Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2006

done BCECE Engineering Solved Paper-2006 Total Questions - 150

• question_answer1) The length of a simple pendulum is about 100 cm known to an accuracy of 1mm. Its period of oscillation is 2s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g?
  A)
   0.2%                                    
  done clear
  B)
          0.5%
  done clear
  C)
          0.1%                                    
  done clear
  D)
          2%
  done clear
  View Answer play_arrow

• question_answer2) Youngs modulus of the material of a wire is V. On pulling the wire by a force F, the increase in its length is x. The potential energy of the stretched wire is:
  A)
   \[\frac{1}{2}Fx\]                             
  done clear
  B)
          \[\frac{1}{2}Yx\]
  done clear
  C)
          \[\frac{1}{2}F{{x}^{2}}\]                              
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer3) A charge situated at a certain distance along the axis of an electric dipole experiences a force F. If the distance of the charge from the dipole is doubled, the force acting on it will become:
  A)
   \[2F\]       
  done clear
  B)
                                          \[\frac{F}{2}\]
  done clear
  C)
                      \[\frac{F}{4}\]                                                  
  done clear
  D)
                         \[\frac{F}{8}\]            
  done clear
  View Answer play_arrow

• question_answer4) Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non- conducting sphere of radius R?
  A)
  
  done clear
  B)
        
  done clear
  C)
        
  done clear
  D)
        
  done clear
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• question_answer5) A certain electrical conductor has a square cross-section, 2.0 mm on side, and is 12 m long. The resistance between its ends is 0.072\[\Omega .\] The resistivity of its material is equal to :
  A)
  \[2.4\times {{10}^{-6}}\Omega m\]                        
  done clear
  B)
          \[1.2\times {{10}^{-6}}\Omega m\]
  done clear
  C)
         \[1.2\times {{10}^{-8}}\Omega m\]                        
  done clear
  D)
          \[2.4\times {{10}^{-8}}\Omega m\]
  done clear
  View Answer play_arrow

• question_answer6) Figure shows three points A, B and C in a region of uniform electric field \[\mathbf{\vec{E}}\]. The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good?
  A)
  \[{{\text{V}}_{\text{A}}}\text{=}{{\text{V}}_{\text{B}}}\text{=}{{\text{V}}_{\text{C}}}\]                              
  done clear
  B)
  \[{{\text{V}}_{\text{A}}}\text{=}{{\text{V}}_{\text{B}}}\text{}{{\text{V}}_{\text{C}}}\]
  done clear
  C)
  \[{{\text{V}}_{\text{A}}}\text{=}{{\text{V}}_{\text{B}}}\text{}{{\text{V}}_{\text{C}}}\]                               
  done clear
  D)
  \[{{\text{V}}_{\text{A}}}\text{}{{\text{V}}_{\text{B}}}\text{=}{{\text{V}}_{\text{C}}}\]
  done clear
  View Answer play_arrow

• question_answer7) The (x, y, z) coordinates of two points A and B are given respectively as (0, 3,-1) and (-2, 6, 4). The displacement vector form A to B may be given by:
  A)
  \[-2\mathbf{\hat{i}}+6\mathbf{\hat{j}}+4\mathbf{\hat{k}}\]                    
  done clear
  B)
          \[-2\mathbf{\hat{i}}+3\mathbf{\hat{j}}+3\mathbf{\hat{k}}\]
  done clear
  C)
         \[-2\mathbf{\hat{i}}+3\mathbf{\hat{j}}+5\mathbf{\hat{k}}\]                    
  done clear
  D)
          \[2\mathbf{\hat{i}}-3\mathbf{\hat{j}}-5\mathbf{\hat{k}}\]
  done clear
  View Answer play_arrow

• question_answer8) In the first second of its flight, rocket ejects 1/60 of its mass with a velocity of \[2400\,\,m{{s}^{-1}}\]. The acceleration of the rocket is:
  A)
   \[19.6\,m{{s}^{-2}}\]                                    
  done clear
  B)
          \[30.2\,m{{s}^{-2}}\]
  done clear
  C)
          \[40\,m{{s}^{-2}}\]                                        
  done clear
  D)
          \[49.8\,\,m{{s}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer9) In the given figure the pulley is assumed massless and frictionless. If the friction force on the object of mass m is \[f\], then its acceleration in terms of the force F will be equal to:            
  A)
  \[(F-f)/m\]                        
  done clear
  B)
  \[\left( \frac{F}{2}-f \right)/m\]
  done clear
  C)
  F/m                                      
  done clear
  D)
  none of these
  done clear
  View Answer play_arrow

• question_answer10) The equivalent resistance between the points P and Q in the network shown in the figure is given by:
  A)
  2.5 \[\Omega \]            
  done clear
  B)
  7.5 \[\Omega \]
  done clear
  C)
  10 \[\Omega \]                                
  done clear
  D)
  12.5 \[\Omega \]
  done clear
  View Answer play_arrow

• question_answer11) The  magnetic  field  amplitude  of an electromagnetic wave is \[2\times {{10}^{-7}}T\], Its electric field amplitude, if the wave is travelling in free space is:
  A)
   \[6\,\,V{{m}^{-1}}\]                                      
  done clear
  B)
          \[60\,\,V{{m}^{-1}}\]
  done clear
  C)
          \[\frac{1}{6}\,V{{m}^{-1}}\]                       
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer12) A can is moving horizontally along a straight line with constant speed 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m. At what speed (relative to the can) must the projectile be fired? (Takes \[=10\,m/{{s}^{2}}\])
  A)
   10 m/s                                
  done clear
  B)
          \[10\sqrt{8}\]m/s
  done clear
  C)
          \[\frac{40}{3}\] m/s                                      
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer13) A boy begins to walk eastward along a street In front of his house, and the graph of his displacement from home is shown in the following figure. His average velocity for the whole time interval is equal to:
  A)
  \[\text{8}\,\text{m/min}\]                         
  done clear
  B)
  \[6\,\text{m/min}\]
  done clear
  C)
  \[\frac{8}{3}\,\text{m/min}\]                    
  done clear
  D)
  \[\text{2}\,\text{m/min}\]
  done clear
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• question_answer14) What is the potential drop between points A and C in the following circuit ? Resistances 1\[\Omega \] and 2\[\Omega \] represent the internal resistances of the respective cells.
  A)
  1.75V                                   
  done clear
  B)
  2.25V
  done clear
  C)
  \[\frac{\text{5}}{\text{4}}\text{V}\]                                      
  done clear
  D)
  \[\frac{4}{5}\text{V}\]
  done clear
  View Answer play_arrow

• question_answer15) The escape velocity of a projectile on the earths surface is \[11.2\,\,km{{s}^{-1}}\]. A body is projected out with thrice this speed. The speed of the body far away from the earth will be:
  A)
   \[22.4\,km{{s}^{-1}}\]                                  
  done clear
  B)
          \[31.7\,km{{s}^{-1}}\]
  done clear
  C)
          \[33.6\,km{{s}^{-1}}\]                                  
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer16) A body moves along a circular pa-h of radius 10 m and the coefficient of friction is 0.5. What should be its angular speed in rad/s, if it is not to slip from the surface? \[(g=9.8\,m{{s}^{-2}})\]
  A)
   5                                            
  done clear
  B)
          10
  done clear
  C)
          0.1                                        
  done clear
  D)
          0.7
  done clear
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• question_answer17) One end of a string of length I is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is:
  A)
  \[T\]                                     
  done clear
  B)
  \[T-\frac{m{{v}^{2}}}{l}\]
  done clear
  C)
  \[T+\frac{m{{v}^{2}}}{l}\]                            
  done clear
  D)
  zero
  done clear
  View Answer play_arrow

• question_answer18) A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to:            
  A)
  \[{{t}^{1/2}}\]                                   
  done clear
  B)
          \[t\]
  done clear
  C)
          \[{{t}^{3/2}}\]                                  
  done clear
  D)
          \[{{t}^{2}}\]
  done clear
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• question_answer19) In the adjacent figure is shown a closed path P. A long straight conductor carrying a current \[I\]passes through O and perpendicular to the plane of the paper. Then which of the following holds good?             
  A)
  \[\int_{P}^{{}}{{\mathbf{\vec{B}}}}\,\mathbf{\vec{d}1}=0\]                     
  done clear
  B)
  \[\int_{P}^{{}}{{\mathbf{\vec{B}}}}\,\mathbf{\vec{d}1}={{\mu }_{0}}I\]
  done clear
  C)
  \[\int_{P}^{{}}{{\mathbf{\vec{B}}}}\,\mathbf{\vec{d}1}>{{\mu }_{0}}I\]                              
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer20) Two circular, similar, coaxial loops carry equal currents in the same direction, if the loops are brought nearer, what will happen?
  A)
   Current will increase in each loop
  done clear
  B)
          Current will decrease in each loop
  done clear
  C)
          Current will remain same in each loop
  done clear
  D)
          Current will increase in one and decrease in the other
  done clear
  View Answer play_arrow

• question_answer21) The figure below shows the plot of \[\frac{PV}{nT}\] versus P for oxygen gas at two different temperatures. Read the following statements concerning the above curves:

  (i) The dotted line corresponds to the ideal gas behaviour.

  (ii) \[{{T}_{1}}>{{T}_{2}}\]

  (iii) The value of \[\frac{PV}{nT}\]at the point where the curves meet on the y-axis is the same for all gases.

  Which of the above statements is true?
  A)
  (i) only                                
  done clear
  B)
  (i) and (ii) only
  done clear
  C)
  All of these                       
  done clear
  D)
  None of these
  done clear
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• question_answer22) The following figure represents the temperature versus time plot for a given amount of a substance when heat energy is supplied to it at a fixed rate and at a constant pressure. Which parts of the above plot represent a phase change?
  A)
  a to b and e to \[f\]       
  done clear
  B)
  b to c and c to d
  done clear
  C)
  d to e and e to \[f\]       
  done clear
  D)
  b to c and d to e
  done clear
  View Answer play_arrow

• question_answer23) A bar magnet has a coercivity \[4\times {{10}^{3}}\,A{{m}^{-1}}\]. It is desired to demagnetise it by inserting it inside a solenoid 12 cm long and having 60 turns. The current carried by the solenoid should be:
  A)
   8 A                                        
  done clear
  B)
          6 A
  done clear
  C)
          4.5 A                                    
  done clear
  D)
          2 A
  done clear
  View Answer play_arrow

• question_answer24) In a series LCR circuit the frequency of a 10 VAC voltage source is adjusted in such a fashion that the reactance of the inductor measures 15 \[\Omega \] and that of capacitor 11\[\Omega \]. If R = 3 \[\Omega \] the potential difference across the series combination of L and C will be:
  A)
   8 V                                        
  done clear
  B)
          10 V
  done clear
  C)
          22 V                                     
  done clear
  D)
          52 V
  done clear
  View Answer play_arrow

• question_answer25) A circuit draws 330 W from a 110 V, 60 Hz AC line. The power factor is 0.6 and the current lags the voltage. The capacitance of a series capacitor that will result in a power factor of unity is equal to:
  A)
   31 \[\mu F\]                                     
  done clear
  B)
          54 \[\mu F\]
  done clear
  C)
          151 \[\mu F\]                                   
  done clear
  D)
          201 \[\mu F\]
  done clear
  View Answer play_arrow

• question_answer26) If the focal length of the lens is 20 cm, what is the distance of the image from the lens in the following figure?
  A)
  5.5 cm                                 
  done clear
  B)
  7.5 cm
  done clear
  C)
  12.0 cm                               
  done clear
  D)
  20.0 cm
  done clear
  View Answer play_arrow

• question_answer27) An open U-tube contains mercury. When 11.2 cm of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm form its initial level?
  A)
   0.56 cm                               
  done clear
  B)
          1.35 cm
  done clear
  C)
          0.41 cm                               
  done clear
  D)
          2.32 cm
  done clear
  View Answer play_arrow

• question_answer28) The change in the entropy of a 1 mole of an ideal gas which went through an isothermal process from an initial state\[({{P}_{1}},{{V}_{1,}}T)\] to the final state \[({{P}_{2}},{{V}_{2,}}T)\] is equal to:
  A)
   zero                                     
  done clear
  B)
          \[\text{R}\,\text{In}\,\text{T}\]
  done clear
  C)
          \[\text{R}\,\text{In}\,\frac{{{\text{V}}_{1}}}{{{\text{V}}_{2}}}\]                              
  done clear
  D)
          \[\text{R}\,\text{In}\,\frac{{{\text{V}}_{\text{2}}}}{{{\text{V}}_{\text{1}}}}\]
  done clear
  View Answer play_arrow

• question_answer29) An unpolarized beam of light is incident on a glass surface at an angle of incidence equal to the polarizing angle of the glass. Read the following statements:

  (i) The reflected beam is completely polarized.

  (ii) The refracted beam is partially polarized.

  (iii) The angle between the reflected and the refracted beams is \[90{}^\circ \].

  Which of the above statements is/are true?
  A)
  (i) only
  done clear
  B)
  (ii) only
  done clear
  C)
  (i) and (iii)
  done clear
  D)
  All the statements are correct
  done clear
  View Answer play_arrow

• question_answer30) The threshold frequency for certain metal is \[3.3\times {{10}^{14}}Hz\]. If light of frequency \[8.2\,\times {{10}^{14}}Hz\] is incident on the metal, the cut-off voltage of the photoelectric current will be:
  A)
   4.9 V                                    
  done clear
  B)
          3.0 V
  done clear
  C)
          2.0 V                                    
  done clear
  D)
          1.0 V
  done clear
  View Answer play_arrow

• question_answer31) Frequencies higher than 10 MHz were found not being reflected by the ionosphere on a particular day at a place. The maximum electron density of the ionosphere on the day was near to:
  A)
   \[1.5\times {{10}^{10}}{{m}^{-3}}\]        
  done clear
  B)
          \[1.24\times {{10}^{12}}{{m}^{-3}}\]
  done clear
  C)
          \[3\times {{10}^{12}}{{m}^{-3}}\]                           
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer32) The de-Broglie wavelength of an electron, \[\alpha \]-particle and a proton all having the same kinetic energy is respectively given as \[{{\lambda }_{e,}}{{\lambda }_{\alpha }}\] and \[{{\lambda }_{P.}}\] Then which of the following is not true ?
  A)
   \[{{\lambda }_{e}}>{{\lambda }_{P}}\]                                 
  done clear
  B)
         \[{{\lambda }_{p}}>{{\lambda }_{\alpha }}\]
  done clear
  C)
         \[{{\lambda }_{e}}>{{\lambda }_{\alpha }}\]                                       
  done clear
  D)
         \[{{\lambda }_{\alpha }}<{{\lambda }_{p}}<{{\lambda }_{e}}\]
  done clear
  View Answer play_arrow

• question_answer33) What is the disintegration constant of radon, if the number of its atoms diminishes by 18% in 24 h?
  A)
   \[2.1\times {{10}^{-3}}{{s}^{-1}}\]                          
  done clear
  B)
          \[2.1\times {{10}^{-4}}{{s}^{-1}}\]
  done clear
  C)
          \[2.1\times {{10}^{-5}}{{s}^{-1}}\]                          
  done clear
  D)
          \[2.1\times {{10}^{-6}}{{s}^{-1}}\]
  done clear
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• question_answer34) Which of the following statements is true for an n-type semiconductor?
  A)
   The donor level lies closely below the bottom of the conduction band
  done clear
  B)
          The donor level lies closely above the top of the valence band
  done clear
  C)
          The donor level lies at the halfway mark of the forbidden energy gap
  done clear
  D)
          None of the above
  done clear
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• question_answer35) Carbon, silicon and germanium have four valence electrons each. These are characterized by valence and conduction bands separated by energy band gap respectively equal to \[{{({{E}_{g}})}_{C}}\] \[{{({{E}_{g}})}_{Si}}\]and \[{{({{E}_{g}})}_{Ge.}}\]. Which of the following statements is true?            
  A)
   \[{{({{E}_{g}})}_{C}}={{({{E}_{g}})}_{Si}}={{({{E}_{g}})}_{Ge}}\]
  done clear
  B)
          \[{{({{E}_{g}})}_{C}}>{{({{E}_{g}})}_{Si}}>{{({{E}_{g}})}_{Ge}}\]
  done clear
  C)
          \[{{({{E}_{g}})}_{C}}<{{({{E}_{g}})}_{Ge}}>{{({{E}_{g}})}_{Si}}\]
  done clear
  D)
          \[{{({{E}_{g}})}_{Si}}<{{({{E}_{g}})}_{Ge}}>{{({{E}_{g}})}_{C}}\]
  done clear
  View Answer play_arrow

• question_answer36) A particle executes SHM of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position?
  A)
   0.5s                                      
  done clear
  B)
          1.0s
  done clear
  C)
          1.5s                                      
  done clear
  D)
          2.0s
  done clear
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• question_answer37) The speed of a wave on a string is 150 m/s when the tension is 120 N. The percentage increase the tension in order to raise the wave speed by 20% is:
  A)
   44%                                      
  done clear
  B)
          40%
  done clear
  C)
          20%                                      
  done clear
  D)
          10%
  done clear
  View Answer play_arrow

• question_answer38) A straight rod of length L has one of its ends at the origin and the other at x - L. If the mass per unit length of the rod is given by A x, where A is constant, where is its mass centre?            
  A)
   \[\frac{L}{3}\]                                  
  done clear
  B)
         \[\frac{L}{2}\]
  done clear
  C)
          \[\frac{2L}{3}\]                                
  done clear
  D)
          \[\frac{3L}{4}\]
  done clear
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• question_answer39) The image of a small electric bulb fixed on the wall of a room is to be obtained on the oppose wall 4 m away by means of a large convex lens. The maximum possible focal length of the lens required for this purpose will be:
  A)
   0.5 m                                   
  done clear
  B)
          1.0 m
  done clear
  C)
          1.5 m                                   
  done clear
  D)
          2.0 m
  done clear
  View Answer play_arrow

• question_answer40) The total energy of a satellite moving with an orbital velocity v around the earth is:
  A)
   \[\frac{1}{2}m{{v}^{2}}\]                            
  done clear
  B)
          \[-\frac{1}{2}m{{v}^{2}}\]
  done clear
  C)
          \[m{{v}^{2}}\]                                 
  done clear
  D)
          \[\frac{3}{2}m{{v}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer41) In hydrogen atom, the electron is moving round the nucleus with velocity \[2.18\,\times {{10}^{6\,}}m/s\] in an orbit of radius \[0.528\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The acceleration of the electron is:            
  A)
   \[9\times {{10}^{18}}m/{{s}^{2}}\]                                      
  done clear
  B)
          \[9\times {{10}^{22}}m/{{s}^{2}}\]
  done clear
  C)
          \[9\times {{10}^{-22}}m/{{s}^{2}}\]            
  done clear
  D)
          \[9\times {{10}^{12}}m/{{s}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer42) When a spring is stretched by a distance x, it exerts a force given by \[F=(-5x-16{{x}^{3}})N\]The work done, when the spring is stretched from 0.1 m to 0.2 m is:            
  A)
   \[\text{8}\text{.7 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}\]                          
  done clear
  B)
          \[\text{12}\text{.2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}\]
  done clear
  C)
          \[\text{8}\text{.1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-1}}}\text{J}\]                          
  done clear
  D)
          \[\text{12}\text{.2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-1}}}\text{J}\]
  done clear
  View Answer play_arrow

• question_answer43) The flow of liquid is laminar or stream line is determined by:
  A)
   rate of flow of liquid
  done clear
  B)
          density of fluid
  done clear
  C)
          radius of the tube
  done clear
  D)
          coefficient of viscosity of liquid
  done clear
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• question_answer44) If boiling point of water is \[95{}^\circ F\], what will be reduction at Celsius scale?
  A)
  \[7{}^\circ C\]                                   
  done clear
  B)
         \[65{}^\circ C\]
  done clear
  C)
         \[63{}^\circ C\]                                 
  done clear
  D)
         \[35{}^\circ C\]
  done clear
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• question_answer45) The motion of a particle varies with time according to the relation \[y=a(\sin \,\omega t\,+\cos \,\omega t).\]
  A)
   The motion is oscillatory but not SHM
  done clear
  B)
          The motion is SHM with amplitude \[a\]
  done clear
  C)
          The motion is SHM with amplitude \[\alpha \sqrt{2}\]
  done clear
  D)
          The motion is SHM with amplitude \[2\alpha \]
  done clear
  View Answer play_arrow

• question_answer46) Two closed organ pipes A and B have the same length. A is wider than B. They resonate in the fundamental mode at frequencies \[{{n}_{A}}\] and \[{{n}_{B}}\] respectively, then:
  A)
   \[{{n}_{A}}={{n}_{B}}\]
  done clear
  B)
          \[{{n}_{A}}>{{n}_{B}}\]
  done clear
  C)
          \[{{n}_{A}}<{{n}_{B}}\]
  done clear
  D)
          either (b) or (c) depending on the ratio of their diameters
  done clear
  View Answer play_arrow

• question_answer47) Two waves having sinusoidal waveforms have different wavelengths and different amplitudes. They will be having:
  A)
   same pitch and different intensity
  done clear
  B)
          same quality and different intensity
  done clear
  C)
          different quality and different intensity
  done clear
  D)
          same quality and different pitch
  done clear
  View Answer play_arrow

• question_answer48) In double slit experiment, the distance between two slits is 0.6 mm and these are illuminated with light of wavelength \[4800\overset{\text{o}}{\mathop{\text{A}}}\,\]. The angular width of first dark fringe on the screen distant 120 cm from slits will be:
  A)
   \[\text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]                                   
  done clear
  B)
          \[\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]
  done clear
  C)
          \[\text{4 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]                                   
  done clear
  D)
          \[\text{16 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\]
  done clear
  View Answer play_arrow

• question_answer49) If there were no atmosphere, the average temperature on the surface of the earth would be:
  A)
   lower                                  
  done clear
  B)
  higher
  done clear
  C)
  same as now   
  done clear
  D)
  \[0{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer50) The ionization energy of 10 times ionized sodium atom is:
  A)
   \[\frac{\text{13}\text{.6}}{\text{11}}\text{eV}\]                             
  done clear
  B)
          \[\frac{\text{13}\text{.6}}{\text{112}}\text{eV}\]
  done clear
  C)
          \[\text{13}\text{.6}\times {{\text{(11)}}^{2}}\,\text{eV}\]         
  done clear
  D)
          \[\text{13}\text{.6}\,\text{eV}\]
  done clear
  View Answer play_arrow

• question_answer51) When \[C{{H}_{3}}COOH\]reacts with \[C{{H}_{3}}-MgX:\]
  A)
  \[C{{H}_{3}}COX\] is formed
  done clear
  B)
   hydrocarbon is formed
  done clear
  C)
   acetone is formed
  done clear
  D)
   alcohol is formed
  done clear
  View Answer play_arrow

• question_answer52) A cyclic hydrocarbon molecule has all the carbon and hydrogen is a single plane. All the carbon-carbon bonds are of same length, less than\[1.54\,\overset{\text{o}}{\mathop{\text{A}}}\,,\] but more than \[1.34\overset{\text{o}}{\mathop{\text{A}}}\,.\] The C-C bond angle will be:
  A)
  \[{{109}^{o}}28\]             
  done clear
  B)
          \[{{100}^{o}}\]
  done clear
  C)
   \[{{180}^{o}}\]
  done clear
  D)
          \[{{120}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer53) Which will reduce zinc oxide to zinc?
  A)
   Mg                                       
  done clear
  B)
   Pb
  done clear
  C)
   Cu                         
  done clear
  D)
          Fe
  done clear
  View Answer play_arrow

• question_answer54) Some chemists at ISRO wished to prepare a saturated solution of a silver compound and they wanted it to have the highest concentration of silver ion possible. Which of the following compounds, would they use? \[{{K}_{sp}}(AgCl)=1.8\times {{10}^{-10}},\] \[{{K}_{sp}}(AgBr)=5.0\times {{10}^{-13}},\] \[{{K}_{sp}}(A{{g}_{2}}Cr{{O}_{4}})=2.4\times {{10}^{-12}}\]
  A)
  \[AgCl\]               
  done clear
  B)
          \[AgBr\]
  done clear
  C)
   \[A{{g}_{2}}Cr{{O}_{4}}\]            
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer55) By Wurtz reaction, a mixture of methyl iodide and ethyl iodide gives :
  A)
   butane
  done clear
  B)
   ethane
  done clear
  C)
   propane
  done clear
  D)
   A mixture of the above three
  done clear
  View Answer play_arrow

• question_answer56) Addition of \[SnC{{l}_{2}}\]to \[\text{HgC}{{\text{l}}_{\text{2}}}\] gives precipitate:
  A)
   white turning to red
  done clear
  B)
   white turning to grey
  done clear
  C)
   black turning to white
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer57) In fermentation by zymase, alcohol and \[C{{O}_{2}}\]are obtained from:       
  A)
   invert sugar      
  done clear
  B)
   glucose
  done clear
  C)
   fructose        
  done clear
  D)
          all of these
  done clear
  View Answer play_arrow

• question_answer58) The stability of ferric ion is due to:
  A)
   half filled \[f-\]orbitals      
  done clear
  B)
   half filled \[d-\]orbitals
  done clear
  C)
   completely filled \[f-\]orbitals
  done clear
  D)
   completely filled \[d-\]orbitals
  done clear
  View Answer play_arrow

• question_answer59) Electron affinity is positive, when:
  A)
   O changes into\[{{O}^{-}}\]
  done clear
  B)
   \[{{O}^{-}}\]changes into \[{{O}^{2-}}\]
  done clear
  C)
   O changes into \[{{O}^{+}}\]
  done clear
  D)
   electron affinity is always negative
  done clear
  View Answer play_arrow

• question_answer60) Ionization potential for a noble gas is:
  A)
   maximum in a period
  done clear
  B)
   minimum in a period
  done clear
  C)
   either minimum or maximum
  done clear
  D)
   constant                                    
  done clear
  View Answer play_arrow

• question_answer61) Ethylamine on a acetylation gives:
  A)
   N-ethyl acetamide
  done clear
  B)
   acetamide
  done clear
  C)
   methyl acetamide
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer62) Strongest oxidizing agent among halogen is:
  A)
   \[{{I}_{2}}\]                                      
  done clear
  B)
  \[B{{r}_{2}}\]
  done clear
  C)
   \[C{{I}_{2}}\]                    
  done clear
  D)
          \[{{F}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer63) Which reagent can convert acetic acid into ethanol?
  A)
  \[\text{Na + alcohol}\]   
  done clear
  B)
  \[LiAl{{H}_{4}}+\text{ether}\]
  done clear
  C)
   \[{{H}_{2}}+Pt\]              
  done clear
  D)
          \[Sn+HCl\]
  done clear
  View Answer play_arrow

• question_answer64) In presence of moisture, \[S{{O}_{2}}\]can:
  A)
   act as oxidant  
  done clear
  B)
   act as reductant
  done clear
  C)
   gain electron   
  done clear
  D)
          not act as reductant
  done clear
  View Answer play_arrow

• question_answer65) Acetals are:
  A)
   ketones             
  done clear
  B)
   diethers
  done clear
  C)
   aldehyde       
  done clear
  D)
          hydroxy aldehydes
  done clear
  View Answer play_arrow

• question_answer66) The principle involved in the classification of basic radicals, is:
  A)
   common ion effect
  done clear
  B)
   solubility product
  done clear
  C)
   valency of radicals
  done clear
  D)
   strength of salt
  done clear
  View Answer play_arrow

• question_answer67) Formation of diethyl ether from ethanol is  based on a:
  A)
   dehydration reaction
  done clear
  B)
   dehydrogenation reaction
  done clear
  C)
   hydrogenation reaction
  done clear
  D)
   homolytic fission reaction
  done clear
  View Answer play_arrow

• question_answer68) Hypo phosphorus acid,\[{{H}_{3}}P{{O}_{2}}\] is:
  A)
   a monobasic acid            
  done clear
  B)
   a tribasic acid
  done clear
  C)
   a dibasic acid   
  done clear
  D)
          not acidic at all
  done clear
  View Answer play_arrow

• question_answer69) What is obtained when acetyl chloride is heated with benzene in presence of anhydrous\[\text{AlC}{{\text{l}}_{\text{3}}}\]?
  A)
   Acetyl benzoic acid
  done clear
  B)
   Anisol
  done clear
  C)
   Acetophenone
  done clear
  D)
   Chlorobenzene
  done clear
  View Answer play_arrow

• question_answer70) Which gas is used in airated water?
  A)
  \[C{{O}_{2}}\]                                   
  done clear
  B)
   \[S{{O}_{2}}\]
  done clear
  C)
   CO                        
  done clear
  D)
          Water vapours
  done clear
  View Answer play_arrow

• question_answer71) The refluxing of \[{{(C{{H}_{3}})}_{2}}NCOC{{H}_{3}}\] with acid gives:
  A)
  \[{{(C{{H}_{3}})}_{2}}NH+C{{H}_{3}}COOH\]
  done clear
  B)
   \[{{(C{{H}_{3}})}_{2}}NCOOH+C{{H}_{4}}\]
  done clear
  C)
   \[2C{{H}_{3}}OH+C{{H}_{3}}CON{{H}_{2}}\]
  done clear
  D)
   \[2C{{H}_{3}}N{{H}_{2}}+C{{H}_{3}}COOH\]
  done clear
  View Answer play_arrow

• question_answer72) Which is obtained on treating phenol with dilute\[HN{{O}_{3}}\]?
  A)
                                                                         
  done clear
  B)
  
  done clear
  C)
                                                 
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer73) Solder is an alloy of lead with:
  A)
   copper                                
  done clear
  B)
   zinc
  done clear
  C)
   nickel                  
  done clear
  D)
          tin
  done clear
  View Answer play_arrow

• question_answer74) Arrange\[NH_{4}^{+},{{H}_{2}}O,{{H}_{3}}{{O}^{+}}.HF\] and \[O{{H}^{-}}\]in increasing order of acidic nature:
  A)
   \[{{H}_{3}}\overset{+}{\mathop{O}}\,<NH_{4}^{+}<HF<O{{H}^{-}}<{{H}_{2}}O\]
  done clear
  B)
   \[NH_{4}^{+}<HF<{{H}_{3}}{{O}^{+}}<{{H}_{2}}O<O{{H}^{-}}\]
  done clear
  C)
   \[H{{O}^{-}}<{{H}_{2}}O<NH_{4}^{+}<HF<{{H}_{3}}{{O}^{+}}\]
  done clear
  D)
   \[{{H}_{3}}O{{\,}^{+}}>HF>{{H}_{2}}O>NH_{4}^{+}>O{{H}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer75) Which of the following radicals gives the apple green flame during flame test?
  A)
  \[B{{a}^{2+}}\]                 
  done clear
  B)
   \[S{{r}^{2+}}\]
  done clear
  C)
   \[C{{a}^{2+}}\]
  done clear
  D)
          \[C{{r}^{3+}}\]
  done clear
  View Answer play_arrow

• question_answer76) When chlorine is passed through concentrated solution of KOH, the compound formed is:
  A)
  \[KCl{{O}_{4}}\]               
  done clear
  B)
          \[KCl{{O}_{3}}\]
  done clear
  C)
   \[KCl{{O}_{2}}\]              
  done clear
  D)
          \[KClO\]
  done clear
  View Answer play_arrow

• question_answer77) The equilibrium constant\[{{K}_{p}}\] for the reaction \[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\]is:
  A)
   more than one                
  done clear
  B)
   less than one
  done clear
  C)
   equal to\[{{K}_{c}}\]     
  done clear
  D)
          zero
  done clear
  View Answer play_arrow

• question_answer78) What is the weight of oxygen that is required the complete combustion of 2.8 kg of ethylene?
  A)
   9.6 kg                                  
  done clear
  B)
   96.0 kg
  done clear
  C)
   6.4 kg                  
  done clear
  D)
          2.8 kg
  done clear
  View Answer play_arrow

• question_answer79) The metal that does not displace hydrogen from an acid is:
  A)
   Ca                                         
  done clear
  B)
   Al
  done clear
  C)
   Zn                         
  done clear
  D)
          Hg
  done clear
  View Answer play_arrow

• question_answer80) The decomposition of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]occurs as, \[\text{2}{{\text{N}}_{2}}{{O}_{5}}\xrightarrow{{}}4{{N}_{2}}+{{O}_{2}},\] and follows Ist order kinetics, hence:
  A)
   the reaction is unimolecular
  done clear
  B)
   the reaction is bimolecular
  done clear
  C)
   \[{{t}_{1/2}}\propto {{a}^{o}}\]
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer81) Atomic radii of F and Ne, in \[\overset{\text{o}}{\mathop{\text{A}}}\,,\]are given by:
  A)
  \[0.72,0.71\]      
  done clear
  B)
         \[~0.72,1.6\]
  done clear
  C)
  \[1.6,\text{ }1.58\]       
  done clear
  D)
         \[~0.71,\text{ }0.72\]
  done clear
  View Answer play_arrow

• question_answer82) Which pair has both members from the same period of periodic table?
  A)
  \[Cl,Br\]                              
  done clear
  B)
  \[~Ca,Cl\]
  done clear
  C)
  \[~Na,Ca\]        
  done clear
  D)
         \[~Na,Cl\]
  done clear
  View Answer play_arrow

• question_answer83) When dilute aqueous solution of \[\text{AgN}{{\text{O}}_{\text{3}}}\](excess) is added to KI solution, positively charged sol of \[\text{AgI}\]is formed due to adsorption of:
  A)
  \[NO_{3}^{-}\]                 
  done clear
  B)
   \[O_{2}^{-}\]
  done clear
  C)
   \[A{{g}^{+}}\]  
  done clear
  D)
          \[{{K}^{+}}\]
  done clear
  View Answer play_arrow

• question_answer84) Which of the following has largest ionic radius?
  A)
  \[C{{s}^{+}}\]                                    
  done clear
  B)
   \[L{{i}^{+}}\]
  done clear
  C)
   \[N{{a}^{+}}\]  
  done clear
  D)
          \[{{K}^{+}}\]
  done clear
  View Answer play_arrow

• question_answer85) For \[CaC{{O}_{3}}(s)CaO(s)+C{{O}_{2}}(g)\]at \[927{{\,}^{o}}C,\]\[\Delta H=176\,kJ\,\text{mol}\,;\]then \[\Delta E\]is:
  A)
   180 kJ                                  
  done clear
  B)
   186.4 kJ
  done clear
  C)
   166.0 kJ              
  done clear
  D)
          160 kJ
  done clear
  View Answer play_arrow

• question_answer86) The charge required to liberate one gram equivalent of an element is:
  A)
   96500 F                               
  done clear
  B)
   1 F
  done clear
  C)
   1 C                        
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer87) The shape of sulphate ion is:
  A)
   square planar                  
  done clear
  B)
   trigonal
  done clear
  C)
   trigonal planar 
  done clear
  D)
          tetrahedral
  done clear
  View Answer play_arrow

• question_answer88) The H-H bond energy is \[430\text{ }kJ\text{ }mo{{l}^{-1}}\] and \[ClCl\]bond energy is \[240\text{ }kJ\text{ }mo{{l}^{-1}},\]\[\Delta H\] for \[HCl\]is \[-\text{ }90\text{ }kJ.\] The \[HCl\]bond energy is about:
  A)
  \[180\text{ }kJ\text{ }mo{{l}^{-1}}\]   
  done clear
  B)
          \[360\text{ }kJ\text{ }mo{{l}^{-1}}\]
  done clear
  C)
  \[~213\text{ }kJ\text{ }mo{{l}^{-1}}\]   
  done clear
  D)
          \[425\text{ }kJ\text{ }mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer89) In the equation \[{{H}_{2}}S+2HN{{O}_{3}}\xrightarrow{{}}2{{H}_{2}}O+2N{{O}_{2}}+S.\]The equivalent weight of hydrogen sulphide is:
  A)
   18                                         
  done clear
  B)
   68
  done clear
  C)
   34                         
  done clear
  D)
          17
  done clear
  View Answer play_arrow

• question_answer90) The energy released in an atom bomb explosion is mainly due to:
  A)
   release of neutrons
  done clear
  B)
   release of electrons
  done clear
  C)
   greater mass of products than initial  material
  done clear
  D)
   lesser mass of products than initial material
  done clear
  View Answer play_arrow

• question_answer91) Highest entropy is in:
  A)
   hydrogen          
  done clear
  B)
   water
  done clear
  C)
   graphite             
  done clear
  D)
          mercury
  done clear
  View Answer play_arrow

• question_answer92) Which one will liberate \[B{{r}_{2}}\]from\[KBr\]?
  A)
  \[{{I}_{2}}\]                                       
  done clear
  B)
   \[S{{O}_{2}}\]
  done clear
  C)
   \[HI\]                  
  done clear
  D)
          \[C{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer93) Nuclides:
  A)
   have specific atomic numbers
  done clear
  B)
   have same number of protons
  done clear
  C)
   have specific atomic number and mass numbers
  done clear
  D)
   are isotopes
  done clear
  View Answer play_arrow

• question_answer94) Arrhenius equation is:
  A)
  \[\Delta H=\Delta E+\Delta {{n}_{g}}RT\]
  done clear
  B)
   \[\Delta G=\Delta H-T.\Delta S\]
  done clear
  C)
                   \[K=A{{e}^{-{{E}_{a}}/RT}}\]
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer95) In which of the following compounds, the oxidation number of iodine is fractional?
  A)
   \[I{{F}_{3}}\]                                    
  done clear
  B)
  \[I{{F}_{5}}\]
  done clear
  C)
   \[I_{3}^{-}\]                     
  done clear
  D)
         \[I{{F}_{7}}\]
  done clear
  View Answer play_arrow

• question_answer96) Non-directional orbital is:
  A)
  \[4p\]        
  done clear
  B)
                          \[4d\]
  done clear
  C)
   \[4f\]                   
  done clear
  D)
          \[3s\]
  done clear
  View Answer play_arrow

• question_answer97) A monoprotic acid in 1.00 M solution is 0.01% ionized. The dissociation constant of this acid is:
  A)
   \[1\times {{10}^{-8}}\]                 
  done clear
  B)
   \[1\times {{10}^{-4}}\]
  done clear
  C)
   \[1\times {{10}^{-6}}\] 
  done clear
  D)
          \[1\times {{10}^{-5}}\]
  done clear
  View Answer play_arrow

• question_answer98) If both oxygen and helium gases are at the same temperature, the rate of diffusion of \[{{O}_{2}}\] is very close to:
  A)
   4 times that of He
  done clear
  B)
   2 times that of He
  done clear
  C)
   0.35 times that of He
  done clear
  D)
   8 times that of He
  done clear
  View Answer play_arrow

• question_answer99) A white substance having alkaline nature in solution is:
  A)
  \[NaN{{O}_{3}}\]            
  done clear
  B)
          \[N{{H}_{4}}Cl\]
  done clear
  C)
   \[N{{a}_{2}}C{{O}_{3}}\]             
  done clear
  D)
          \[F{{e}_{2}}{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer100) A solution of \[\text{FeC}{{\text{l}}_{\text{3}}}\]in water acts as acidic solution due to:
  A)
   hydrolysis of \[\text{FeC}{{\text{l}}_{\text{3}}}\]
  done clear
  B)
   acidic impurities
  done clear
  C)
   dissociation
  done clear
  D)
   ionization
  done clear
  View Answer play_arrow

• question_answer101) The units place digit in the number \[{{13}^{25}}+{{11}^{25}}-{{3}^{25}}\]is:
  A)
   0                                            
  done clear
  B)
   1                            
  done clear
  C)
   2                            
  done clear
  D)
          3
  done clear
  View Answer play_arrow

• question_answer102) The angle of intersection of the curves \[y={{x}^{2}},6y=7-{{x}^{3}}\]at \[(1,1)\]is:
  A)
  \[\frac{\pi }{4}\]                              
  done clear
  B)
          \[\frac{\pi }{3}\]                             
  done clear
  C)
   \[\frac{\pi }{2}\]                             
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer103) The value of \[x\] for which the equation \[1+r+{{r}^{2}}+...+{{r}^{x}}\] \[=(1+r)(1+{{r}^{2}})(1+{{r}^{4}})(1+{{r}^{8}})\] holds is:
  A)
   12                         
  done clear
  B)
          13                         
  done clear
  C)
   14                         
  done clear
  D)
          15
  done clear
  View Answer play_arrow

• question_answer104) If \[f(x)=\frac{{{x}^{2}}-1}{{{x}^{2}}+1},\] for every real number \[x;\]then minimum value of \[f(x):\]
  A)
   does not exist  
  done clear
  B)
          is equal to 1      
  done clear
  C)
          is equal- to 0    
  done clear
  D)
          is equal to \[-1\]
  done clear
  View Answer play_arrow

• question_answer105) The value of d for which the sum of the squares of the roots of the equation \[{{x}^{2}}-(a-2)x-a-1=0\] assumes the least value is:
  A)
   0                            
  done clear
  B)
          1                            
  done clear
  C)
          2                            
  done clear
  D)
          3
  done clear
  View Answer play_arrow

• question_answer106) A particle is dropped under gravity from rest from a height \[h(g=9.8\,m/{{s}^{2}})\]and it travels a distance \[\frac{9h}{25}\] in the last second the height \[h\]is:
  A)
   100 m                                  
  done clear
  B)
   122.5 m              
  done clear
  C)
          145 m                  
  done clear
  D)
          167.5 m
  done clear
  View Answer play_arrow

• question_answer107) The number of onto mappings from the set A\[A=\{1,2,......,100\}\]to set \[B=\{1,2\}\]is:
  A)
  \[{{2}^{100}}-2\]              
  done clear
  B)
          \[{{2}^{100}}\]                 
  done clear
  C)
   \[{{2}^{99}}-2\]               
  done clear
  D)
          \[{{2}^{99}}\]
  done clear
  View Answer play_arrow

• question_answer108) Which of the following functions is inverse of itself?
  A)
   \[f(x)=\frac{1-x}{1+x}\]
  done clear
  B)
          \[f(x)={{3}^{\log x}}\]                  
  done clear
  C)
   \[f(x)={{3}^{x(x+1)}}\]
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer109) If \[f(x)=\log (x+\sqrt{{{x}^{2}}+1}),\]then \[f(x)\]is:1
  A)
   even function  
  done clear
  B)
          odd function
  done clear
  C)
          periodic function
  done clear
  D)
         none of these
  done clear
  View Answer play_arrow

• question_answer110) The solution of \[{{\log }_{99}}\{{{\log }_{2}}({{\log }_{3}}x)\}=0\]is:
  A)
   4                            
  done clear
  B)
          9           
  done clear
  C)
          44                         
  done clear
  D)
          99          
  done clear
  View Answer play_arrow

• question_answer111) If \[n=1000!,\]then the value of sum \[\frac{1}{{{\log }_{2}}n}+\frac{1}{{{\log }_{3}}n}+...+\frac{1}{{{\log }_{1000}}n}\]is:
  A)
   0                            
  done clear
  B)
          1                            
  done clear
  C)
   10                         
  done clear
  D)
         \[{{10}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer112) If \[\omega \] and \[{{\omega }^{2}}\]are the two imaginary cube root unity, then the equation whose roots are \[a{{\omega }^{317}}\]and \[a{{\omega }^{382}}\]is:
  A)
  \[{{x}^{2}}+ax-{{a}^{2}}=0\]
  done clear
  B)
          \[{{x}^{2}}+{{a}^{2}}x+a=0\]
  done clear
  C)
          \[{{x}^{2}}+ax+{{a}^{2}}=0\]
  done clear
  D)
          \[{{x}^{2}}-{{a}^{2}}x+a=0\]
  done clear
  View Answer play_arrow

• question_answer113) The value of \[1+\sum\limits_{k=0}^{14}{\left\{ \cos \frac{2k+1}{15}\pi +i\sin \frac{(2k+1)}{15}\pi  \right\}}\]is:
  A)
   0                            
  done clear
  B)
          \[-1\]   
  done clear
  C)
   1                            
  done clear
  D)
          \[i\]
  done clear
  View Answer play_arrow

• question_answer114) If \[1,{{a}_{1}},{{a}_{2}},....,{{a}_{n-1}}\] are roots of unity, then the value of \[(1-{{a}_{1}})(1-{{a}_{2}})...(1-{{a}_{n-1}})\]is:
  A)
   0                            
  done clear
  B)
          1                            
  done clear
  C)
  \[n\]                                     
  done clear
  D)
   \[{{n}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer115) If \[\alpha ,\beta \]are the roots of \[a{{x}^{2}}+bx+c=0,\alpha +h,\beta +h\] are roots of \[p{{x}^{2}}+qx+r=0;\]and\[{{D}_{1}},{{D}_{2}}\]are the respective discriminants of the equations, then \[{{D}_{1}}:{{D}_{2}}\]is equal to:
  A)
  \[\frac{{{a}^{2}}}{{{p}^{2}}}\]                    
  done clear
  B)
          \[\frac{{{b}^{2}}}{{{q}^{2}}}\]                   
  done clear
  C)
   \[\frac{{{c}^{2}}}{{{r}^{2}}}\]                     
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer116) If a, b, c are three unequal numbers such that b, care in AP and \[b-a,c-b,a\] are in GP, then a: b: c is:
  A)
   1 : 2 : 3                
  done clear
  B)
          1 : 3 : 4
  done clear
  C)
          2 : 3 : 4                
  done clear
  D)
          1 : 2 : 4
  done clear
  View Answer play_arrow

• question_answer117) The number of divisors of \[3\times {{7}^{3}},7\times {{11}^{2}}\]and  \[2\times 61\]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_answer118) Suppose a, b, c are in AP and | a|, | b|, | c| < 1. If \[x=1+a+{{a}^{2}}+....\,to\,\infty ,\] \[y=1+b+{{b}^{2}}+....\,\text{to}\,\infty ,\] \[z=-1+c+{{c}^{2}}+...\,\text{to}\,\infty \] then \[x,y,z\]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_answer119) \[1+\frac{4}{5}+\frac{7}{{{5}^{3}}}+....to\infty \]is:
  A)
   \[\frac{16}{35}\]                             
  done clear
  B)
          \[\frac{11}{8}\]               
  done clear
  C)
          \[\frac{35}{16}\]                             
  done clear
  D)
          \[\frac{7}{16}\]
  done clear
  View Answer play_arrow

• question_answer120) If the sum of first \[n\]natural numbers is \[\frac{1}{78}\] times the sum of their cubes, then the value of \[n\] is:
  A)
   11                         
  done clear
  B)
          12                         
  done clear
  C)
          13                         
  done clear
  D)
          14
  done clear
  View Answer play_arrow

• question_answer121) If \[p=\cos {{55}^{o}},q=\cos {{65}^{o}}\] and \[r=\cos {{175}^{o}},\] then the value of\[\frac{1}{p}+\frac{1}{q}+\frac{r}{pq}\]is:
  A)
   0                            
  done clear
  B)
                                          \[-1\]                   
  done clear
  C)
          1                            
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer122) The value of\[\sin {{20}^{o}}(4+sec{{20}^{o}})\]is:
  A)
   0                            
  done clear
  B)
          1                            
  done clear
  C)
                         \[\sqrt{2}\]                        
  done clear
  D)
         \[\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer123) If\[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\] then \[x\]is equal to:
  A)
   0                                            
  done clear
  B)
   1/2                       
  done clear
  C)
   \[-1/2\]                              
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer124) If the line \[\frac{x}{a}+\frac{y}{b}=1\]  moves such that \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}},\] where c is a constant, then the locus of the foot of the perpendicular from the origin to the line is:
  A)
   straight line     
  done clear
  B)
          circle    
  done clear
  C)
          parabola        
  done clear
  D)
          ellipse
  done clear
  View Answer play_arrow

• question_answer125) The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts, passes through the point:
  A)
   (1, 1)                    
  done clear
  B)
          (2, 2)    
  done clear
  C)
          (3, 3)                    
  done clear
  D)
          (4, 4)
  done clear
  View Answer play_arrow

• question_answer126) If the circle \[{{x}^{2}}+{{y}^{2}}+4x+22y+c=0\]bisects  the circumference of the circle \[{{x}^{2}}+{{y}^{2}}-2x+8y-d=0,\] then \[c+d\]is equal to :
  A)
   60                         
  done clear
  B)
          50                         
  done clear
  C)
   40                         
  done clear
  D)
          30
  done clear
  View Answer play_arrow

• question_answer127) The radius of the circle whosc1 tangents at \[x+3y-5=0,\,\,2x+6y+30=0\]is:
  A)
   \[\sqrt{5}\]unit               
  done clear
  B)
          \[\sqrt{10}\]unit             
  done clear
  C)
          \[\sqrt{15}\]unit             
  done clear
  D)
          \[\sqrt{20}\]unit
  done clear
  View Answer play_arrow

• question_answer128) The latusrectum of the parabola \[{{y}^{2}}=4ax\]whose focal chord is \[PSQ\]such that \[SP=3\]and \[SQ=2\]is given by:
  A)
   24/5                                     
  done clear
  B)
   12/5                     
  done clear
  C)
   6/5                       
  done clear
  D)
          1/5
  done clear
  View Answer play_arrow

• question_answer129) If \[{{M}_{1}}\]and \[{{M}_{2}}\]are the feet of the perpendiculars from the foci \[{{S}_{1}}\]and \[{{S}_{2}}\]of the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=1\] on the tangent at a point P on the ellipse, then \[({{S}_{1}}{{M}_{1}})({{S}_{2}}{{M}_{2}})\]is equal to:
  A)
   16                         
  done clear
  B)
          9                            
  done clear
  C)
   4                            
  done clear
  D)
          3
  done clear
  View Answer play_arrow

• question_answer130) If the chords of contact of tangents from two points \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\] to the hyperbola  \[4{{x}^{2}}-9y-36=0\] are at right angles, then \[\frac{{{x}_{1}}{{x}_{2}}}{{{y}_{1}}{{y}_{2}}}\] is equal to:
  A)
  \[\frac{9}{4}\]                   
  done clear
  B)
          \[-\frac{9}{4}\]                
  done clear
  C)
   \[\frac{81}{16}\]                             
  done clear
  D)
          \[-\frac{81}{16}\]
  done clear
  View Answer play_arrow

• question_answer131) The solution of \[x\,dy-ydx+{{x}^{2}}{{e}^{x}}dx=0\]is:
  A)
  \[\frac{y}{x}+{{e}^{x}}=c\]          
  done clear
  B)
          \[\frac{x}{y}+{{e}^{x}}=c\]         
  done clear
  C)
          \[x+{{e}^{y}}=c\]           
  done clear
  D)
          \[y+{{e}^{x}}=c\]
  done clear
  View Answer play_arrow

• question_answer132) The coefficient of\[{{x}^{2}}\] in the binomial expansion of \[{{\left( \frac{1}{3}{{x}^{1/2}}+{{x}^{-1/4}} \right)}^{10}}\]is:
  A)
   \[\frac{70}{243}\]           
  done clear
  B)
          \[\frac{60}{423}\]           
  done clear
  C)
          \[\frac{50}{13}\]                             
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer133) The solution set of the equation \[{{\left[ 4\left( 1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+... \right) \right]}^{{{\log }_{2}}x}}\] \[={{\left[ 54\left( 1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+... \right) \right]}^{{{\log }_{x}}2}}\]is:
  A)
   \[\left\{ 4,\frac{1}{4} \right\}\]
  done clear
  B)
          \[\left\{ 2,\frac{1}{2} \right\}\]
  done clear
  C)
          \[\{1,2\}\]         
  done clear
  D)
          \[\left\{ 8,\frac{1}{8} \right\}\]
  done clear
  View Answer play_arrow

• question_answer134) If \[y=x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}-\frac{{{x}^{4}}}{4}+....\]and if \[|x|\,<1,\]then:
  A)
  \[x=1-y+\frac{{{y}^{2}}}{2}-\frac{{{y}^{3}}}{3}+....\]
  done clear
  B)
   \[x=1+y+\frac{{{y}^{2}}}{2}+\frac{{{y}^{3}}}{3}+....\]
  done clear
  C)
   \[x=y-\frac{{{y}^{2}}}{2!}+\frac{{{y}^{3}}}{3!}-\frac{{{y}^{4}}}{4!}+....\]
  done clear
  D)
   \[x=y+\frac{{{y}^{2}}}{2!}+\frac{{{y}^{3}}}{3!}+\frac{{{y}^{4}}}{4!}+....\]
  done clear
  View Answer play_arrow

• question_answer135) The length of perpendicular from (1, 6, 3) to  the\[\text{line}\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\]is:
  A)
   3                            
  done clear
  B)
          \[\sqrt{11}\]     
  done clear
  C)
          \[\sqrt{13}\]                     
  done clear
  D)
   5
  done clear
  View Answer play_arrow

• question_answer136) The plane\[2x+3y+4z=1\]meets the coordinate axes in A, B, C. The centroid of the triangle ABC is:
  A)
   (2, 3, 4)               
  done clear
  B)
          \[\left( \frac{1}{2},\frac{1}{3},\frac{1}{4} \right)\]           
  done clear
  C)
          \[\left( \frac{1}{6},\frac{1}{9},\frac{1}{12} \right)\]         
  done clear
  D)
          \[\left( \frac{1}{2},\frac{3}{3},\frac{3}{4} \right)\]
  done clear
  View Answer play_arrow

• question_answer137) The vector equation of the sphere whose centre is the point (1, 0, 1) and radius is 4, is:
  A)
  \[|\vec{r}-(\hat{i}+\hat{k})|=4\]
  done clear
  B)
   \[|\vec{r}+(\hat{i}+\hat{k})|={{4}^{2}}\]            
  done clear
  C)
   \[\vec{r}(\hat{i}+\hat{k})=4\]  
  done clear
  D)
          \[\vec{r}(\hat{i}+\hat{k})={{4}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer138) The plane \[2\lambda x-(1+\lambda )y+3z=0\]passes through the intersection of the planes:
  A)
  \[2x-y=0\]and \[y+3z=0\]
  done clear
  B)
   \[2x-y=0\]and \[y-3z=0\]
  done clear
  C)
   \[2x+3z=0\]and \[y=0\]
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer139) If \[\vec{a}+\vec{b}+\vec{c}=\vec{0}\]and \[|\vec{a}|=\sqrt{37},|\vec{b}|\]\[=3,|\vec{c}|=4,\] then angle between \[\vec{b}\]and \[\vec{c}\] is:
  A)
   \[{{30}^{o}}\]                   
  done clear
  B)
          \[{{45}^{o}}\]                   
  done clear
  C)
          \[{{60}^{o}}\]                   
  done clear
  D)
          \[{{90}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer140) If \[\vec{a}=\hat{i}+\hat{j}-\hat{k},\,\vec{b}=-\hat{i}+\hat{k},\,\vec{c}=2\hat{i}+\hat{j}\]the value of \[\lambda \]such that \[\vec{a}+\lambda \,\vec{c}\]is perpendicular  to \[\vec{b}\]is
  A)
   1                            
  done clear
  B)
          \[-1\]                   
  done clear
  C)
   0                            
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer141) The total work done by two forces \[{{\vec{F}}_{1}}=2\hat{i}-\hat{j}\]at \[{{\vec{F}}_{2}}=3\hat{i}+2\hat{j}-\hat{k}\]acting on a particle when it is displace from the point \[3\hat{i}+2\hat{j}+\hat{k}\]to \[5\hat{i}+5\hat{j}+3\hat{k}\]is:
  A)
   8 unit                   
  done clear
  B)
          9 unit   
  done clear
  C)
          10 unit                
  done clear
  D)
          11 unit
  done clear
  View Answer play_arrow

• question_answer142) Let \[\vec{a},\vec{b}\]and \[\vec{c}\]be three non-coplanar vectors, and let \[\vec{p}\]and \[\vec{r}\]be vectors defined by the relations \[\vec{P}=\frac{\vec{b}\times \vec{c}}{[\vec{a}\vec{b}\vec{c}]}.\vec{q}=\frac{\vec{c}\times \vec{a}}{[\vec{a}\vec{b}\vec{c}]}\]and \[\vec{r}=\frac{\vec{a}\times \vec{b}}{[\vec{a}\vec{b}\vec{c}]}\] Then, the value of the egression        \[(\vec{a}+\vec{b}).\vec{p}+(\vec{b}+\vec{c}).\vec{q}+(\vec{c}+\vec{a}).\vec{r}\]is equal to:
  A)
   0                                                                            
  done clear
  B)
   1                            
  done clear
  C)
                          2                            
  done clear
  D)
          3
  done clear
  View Answer play_arrow

• question_answer143) If \[\left| \begin{matrix}   {{x}^{n}} & {{x}^{n+2}} & {{x}^{n+3}}  \\    {{y}^{n}} & {{y}^{n+2}} & {{y}^{n+3}}  \\    {{z}^{n}} & {{z}^{n+2}} & {{z}^{n+3}}  \\ \end{matrix} \right|\]\[=(y-z)(z-x)(x-y)\left( \frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right),\]then \[n\]is equal to:
  A)
   2                            
  done clear
  B)
         \[-2\]                    
  done clear
  C)
         \[-1\]                    
  done clear
  D)
          1
  done clear
  View Answer play_arrow

• question_answer144) If \[{{a}_{1}},{{a}_{2}},....,{{a}_{n}},...\] are in GP and \[{{a}_{1}}>0\]for each i, then determinant \[\Delta =\left| \begin{matrix}    \log \,{{a}_{n}} & \log {{a}_{n+2}} & \log {{a}_{n+4}}  \\    \log {{a}_{n+6}} & \log {{a}_{n+8}} & \log {{a}_{n+10}}  \\    \log {{a}_{n+12}} & \log {{a}_{n+14}} & \log {{a}_{n+16}}  \\ \end{matrix} \right|\] is equal to:
  A)
   0                              
  done clear
  B)
          1                            
  done clear
  C)
                          2                              
  done clear
  D)
          \[n\]
  done clear
  View Answer play_arrow

• question_answer145) The values of a for which the system of equation\[x+y+z=0,\]\[x+ay+az=0,\]\[x-ay+z=0,\] possess non-zero solutions, are given by:
  A)
   1, 2                       
  done clear
  B)
         \[1,-1\]                               
  done clear
  C)
   1, 0                       
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer146) If a square matrix A is such that \[A{{A}^{T}}=I={{A}^{T}}A,\] then \[|A|\] is equal to:
  A)
   0                                            
  done clear
  B)
   \[\pm \,1\]                       
  done clear
  C)
  \[\pm \,2\]                        
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer147) \[\int_{a}^{b}{\frac{|x|}{x}}dx,a<0<b,\] is equal to:
  A)
   \[|b|-|a|\]       
  done clear
  B)
          \[|b|+|a|\]      
  done clear
  C)
          \[|a-b|\]           
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer148) A and B are two events. Odds against A are 2 to Odds in favour of \[A\cup B\]are 3 to 1. If  \[x\le P(B)\le y,\] then ordered pair \[(x,y)\] is:
  A)
   \[\left( \frac{5}{12},\frac{3}{4} \right)\]
  done clear
  B)
          \[\left( \frac{2}{3},\frac{3}{4} \right)\]  
  done clear
  C)
          \[\left( \frac{1}{3},\frac{3}{4} \right)\]  
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer149) In a series of three trials, the probability of exactly two successes in nine times is as large as the probability of three successes. Then, the probability of success in each trial is :
  A)
   \[\frac{1}{2}\]                  
  done clear
  B)
          \[\frac{1}{3}\]                  
  done clear
  C)
   \[\frac{1}{4}\]                  
  done clear
  D)
          \[\frac{3}{4}\]  
  done clear
  View Answer play_arrow

• question_answer150) An integer is chosen at random from first two hundred numbers. Then, the probability that the integer chosen is divisible by 6 or 8 is:
  A)
   \[\frac{1}{4}\]                  
  done clear
  B)
          \[\frac{2}{4}\]                  
  done clear
  C)
   \[\frac{3}{4}\]                  
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow