Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2011

done JCECE Engineering Solved Paper-2011 Total Questions - 150

• question_answer1) The dimension of \[\frac{p}{a}\] in the equation\[p=\frac{b-{{t}^{2}}}{ax}\] where \[p\] is pressure, \[x\] is distance and \[t\] is time are
  A)
  \[[ML{{T}^{-2}}]\]                           
  done clear
  B)
  \[[M{{T}^{-2}}]\]
  done clear
  C)
  \[[M{{L}^{3}}{{T}^{-2}}]\]                            
  done clear
  D)
   \[[L{{T}^{-3}}]\]
  done clear
  View Answer play_arrow

• question_answer2) A body moving with uniform acceleration describes \[12\,\,m\] in the third second of its motion and \[20\,\,m\] in the \[5th\] second. Find the velocity after \[10th\] second.
  A)
  \[40\,\,m/s\]                    
  done clear
  B)
  \[42\,\,m/s\]
  done clear
  C)
   \[52\,\,m/s\]                   
  done clear
  D)
   \[4\,\,m/s\]
  done clear
  View Answer play_arrow

• question_answer3) A ball rolls of the top of a stair way with a horizontal velocity\[u\,\,m{{s}^{-1}}\]. If the steps are \[h\] metre high and \[b\] metre wide, the ball will hit the edge of the nth step, where \[n\] is
  A)
  \[\frac{2hu}{g{{b}^{2}}}\]                                            
  done clear
  B)
  \[\frac{2h{{u}^{2}}}{g{{b}^{2}}}\]
  done clear
  C)
  \[\frac{2h{{u}^{2}}}{gb}\]                            
  done clear
  D)
   \[\frac{h{{u}^{2}}}{g{{b}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer4) A man slides down a light rope whose breaking strength is \[\eta \] times his weight. What should be his maximum acceleration so that the rope just not breaks?
  A)
  \[g(1-\eta )\]                    
  done clear
  B)
  \[\eta g\]
  done clear
  C)
   \[\frac{g}{1+\eta }\]                     
  done clear
  D)
   \[\frac{g}{1-\eta }\]
  done clear
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• question_answer5) The motor of an engine is rotating about its axis with an angular velocity of\[100\,\,rev/m\]. It comes to rest in\[15\,\,s\], after being switched off. Assuming constant angular deceleration. What are the numbers of revolutions made by it before coming to rest?
  A)
  \[12.5\]                               
  done clear
  B)
  \[40\]
  done clear
  C)
   \[32.6\]                                              
  done clear
  D)
   \[15.6\]
  done clear
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• question_answer6) By what percent the energy of a satellite has to be increased to shift it from an orbit of radius\[r\]to\[3r\]?
  A)
  \[22.3%\]                            
  done clear
  B)
  \[33.3%\]
  done clear
  C)
  \[66.7%\]                            
  done clear
  D)
   \[100%\]
  done clear
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• question_answer7) To maintain a rotar at uniform angular speed of\[200\,\,rad/s\], an engine needs to transmit a torque of\[180\,\,Nm\]. What is the power required by engine? (Assume efficiency of engine to be \[80%)\]
  A)
  \[36\,\,kW\]                      
  done clear
  B)
  \[18\,\,kW\]
  done clear
  C)
   \[45\,\,kW\]                     
  done clear
  D)
   \[54\,\,kW\]
  done clear
  View Answer play_arrow

• question_answer8) Two pendulum have time period \[T\] and \[\frac{5T}{4}\] they start \[SHM\] at the same time form the mean position. What will be the phase difference between them after the bigger pendulum completed one oscillation
  A)
  \[{{45}^{o}}\]                                    
  done clear
  B)
  \[{{90}^{o}}\]
  done clear
  C)
   \[{{60}^{o}}\]                                   
  done clear
  D)
   \[{{30}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer9) An open pipe of length \[33\,\,cm\] resonates with frequency of\[1000\,\,Hz\]. If the speed of sound is \[333\,\,m{{s}^{-1}}\], then this frequency is
  A)
   fundamental frequency of the pipe
  done clear
  B)
   third harmonic of the pipe
  done clear
  C)
    second harmonic of the pipe
  done clear
  D)
    fourth harmonic of the pipe
  done clear
  View Answer play_arrow

• question_answer10) Water rises to a height h in a capillary at the surface of earth on the surface of the moon the height of water column in the same capillary will be
  A)
  \[6h\]                                   
  done clear
  B)
  \[h/6\]
  done clear
  C)
   \[h\]                                    
  done clear
  D)
   \[zero\]
  done clear
  View Answer play_arrow

• question_answer11) The molar heat capacity in a process of a diatomic gas, if it does a work of \[Q/4\] when heat \[Q\] is supplied to it, is
  A)
  \[\frac{2}{5}R\]                                
  done clear
  B)
  \[\frac{10}{3}R\]
  done clear
  C)
   \[\frac{5}{3}R\]                                               
  done clear
  D)
   \[\frac{6}{5}R\]
  done clear
  View Answer play_arrow

• question_answer12) A black body has maximum energy at wavelength \[{{\lambda }_{m}}\] at temperature\[2000\,\,K\]. The corresponding wavelength at a temperature of \[3000\,\,K\] will be
  A)
  \[\frac{3}{2}{{\lambda }_{m}}\]                                
  done clear
  B)
  \[\frac{2}{3}{{\lambda }_{m}}\]
  done clear
  C)
  \[\frac{4}{9}{{\lambda }_{m}}\]                                
  done clear
  D)
   \[\frac{9}{4}{{\lambda }_{m}}\]
  done clear
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• question_answer13) The potential field of an electric field \[\mathbf{E}=(y\mathbf{i}+x\mathbf{j})\] is
  A)
  \[V=-(x+y)+\]constant
  done clear
  B)
  \[V=\]constant
  done clear
  C)
   \[V=-({{x}^{2}}+{{y}^{2}})+\]constant
  done clear
  D)
   \[V=-xy+\]constant
  done clear
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• question_answer14) The \[80\,\,\Omega \] galvanometer deflects full scale for a potentials of\[20\,\,mV\]. A voltmeter deflecting full scale of \[5\,\,V\] is to made using this galvanometer. We must connect
  A)
   a resistance of \[19.92\,\,k\Omega \] parallel to the galvanometer
  done clear
  B)
   assistance of \[19.92\,\,k\Omega \] in series with the galvanometer
  done clear
  C)
    a resistance of \[20\,\,k\Omega \] parallel to the galvanometer
  done clear
  D)
    a resistance of \[20\,\,k\Omega \] in series with galvanometer
  done clear
  View Answer play_arrow

• question_answer15) A current of \[1\,\,A\] is passed through a straight wire of length\[20\,\,m\]. The magnetic field at a point air at a distance of \[3\,\,m\] from either end of wire and lying on the axis of wire will be
  A)
  \[\frac{{{\mu }_{0}}}{2\pi }\]                                      
  done clear
  B)
  \[\frac{{{\mu }_{0}}}{4\pi }\]
  done clear
  C)
   \[\frac{{{\mu }_{0}}}{8\pi }\]                                     
  done clear
  D)
   \[zero\]
  done clear
  View Answer play_arrow

• question_answer16) A short bar magnet placed with its axis at \[{{30}^{o}}\] with a uniform external magnetic field of \[0.16\,\,T\] experience a torque of magnitude\[0.032\,\,J\]. The magnetic moment of the bar magnet will be
  A)
  \[0.23\,\,J{{T}^{-1}}\]                    
  done clear
  B)
  \[0.40\,\,J{{T}^{-1}}\]
  done clear
  C)
  \[0.80\,\,J{{T}^{-1}}\]                    
  done clear
  D)
   \[zero\]
  done clear
  View Answer play_arrow

• question_answer17) A coil has an area of \[0.05\,\,{{m}^{2}}\] and has \[800\] turns. After placing the coil in a magnetic field of strength \[4\times {{10}^{-5}}Wb{{m}^{-2}}\] perpendicular to the field, the coil is rotated through \[{{90}^{o}}\] in\[0.1\,\,s\]. The average emf induced is
  A)
  \[zero\]                                               
  done clear
  B)
  \[0.016\,\,V\]
  done clear
  C)
   \[0.01\,\,V\]                     
  done clear
  D)
   \[0.032\,\,V\]
  done clear
  View Answer play_arrow

• question_answer18) An alternating voltage (in volt) given by \[V=200\sqrt{2}\sin (100t)\] is connected to \[1\,\,\mu F\] capacitor through an \[AC\] ammeter. The reading of the ammeter will be
  A)
  \[10\,\,mA\]                     
  done clear
  B)
  \[20\,\,mA\]
  done clear
  C)
   \[40\,\,mA\]                    
  done clear
  D)
   \[80\,\,mA\]
  done clear
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• question_answer19) Instantaneous displacement current of \[1.0\,\,A\] in the space between the parallel plates of \[1\,\,\mu F\] capacitor can be established by changing potential difference of
  A)
  \[{{10}^{-6}}V/s\]                           
  done clear
  B)
  \[{{10}^{6}}V/s\]
  done clear
  C)
  \[{{10}^{-8}}V/s\]                           
  done clear
  D)
   \[{{10}^{8}}V/s\]
  done clear
  View Answer play_arrow

• question_answer20) The maximum magnification that can be obtained with a convex lens of focal length \[2.5\,\,cm\] is least distance of distinct vision is \[25\,\,cm\]
  A)
  \[10\]                                   
  done clear
  B)
  \[0.1\]
  done clear
  C)
   \[62.5\]                                              
  done clear
  D)
   \[11\]
  done clear
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• question_answer21) The magnifying power of an astronomical telescope is \[8\] and the distance between the two lenses is\[54\,\,cm\]. The focal length of eye lens and objective lens will be respectively
  A)
   6 cm and 48 cm               
  done clear
  B)
   48 cm and 6 cm
  done clear
  C)
    8 cm and 64 cm              
  done clear
  D)
    6 cm and 60 cm
  done clear
  View Answer play_arrow

• question_answer22) The path difference between two wave fronts emitted by coherent sources of wavelength \[5460\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\] is \[2.1\] micron. The phase difference between the wave fronts at that point is
  A)
  \[7.692\,\,rad\]                
  done clear
  B)
  \[7.692\,\,\pi \,\,rad\]
  done clear
  C)
   \[\frac{7.692}{\pi }rad\]                              
  done clear
  D)
   \[\frac{7.692}{3\pi }rad\]
  done clear
  View Answer play_arrow

• question_answer23) A photocell with a constant potential difference of \[V\] volt across it is illuminated by a point source from a distance of\[25\,\,cm\]. When the source is moved to a distance of\[1\,\,m\], the electrons emitted by the photocell
  A)
   carry 1/4th their previous energy
  done clear
  B)
   are 1/6th as numerous as before
  done clear
  C)
    are 1/4th as numerous as before
  done clear
  D)
    carry 1/4th their previous momentum
  done clear
  View Answer play_arrow

• question_answer24) When an electron in hydrogen atom is excited from its 4th to 5th stationary orbit, the change in angular momentum of electron is (Planck's constant\[h=6.6\times {{10}^{-34}}Js)\]
  A)
  \[4.16\times {{10}^{-34}}Js\]
  done clear
  B)
  \[3.32\times {{10}^{-34}}Js\]
  done clear
  C)
   \[1.05\times {{10}^{-34}}Js\]
  done clear
  D)
   \[2.08\times {{10}^{-34}}Js\]
  done clear
  View Answer play_arrow

• question_answer25) Let \[T\] be the mean life of a radioactive sample. \[75%\] of the active nuclei present in the sample initially will decay in time
  A)
  \[2T\]                                   
  done clear
  B)
  \[\frac{1}{2}(\ln 2)T\]
  done clear
  C)
   \[4T\]                                  
  done clear
  D)
   \[2(\ln 2)T\]
  done clear
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• question_answer26) A potential barrier of 0.50 V exists across a \[p-n\] junction. If the depletion region is \[5.0\times {{10}^{-7}}m\] wide, the strength of electric field in this region is
  A)
  \[1.0\times {{10}^{6}}V/m\]       
  done clear
  B)
  \[1.0\times {{10}^{5}}V/m\]
  done clear
  C)
   \[2.0\times {{10}^{5}}V/m\]      
  done clear
  D)
   \[2.0\times {{10}^{6}}V/m\]
  done clear
  View Answer play_arrow

• question_answer27) What is an \[AND\] gate?
  A)
   It has not equivalence to switching circuit
  done clear
  B)
   It is equivalent to series switching circuit
  done clear
  C)
    It is equivalent to parallel switching circuit
  done clear
  D)
   It is a mixture of series and parallel switching
  done clear
  View Answer play_arrow

• question_answer28) A parachutist, drops first freely from an aero plane for \[10\,\,s\] and then parachute opens out. Now he descends with a net retardation of\[2.5\,\,m/{{s}^{2}}\]. If. he bails out of the plane at a height of \[2495\,\,m\] and \[g=10\,\,m/{{s}^{2}}\], his velocity on reaching the ground will be
  A)
  \[5\,\,m/s\]                       
  done clear
  B)
  \[10\,\,m/s\]
  done clear
  C)
   \[15\,\,m/s\]                   
  done clear
  D)
   \[20\,\,m/s\]
  done clear
  View Answer play_arrow

• question_answer29) A particle is moving along a circular path with uniform speed. Through what angle does it angular velocity change when it completes half of the circular path?
  A)
  \[{{0}^{o}}\]                                      
  done clear
  B)
  \[{{45}^{o}}\]
  done clear
  C)
   \[{{180}^{o}}\]                                
  done clear
  D)
   \[{{360}^{o}}\]
  done clear
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• question_answer30) Tick out the wrong statement.
  A)
   Transverse waves can be generated in solids.
  done clear
  B)
   A system having ice floating on water has the same volume even after the ice is melted.
  done clear
  C)
   Heat radiations have the velocity of light.
  done clear
  D)
    Phase will not change when sound or light waves are reflected back.
  done clear
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• question_answer31) Two particles \[P\] and \[Q\] describe \[SHM\] of same amplitude\[a\], frequency \[v\] along the same Straight line. The maximum distance between the two particles is\[a\sqrt{2}\]. The initial phase difference between the particles is
  A)
  \[zero\]                                               
  done clear
  B)
  \[\pi /2\]
  done clear
  C)
  \[\pi /6\]                                             
  done clear
  D)
   \[\pi /3\]
  done clear
  View Answer play_arrow

• question_answer32) The magnitude of electric intensity \[E\] is such that an electron placed in it would experience an electrical force equal to its weight. \[E\] is given by
  A)
  \[mge\]                                               
  done clear
  B)
  \[\frac{e}{mg}\]
  done clear
  C)
   \[\frac{mg}{e}\]                                             
  done clear
  D)
   \[\frac{{{e}^{2}}g}{{{m}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer33) In the figure, charge and the potential difference across the 4uF capacitor will be nearly
  A)
  \[600\mu C,\,\,150\,\,V\]            
  done clear
  B)
  \[300\,\,\mu C,\,\,75\,\,V\]
  done clear
  C)
   \[800\,\,\mu C,\,\,200\,\,V\]    
  done clear
  D)
   \[580\,\,\mu C,\,\,145\,\,V\]
  done clear
  View Answer play_arrow

• question_answer34) A dip circle lies initially in the magnetic meridian. If it is now rotated through angle \[\theta \] in the horizontal plane, then tangent of the angle of dip is changed in the ratio
  A)
  \[1:\cos \theta \]                            
  done clear
  B)
  \[\cos \theta :1\]
  done clear
  C)
   \[1:\sin \theta \]                            
  done clear
  D)
   \[\sin \theta :1\]
  done clear
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• question_answer35) A \[5\,\,cm\] long solenoid having \[10\,\,\Omega \] resistance and \[5\,\,mH\] inductance is joined to a \[10\,\,V\] battery. At steady state, the current through the solenoid  (in ampere) will be
  A)
  \[5\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
   \[1\]                                    
  done clear
  D)
   \[zero\]
  done clear
  View Answer play_arrow

• question_answer36) A convex lens makes a real image \[4\,\,cm\] long on a screen. When the lens is shifted to a new position without disturbing the object, we again get a real image on the screen which is \[16\,\,cm\] tall. The length of the object must be
  A)
  \[\frac{1}{4}cm\]                             
  done clear
  B)
  \[8\,\,cm\]
  done clear
  C)
   \[12\,\,cm\]                     
  done clear
  D)
   \[20\,\,cm\]
  done clear
  View Answer play_arrow

• question_answer37) For a particle of mass \[m\] enclosed in a one-dimensional box of length\[L\], the de-Broglie concept would lead to stationary waves, with nodes at the two ends. The energy values allowed for such a system (with \[n\] as integer) will be
  A)
  \[\frac{{{h}^{2}}}{8m{{L}^{2}}}{{n}^{2}}\]                             
  done clear
  B)
  \[\frac{{{h}^{2}}}{4m{{L}^{2}}}{{n}^{2}}\]
  done clear
  C)
  \[\frac{h}{4mL}n\]                          
  done clear
  D)
   \[\frac{{{h}^{2}}}{4m{{L}^{2}}}{{n}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer38) If no is the original mass of the substance of half-life period\[{{t}_{1/5}}=5\,\,yrs\], then the amount of substance left after 15 days is
  A)
  \[\frac{{{N}_{0}}}{8}\]                                   
  done clear
  B)
  \[\frac{{{N}_{0}}}{16}\]
  done clear
  C)
   \[\frac{{{N}_{0}}}{2}\]                                  
  done clear
  D)
   \[\frac{{{N}_{0}}}{4}\]
  done clear
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• question_answer39) A doubled layered wall has layer\[A\], \[10\,\,cm\] thick and B, \[20\,\,cm\] thick. The thermal conductivity of \[A\] is thrice that of\[B\]. In the steady state, the temperature difference across the wall is\[{{35}^{o}}C\]. The temperature difference across the layer \[A\] is
  A)
  \[{{28}^{o}}C\]                 
  done clear
  B)
  \[{{14}^{o}}C\]
  done clear
  C)
   \[{{7}^{o}}C\]                                  
  done clear
  D)
   \[{{5}^{o}}C\]
  done clear
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• question_answer40) The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is
  A)
  \[\sqrt{3}v\]                                      
  done clear
  B)
  \[\sqrt{2}v\]
  done clear
  C)
   \[\sqrt{5}v\]                                     
  done clear
  D)
   \[\sqrt{12}v\]
  done clear
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• question_answer41) Power supplied to a particle of mass \[2\,\,kg\] varies with time as\[P=\frac{3{{t}^{2}}}{2}W\]. Here \[t\] is in second. If velocity of particle at \[t=0\] is\[v=0\], the velocity of particle at time\[t=2\,\,s\]  will be
  A)
  \[1\,\,m/s\] 
  done clear
  B)
  \[4\,\,m/s\]
  done clear
  C)
   \[2\,\,m/s\]
  done clear
  D)
   \[2\sqrt{2}\,\,m/s\]
  done clear
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• question_answer42) A particle is projected from the ground with an initial speed of \[v\] at an angle \[\theta \] with horizontally. The average velocity of the particle between its point of projection and highest point of trajectory is
  A)
  \[\frac{v}{2}\sqrt{1+2{{\cos }^{2}}\theta }\]       
  done clear
  B)
  \[\frac{v}{2}\sqrt{1+2{{\cos }^{2}}\theta }\]
  done clear
  C)
   \[\frac{v}{2}\sqrt{1+3{{\cos }^{2}}\theta }\]      
  done clear
  D)
   \[v\cos \theta \]
  done clear
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• question_answer43) Given \[\sigma \] is the compressibility of water, \[p\] is the density of water and \[k\] is the bulk modulus of water. What is the energy density of water at the bottom of a lake \[h\] metre deep?
  A)
  \[\frac{1}{2}\sigma {{(h\rho g)}^{2}}\]                   
  done clear
  B)
  \[\frac{1}{2}\sigma (h\rho g)\]
  done clear
  C)
   \[\frac{1}{2}\frac{h\rho g}{\sigma }\]                    
  done clear
  D)
   \[\frac{h\rho g}{\sigma }\]
  done clear
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• question_answer44) An ideal gas heat engine operates in a Carnot cycle between \[{{227}^{o}}C\] and\[{{127}^{o}}C\]. It absorbs \[6.0\times {{10}^{4}}\,\,cal\] at the higher temperature. The amount of heat converted into work is equal to
  A)
  \[4.8\times {{10}^{4}}cal\]                          
  done clear
  B)
  \[3.5\times {{10}^{4}}cal\]
  done clear
  C)
   \[1.6\times {{10}^{4}}cal\]                         
  done clear
  D)
   \[1.2\times {{10}^{4}}cal\]
  done clear
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• question_answer45) The latent heat of vaporisation of water is\[2240\,\,J\]. If the work done in the process of vaporisation of \[1\,\,g\] is\[168\,\,J\], then increases in internal energy is
  A)
  \[2408\,\,J\]                      
  done clear
  B)
  \[2240\,\,J\]
  done clear
  C)
   \[2072\,\,J\]                     
  done clear
  D)
   \[1904\,\,J\]
  done clear
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• question_answer46) A body dropped from the top of a tower covers a distance \[7x\] in the last second of its journey, where \[x\] is the distance; covered in first second. How much time does it take to reach the ground?
  A)
  \[3\,\,s\]                                             
  done clear
  B)
  \[4\,\,s\]
  done clear
  C)
   \[5\,\,s\]                                            
  done clear
  D)
   \[6\,\,s\]
  done clear
  View Answer play_arrow

• question_answer47) A body just dropped from a tower explodes into two pieces of equal mass in mid-air. Which of the following is not possible?
  A)
   Each part will follow parabolic path
  done clear
  B)
   Only one part will follow parabolic path
  done clear
  C)
    Both parts move along a vertical line
  done clear
  D)
    One part reaches the ground earlier than the other
  done clear
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• question_answer48) Moment of inertia of a uniform circular disc about a diameter is\[I\]. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be
  A)
  \[5\,\,I\]                                             
  done clear
  B)
  \[3\,\,I\]
  done clear
  C)
   \[6\,\,I\]                                            
  done clear
  D)
   \[4\,\,I\]
  done clear
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• question_answer49) Two sources \[A\] and \[B\] are sounding notes of frequency\[680\,\,Hz\]. A listener moves from \[A\] to \[B\] with a constant velocity\[u\]. If the speed of sound\[340\,\,m/s\], what must be the value of \[u\] so that he hears \[10\] beats per second?
  A)
  \[2.0\,\,m/s\]                   
  done clear
  B)
  \[2.5\,\,m/s\]
  done clear
  C)
   \[3.0\,\,m/s\]                  
  done clear
  D)
   \[3.5\,\,m/s\]
  done clear
  View Answer play_arrow

• question_answer50) A current of \[1\,\,A\] flows in a circular area of wire which subtends an angle of \[\left( \frac{3\pi }{4} \right)rad\] at its centre, whose radius is\[R\]. The magnetic induction \[B\] at the centre is
  A)
  \[\frac{{{\mu }_{0}}I}{R}\]                                           
  done clear
  B)
   \[\frac{{{\mu }_{0}}I}{2R}\]
  done clear
  C)
   \[\frac{2{{\mu }_{0}}I}{R}\]                       
  done clear
  D)
   \[\frac{3{{\mu }_{0}}I}{8R}\]
  done clear
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• question_answer51) Which of the following compounds corresponds to van't Hoff factor \[(i)\] to be equal to \[2\] for dilute solution?
  A)
  \[{{K}_{2}}S{{O}_{4}}\]                 
  done clear
  B)
  \[NaHS{{O}_{4}}\]
  done clear
  C)
  \[Sugar\]                            
  done clear
  D)
  \[MgS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer52) \[0.1\,\,M\,\,NaCI\] and \[0.1\,\,M\,\,C{{H}_{3}}COOH\] are kept in separate containers. If their osmotic pressures are \[{{p}_{1}}\] and \[{{p}_{2}}\] respectively then what is the correct statement?
  A)
  \[{{p}_{1}}>{{p}_{2}}\]                  
  done clear
  B)
  \[{{p}_{1}}={{p}_{2}}\]
  done clear
  C)
  \[{{p}_{1}}<{{p}_{2}}\]                  
  done clear
  D)
  \[{{p}_{1}}={{p}_{2}}=0\,\,atm\]
  done clear
  View Answer play_arrow

• question_answer53) Primary, secondary and tertiary alcohols may be distinguished by
  A)
   Fehling solution              
  done clear
  B)
   Victor-Meyer test
  done clear
  C)
   Hofmann test                  
  done clear
  D)
   Beilstein test
  done clear
  View Answer play_arrow

• question_answer54) Which of the following will respond to Cannizaro's reaction?
  A)
   \[2,\,\,2-\]dimethylpropanal
  done clear
  B)
   Acetaldehyde
  done clear
  C)
   Propionaldehyde
  done clear
  D)
   Cinnamaldehyde
  done clear
  View Answer play_arrow

• question_answer55) Which one of the following will increase the voltage of the cell? \[Sn(s)+2A{{g}^{+}}(aq)\xrightarrow{{}}S{{n}^{2+}}+(aq)+2Ag(s)\]
  A)
   Increase in the size of silver rod
  done clear
  B)
   Increasing the size of plate
  done clear
  C)
   Increase in the concentration of \[A{{g}^{+}}\] ions
  done clear
  D)
   Increase in the concentration of \[S{{n}^{2+}}\] ions
  done clear
  View Answer play_arrow

• question_answer56) Which among the following can be purified by steam distillation?
  A)
   Phenol                
  done clear
  B)
   Aniline
  done clear
  C)
   Benzoic acid                     
  done clear
  D)
   \[p-\]nitrophenol
  done clear
  View Answer play_arrow

• question_answer57) For a chemical reaction\[A+BC\], the thermodynamic equilibrium constant \[{{K}_{p}}\] is
  A)
   in\[at{{m}^{-2}}\]                          
  done clear
  B)
   in\[at{{m}^{-3}}\]
  done clear
  C)
   in\[at{{m}^{-1}}\]                          
  done clear
  D)
   dimensionless
  done clear
  View Answer play_arrow

• question_answer58) If the equivalent, weight of a trivalent metal is \[32.7\], the molecular weight of its chloride is
  A)
  \[68.2\]                               
  done clear
  B)
  \[103.7\]
  done clear
  C)
  \[204.6\]                             
  done clear
  D)
  \[32.7\]
  done clear
  View Answer play_arrow

• question_answer59) Conjugate base of hydrazoic acid is
  A)
  \[HN_{3}^{-}\]                 
  done clear
  B)
  \[N_{2}^{-}\]
  done clear
  C)
  \[N_{3}^{-}\]                                    
  done clear
  D)
  \[{{N}^{3-}}\]
  done clear
  View Answer play_arrow

• question_answer60) The geometrical arrangement and shape of\[I_{3}^{-}\] are respectively
  A)
   trigonal bipyramidal geometry, linear shape
  done clear
  B)
   hexagonal geometry, T-shape
  done clear
  C)
   triangular planar geometry, triangular shape
  done clear
  D)
   tetrahedral geometry, pyramidal shape
  done clear
  View Answer play_arrow

• question_answer61) Sodium reacts with water more vigorously than \[Li\] because it has
  A)
   higher atomic mass
  done clear
  B)
   more electropositive character
  done clear
  C)
   metallic nature
  done clear
  D)
   more electronegative character
  done clear
  View Answer play_arrow

• question_answer62) When sodium is treated with sufficient oxygen/air, the product obtained is
  A)
  \[N{{a}_{2}}O\]                
  done clear
  B)
  \[N{{a}_{2}}{{O}_{2}}\]
  done clear
  C)
  \[Na{{O}_{2}}\]                
  done clear
  D)
  \[NaO\]
  done clear
  View Answer play_arrow

• question_answer63) Gallium arsenide is purified by
  A)
   froth floatation process
  done clear
  B)
   van-Arkel method
  done clear
  C)
   zone refining method
  done clear
  D)
    electrolytic method
  done clear
  View Answer play_arrow

• question_answer64) Which ion has the lowest radius from the following ions?
  A)
  \[N{{a}^{+}}\]                                   
  done clear
  B)
  \[M{{g}^{2+}}\]
  done clear
  C)
  \[A{{l}^{3+}}\]                                  
  done clear
  D)
  \[S{{i}^{4+}}\]
  done clear
  View Answer play_arrow

• question_answer65) The extraction of which of the following metals involves bessemerisation?
  A)
   Iron                                      
  done clear
  B)
   Copper
  done clear
  C)
   Aluminium       
  done clear
  D)
   Silver
  done clear
  View Answer play_arrow

• question_answer66) Terylene is made by polymerisation of terephthalic acid with
  A)
   ethylene glycol               
  done clear
  B)
   phenol
  done clear
  C)
   ethanol              
  done clear
  D)
   catechol
  done clear
  View Answer play_arrow

• question_answer67) Treatment of ammonia with excess of ethyl iodide will yield
  A)
   diethylamine
  done clear
  B)
   ethylamine
  done clear
  C)
   triethylamine
  done clear
  D)
   tetraethylammonium iodide
  done clear
  View Answer play_arrow

• question_answer68) In the combustion of \[2.0\,\,g\] \[\text{of}\] methane, \[25\,\,kcal\] heat is liberated. Heat of combustion of methane would be
  A)
  \[150\,\,kcal\]                  
  done clear
  B)
  \[200\,\,kcal\]
  done clear
  C)
  \[250\,\,kcal\]                  
  done clear
  D)
  \[350\,\,kcal\]
  done clear
  View Answer play_arrow

• question_answer69) Arsenic sulphide is a negative sol. The reagent with least precipitating power is
  A)
  \[AlC{{l}_{3}}\]                 
  done clear
  B)
  \[NaCl\]
  done clear
  C)
  \[Ca{{F}_{2}}\]                 
  done clear
  D)
   glucose
  done clear
  View Answer play_arrow

• question_answer70) Which of the following salt when dissolved in water gets hydrolysed?
  A)
  \[NaCl\]                              
  done clear
  B)
  \[N{{H}_{4}}Cl\]
  done clear
  C)
  \[KCl\]                                 
  done clear
  D)
  \[N{{a}_{2}}S{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer71) \[20\,\,mL\] of a \[HCl\] solution exactly neutralises \[40\,\,mL\] of \[0.005\,\,N\,\,NaOH\] solution. The\[pH\] of\[HCl\]. solution is
  A)
  \[2.5\]                                  
  done clear
  B)
  \[2.0\]
  done clear
  C)
  \[1.5\]                                  
  done clear
  D)
  \[1\]
  done clear
  View Answer play_arrow

• question_answer72) Which of the following is used for inducing sleep?
  A)
   Paracetamol
  done clear
  B)
   Chloroquine
  done clear
  C)
   Bithional
  done clear
  D)
   Barbituric acid derivatives
  done clear
  View Answer play_arrow

• question_answer73) Which of the following acids has the smallest dissociation constant?
  A)
  \[C{{H}_{3}}CHFCOOH\]               
  done clear
  B)
  \[FC{{H}_{2}}C{{H}_{2}}COOH\]
  done clear
  C)
  \[BrC{{H}_{2}}C{{H}_{2}}COOH\]              
  done clear
  D)
  \[C{{H}_{3}}CBrCOOH\]
  done clear
  View Answer play_arrow

• question_answer74) Hydrolysis of benzonitrile by dilute \[HCl\] yields
  A)
   aniline                 
  done clear
  B)
   benzoic acid
  done clear
  C)
   berizamide       
  done clear
  D)
   benzaldehyde
  done clear
  View Answer play_arrow

• question_answer75) Anti-Markownikoff's addition of \[HBr\] is not observed in
  A)
   propene            
  done clear
  B)
   1-butene
  done clear
  C)
   but-2-ene         
  done clear
  D)
   pent-2-ene
  done clear
  View Answer play_arrow

• question_answer76) Kjeldahl's method can be used for estimation of nitrogen in
  A)
  \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}\]
  done clear
  B)
   pyridine
  done clear
  C)
  \[{{C}_{6}}{{H}_{5}}-N=N-{{C}_{6}}{{H}_{5}}\]
  done clear
  D)
  \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer77) How many electrons in \[19\,\,K\] have\[n=3;\,\,l=0?\]
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[4\]                                     
  done clear
  D)
  \[3\]
  done clear
  View Answer play_arrow

• question_answer78) Metallic bond is
  A)
   similar to ionic bond
  done clear
  B)
   similar to covalent bond
  done clear
  C)
   neither similar to ionic nor covalent bond
  done clear
  D)
   formed by the movement of positively charged spheres in a sea of electrons
  done clear
  View Answer play_arrow

• question_answer79) Which of the following is not a Lewis base?
  A)
  \[C{{N}^{-}}\]                                   
  done clear
  B)
  \[ROH\]
  done clear
  C)
  \[N{{H}_{3}}\]                                  
  done clear
  D)
  \[AlC{{l}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer80) Hydrogen can have oxidation number/s of
  A)
  \[-1\]only          
  done clear
  B)
   \[+1\]only
  done clear
  C)
  \[0\]only                             
  done clear
  D)
  \[-1,\,\,0,\,\,+1\]
  done clear
  View Answer play_arrow

• question_answer81) \[250\,\,mL\] of a sodium carbonate solution contains \[2.65\,\,g\] of\[N{{a}_{2}}C{{O}_{3}}\]. If \[10\,\,mL\] of this solution is diluted to\[1\,\,L\], what is the concentration of the resultant solution? (Mol. wt. of\[N{{a}_{2}}C{{O}_{3}}=106)\]
  A)
  \[0.1\,\,M\]                       
  done clear
  B)
  \[0.001\,\,M\]
  done clear
  C)
  \[0.01\,\,M\]                    
  done clear
  D)
  \[{{10}^{-4}}M\]
  done clear
  View Answer play_arrow

• question_answer82) At constant temperature, in a given mass of an ideal gas
  A)
   the ratio of pressure and volume always remains constant
  done clear
  B)
   volume always remains constant
  done clear
  C)
   pressure always remains Constant
  done clear
  D)
   the product of pressure and volume always remains constant
  done clear
  View Answer play_arrow

• question_answer83) The rate of the reaction intermediates can be determined by the study of
  A)
   catalyst effects
  done clear
  B)
   concentration of the reactants
  done clear
  C)
   temperature effects
  done clear
  D)
    solvent effects
  done clear
  View Answer play_arrow

• question_answer84) Order of reaction is decided by
  A)
   temperature
  done clear
  B)
   mechanism of reaction
  done clear
  C)
   molecularity
  done clear
  D)
   pressure
  done clear
  View Answer play_arrow

• question_answer85) Which of the following conditions will always lead to a non-spontaneous change?
  A)
   \[+ve\Delta H\] and\[+ve\Delta S\]
  done clear
  B)
   \[-ve\Delta H\]and\[-ve\Delta S\]
  done clear
  C)
  \[+ve\Delta H\] and\[-ve\Delta S\]
  done clear
  D)
  \[-ve\Delta H\]and\[+ve\Delta S\]
  done clear
  View Answer play_arrow

• question_answer86) The passage of current liberates \[{{H}_{2}}\] at cathode and \[C{{l}_{2}}\] at anode. The solution is
  A)
   copper chloride in water
  done clear
  B)
   \[NaCl\] in water
  done clear
  C)
   ferric chloride in water
  done clear
  D)
   \[AuC{{l}_{3}}\] in water
  done clear
  View Answer play_arrow

• question_answer87) Compounds with \[{{C}_{4}}{{H}_{11}}N\] as molecular formula can exhibit
  A)
   position isomerism
  done clear
  B)
   metamerism
  done clear
  C)
   functional isomerism
  done clear
  D)
   All the three
  done clear
  View Answer play_arrow

• question_answer88) Which of the following species is nucleophile?
  A)
  \[\overset{+}{\mathop{N}}\,{{O}_{2}}\]                                              
  done clear
  B)
  \[:C{{X}_{2}}\]
  done clear
  C)
  \[:\overset{\bullet \,\,\,\bullet }{\mathop{NH_{2}^{-}}}\,\]                        
  done clear
  D)
  \[\bullet C{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer89) Which of the following carbocation is most stable?
  A)
  \[C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]                           
  done clear
  B)
  \[C{{H}_{2}}=\overset{+}{\mathop{C}}\,H\]
  done clear
  C)
  \[CH\equiv {{C}^{+}}\]                  
  done clear
  D)
  \[{{C}_{6}}H_{5}^{+}\]
  done clear
  View Answer play_arrow

• question_answer90) Brown colour in \[HN{{O}_{3}}\] can be removed by
  A)
   adding \[Mg\] powder
  done clear
  B)
   boiling the acid
  done clear
  C)
   passing \[N{{H}_{3}}\] through acid
  done clear
  D)
   passing air through warm acid
  done clear
  View Answer play_arrow

• question_answer91) What products are expected from the disproportionation reaction of hypochlorous acid?
  A)
  \[HCl{{O}_{3}}\]and\[C{{l}_{2}}O\]          
  done clear
  B)
  \[HCl{{O}_{2}}\]and\[HCl{{O}_{4}}\]
  done clear
  C)
  \[HCl\]and\[C{{l}_{2}}O\]            
  done clear
  D)
  \[HCl\]and\[HCl{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer92) Which of the following is not a wax?
  A)
   Myricyl palmitate           
  done clear
  B)
   Tripalmitin
  done clear
  C)
   Myricyl cerotate             
  done clear
  D)
   Cetyl palmitate
  done clear
  View Answer play_arrow

• question_answer93) Which of the following ions forms most stable complex compound?
  A)
  \[F{{e}^{3+}}\]                                 
  done clear
  B)
  \[M{{n}^{2+}}\]
  done clear
  C)
  \[N{{i}^{2+}}\]                                  
  done clear
  D)
  \[C{{u}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer94) Silver plating is carried out from which of the following?
  A)
  \[AgN{{O}_{3}}\]                             
  done clear
  B)
  \[AgCl\]
  done clear
  C)
  \[K[Ag{{(CN)}_{2}}]\]    
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer95) Which one of the following is an example of non-typical transition elements?
  A)
  \[Li,\,\,K,\,\,Na\]                            
  done clear
  B)
  \[Be,\,\,Al,\,\,Pb\]
  done clear
  C)
  \[Zn,\,\,Cd,\,\,Hg\]                        
  done clear
  D)
  \[Ba,\,\,Ga,\,\,Sr\]
  done clear
  View Answer play_arrow

• question_answer96) In the reaction,\[{{C}_{6}}{{H}_{6}}\xrightarrow[AlC{{l}_{3}}]{C{{H}_{3}}Cl}A\xrightarrow{KMn{{O}_{4}}}B\], \[B\]is
  A)
   benzoic acid                     
  done clear
  B)
   benzoyl chloride
  done clear
  C)
   benzaldehyde                 
  done clear
  D)
   chlorobenzene
  done clear
  View Answer play_arrow

• question_answer97) The reaction,\[{{C}_{6}}{{H}_{5}}OH\xrightarrow[Pyridine]{C{{H}_{3}}COCl}{{C}_{6}}{{H}_{5}}COC{{H}_{3}}\]is called
  A)
   Reimer-Tiemann reaction
  done clear
  B)
   Schotten-Baumann reaction
  done clear
  C)
   acetylation
  done clear
  D)
   benzoylation
  done clear
  View Answer play_arrow

• question_answer98) Which of the following enzymes is not useful in the digestion of proteins?
  A)
   Chymotripsin                   
  done clear
  B)
   Pepsin
  done clear
  C)
   Tripsin                 
  done clear
  D)
   Lipase
  done clear
  View Answer play_arrow

• question_answer99) Which are isomers?
  A)
   Ethyl alcohol and dimethyl ether
  done clear
  B)
   Acetone and acetaldehyde
  done clear
  C)
   Propionic acid and propanone
  done clear
  D)
   Methyl alcohol and dimethyl ether
  done clear
  View Answer play_arrow

• question_answer100) The dative bond is present in
  A)
  \[N{{H}_{3}}\]                                  
  done clear
  B)
  \[S{{O}_{3}}\]
  done clear
  C)
  \[PC{{l}_{5}}\]                                  
  done clear
  D)
  \[B{{F}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer101) The sum of \[i-2-3i+4...\] up to \[100\] terms, where\[i=\sqrt{-1}\]is
  A)
  \[50(1-i)\]                           
  done clear
  B)
  \[25i\]
  done clear
  C)
  \[25(1+i)\]                          
  done clear
  D)
  \[100(1-i)\]
  done clear
  View Answer play_arrow

• question_answer102) In a college examination, a candidate is required to answer \[6\] out of \[10\] questions which are divided into sections each containing \[5\] questions. Further the candidate is not permitted to attempt more than \[4\] questions from either of the section. The number of ways in which he can make up a choice of \[6\] questions, is
  A)
  \[200\]                                 
  done clear
  B)
  \[150\]
  done clear
  C)
  \[100\]                                 
  done clear
  D)
  \[50\]
  done clear
  View Answer play_arrow

• question_answer103) For the equations\[x+2y+3z=1\],\[2x+y+3z=2\], \[5x+5y+9z=4\]
  A)
   there is only one solution
  done clear
  B)
   there exists infinitely many solution
  done clear
  C)
   there is no solution
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer104) If\[a\ne p,\,\,b\ne q,\,\,c\ne r\]and\[\left| \begin{matrix}    p & b & c  \\    a & q & c  \\    a & b & r  \\ \end{matrix} \right|=0\]. Then, the value of\[\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}\]is
  A)
  \[0\]                                     
  done clear
  B)
  \[1\]
  done clear
  C)
  \[-1\]                                    
  done clear
  D)
  \[2\]
  done clear
  View Answer play_arrow

• question_answer105) If\[\tan (\pi cos\theta )=cot(\pi sin\theta )\], then the value\[(s)\] of\[\cos \left( \theta -\frac{\pi }{4} \right)\]is/are
  A)
  \[\frac{1}{2}\]                                   
  done clear
  B)
  \[\frac{1}{\sqrt{2}}\]
  done clear
  C)
  \[\pm \frac{1}{2\sqrt{2}}\]                         
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer106) Form the top of a light house \[60\,\,m\] high with its base at the sea level, the angle of depression of a boat is\[{{15}^{o}}\]. The distance of the boat form the foot of the light house is
  A)
  \[\left( \frac{\sqrt{3}-1}{\sqrt{3}+1} \right)60\,\,m\]      
  done clear
  B)
  \[\left( \frac{\sqrt{3}+1}{\sqrt{3}-1} \right)60\,\,m\]
  done clear
  C)
  \[\left( \frac{\sqrt{3}+1}{\sqrt{3}-1} \right)m\]                 
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer107) Three lines \[px+qy+r=0,\,\,qx+ry+p=0\] and \[rx+py+q=0\] are concurrent, if
  A)
  \[p+q+r=0\]
  done clear
  B)
  \[{{p}^{2}}+{{q}^{2}}+{{r}^{2}}=pq+qr+rp\]
  done clear
  C)
  \[{{p}^{3}}+{{q}^{3}}+{{r}^{3}}=3pqr\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer108) Find the angle between the lines represented by the equation\[{{x}^{2}}-2pxy+{{y}^{2}}=0\]
  A)
  \[{{\cos }^{-1}}(p)\]                       
  done clear
  B)
  \[{{\sec }^{-1}}(p)\]
  done clear
  C)
  \[{{\sec }^{-1}}(-p)\]                      
  done clear
  D)
  \[{{\sec }^{-1}}(\pm p)\]
  done clear
  View Answer play_arrow

• question_answer109) The length of the chord of the parabola \[{{x}^{2}}=4ay\] passing through the vertex and having slope \[\tan \alpha \] is
  A)
  \[4a\cos \text{ec}\alpha \cdot \cot \alpha \]      
  done clear
  B)
  \[4a\tan \alpha \cdot \sec \alpha \]
  done clear
  C)
  \[4a\cos \alpha \cdot \cot \alpha \]        
  done clear
  D)
  \[4a\sin \alpha \cdot \tan \alpha \]
  done clear
  View Answer play_arrow

• question_answer110) If any tangent to the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] intercepts equal lengths I on the axes, then equals to
  A)
  \[{{a}^{2}}+{{b}^{2}}\]                  
  done clear
  B)
  \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
  done clear
  C)
  \[{{({{a}^{2}}+{{b}^{2}})}^{2}}\]                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer111) If the normal at \[\left( ct,\,\,\frac{c}{t} \right)\] on the curve\[xy={{c}^{2}}\] meets the curve again in\[V\] , then
  A)
  \[t'=\frac{-1}{{{t}^{3}}}\]                             
  done clear
  B)
  \[t'=\frac{-1}{t}\]
  done clear
  C)
  \[t'=\frac{1}{{{t}^{2}}}\]                               
  done clear
  D)
  \[t{{'}^{2}}=\frac{-1}{{{t}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer112) The line \[\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}\] intersects the curve\[xy=c,\,\,z=0\], if \[c\] equals to
  A)
  \[\pm 1\]                                            
  done clear
  B)
  b)\[\pm \frac{1}{3}\]
  done clear
  C)
  \[\pm \sqrt{5}\]                                              
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer113) If\[f(x)=\frac{1-x}{1+x}\], the domain of\[{{f}^{-1}}(x)\]is
  A)
  \[R\]                                     
  done clear
  B)
  \[R-\{-1\}\]
  done clear
  C)
  \[(-\infty ,\,\,-1)\]                          
  done clear
  D)
  \[(-1,\,\,\infty )\]
  done clear
  View Answer play_arrow

• question_answer114) If\[f'(2)=2\],\[f''(2)=1\], then\[\underset{x\to 2}{\mathop{\lim }}\,\frac{2{{x}^{2}}-4f'(x)}{x-2}\] is
  A)
  \[4\]                                     
  done clear
  B)
  \[0\]
  done clear
  C)
  \[2\]                                     
  done clear
  D)
  \[\infty \]
  done clear
  View Answer play_arrow

• question_answer115) A function is denned as follows\[f(x)=\left\{ \begin{matrix}    {{x}^{m}}\sin \left( \frac{1}{x} \right), & x\ne 0  \\    0, & x=0  \\ \end{matrix} \right\}\]what condition should be imposed on m, so that \[f(x)\] may be continuous\[x=0?\]
  A)
  \[m>0\]                               
  done clear
  B)
  \[m<0\]
  done clear
  C)
  \[m=0\]                               
  done clear
  D)
   any value of\[m\]
  done clear
  View Answer play_arrow

• question_answer116) The value of\[\lim {{(\cos x+a\sin bx)}^{1/x}}\]is
  A)
  \[1\]                                     
  done clear
  B)
  \[ab\]
  done clear
  C)
  \[{{e}^{ab}}\]                                   
  done clear
  D)
  \[{{e}^{b/a}}\]
  done clear
  View Answer play_arrow

• question_answer117) \[\int{{{e}^{x}}}\left( \frac{x-1}{{{(x+1)}^{3}}} \right)dx\]
  A)
  \[\frac{{{e}^{x}}}{x+1}+C\]                         
  done clear
  B)
  \[\frac{{{e}^{x}}}{{{(x+1)}^{2}}}+C\]
  done clear
  C)
  \[\frac{-{{e}^{x}}}{(x+1)}+C\]                    
  done clear
  D)
  \[\frac{-{{e}^{x}}}{{{(x+1)}^{2}}}+C\]
  done clear
  View Answer play_arrow

• question_answer118) For which of the following values of\[m\], is the area of the region bounded by the curve \[y=x-{{x}^{2}}\] and the line \[y=mx\] equals\[9/2\].
  A)
  \[-4\]                                    
  done clear
  B)
  \[3\]
  done clear
  C)
  \[2\]                                     
  done clear
  D)
  \[4\]
  done clear
  View Answer play_arrow

• question_answer119) Three numbers are chosen from \[1\] to\[30\]. Find the probability that they are not consecutive.
  A)
  \[\frac{16}{81}\]                                              
  done clear
  B)
  \[\frac{144}{145}\]
  done clear
  C)
  \[\frac{80}{145}\]                                            
  done clear
  D)
  \[\frac{65}{81}\]
  done clear
  View Answer play_arrow

• question_answer120) If\[\frac{1+4p}{p},\,\,\frac{1-p}{2},\,\,\frac{1-2p}{2}\]are probabilities of three mutually exclusive events, then
  A)
  \[\frac{1}{3}\le p\le \frac{1}{2}\]                              
  done clear
  B)
  \[\frac{1}{2}\le p\le \frac{2}{3}\]
  done clear
  C)
  \[\frac{1}{6}\le p\le \frac{1}{2}\]                              
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer121) A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in nth second to the distance covered in a n second is
  A)
  \[\frac{2}{n}-\frac{1}{{{n}^{2}}}\]                            
  done clear
  B)
  \[\frac{1}{{{n}^{2}}}-\frac{1}{n}\]
  done clear
  C)
  \[\frac{2}{{{n}^{2}}}-\frac{1}{n}\]                            
  done clear
  D)
  \[\frac{2}{n}+\frac{1}{{{n}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer122) The equation \[{{x}^{3}}-3x+4=0\] has only one real root. What is its first approximate value as obtained by the method of false position in\[(-3,\,\,-2)\]?
  A)
  \[-2.125\]                           
  done clear
  B)
  \[2.125\]
  done clear
  C)
  \[-2.812\]                           
  done clear
  D)
  \[2.812\]
  done clear
  View Answer play_arrow

• question_answer123) If\[z+{{z}^{-1}}=1\], then \[{{z}^{100}}+{{z}^{-100}}\] is equal to
  A)
  \[i\]                                       
  done clear
  B)
  \[-i\]
  done clear
  C)
  \[1\]                                     
  done clear
  D)
  \[-1\]
  done clear
  View Answer play_arrow

• question_answer124) If \[a,\,\,b,\,\,c\] are in\[G\,\,P\], then the equations \[a{{x}^{2}}+2bx+c=0\] and \[d{{x}^{2}}+2ex+f=0\] have a common root, if\[\frac{d}{a},\,\,\frac{e}{b},\,\,\frac{f}{c}\]are in
  A)
  \[AP\]                                  
  done clear
  B)
  \[GP\]
  done clear
  C)
  \[HP\]                                  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer125) If the roots of the equation\[\frac{1}{x+a}+\frac{1}{x+b}=\frac{1}{c}\] are equal in magnitude but opposite in sign, then their product is
  A)
  \[\frac{1}{2}({{a}^{2}}+{{b}^{2}})\]                          
  done clear
  B)
  \[-\frac{1}{2}({{a}^{2}}+{{b}^{2}})\]
  done clear
  C)
  \[\frac{1}{2}ab\]                                              
  done clear
  D)
  \[-\frac{1}{2}ab\]
  done clear
  View Answer play_arrow

• question_answer126) The coefficient of \[y\] in expansion of\[{{\left( {{y}^{2}}+\frac{c}{y} \right)}^{2}}\] is
  A)
  \[29c\]                                 
  done clear
  B)
  \[10c\]
  done clear
  C)
  \[10{{c}^{3}}\]                                  
  done clear
  D)
  \[20{{c}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer127) In the expansion of\[{{(1+x)}^{50}}\], the sum of the coefficients of odd powers of \[x\] is
  A)
  \[0\]                                     
  done clear
  B)
  \[{{2}^{49}}\]
  done clear
  C)
  \[{{2}^{50}}\]                                    
  done clear
  D)
  \[{{2}^{51}}\]
  done clear
  View Answer play_arrow

• question_answer128) If\[\cos A=\tan B,\,\,\,\cos B=\tan C,\,\,\,\cos C=\tan A\], then \[\sin A\] is equal to
  A)
  \[\sin {{18}^{o}}\]                           
  done clear
  B)
  \[2\sin {{18}^{o}}\]
  done clear
  C)
  \[2\cos {{18}^{o}}\]                        
  done clear
  D)
  \[2\cos {{36}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer129) If in a\[\Delta ABC\],\[\frac{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos c}{c}=\frac{a}{bc}+\frac{b}{ca}\] then the value of the \[\angle A\] is
  A)
  \[\frac{\pi }{3}\]                                              
  done clear
  B)
  \[\frac{\pi }{4}\]
  done clear
  C)
  \[\frac{\pi }{2}\]                                              
  done clear
  D)
  \[\frac{\pi }{6}\]
  done clear
  View Answer play_arrow

• question_answer130) If\[\tan (x+y)=33\]and\[x={{\tan }^{-1}}3\], then\[y\]will be
  A)
  \[0.3\]                                  
  done clear
  B)
  \[{{\tan }^{-1}}(1.3)\]
  done clear
  C)
  \[{{\tan }^{-1}}(0.3)\]                    
  done clear
  D)
  \[{{\tan }^{-1}}\left( \frac{1}{18} \right)\]
  done clear
  View Answer play_arrow

• question_answer131) If the algebraic sum of the perpendicular distances from the points \[(2,\,\,0),\,\,\,(0,\,\,2)\] and \[(1,\,\,1)\] to a variable straight line be zero, then the line passes through the point
  A)
  \[(-1,\,\,1)\]                      
  done clear
  B)
  \[(1,\,\,1)\]
  done clear
  C)
  \[(1,\,\,-1)\]                      
  done clear
  D)
  \[(-1,\,\,-1)\]
  done clear
  View Answer play_arrow

• question_answer132) If the circles\[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{c}^{2}}\]and\[{{(x-b)}^{2}}+{{(y-a)}^{2}}={{c}^{2}}\]touch each other, then
  A)
  \[a=b\pm 2c\]  
  done clear
  B)
  \[a=b\pm \sqrt{2}c\]
  done clear
  C)
  \[a=b\pm c\]                    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer133) The number of common tangents of the circles \[{{x}^{2}}+{{y}^{2}}-2x-1=0\]and\[{{x}^{2}}+{{y}^{2}}-2y-7=0\] is
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[3\]                                     
  done clear
  D)
  \[4\]
  done clear
  View Answer play_arrow

• question_answer134) If\[S=\sum\limits_{n=2}^{\infty }{^{n}{{C}_{2}}}\frac{{{3}^{n-2}}}{n!}\], then\[2s\]equals to
  A)
  \[{{e}^{3/2}}\]                                  
  done clear
  B)
  \[{{e}^{3}}\]
  done clear
  C)
  \[{{e}^{-3/2}}\]                                
  done clear
  D)
  \[{{e}^{-3}}\]
  done clear
  View Answer play_arrow

• question_answer135) The sum of the series \[\frac{1}{2}{{x}^{2}}+\frac{2}{3}{{x}^{3}}+\frac{3}{4}{{x}^{4}}+\frac{4}{5}{{x}^{5}}+...\]is
  A)
  \[\frac{x}{1+x}+\log (1+x)\]
  done clear
  B)
  \[\frac{x}{1-x}+\log (1-x)\]
  done clear
  C)
  \[-\frac{x}{1+x}+\log (1+x)\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer136) For any vector \[\mathbf{a},\,\,|\mathbf{a}\times \mathbf{i}{{|}^{2}}+|\mathbf{a}\times \mathbf{j}{{|}^{2}}+|\mathbf{a}+\mathbf{k}{{|}^{2}}\] is equal to
  A)
  \[|\mathbf{a}{{|}^{2}}\]                                             
  done clear
  B)
  \[2|\mathbf{a}{{|}^{2}}\]
  done clear
  C)
  \[3|\mathbf{a}{{|}^{2}}\]                           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer137) If the unit vectors \[a\] and \[b\] are inclined at an angle \[2\theta \] such that \[|a-b|\,\,<1\] and\[0\le \theta \le \pi \], then \[\theta \] lies in the interval
  A)
  \[\left[ 0,\,\,\frac{\pi }{6} \right)\]                          
  done clear
  B)
  \[\left[ \frac{5\pi }{6},\,\,\pi  \right]\]
  done clear
  C)
  \[\left[ \frac{\pi }{6},\,\,\frac{\pi }{2} \right]\]                   
  done clear
  D)
  \[\left[ \frac{\pi }{2},\,\,\frac{5\pi }{6} \right]\]
  done clear
  View Answer play_arrow

• question_answer138) The vectors\[\mathbf{a}=x\mathbf{i}+(x+1)\mathbf{j}+(x+2)\mathbf{k}\],\[\mathbf{b}=(x+3)\mathbf{i}+(x+4)\mathbf{j}+(x+5)\mathbf{k}\] and\[\mathbf{c}=(x+6)\mathbf{i}+(x+7)\mathbf{j}+(x+8)\mathbf{k}\]are coplanar for
  A)
   all values of\[x\]             
  done clear
  B)
   only\[x=1\]
  done clear
  C)
   only\[x=0\]                       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer139) If\[y={{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}+\sqrt{1-{{x}^{2}}}}{\sqrt{1+{{x}^{2}}}-\sqrt{1-{{x}^{2}}}} \right)\], then\[\frac{dy}{dx}\] equals to
  A)
  \[\frac{1}{\sqrt{1-{{x}^{4}}}}\]                  
  done clear
  B)
  \[\frac{-1}{\sqrt{1-{{x}^{4}}}}\]
  done clear
  C)
  \[\frac{x}{\sqrt{1-{{x}^{4}}}}\]                  
  done clear
  D)
  \[\frac{-x}{\sqrt{1-{{x}^{4}}}}\]
  done clear
  View Answer play_arrow

• question_answer140) If the parametric equation of a curve given by\[x={{e}^{t}}\cos t,\,\,y={{e}^{t}}\sin t\], then the tangent to the curve at the point \[=\frac{\pi }{4}\] makes with axis of \[x\], the angle is
  A)
  \[0\]                                     
  done clear
  B)
  \[\frac{\pi }{4}\]
  done clear
  C)
  \[\frac{\pi }{3}\]                                              
  done clear
  D)
  \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer141) The function \[f(x)=\frac{x}{\log x}\] increases on the interval
  A)
  \[(0,\,\,\infty )\]                              
  done clear
  B)
  \[(0,\,\,e)\]
  done clear
  C)
  \[(e,\,\,\infty )\]                             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer142) If\[f(x)={{\tan }^{-1}}\left\{ \frac{\log \left( \frac{e}{{{x}^{2}}} \right)}{\log (e{{x}^{2}})} \right\}+{{\tan }^{-1}}\left( \frac{1+2\log x}{1-2\log x} \right)\], then\[\frac{dy}{dx}\]is
  A)
  \[{{\tan }^{-1}}(\log x)\]                               
  done clear
  B)
  \[0\]
  done clear
  C)
  \[\frac{1}{2}\]                                   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer143) If\[{{I}_{m}}=\int_{1}^{x}{{{(\log x)}^{m}}dx}\]satisfies the relation \[{{I}_{m}}=K-l{{I}_{m-1}}\],then
  A)
  \[K=e\]                
  done clear
  B)
  \[l=m\]
  done clear
  C)
  \[K=\frac{1}{e}\]                             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer144) Let\[I=\int_{0}^{1}{\frac{{{e}^{x}}}{x+1}dx}\], then the value of the integral    \[\int_{0}^{1}{\frac{x{{e}^{{{x}^{2}}}}}{{{x}^{2}}+1}dx}\]is
  A)
  \[{{I}^{2}}\]                                       
  done clear
  B)
  \[\frac{1}{2}I\]
  done clear
  C)
  \[2I\]                                    
  done clear
  D)
  \[\frac{1}{2}{{I}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer145) \[\int_{0}^{1}{|\sin 2\pi x|dx}\]is equal to
  A)
  \[0\]                                     
  done clear
  B)
  \[-\frac{1}{\pi }\]
  done clear
  C)
  \[\frac{1}{\pi }\]                                              
  done clear
  D)
  \[\frac{2}{\pi }\]
  done clear
  View Answer play_arrow

• question_answer146) The differential equation of all conies whose centre is lie at the origin is of order
  A)
  \[2\]                                     
  done clear
  B)
  \[3\]
  done clear
  C)
  \[4\]                                     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer147) The curve satisfying \[y\,dx-xdx+\log \,\,x\,dx=0\] for \[x>0\] and passing through\[(1,\,\,-1)\]is
  A)
  \[y=-1-\log x\]
  done clear
  B)
  \[y+\log x=0\]
  done clear
  C)
  \[y={{e}^{x}}-1\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer148) The differential equation of\[y=cx+2{{c}^{2}}\]is
  A)
  \[y=x{{y}_{1}}+2y_{1}^{2}\]                       
  done clear
  B)
  \[y=x{{y}_{1}}-2y_{1}^{2}\]
  done clear
  C)
  \[y+x{{y}_{1}}=2y_{1}^{2}\]                       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer149) Variance is independent to charge of
  A)
   origin only
  done clear
  B)
   scale only
  done clear
  C)
   origin and scale both
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer150) The contrapositive of the statement\[(\tilde{\ }p\Rightarrow \tilde{\ }q)\] is
  A)
  \[p\Rightarrow q\]                         
  done clear
  B)
  \[q\Rightarrow p\]
  done clear
  C)
  \[\tilde{\ }q\Rightarrow \tilde{\ }p\]                      
  done clear
  D)
  \[\tilde{\ }p\Rightarrow q\]
  done clear
  View Answer play_arrow