the halogen atoms in a molecule is called
  A)
   ionization potential
  done clear
  B)
   electron affinity
  done clear
  C)
    electronegativity
  done clear
  D)
    electronic attraction
  done clear
  View Answer play_arrow

• question_answer73) A reversible chemical reaction is having two reactants, in equilibrium. If the concentration of the reactants are doubled then the equilibrium constant will
  A)
   be doubled
  done clear
  B)
   become one fourth
  done clear
  C)
   be halved
  done clear
  D)
   remain the same
  done clear
  View Answer play_arrow

• question_answer74) The strongest Bronsted base is
  A)
  \[ClO_{3}^{-}\]                 
  done clear
  B)
   \[ClO_{2}^{-}\]
  done clear
  C)
   \[ClO_{4}^{-}\]                
  done clear
  D)
   \[Cl{{O}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer75) A solution contains \[10\,\,mL\] \[0.1\,\,N\,\,NaOH\] and NH\[10\,\,mL\,\,0.05\,\,N\,\,{{H}_{2}}S{{O}_{4}}\], \[pH\] of this solution is
  A)
   less than\[7\]                  
  done clear
  B)
  \[7\]
  done clear
  C)
    zero                                    
  done clear
  D)
    greater than\[7\]
  done clear
  View Answer play_arrow

• question_answer76) For which one of the following reactions\[{{K}_{p}}={{K}_{c}}\]?
  A)
  \[PC{{l}_{5}}PC{{l}_{3}}+C{{l}_{2}}\]
  done clear
  B)
  \[{{N}_{2}}+{{O}_{2}}2NO\]
  done clear
  C)
  \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}\]
  done clear
  D)
  \[2S{{O}_{3}}2S{{O}_{2}}+{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer77) What is the molarity of \[0.2\,\,N\,\,N{{a}_{2}}C{{O}_{3}}\] solution?
  A)
  \[0.1\,\,M\]                       
  done clear
  B)
  \[0\,\,M\]
  done clear
  C)
  \[0.4\,\,M\]                       
  done clear
  D)
  \[0.2\,\,M\]
  done clear
  View Answer play_arrow

• question_answer78) The order of a reaction with rate equal to \[kC_{A}^{3/2}C_{B}^{-1/2}\]is
  A)
  \[1\]                                     
  done clear
  B)
  \[-\frac{1}{2}\]
  done clear
  C)
  \[-\frac{3}{2}\]                                 
  done clear
  D)
  \[2\]
  done clear
  View Answer play_arrow

• question_answer79) A simple method to remove peroxides from ethers is to treat them with an aqueous solution of
  A)
  \[KI\]                                    
  done clear
  B)
  \[KCNS\]
  done clear
  C)
   \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]                              
  done clear
  D)
  \[B{{r}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer80) Which of the following is the predominant product in the reaction of \[HOBr\] with propene?
  A)
   2-bromo-1-propanol
  done clear
  B)
   3-bromo-1-propanol
  done clear
  C)
   2-bromo-2-propanol
  done clear
  D)
   1-bromo-2-propanol
  done clear
  View Answer play_arrow

• question_answer81) Most stable carbonium ion is
  A)
  \[{{\overset{+}{\mathop{C}}\,}_{2}}{{H}_{5}}\]                
  done clear
  B)
  \[{{(C{{H}_{3}})}_{3}}\overset{+}{\mathop{C}}\,\]
  done clear
  C)
  \[{{({{C}_{6}}{{H}_{5}})}_{3}}\overset{+}{\mathop{C}}\,\]                           
  done clear
  D)
  \[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer82) In aqueous solutions, the basic strength of amines decreases in the order
  A)
  \[C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{2}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N\]
  done clear
  B)
  \[{{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}\]
  done clear
  C)
  \[{{(C{{H}_{3}})}_{3}}N>{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}\]
  done clear
  D)
   \[{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N\]
  done clear
  View Answer play_arrow

• question_answer83) The most reactive compound towards formation of cyanohydrin on treatment with HCN followed by acidification is
  A)
   benzaldehyde
  done clear
  B)
   \[p-\]nitrobenzaldehyde
  done clear
  C)
   phenylacetaldehyde
  done clear
  D)
    \[p-\]hydroxybenzaldehyde
  done clear
  View Answer play_arrow

• question_answer84) Producer gas is the mixture of
  A)
  \[CO+{{N}_{2}}\]
  done clear
  B)
  \[CO+{{H}_{2}}\]
  done clear
  C)
  \[CO+\]water vapour
  done clear
  D)
   \[{{N}_{2}}+C{{H}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer85) What is the freezing point of a solution containing  \[8.1\,\,g\,\,HBr\] in \[100\,\,g\] water assuming the acid to be \[90%\] ionised? \[({{k}_{f}}\] for water\[=1.86\,\,K\,\,mo{{l}^{-1}})\]
  A)
  \[{{0.85}^{o}}C\]                             
  done clear
  B)
   \[-{{3.53}^{o}}C\]
  done clear
  C)
   \[{{0}^{o}}C\]                                  
  done clear
  D)
   \[-{{0.35}^{o}}C\]
  done clear
  View Answer play_arrow

• question_answer86) Number of elements presents in the fifth period of Periodic Table is
  A)
  \[32\]                                   
  done clear
  B)
  \[10\]
  done clear
  C)
   \[18\]                                  
  done clear
  D)
   \[8\]
  done clear
  View Answer play_arrow

• question_answer87) \[{{[Sc({{H}_{2}}{{O}_{6}})]}^{3+}}\]ion is
  A)
   colourless and diamagnetic
  done clear
  B)
   coloured and octahedral
  done clear
  C)
   colourless and paramagnetic
  done clear
  D)
    coloured and paramagnetic
  done clear
  View Answer play_arrow

• question_answer88) Which one has the highest boiling point?
  A)
  \[{{H}_{2}}\]                                      
  done clear
  B)
  \[Xe\]
  done clear
  C)
  \[C{{H}_{4}}\]                                   
  done clear
  D)
  \[He\]
  done clear
  View Answer play_arrow

• question_answer89) Benzaldehyde reacts with ammonia to form
  A)
   benzaldehyde ammonia
  done clear
  B)
   urotropine
  done clear
  C)
   hydrobenzamide
  done clear
  D)
   ammonium chloride
  done clear
  View Answer play_arrow

• question_answer90) Identify \[Z\] in the sequence\[C{{H}_{3}}COON{{H}_{4}}\xrightarrow{\Delta }X\xrightarrow[\Delta ]{{{P}_{2}}{{O}_{5}}}Y\xrightarrow{{{H}_{2}}O/{{H}^{+}}}Z\]
  A)
  \[C{{H}_{3}}C{{H}_{2}}CON{{H}_{2}}\]   
  done clear
  B)
  \[C{{H}_{3}}CN\]
  done clear
  C)
  \[C{{H}_{3}}COOH\]                       
  done clear
  D)
  \[{{(C{{H}_{3}}CO)}_{2}}O\]
  done clear
  View Answer play_arrow

• question_answer91) Acetic anhydride reacts with diethyl ether in the presence of anhydrous \[AlC{{l}_{3}}\] to give
  A)
  \[C{{H}_{3}}C{{H}_{2}}COOH\]
  done clear
  B)
  \[C{{H}_{3}}C{{H}_{2}}COOC{{H}_{2}}C{{H}_{3}}\]
  done clear
  C)
   \[C{{H}_{3}}COOC{{H}_{3}}\]
  done clear
  D)
  \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer92) Denaturation of proteins leads to loss of its biological activity by
  A)
   formation of amino acids
  done clear
  B)
   loss of primary structure
  done clear
  C)
   loss of both primary and secondary structures
  done clear
  D)
   loss of both secondary and tertiary structures
  done clear
  View Answer play_arrow

• question_answer93) The compound with highest boiling point
  A)
   n-hexane
  done clear
  B)
   n-pentane
  done clear
  C)
   2, 2-dimethylpropane
  done clear
  D)
   2-methylbutane
  done clear
  View Answer play_arrow

• question_answer94) Which of the following statements concerning transition elements is false?
  A)
   They are all metals
  done clear
  B)
   They easily form complex coordination compounds
  done clear
  C)
   Compounds containing their ions are mostly coloured
  done clear
  D)
    They show multiple oxidation states always differing by units of two
  done clear
  View Answer play_arrow

• question_answer95) In the manufacture of bromine from sea water, the mother liquor containing bromide is treated with
  A)
   carbon dioxide                
  done clear
  B)
   chlorine
  done clear
  C)
   iodine                                 
  done clear
  D)
    sulphur dioxide
  done clear
  View Answer play_arrow

• question_answer96) A transition element X has the configuration \[[Ar]{{d}^{4}}\] in its \[+3\] oxidation state. It?s atomic number is
  A)
  \[25\]                                   
  done clear
  B)
  \[26\]
  done clear
  C)
  \[22\]                                   
  done clear
  D)
  \[19\]
  done clear
  View Answer play_arrow

• question_answer97) The element with the electronic configuration as \[[Ar]3{{d}^{10}}4{{s}^{2}}4{{p}^{3}}\] represents a
  A)
   metal
  done clear
  B)
   non-metal
  done clear
  C)
   metalloid
  done clear
  D)
   transition element
  done clear
  View Answer play_arrow

• question_answer98) The number of moles of\[{{H}_{2}}\]in\[0.224\] hydrogen gas at\[STP\,\,(273\,\,K,\,\,1\,\,atm)\], is
  A)
  \[0.1\]                                  
  done clear
  B)
   \[0.01\]
  done clear
  C)
  \[0.001\]                             
  done clear
  D)
   \[1\]
  done clear
  View Answer play_arrow

• question_answer99) The molecule which has zero dipole moment is
  A)
  \[C{{H}_{3}}Cl\]               
  done clear
  B)
  \[N{{F}_{3}}\]
  done clear
  C)
  \[B{{F}_{3}}\]                                    
  done clear
  D)
   \[Cl{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer100) Greenhouse effect is caused by
  A)
  \[N{{O}_{2}}\]                                  
  done clear
  B)
  \[CO\]
  done clear
  C)
  \[NO\]                                 
  done clear
  D)
  \[C{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer101) If\[y=\sin x\], then\[\frac{{{d}^{2}}}{d{{y}^{2}}}({{\cos }^{7}}x)\]is equal to
  A)
  \[7{{\cos }^{5}}x+35{{\cos }^{3}}x\]
  done clear
  B)
  \[7{{\cos }^{5}}x+35{{\cos }^{2}}x\]
  done clear
  C)
  \[-7{{\cos }^{5}}x+35{{\cos }^{2}}x\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer102) The equation of ellipse whose axes are coincident with the coordinate axes and which   touches   the   straight   lines \[3x-2y-20=0\] and\[x+6y-20=0\], is
  A)
  \[\frac{{{x}^{2}}}{5}+\frac{{{y}^{2}}}{8}=1\]                        
  done clear
  B)
  \[\frac{{{x}^{2}}}{40}+\frac{{{y}^{2}}}{10}=10\]
  done clear
  C)
  \[\frac{{{x}^{2}}}{40}+\frac{{{y}^{2}}}{10}=1\]                   
  done clear
  D)
  \[\frac{{{x}^{2}}}{10}+\frac{{{y}^{2}}}{40}=1\]
  done clear
  View Answer play_arrow

• question_answer103) The equation of the radical axis of the circles \[2{{x}^{2}}+2{{y}^{2}}+14x-18y+15=0\]and\[4{{x}^{2}}+4{{y}^{2}}-3x-y+5=0\], is
  A)
  \[31x+35y-25=0\]
  done clear
  B)
  \[31x-35y+25=0\]
  done clear
  C)
  \[35x+31y-25=0\]
  done clear
  D)
  \[35x-31y+25=0\]
  done clear
  View Answer play_arrow

• question_answer104) SS\[\underset{x\to 1}{\mathop{\lim }}\,\frac{1+\log x-x}{1-2x+{{x}^{2}}}\]is equal to
  A)
  \[1\]                                     
  done clear
  B)
  \[-1\]
  done clear
  C)
  \[0\]                                     
  done clear
  D)
  \[-\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer105) \[\int_{0}^{\pi /2}{{{\cos }^{5}}\left( \frac{x}{2} \right)}\sin x\,\,dx\]is equal to
  A)
  \[\frac{2}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)\]                
  done clear
  B)
  \[-\frac{4}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)\]
  done clear
  C)
  \[\frac{4}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)\]                
  done clear
  D)
  \[-\frac{2}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)\]
  done clear
  View Answer play_arrow

• question_answer106) The area of the region bounded by the curve \[y=\frac{{{a}^{3}}}{{{x}^{2}}+{{a}^{2}}}\]and \[x-axis\] is
  A)
  \[\pi {{a}^{2}}sq\,\,unit\]                            
  done clear
  B)
  \[2\pi {{a}^{2}}sq\,\,unit\]
  done clear
  C)
  \[3\pi {{a}^{2}}sq\,\,unit\]                          
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer107) If the constant forces\[2\widehat{\mathbf{i}}-5\widehat{\mathbf{j}}+6\widehat{\mathbf{k}}\]and \[-\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}-\widehat{\mathbf{k}}\]act on a particle due to which it is displaced from a point\[A(4,\,\,-3,\,\,-2)\]to a point\[B(6,\,\,1,\,\,-3)\]then the work done by the force is
  A)
  \[25\,\,unit\]                    
  done clear
  B)
  \[-15\,\,unit\]
  done clear
  C)
  \[9\,\,unit\]                       
  done clear
  D)
  \[-9\,\,unit\]
  done clear
  View Answer play_arrow

• question_answer108) The equation of the line which passes through the point \[(3,\,\,4)\] and the sum of its intercepts on the axes is\[14\], is
  A)
  \[x+y=7\]and\[4x+3y=24\]
  done clear
  B)
  \[x+y=24\]and\[4x+3y=7\]
  done clear
  C)
  \[x-y=7\]and\[4x-3y=24\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer109) If\[{{x}^{2}}-x+1=0\],  then  the  value  of\[\sum\limits_{n=1}^{5}{{{\left( {{x}^{n}}+\frac{1}{{{x}^{n}}} \right)}^{2}}}\]is
  A)
  \[8\]                                     
  done clear
  B)
  \[10\]
  done clear
  C)
  \[12\]                                   
  done clear
  D)
  \[14\]
  done clear
  View Answer play_arrow

• question_answer110) Minimum value of\[{{4}^{x}}-{{4}^{1-x}},\,\,x\in R\]is
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[3\]                                     
  done clear
  D)
  \[4\]
  done clear
  View Answer play_arrow

• question_answer111) If \[\alpha ,\,\,\beta \] are the roots of equation\[8{{x}^{2}}-3x+27=0\], then the value of\[{{\left( \frac{{{\alpha }^{2}}}{\beta } \right)}^{1/3}}+{{\left( \frac{{{\beta }^{2}}}{\alpha } \right)}^{1/3}}\]is
  A)
  \[\frac{1}{3}\]                                   
  done clear
  B)
  \[\frac{1}{4}\]
  done clear
  C)
  \[\frac{7}{2}\]                                   
  done clear
  D)
  \[4\]
  done clear
  View Answer play_arrow

• question_answer112) There are four candidates for the post of a lecturer in Mathematics and one is to be selected by votes of \[5\] men. The number of ways in which the votes can be given is
  A)
  \[1048\]                                              
  done clear
  B)
  \[1072\]
  done clear
  C)
  \[1024\]                              
  done clear
  D)
  \[1064\]
  done clear
  View Answer play_arrow

• question_answer113) The coefficient of \[{{x}^{4}}\] in the expansion of\[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{11}}\], is
  A)
  \[990\]                                 
  done clear
  B)
  \[605\]
  done clear
  C)
  \[810\]                                 
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer114) If the matrix\[\left[ \begin{matrix}    0 & 2\beta  & \gamma   \\   \alpha  & \beta  & -\gamma   \\    \alpha  & -\beta  & \gamma   \\ \end{matrix} \right]\]is orthogonal, then
  A)
  \[\alpha =\pm \frac{1}{\sqrt{2}}\]                           
  done clear
  B)
  \[\beta =\pm \frac{1}{\sqrt{6}}\]
  done clear
  C)
  \[\gamma =\pm \frac{1}{\sqrt{3}}\]                       
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer115) The sum of the series \[{{\log }_{4}}2-{{\log }_{8}}2+{{\log }_{16}}2-....\infty \], is
  A)
  \[{{e}^{2}}\]                                      
  done clear
  B)
  \[{{\log }_{e}}2+1\]
  done clear
  C)
  \[{{\log }_{e}}2-1\]                         
  done clear
  D)
  \[1-{{\log }_{e}}2\]
  done clear
  View Answer play_arrow

• question_answer116) The range of the function\[f(x)=\frac{x-2}{2-x}\], when\[x\ne 2\]is
  A)
  \[R\]                                     
  done clear
  B)
  \[R-\{1\}\]
  done clear
  C)
  \[\{-1\}\]                                            
  done clear
  D)
  \[R-\{-1\}\]
  done clear
  View Answer play_arrow

• question_answer117) If \[A\] and \[B\] are two independent events such that \[P(A)=\frac{1}{2}\] and \[P(B)=\frac{1}{5},\] then which of the following is/are correct?
  A)
  \[P(A\cup B)=\frac{5}{3}\]          
  done clear
  B)
  \[P\left( \frac{A}{B} \right)=\frac{1}{3}\]
  done clear
  C)
  \[P\left( \frac{A}{A\cup B} \right)=\frac{5}{6}\]
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer118) The probability of \[A\] to fail in an examination is \[\frac{1}{5}\] and that of \[B\] is\[\frac{3}{10}\], then the probability that either \[A\] or \[B\] fails is
  A)
  \[\frac{1}{2}\]                                   
  done clear
  B)
  \[\frac{11}{25}\]
  done clear
  C)
  \[\frac{19}{50}\]                                              
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer119) The value of \[\cos y\cos \left( \frac{\pi }{2}-x \right)-\cos \left( \frac{\pi }{2}-y \right)\cos x\] \[+\sin y\cos \left( \frac{\pi }{2}-x \right)+\cos x\sin \left( \frac{\pi }{2}-y \right)\]is zero, if
  A)
  \[x=0\]                
  done clear
  B)
  \[y=0\]
  done clear
  C)
  \[x=y\]                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer120) The value of\[\sin [{{\cot }^{-1}}\{{{\cot }^{-1}}({{\cos }^{-1}}x)\}]\]is equal to
  A)
  \[\frac{\sqrt{1-{{x}^{2}}}}{x}\]                  
  done clear
  B)
  \[\frac{x}{\sqrt{1-{{x}^{2}}}}\]
  done clear
  C)
  \[x\]                                     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer121) . The maximum value of \[P=6x+8y\] subject to constraints\[2x+y\le 30,\,\,x+2y\le 24\]and\[x\ge 0,\,\,y\ge 0\]is
  A)
  \[90\]                                   
  done clear
  B)
  \[120\]
  done clear
  C)
  \[96\]                                   
  done clear
  D)
  \[240\]
  done clear
  View Answer play_arrow

• question_answer122) With the help of trapezoidal rule for numerical integration and the following table.

  \[x\]	\[0\]	\[0.25\]	\[0.50\]	\[0.75\]	\[1\]
  \[f(x)\]	\[0\]	\[0.625\]	\[0.2500\]	\[0.5625\]	\[1\]

  The value of\[\int_{0}^{1}{f(x)}\,\,dx\]is
  A)
  \[0.35342\]                        
  done clear
  B)
  \[0.34375\]
  done clear
  C)
  \[0.34457\]                        
  done clear
  D)
  \[0.33334\]
  done clear
  View Answer play_arrow

• question_answer123) If \[B\] is an idempotent matrix and\[A=I-B\],  then
  A)
  \[{{A}^{2}}=A\]
  done clear
  B)
  \[AB=0\]
  done clear
  C)
  \[BA=0\]
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer124) The coefficient of \[{{x}^{20}}\] in the expansion of\[{{(1+{{x}^{2}})}^{40}}{{\left( {{x}^{2}}+2+\frac{1}{{{x}^{2}}} \right)}^{-5}}\], is
  A)
  \[^{30}{{C}_{10}}\]                                         
  done clear
  B)
  \[^{30}{{C}_{25}}\]
  done clear
  C)
  \[1\]                                     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer125) For what values of\[k\in R\], the expression \[2{{x}^{2}}+kxy+3{{y}^{2}}-5y-2\] can be expressed as\[({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}})\cdot ({{a}_{2}}x+{{b}_{2}}y+{{c}_{2}})\]?
  A)
  \[-3,\,\,-4\]                        
  done clear
  B)
  \[2,\,\,3\]
  done clear
  C)
  \[3,\,\,4\]                                           
  done clear
  D)
  \[7,\,\,-7\]
  done clear
  View Answer play_arrow

• question_answer126) If \[a,\,\,\,b,\,\,\,c\] are the sides of a \[\Delta \,\,ABC\] which are in\[AP\], then \[\cot \frac{C}{2}\] is equal to
  A)
  \[3\tan \frac{A}{2}\]                      
  done clear
  B)
  \[3\tan \frac{B}{2}\]
  done clear
  C)
  \[3\cot \frac{A}{2}\]                      
  done clear
  D)
  \[2\cot \frac{B}{2}\]
  done clear
  View Answer play_arrow

• question_answer127) The continued product of the four values of \[{{\left[ \cos \left( \frac{\pi }{3} \right)+i\sin \left( \frac{\pi }{3} \right) \right]}^{3/4}}\], is
  A)
  \[-1\]                                    
  done clear
  B)
  \[1\]
  done clear
  C)
  \[2\]                                     
  done clear
  D)
  \[-2\]
  done clear
  View Answer play_arrow

• question_answer128) For the given line\[3x-4y=8\], the points \[(2,\,\,3)\] and \[(-4,\,\,5)\] are on the
  A)
   same side          
  done clear
  B)
   opposite side
  done clear
  C)
   lie on the line                   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer129) The abscissae and ordinates of the points \[A\] and \[B\] are the roots of the equations\[{{x}^{2}}+2ax+b=0\]and\[{{x}^{2}}+2cx+d=0\] respective, then the equation, of circle with \[AB\] is diameter, is
  A)
  \[{{x}^{2}}+{{y}^{2}}+2ax+2cy+b+d=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}-2ax-2cy-b-d=0\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}+2ax+2cy-b-d=0\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}-2ax-2cy+b+d=0\] 
  done clear
  View Answer play_arrow

• question_answer130) If \[2x+y+k=0\]is a normal to the parabola\[{{y}^{2}}=-8x\], then the value of \[k\] is
  A)
  \[-16\]                                 
  done clear
  B)
  \[-8\]
  done clear
  C)
  \[-24\]                                 
  done clear
  D)
  \[24\]
  done clear
  View Answer play_arrow

• question_answer131) The equation of tangent parallel to \[y=x\] drawn to\[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\], is
  A)
  \[x-y+1=0\]                       
  done clear
  B)
  \[x-y+2=0\]
  done clear
  C)
  \[x+y-1=0\]                       
  done clear
  D)
  \[x+y-2=0\]
  done clear
  View Answer play_arrow

• question_answer132) The domain of the function\[f(x)=\sqrt{3-x}+{{\cos }^{-1}}\left( \frac{3-2x}{5} \right)\], is
  A)
  \[[-1,\,\,3]\]                      
  done clear
  B)
  \[(-1,\,\,3]\]
  done clear
  C)
  \[[-1,\,\,3)\]                      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer133) If \[f(x)\] is differentiable in the interval \[[2,\,\,5]\] where\[f(2)=\frac{1}{5}\]and\[f(5)=\frac{1}{2}\], then there exist a number \[c,\,\,2<c<5\] for which \[f'(c)\] is equal to
  A)
  \[\frac{1}{2}\]                                   
  done clear
  B)
  \[\frac{1}{5}\]
  done clear
  C)
  \[\frac{1}{10}\]                                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer134) If the line \[ax+by+c=0\]is a normal to the curve\[xy=1\], then
  A)
  \[a>0,\,\,b>0\]                 
  done clear
  B)
  \[a>0,\,\,b<0\]
  done clear
  C)
  \[a<0,\,\,b<0\]                 
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer135) \[\int{{{\sec }^{3}}x}\,\,dx\]is equal to
  A)
  \[\sec x\tan x+\log |\sec x+\tan x|+c\]
  done clear
  B)
  \[\frac{1}{2}\sec x\tan x+\frac{1}{2}\log |\sec x+\tan x|+c\]
  done clear
  C)
  \[{{\sec }^{3}}x\tan x+\log |{{\sec }^{3}}x+\tan x|+c\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer136) The order and. degree of the differential equation\[{{\left( 1+3\frac{dy}{dx} \right)}^{2/3}}=4\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)\]are
  A)
  \[1,\,\,\frac{2}{3}\]                                        
  done clear
  B)
  \[3,\,\,1\]
  done clear
  C)
  \[3,\,\,3\]                                           
  done clear
  D)
  \[1,\,\,2\]
  done clear
  View Answer play_arrow

• question_answer137) If \[\sin x\] is an integrating factor of the differential equation\[\frac{dy}{dx}+Py=Q\], then \[P\] can be
  A)
  \[\log \sin x\]                    
  done clear
  B)
  \[\cot x\]
  done clear
  C)
  \[\sin x\]                                             
  done clear
  D)
  \[\log \cos x\]
  done clear
  View Answer play_arrow

• question_answer138) Let\[\overset{\to }{\mathop{\mathbf{a}}}\,=\widehat{\mathbf{i}}-\widehat{\mathbf{k}},\,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,=x\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+(1-x)\widehat{\mathbf{k}}\]and\[\overset{\to }{\mathop{\mathbf{c}}}\,=y\widehat{\mathbf{i}}+x\widehat{\mathbf{j}}+(1+x-y)\widehat{\mathbf{k}}\]. Then,\[[\overrightarrow{\mathbf{a}}\overrightarrow{\mathbf{b}}\overrightarrow{\mathbf{c}}]\] depends on,
  A)
   only\[x\]                            
  done clear
  B)
   only\[y\]
  done clear
  C)
   neither\[x\]nor\[y\]     
  done clear
  D)
   both \[x\] and\[y\]
  done clear
  View Answer play_arrow

• question_answer139) If the planes\[\overset{\to }{\mathop{\mathbf{r}}}\,\cdot (2\widehat{\mathbf{i}}-\lambda \widehat{\mathbf{j}}+\widehat{\mathbf{k}})=3\]and\[\overset{\to }{\mathop{\mathbf{r}}}\,\cdot (4\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\mu \widehat{\mathbf{k}})=5\]are parallel, then the value of \[\lambda \] and \[\mu \] are
  A)
  \[\frac{1}{2},\,\,-2\]                       
  done clear
  B)
  \[-\frac{1}{2},\,\,2\]
  done clear
  C)
  \[-\frac{1}{2},\,\,-2\]                     
  done clear
  D)
  \[\frac{1}{2},\,\,2\]
  done clear
  View Answer play_arrow

• question_answer140) Two forces \[P\] and \[Q\] acting at a point have a resultant\[R\]. The resolved of \[R\] in the direction of \[P\] is a magnitude\[Q\]. Then, the angle between the forces and the magnitude of the resultant are
  A)
  \[\theta ={{\cos }^{-1}}\left( \frac{P-Q}{Q} \right),\,\,R=\sqrt{{{P}^{2}}-{{Q}^{2}}+2PQ}\]
  done clear
  B)
  \[\theta ={{\cos }^{-1}}\left( \frac{Q-P}{Q} \right),\,\,R=\sqrt{{{Q}^{2}}-{{P}^{2}}+2PQ}\]
  done clear
  C)
  \[\theta ={{\cos }^{-1}}\left( \frac{P-Q}{P} \right),\,\,R=\sqrt{2{{P}^{2}}-{{Q}^{2}}+2PQ}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer141) A point is moving in a straight line with uniform acceleration describes \[a\] and \[b\] feet in successive intervals of \[{{t}_{1}}\] and \[{{t}_{2}}\] seconds. Then, the acceleration is
  A)
  \[\frac{2(b{{t}_{1}}-a{{t}_{2}})}{{{t}_{1}}{{t}_{2}}({{t}_{1}}+{{t}_{2}})}\]                 
  done clear
  B)
  \[\frac{b{{t}_{2}}-a{{t}_{1}}}{{{t}_{1}}{{t}_{2}}({{t}_{1}}+{{t}_{2}})}\]
  done clear
  C)
  \[\frac{b{{t}_{2}}-a{{t}_{1}}}{2{{t}_{1}}{{t}_{2}}({{t}_{1}}+{{t}_{2}})}\]                    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer142) If\[2f(x)+3f\left( \frac{1}{x} \right)=\frac{1}{x}-2,\,\,x\ne 0\], then\[\int_{1}^{2}{f(x)}\,\,dx\]equal to
  A)
  \[-\frac{2}{5}\log 2+\frac{1}{2}\]                              
  done clear
  B)
  \[-\frac{2}{5}\log 2-\frac{1}{2}\]
  done clear
  C)
  \[\frac{2}{5}\log 2+\frac{1}{2}\]                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer143) The maximum value of the function \[y=x{{(x-1)}^{2}}\], is
  A)
  \[0\]                                     
  done clear
  B)
  \[\frac{4}{27}\]
  done clear
  C)
  \[-4\]                                    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer144) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{x}}{\sqrt{4-\sqrt{x}}-\sqrt{x}}\]is equal to
  A)
  \[0\]                                     
  done clear
  B)
  \[1\]
  done clear
  C)
  \[-1\]                                    
  done clear
  D)
   does not exist
  done clear
  View Answer play_arrow

• question_answer145) If\[\frac{d}{dx}\left( \frac{1+{{x}^{4}}+{{x}^{8}}}{1+{{x}^{2}}+{{x}^{4}}} \right)=a{{x}^{3}}+bx\], then
  A)
  \[a=4,\,\,b=2\]                 
  done clear
  B)
  \[a=4,\,\,b=-2\]
  done clear
  C)
  \[a=-2,\,\,b=4\]                               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer146) If\[y={{x}^{n-1}}\log x\], then\[{{x}^{2}}{{y}_{2}}+(3-2n)x{{y}_{1}}\]is equal to
  A)
  \[-{{(n-1)}^{2}}y\]                           
  done clear
  B)
  \[{{(n-1)}^{2}}y\]
  done clear
  C)
  \[-{{n}^{2}}y\]                  
  done clear
  D)
  \[{{n}^{2}}y\]
  done clear
  View Answer play_arrow

• question_answer147) The length of latusrectum of the ellipse\[2{{x}^{2}}+{{y}^{2}}-8x+2y+7=0\], is
  A)
  \[\sqrt{2}\]                                        
  done clear
  B)
  \[2\]
  done clear
  C)
  \[8\]                                     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer148) The angle between the pair of tangents from the point \[\left( 1,\,\,\frac{1}{2} \right)\] to the circle\[{{x}^{2}}+{{y}^{2}}+4x+2y-4=0\], is
  A)
  \[{{\cos }^{-1}}\left( \frac{4}{5} \right)\]                               
  done clear
  B)
  \[{{\sin }^{-1}}\left( \frac{4}{5} \right)\]
  done clear
  C)
  \[{{\tan }^{-1}}\left( \frac{4}{5} \right)\]                               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer149) The value of\[\cos \left( \frac{\pi }{7} \right)\cos \left( \frac{4\pi }{7} \right)\cos \left( \frac{5\pi }{7} \right)\]is equal to
  A)
  \[\frac{1}{2}\]                                   
  done clear
  B)
  \[\frac{1}{4}\]
  done clear
  C)
  \[-\frac{1}{8}\]                                 
  done clear
  D)
  \[\frac{1}{8}\]
  done clear
  View Answer play_arrow

• question_answer150) The vertical poles, \[AB\] of length \[2\,\,m\] and \[CD\] of length \[20\,\,m\] are erected with base \[B\] and \[D\] respectively. It is given that distance between the poles is more than \[20\,\,m\] and \[(\angle ACB)=\frac{2}{77}\], then distance between the poles is
  A)
  \[68\,\,m\]                        
  done clear
  B)
  \[24\,\,m\]
  done clear
  C)
  \[72\,\,m\]                        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow