Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2011

done CET - Karnataka Engineering Solved Paper-2011 Total Questions - 180

• question_answer1) If C be the capacitance and V be the electric potential, then the dimensional formula of \[C{{V}^{2}}\] is
  A)
   \[[M{{L}^{2}}{{T}^{-2}}{{A}^{0}}]\]         
  done clear
  B)
   \[[ML{{T}^{-2}}{{A}^{-1}}]\]
  done clear
  C)
   \[[{{M}^{0}}L{{T}^{-2}}{{A}^{0}}]\]         
  done clear
  D)
   \[[M{{L}^{-3}}TA]\]
  done clear
  View Answer play_arrow

• question_answer2) The displacement-time graph of two moving particles make angles of \[{{30}^{o}}\] and \[{{45}^{o}}\] with the X-axis. The ratio of their velocities is
  A)
   \[\sqrt{3}:2\]                                   
  done clear
  B)
   \[1:1\]
  done clear
  C)
   \[1:2\]                                 
  done clear
  D)
   \[1:\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer3) Block A of mass of 2 kg is placed over block B of mass 8 kg. The combination is placed over a rough horizontal surface. Coefficient of friction between B and the floor is 0.5. Coefficient of friction between blocks A and B is 0.4. A horizontal force of 10 N is applied on block B. The force of friction between blocks A and B is \[(g=10\,m{{s}^{-2}})\]
  A)
   100 N                                   
  done clear
  B)
   40 N
  done clear
  C)
   50 N                                     
  done clear
  D)
   Zero
  done clear
  View Answer play_arrow

• question_answer4) The height y and the distance \[x\] along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by \[y=8\text{ }t5\text{ }{{t}^{2}}m\] and \[x=6t\text{ }m\], where t is in seconds. The velocity with which the projectile is projected is
  A)
   \[6\text{ }m{{s}^{-1}}\]                               
  done clear
  B)
   \[8\text{ }m{{s}^{-1}}\]
  done clear
  C)
   \[10\text{ }m{{s}^{-1}}\]             
  done clear
  D)
   \[14\text{ }m{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer5) A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity \[=9.8\text{ }m{{s}^{-2}}\])
  A)
   5 m                                       
  done clear
  B)
   2.5 m
  done clear
  C)
   10 m                                    
  done clear
  D)
   12.5 m
  done clear
  View Answer play_arrow

• question_answer6) A solid sphere of mass m rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is v. The kinetic energy of the sphere at the bottom is
  A)
   \[\frac{1}{2}m{{v}^{2}}\]                            
  done clear
  B)
   \[\frac{5}{3}m{{v}^{2}}\]
  done clear
  C)
   \[\frac{2}{5}m{{v}^{2}}\]                            
  done clear
  D)
   \[\frac{7}{10}m{{v}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer7) Two satellites of mass m and 9m are orbiting a planet in orbits of radius R. Their periods of revolution will be in the ratio of
  A)
   \[9:1\]                                 
  done clear
  B)
   \[3:1\]
  done clear
  C)
   \[1:1\]                                 
  done clear
  D)
   \[1:3\]
  done clear
  View Answer play_arrow

• question_answer8) The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension, when the same tension is applied?
  A)
   \[L=100\text{ }cm,\text{ }r=0.2\text{ }mm\]
  done clear
  B)
                   \[L=200\text{ }cm,\text{ }r=0.4\text{ }mm\]
  done clear
  C)
   \[L=300\text{ }cm,\text{ }r=0.6\text{ }mm\]
  done clear
  D)
   \[L=400\text{ }cm,\text{ }r=0.8\text{ }mm\]
  done clear
  View Answer play_arrow

• question_answer9) The resultant of two forces acting at an angle of \[{{120}^{o}}\] is 10 kg-wt and is perpendicular to one of the forces. That force is
  A)
   \[10\sqrt{3}\,kg-wt\]                   
  done clear
  B)
   \[20\sqrt{3}\,kg-wt\]
  done clear
  C)
   10 kg-wt             
  done clear
  D)
    \[\frac{10}{\sqrt{3}}\,kg-wt\]
  done clear
  View Answer play_arrow

• question_answer10) Eight equal drops of water are falling through air with a steady velocity of \[10\text{ }cm\text{ }{{s}^{-1}}\]. If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is
  A)
   \[40\text{ }cm{{s}^{-1}}\]           
  done clear
  B)
   \[10\text{ }cm{{s}^{-1}}\]
  done clear
  C)
   \[30\text{ }cm{{s}^{-1}}\]           
  done clear
  D)
   \[80\text{ }cm{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer11) Two capillary tubes of different diameters are dipped in water. The rise of water is
  A)
   the same in both tubes
  done clear
  B)
   greater in the tube of larger diameter
  done clear
  C)
   greater in the tube of smaller diameter
  done clear
  D)
   independent of the diameter of the tube
  done clear
  View Answer play_arrow

• question_answer12) A perfect gas at \[{{27}^{o}}C\] is heated at constant pressure so as to double its volume. The increase in temperature of the gas will be
  A)
   \[{{600}^{o}}C\]                              
  done clear
  B)
   \[{{327}^{o}}C\]
  done clear
  C)
   \[{{54}^{o}}C\]                                
  done clear
  D)
   \[{{300}^{o}}C\]
  done clear
  View Answer play_arrow

• question_answer13) Three identical rods A, B and C are placed end to end. A temperature difference is maintained between the free ends of A and C. The thermal conductivity of B is thrice that of C and half of that of A. The effective thermal conductivity of the system will be (\[{{K}_{A}}\]a is the thermal conductivity of rod A)
  A)
   \[\frac{1}{3}{{K}_{A}}\]                               
  done clear
  B)
   \[3{{K}_{A}}\]
  done clear
  C)
   \[2{{K}_{A}}\]                  
  done clear
  D)
   \[\frac{2}{3}{{K}_{A}}\]
  done clear
  View Answer play_arrow

• question_answer14) The quantities of heat required to raise the temperatures of two copper spheres of radii \[{{r}_{1}}\] and \[{{r}_{2}}\] \[({{r}_{1}}=1.5\text{ }{{r}_{2}})\] through 1 K are in the ratio
  A)
   \[\frac{27}{8}\]                               
  done clear
  B)
   \[\frac{9}{4}\]
  done clear
  C)
   \[\frac{3}{2}\]                                  
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer15) Which one of the following is\[{{v}_{m}}\].T graph for perfectly black body? \[{{v}_{m}}\] is the frequency of radiation with maximum intensity. T is the absolute temperature.
  A)
   A                                           
  done clear
  B)
   B
  done clear
  C)
   C                                           
  done clear
  D)
   D
  done clear
  View Answer play_arrow

• question_answer16) A particle executing a simple harmonic motion has a period of 6 s. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is
  A)
   \[\frac{3}{2}s\]                                                
  done clear
  B)
   \[\frac{1}{2}s\]
  done clear
  C)
   \[\frac{3}{4}s\]                                                
  done clear
  D)
   \[\frac{1}{4}s\]
  done clear
  View Answer play_arrow

• question_answer17) The equation of a wave is given by\[y=10\sin \left( \frac{2\pi }{45}t+\alpha  \right).\]If the displacement is 5 cm at \[t=0\], then the total phase at \[t=7.5\text{ }s\]is
  A)
   \[\frac{\pi }{3}\]                                             
  done clear
  B)
   \[\frac{\pi }{2}\]
  done clear
  C)
   \[\frac{\pi }{6}\]                                             
  done clear
  D)
   \[\pi \]
  done clear
  View Answer play_arrow

• question_answer18) Two tuning forks A and B, produce notes of frequencies 258 Hz and 262 Hz. An unknown note sounded with A produces certain beats. When the same note is sounded with B, the beat frequency gets doubled. The unknown frequency is
  A)
   250 Hz                                 
  done clear
  B)
   252 Hz
  done clear
  C)
   254 Hz                                 
  done clear
  D)
   256 Hz
  done clear
  View Answer play_arrow

• question_answer19) A wire under tension vibrates with a fundamental frequency of 600 Hz. If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one - ninth the tension. Then the fundamental frequency will become
  A)
   200 Hz                                 
  done clear
  B)
   300 Hz
  done clear
  C)
   600 Hz                                 
  done clear
  D)
   400 Hz
  done clear
  View Answer play_arrow

• question_answer20) Faintest stars are called
  A)
   zero magnitude stars
  done clear
  B)
   second magnitude stars
  done clear
  C)
   sixth magnitude stars
  done clear
  D)
   dwarfs
  done clear
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• question_answer21) Wavelength of given light waves in air and in a medium are \[6000\overset{o}{\mathop{A}}\,\]and \[4000\overset{o}{\mathop{A}}\,\] respectively. The critical angle is
  A)
   \[{{\tan }^{-1}}\left( \frac{2}{3} \right)\]                              
  done clear
  B)
   \[{{\tan }^{-1}}\left( \frac{3}{2} \right)\]
  done clear
  C)
   \[{{\tan }^{-1}}\left( \frac{2}{3} \right)\]                              
  done clear
  D)
   \[{{\sin }^{-1}}\left( \frac{3}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer22) The time required for the light to pass through a glass slab (refractive index = 1.5) of thickness 4 mm is (\[c=3\times {{10}^{8}}m{{s}^{-1}}\] speed of light in free space)
  A)
   \[{{10}^{-11}}s\]                             
  done clear
  B)
   \[2\times {{10}^{-11}}s\]
  done clear
  C)
   \[2\times {{10}^{11}}s\]                              
  done clear
  D)
   \[2\times {{10}^{-5}}s\]
  done clear
  View Answer play_arrow

• question_answer23) A prism having refractive index 1.414 and refracting angle \[{{30}^{o}}\] has one of the refracting surfaces silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is
  A)
   \[{{0}^{o}}\]                                     
  done clear
  B)
   \[{{30}^{o}}\]
  done clear
  C)
   \[{{60}^{o}}\]                                   
  done clear
  D)
   \[{{45}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer24) A plano convex lens has a maximum thickness of 6 cm. When placed on a horizontal table with the curved surface in contact with the table surface, the apparent depth of the bottommost point of the lens is found to be 4 cm. If the lens is inverted such that the plane face of the lens is in contact with the surface of the table, the apparent depth of the centre of the plane face is found to be \[\left( \frac{17}{4} \right)\]cm. The radius of curvature of the lens is
  A)
   68 cm                                  
  done clear
  B)
   75 cm
  done clear
  C)
   128 cm                                
  done clear
  D)
   34 cm
  done clear
  View Answer play_arrow

• question_answer25) Two thin lenses have a combined power of +9 D. When they are separated by a distance of 20 cm, their equivalent power becomes +\[+\frac{27}{5}D\]. Their individual powers (in dioptre) are
  A)
   1, 8                                       
  done clear
  B)
   2, 7
  done clear
  C)
   3, 6                                       
  done clear
  D)
   4, 5
  done clear
  View Answer play_arrow

• question_answer26) Wave front is the locus of all points, where the particles of the medium vibrate with the same
  A)
   phase                                  
  done clear
  B)
   amplitude
  done clear
  C)
   frequency         
  done clear
  D)
   period
  done clear
  View Answer play_arrow

• question_answer27) Two monochromatic light waves of amplitudes 3 A and 2 A interfering at a point have a phase difference of \[{{60}^{o}}\]. The intensity at that point will be proportional to
  A)
   \[5{{A}^{2}}\]                                  
  done clear
  B)
   \[13{{A}^{2}}\]
  done clear
  C)
   \[7{{A}^{2}}\]                                  
  done clear
  D)
   \[19{{A}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer28) Consider the following statements in case of Young's double slit experiment.

  (1) A slit S is necessary if we use an ordinary extended source of light.

  (2) A slit S is not needed if we use an ordinary but well collimated beam of light.

  (3) A slit S is not needed if we use a spatially coherent source of light.

  Which of the above statements are correct?
  A)
   (1), (2) and (3)                 
  done clear
  B)
   (1) and (2)
  done clear
  C)
   (2) and (3)                         
  done clear
  D)
   (1) and (3)
  done clear
  View Answer play_arrow

• question_answer29) A parallel beam of light of wavelength 6000 A gets diffracted by a single slit of width 0.3 mm. The angular position of the first minima of diffracted light is
  A)
   \[2\times {{10}^{-3}}rad\]          
  done clear
  B)
   \[3\times {{10}^{-3}}rad\]
  done clear
  C)
   \[1.8\times {{10}^{-3}}rad\]      
  done clear
  D)
   \[6\times {{10}^{-3}}rad\]
  done clear
  View Answer play_arrow

• question_answer30) The critical angle of a certain medium is\[si{{n}^{-1}}\left( \frac{3}{5} \right)\]. The polarizing angle of the medium is
  A)
   \[{{\sin }^{-1}}\left( \frac{4}{5} \right)\]                               
  done clear
  B)
   \[ta{{n}^{-1}}\left( \frac{5}{3} \right)\]
  done clear
  C)
   \[{{\tan }^{-1}}\left( \frac{3}{4} \right)\]                              
  done clear
  D)
   \[{{\tan }^{-1}}\left( \frac{4}{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer31) Two identical charged spheres of material density p, suspended from the same point by inextensible strings of equal length make an angle 6 between the strings. When suspended in a liquid of density o the angle 9 remains the same. The dielectric constant K of the liquid is
  A)
   \[\frac{\rho }{\rho -\sigma }\]                  
  done clear
  B)
   \[\frac{\rho -\sigma }{\rho }\]
  done clear
  C)
   \[\frac{\rho }{\rho +\sigma }\]                 
  done clear
  D)
   \[\frac{\rho +\sigma }{\rho }\]
  done clear
  View Answer play_arrow

• question_answer32) The electric field at a point due to an electric dipole, on an axis inclined at an angle\[\theta \left( <{{90}^{0}} \right)\] to the dipole axis, is perpendicular to the dipole axis, if the angle \[\theta \]is
  A)
   \[{{\tan }^{-1}}\left( 2 \right)\]                
  done clear
  B)
   \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]
  done clear
  C)
   \[{{\tan }^{-1}}\left( \sqrt{2} \right)\]                   
  done clear
  D)
   \[{{\tan }^{-1}}\left( \frac{1}{\sqrt{2}} \right)\]
  done clear
  View Answer play_arrow

• question_answer33) In the circuit shown, the currents \[{{i}_{1}}\] and \[{{i}_{2}}\]are
  A)
   \[{{i}_{1}}=1.5A,{{i}_{2}}=0.5A\]
  done clear
  B)
   \[{{i}_{1}}=0.5A,{{i}_{2}}=1.5A\]
  done clear
  C)
   \[{{i}_{1}}=1A,{{i}_{2}}=3A\]
  done clear
  D)
   \[{{i}_{1}}=3A,{{i}_{2}}=1A\]
  done clear
  View Answer play_arrow

• question_answer34) In the given network, the valve of C, so that  an equivalent capacitance between points A and B is \[3\,\mu F\], is
  A)
   \[\frac{1}{5}\mu F\]      
  done clear
  B)
   \[\frac{31}{5}\mu F\]
  done clear
  C)
   \[48\mu F\]                      
  done clear
  D)
   \[36\mu F\]
  done clear
  View Answer play_arrow

• question_answer35) A conductor wire having \[{{10}^{29}}\] free electrons 1 \[{{m}^{3}}\] carries a current of 20A. If the cross-section of the wire is \[1\text{ }m{{m}^{2}}\], then the drift velocity of electrons will be \[(e=1.6\times {{10}^{-19}})\]
  A)
   \[1.25\times {{10}^{-4}}m{{s}^{-1}}\]    
  done clear
  B)
   \[1.25\times {{10}^{-3}}m{{s}^{-1}}\]
  done clear
  C)
   \[1.25\times {{10}^{-5}}m{{s}^{-1}}\]       
  done clear
  D)
   \[6.25\times {{10}^{-3}}m{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer36) A resistor has a colour code of green, blue, brown and silver. What is its resistance?
  A)
   \[56\,\Omega ~\,\pm 5%\]       
  done clear
  B)
   \[560\,\Omega ~\,\pm 10%\]
  done clear
  C)
   \[560\,\Omega ~\,\pm 5%\]    
  done clear
  D)
   \[5600\,\Omega ~\,\pm 10%\]
  done clear
  View Answer play_arrow

• question_answer37) The voltage V and current \[I\] graph for a conductor at two different temperatures \[{{T}_{1}}\]and \[{{T}_{2}}\] and shown in the figure. The relation between \[{{T}_{1}}\] and \[{{T}_{2}}\] is                
  A)
   \[{{T}_{1}}>{{T}_{2}}\]                 
  done clear
  B)
   \[{{T}_{1}}<{{T}_{2}}\]
  done clear
  C)
   \[{{T}_{1}}={{T}_{2}}\]                 
  done clear
  D)
   \[{{T}_{1}}=\frac{1}{{{T}_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer38) Consider the following statements regarding the network shown in the figure.

  (1) The equivalent resistance of the network between points A and B is independent of value of G.

  (2) The equivalent resistance of the network between points A and B is \[\frac{4}{3}R\]

  (3) The current through G is zero.

  Which of the above statements is/are true?
  A)
   (1) alone            
  done clear
  B)
   (2) alone
  done clear
  C)
   (2) and (3)         
  done clear
  D)
   (1), (2) and (3)
  done clear
  View Answer play_arrow

• question_answer39) The torque required to hold a small circular coil of 10 turns, area \[1\text{ }mm2\] and carrying a current of \[\left( \frac{21}{44} \right)\]A in the middle of a long  solenoid of \[{{10}^{3}}\] turns/m carrying a current of 2.5 A, with its axis perpendicular to the axis of the solenoid is
  A)
   \[1.5\times {{10}^{-6}}N-m\]    
  done clear
  B)
   \[1.5\times {{10}^{-8}}N-m\]
  done clear
  C)
   \[1.5\times {{10}^{+6}}N-m\]   
  done clear
  D)
   \[1.5\times {{10}^{+8}}N-m\]
  done clear
  View Answer play_arrow

• question_answer40) A particle of charge e and mass m moves with a velocity v in a magnetic field B applied perpendicular to the motion of the particle. The radius r of its path in the field is
  A)
   \[\frac{mv}{Be}\]                                           
  done clear
  B)
   \[\frac{Be}{mv}\]
  done clear
  C)
   \[\frac{ev}{Bm}\]                           
  done clear
  D)
   \[\frac{Bv}{em}\]
  done clear
  View Answer play_arrow

• question_answer41) A neutron, a proton, an electron and an \[\alpha \]-particle enter a region of uniform magnetic field with the same velocities. The magnetic field is perpendicular and directed into the plane of the paper. The tracks of the particles are labelled in the figure. The electron follows the track.
  A)
   A                                           
  done clear
  B)
   B
  done clear
  C)
   C                                           
  done clear
  D)
   D
  done clear
  View Answer play_arrow

• question_answer42) The deflection in a moving coil galvanometer is reduced to half when it is shunted with a \[40\,\Omega \] coil. The resistance of the galvanometer is
  A)
   \[80\,\Omega \]                             
  done clear
  B)
   \[40\,\Omega \]
  done clear
  C)
   \[20\,\Omega \]                             
  done clear
  D)
   \[15\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer43) A current of \[\left( \frac{2}{\sqrt{3}} \right)A\], produces a deflection of \[{{60}^{o}}\] in a tangent galvanometer. The reduction factor is
  A)
   \[\left( \frac{2}{\sqrt{3}} \right)A\]                        
  done clear
  B)
   \[\left( \frac{2}{3} \right)A\]
  done clear
  C)
   2 A                                       
  done clear
  D)
   \[\left( \frac{3}{2} \right)A\]
  done clear
  View Answer play_arrow

• question_answer44) In an AC circuit, V and \[I\] are given by \[V=150\sin \left( 150t \right)\] volt and \[I=150\sin \left( 150t+\frac{\pi }{3} \right)\] amp. The power dissipated in the circuit is
  A)
   106 W                                  
  done clear
  B)
   150 W
  done clear
  C)
   5625 W                               
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer45) In the series L-C-R circuit shown, the impedance is
  A)
   \[200\,\Omega \]                           
  done clear
  B)
   \[100\,\Omega \]
  done clear
  C)
   \[300\,\Omega \]                           
  done clear
  D)
   \[500\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer46) The energy stored in an inductor of self inductance L henry carrying a current of \[I\]ampere is
  A)
   \[\frac{1}{2}{{L}^{2}}I\]                               
  done clear
  B)
   \[\frac{1}{2}L{{I}^{2}}\]
  done clear
  C)
   \[L{{I}^{2}}\]                                    
  done clear
  D)
   \[{{L}^{2}}I\]
  done clear
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• question_answer47) A transformer works on the principle of
  A)
  self - induction
  done clear
  B)
  electrical inertia
  done clear
  C)
  mutual induction
  done clear
  D)
  magnetic effect of the electrical current
  done clear
  View Answer play_arrow

• question_answer48) Flash spectrum confirms a/an
  A)
   total solar eclipse
  done clear
  B)
   lunar eclipse
  done clear
  C)
   earthquake
  done clear
  D)
   magnetic storm
  done clear
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• question_answer49) The photoelectric threshold wavelength for silver is \[{{\lambda }_{0}}\]. The energy of the electron ejected from the surface of silver by an incident wavelength \[\lambda \left( \lambda <{{\lambda }_{0}} \right)\] will be
  A)
   \[hc\left( {{\lambda }_{0}}<\lambda  \right)\]                   
  done clear
  B)
   \[\frac{hc}{{{\lambda }_{0}}-\lambda }\]
  done clear
  C)
   \[\frac{h}{c}\left( \frac{{{\lambda }_{0}}-\lambda }{\lambda {{\lambda }_{0}}} \right)\]                                
  done clear
  D)
   \[hc\left( \frac{{{\lambda }_{0}}-\lambda }{\lambda {{\lambda }_{0}}} \right)\]
  done clear
  View Answer play_arrow

• question_answer50) Rutherford's atomic model could account for
  A)
   stability of atoms
  done clear
  B)
   origin of spectra
  done clear
  C)
   the positive charged central can of an atom
  done clear
  D)
   concept of stationary orbits
  done clear
  View Answer play_arrow

• question_answer51) When an electron jumps from the orbit \[n=2\]to \[n=4\], then wavelength of the radiations absorbed will be (R is Rydberg's constant)
  A)
   \[\frac{16}{3R}\]                                             
  done clear
  B)
   \[\frac{16}{5R}\]
  done clear
  C)
   \[\frac{5R}{16}\]                                             
  done clear
  D)
   \[\frac{3R}{16}\]
  done clear
  View Answer play_arrow

• question_answer52) The thermonuclear reaction of hydrogen inside the stars is taking place by a cycle of operations. The particular element which acts as a catalyst is
  A)
   Nitrogen            
  done clear
  B)
   Oxygen
  done clear
  C)
   Helium                                
  done clear
  D)
   Carbon
  done clear
  View Answer play_arrow

• question_answer53) The ratio of minimum wavelengths of Lyman and Balmer series will be
  A)
   1.25                                      
  done clear
  B)
   0.25
  done clear
  C)
   5                                            
  done clear
  D)
   10
  done clear
  View Answer play_arrow

• question_answer54) The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half-life of the radioactive sample is
  A)
   \[\frac{1}{4}\]                                  
  done clear
  B)
   \[\frac{1}{2\sqrt{2}}\]
  done clear
  C)
   \[\frac{1}{2}\]                                  
  done clear
  D)
   \[\frac{1}{\sqrt{2}}\]
  done clear
  View Answer play_arrow

• question_answer55) 1 curie represents
  A)
                   \[3.7\times {{10}^{7}}\] disintegrations per second
  done clear
  B)
   \[3.7\times {{10}^{10}}\] disintegrations per second
  done clear
  C)
   \[{{10}^{6}}\] disintegrations per second
  done clear
  D)
   1 disintegrations per second
  done clear
  View Answer play_arrow

• question_answer56) An n-p-n transistor can be considered to be equivalent to two diodes, connected. Which of the following figures is the correct one?
  A)
    
  done clear
  B)
   
  done clear
  C)
     
  done clear
  D)
     
  done clear
  View Answer play_arrow

• question_answer57) In the case of forward biasing of a p-n junction diode, which one of the following figures correctly depicts the direction of conventional current (indicated by an arrow mark)?
  A)
   
  done clear
  B)
     
  done clear
  C)
                   
  done clear
  D)
    
  done clear
  View Answer play_arrow

• question_answer58) An electron of mass me and a proton of mass \[{{m}_{p}}\] are moving with the same speed. The ratio of their de-Broglie's wavelengths \[{{\lambda }_{e}}/{{\lambda }_{p}}\]is
  A)
   1                                            
  done clear
  B)
   1836
  done clear
  C)
   1836                                     
  done clear
  D)
   918
  done clear
  View Answer play_arrow

• question_answer59) The output of given logic circuit is
  A)
   A . (B + C)                          
  done clear
  B)
   A . (B . C)
  done clear
  C)
   (A + B) . (A + C)
  done clear
  D)
   A + B + C
  done clear
  View Answer play_arrow

• question_answer60) If the scattering intensity of a liquid is 8 units at a wavelength of 500 nm, then the scattering intensity at a wavelength of 400 nm will be approximately
  A)
   13 units                              
  done clear
  B)
   16 units
  done clear
  C)
   20 units                              
  done clear
  D)
   24 units
  done clear
  View Answer play_arrow

• question_answer61) Which one of the following statements is false?
  A)
   During roasting, moisture is removed from the ore
  done clear
  B)
   The ore is freed from almost all non-metallic impurities
  done clear
  C)
   Calcination of ore is carried out in the absence of any blast of air
  done clear
  D)
   The concentrated zinc blende is subjected to calcination during its extraction by pyrometallurgy
  done clear
  View Answer play_arrow

• question_answer62) Which one of the following sets of quantum numbers represents the highest energy level in an atom?
  A)
   \[n=4,\,\,l=0,\,m=0,\,\,s=+\frac{1}{2}\]
  done clear
  B)
   \[n=3,\,\,l=1,\,m=1,\,\,s=+\frac{1}{2}\]
  done clear
  C)
   \[n=3,\,\,l=2,\,m=-2,\,\,s=+\frac{1}{2}\]
  done clear
  D)
   \[n=3,\,\,l=0,\,m=0,\,\,s=+\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer63) When \[{{O}_{2}}\] is converted into \[O_{2}^{+}\]
  A)
   both paramagnetic character and bond order increase
  done clear
  B)
   bond order decreases
  done clear
  C)
   paramagnetic character increases
  done clear
  D)
   paramagnetic character decreases and the bond order increases
  done clear
  View Answer play_arrow

• question_answer64) In chromite ore, the oxidation number of iron  and chromium are respectively
  A)
   +3, +2                                  
  done clear
  B)
   +3, +6
  done clear
  C)
   +2, +6                                  
  done clear
  D)
   +2, +3
  done clear
  View Answer play_arrow

• question_answer65) The number of naturally occurring p-block elements that are diamagnetic is
  A)
   18                                         
  done clear
  B)
   6
  done clear
  C)
   5                                            
  done clear
  D)
   7
  done clear
  View Answer play_arrow

• question_answer66) If the energies of the two photons in the ratio of \[3:2\], their wavelength will be in the ratio of
  A)
   \[2:3\]                                 
  done clear
  B)
   \[9:4\]
  done clear
  C)
   \[3:2\]                                 
  done clear
  D)
   \[1:2\]
  done clear
  View Answer play_arrow

• question_answer67) Which one of these is not true for benzene?
  A)
   It forms only one type of mono substituted product
  done clear
  B)
   There are three carbon-carbon single bonds and three carbon-carbon double bonds
  done clear
  C)
   Heat of hydrogenation of benzene is less than its theoretical value
  done clear
  D)
   The bond angle between carbon-carbon bonds is \[{{120}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer68) Generally, the first ionization energy increases along a period. But there are some exceptions. The one which is not an exception is
  A)
   Be and B
  done clear
  B)
   Na and Mg
  done clear
  C)
   Mg and Al
  done clear
  D)
   N and O
  done clear
  View Answer play_arrow

• question_answer69) Out of the given two compounds, the vapour pressure of B at a particular temperature is
  A)
   higher than that of A
  done clear
  B)
   lower than that of A
  done clear
  C)
   higher or lower than A depending on the size of the vessel
  done clear
  D)
   same as that of A
  done clear
  View Answer play_arrow

• question_answer70) Increasing order of carbon-carbon bond length for the following is \[\underset{(A)}{\mathop{{{C}_{2}}{{H}_{4}}}}\,\]                \[\underset{(B)}{\mathop{{{C}_{2}}{{H}_{2}}}}\,\]                \[\underset{(C)}{\mathop{{{C}_{6}}{{H}_{6}}}}\,\]                 \[\underset{(D)}{\mathop{{{C}_{2}}{{H}_{6}}}}\,\]
  A)
   \[C<B<A<D\]
  done clear
  B)
   \[B<C<A<D\]
  done clear
  C)
   \[D<C<A<B\]
  done clear
  D)
   \[B<A<C<D\]
  done clear
  View Answer play_arrow

• question_answer71) A mixture of \[CaC{{l}_{2}}\] and \[NaCl\] weighing 4.44 g is treated with sodium carbonate solution to precipitate all the calcium ions as calcium carbonate. The calcium carbonate so obtained is heated strongly to get 0.56 g of \[CaO\]. The percentage of \[NaCl\] in the mixture is (atomic mass of \[Ca=40\])
  A)
   75                                         
  done clear
  B)
   31.5
  done clear
  C)
   40.2                                      
  done clear
  D)
   25
  done clear
  View Answer play_arrow

• question_answer72) \[50\text{ }c{{m}^{3}}\] of \[0.2\text{ }N\text{ }HCl\] is titrated against\[0.1\text{ }N\text{ }NaOH\] solution. The titration was discontinued after adding \[50\text{ }c{{m}^{3}}\] of \[NaOH\]. The remaining titration is completed by adding \[0.5\text{ }N\text{ }KOH\]. The volume of \[KOH\]required for completing the titration is
  A)
   \[12\,\,c{{m}^{3}}\]                                      
  done clear
  B)
   \[10\,\,c{{m}^{3}}\]
  done clear
  C)
   \[21.0\,\,c{{m}^{3}}\]                   
  done clear
  D)
   \[16.2\,\,c{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer73) The rms velocity of hydrogen is \[\sqrt{7}\] times the rms velocity of nitrogen. If T is the temperature of the gas, which of the following is true?
  A)
   \[{{T}_{{{H}_{2}}}}=\sqrt{7}\,{{T}_{{{N}_{2}}}}\]               
  done clear
  B)
   \[{{T}_{{{N}_{2}}}}=\,{{T}_{{{H}_{2}}}}\]
  done clear
  C)
   \[{{T}_{{{N}_{2}}}}=\sqrt{7}{{T}_{{{H}_{2}}}}\] 
  done clear
  D)
   \[{{T}_{{{N}_{2}}}}=2{{T}_{{{H}_{2}}}}\]
  done clear
  View Answer play_arrow

• question_answer74) 25 g of each of the following gasses are taken at \[{{27}^{o}}C\] and 600 mm pressure. Which of these will have the least volume?
  A)
   \[HCl\]                
  done clear
  B)
   \[HBr\]
  done clear
  C)
   \[HI\]                                  
  done clear
  D)
   \[HF\]
  done clear
  View Answer play_arrow

• question_answer75) The amount of heat evolved when \[500\text{ }c{{m}^{3}}\] of \[M\text{ }HCl\] is mixed with \[200\text{ }c{{m}^{3}}\] of \[0.2\text{ }M\text{ }NaOH\] is
  A)
   2.292kJ                               
  done clear
  B)
   1.292 kJ
  done clear
  C)
   22.9 kJ                                 
  done clear
  D)
   0.292 kJ
  done clear
  View Answer play_arrow

• question_answer76) The enthalpy of vaporization of benzene is +35.3 kJ/mol at its boiling point, \[{{80}^{o}}C\]. The entropy change in the transition of vapour to liquid at its boiling point is
  A)
   - 100                                    
  done clear
  B)
   + 100
  done clear
  C)
   + 342                                   
  done clear
  D)
   ? 342
  done clear
  View Answer play_arrow

• question_answer77) Based on the first law of thermodynamics, which one of the following is correct?
  A)
   For an isothermal process, Q = + W
  done clear
  B)
   For an isochoric process, \[\Delta U=-Q\]
  done clear
  C)
   For an adiabatic process, \[\Delta U=-W\]
  done clear
  D)
   For a cyclic process, \[\Delta U=-W\]
  done clear
  View Answer play_arrow

• question_answer78) Consider the following gaseous equilibria with equilibrium constants \[{{K}_{1}}\] and \[{{K}_{2}}\]respectively,                 \[S{{O}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)S{{O}_{3}}(g)\]                 \[2S{{O}_{3}}(g)2S{{O}_{2}}(g)+{{O}_{2}}(g)\] The equilibrium constants are related as
  A)
   \[2{{K}_{1}}=K_{2}^{2}\]                             
  done clear
  B)
   \[K_{1}^{2}=\frac{1}{{{K}_{2}}}\]
  done clear
  C)
   \[K_{2}^{2}=\frac{1}{{{K}_{1}}}\]                            
  done clear
  D)
   \[{{K}_{2}}=\frac{2}{K_{1}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer79) During the adsorption of krypton on activated charcoal at low temperature
  A)
   \[\Delta H<0\] and \[\Delta S<0\]
  done clear
  B)
   \[\Delta H>0\] and \[\Delta S<0\]
  done clear
  C)
                   \[\Delta H>0\] and \[\Delta S>0\]
  done clear
  D)
   \[\Delta H<0\] and \[\Delta S>0\]
  done clear
  View Answer play_arrow

• question_answer80) For the reversible reaction,\[A\,(s)+B\,(g)\]  \[C\,\,(g)+D(g),\,\Delta {{G}^{o}}=-350\,kJ\], which one of the following statements is true?
  A)
   The reaction is thermodynamically non-feasible
  done clear
  B)
   The entropy change is negative
  done clear
  C)
   Equilibrium constant is greater than one
  done clear
  D)
   The reaction should be instantaneous
  done clear
  View Answer play_arrow

• question_answer81) Identify B and D in the following sequence of reactions.
  A)
   methanol and bromoethane
  done clear
  B)
   ethyl hydrogen sulphate and alcoholic KOH
  done clear
  C)
   ethyl hydrogen sulphate and aqueous KOH
  done clear
  D)
   ethanol and alcoholic KOH
  done clear
  View Answer play_arrow

• question_answer82) The compound which gives turbidity immediately with Lucas reagent at room temperature is
  A)
   butan-1-ol
  done clear
  B)
   butan-2-ol
  done clear
  C)
   2-methyl propan-2-ol
  done clear
  D)
   2-methyl propan-1-ol
  done clear
  View Answer play_arrow

• question_answer83) Ethyl benzene cannot be prepared by
  A)
   Wurtz reaction
  done clear
  B)
   Wurtz-Fittig reaction
  done clear
  C)
                   Friedel-Craft's reaction
  done clear
  D)
   Clemmensen reduction
  done clear
  View Answer play_arrow

• question_answer84) 1.2 g of organic compound of Kjeldahlization liberates ammonia which consumes \[30\,\,c{{m}^{3}}\]of\[1\text{ }N\text{ }HCl\]. The percentage of nitrogen in the organic compound is
  A)
   30                                         
  done clear
  B)
   35
  done clear
  C)
   46.67                                   
  done clear
  D)
   20.8
  done clear
  View Answer play_arrow

• question_answer85) Carbon cannot reduce \[F{{e}_{2}}C{{O}_{3}}\] to Fe at a temperature below 983 K because
  A)
   free energy change for the formation of CO is more negative than that of \[F{{e}_{2}}{{O}_{3}}\]
  done clear
  B)
   CO is thermodynamically more stable than \[F{{e}_{2}}{{O}_{3}}\]
  done clear
  C)
   carbon has higher affinity towards oxygen than iron
  done clear
  D)
   iron has higher affinity towards oxygen than carbon
  done clear
  View Answer play_arrow

• question_answer86) The yellow precipitate formed during the chromyl chloride test is chemically
  A)
   chromic acid    
  done clear
  B)
   lead chromate
  done clear
  C)
   lead acetate    
  done clear
  D)
   sodium chromate
  done clear
  View Answer play_arrow

• question_answer87) 1 g of silver gets distributed between \[10\,\,c{{m}^{3}}\]of molten zinc and \[100\,\,c{{m}^{3}}\] of molten lead at\[{{800}^{o}}C\]. The percentage of silver still left in the lead layer is approximately
  A)
   2                                            
  done clear
  B)
   5
  done clear
  C)
   3                                            
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer88) Which one of the following is true?
  A)
   \[NaOH\] is used in the concentration of bauxite ore
  done clear
  B)
   \[NaOH\] is a primary standard in volumetric analysis
  done clear
  C)
   Manganous hydroxide is soluble in excess of \[NaOH\]solution
  done clear
  D)
   \[NaOH\] solution does not react with \[Cl\]
  done clear
  View Answer play_arrow

• question_answer89) In Ramsay and Rayleigh's isolation of noble gases from air, the nitrogen of the air is finally converted into
  A)
   \[NaN{{O}_{2}}\]only
  done clear
  B)
   NO and \[N{{O}_{2}}\]
  done clear
  C)
                   \[NaN{{O}_{3}}\] only
  done clear
  D)
   \[NaN{{O}_{2}}\] and \[NaN{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer90) The spin only magnetic moment of \[F{{e}^{2+}}\] ion (in BM) is approximately
  A)
   4                                            
  done clear
  B)
   7
  done clear
  C)
   5                                            
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer91) The IUPAC name of the complex\[[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl\] is
  A)
   dichloro tetraammine cobalt (III) chloride
  done clear
  B)
   tetraammine dichloro cobalt (III) chloride
  done clear
  C)
   tetraammine dichloro cobalt (II) chloride
  done clear
  D)
   tetraammine dichloro cobalt (IV) chloride
  done clear
  View Answer play_arrow

• question_answer92) Excess of silver nitrate solution is added to 100 mL of 0.01 M pentaaqua chloro chromium (III) chloride solution. The mass of silver chloride obtained in grams is [Atomic mass of silver is 108].
  A)
   \[287\times {{10}^{-3}}\]
  done clear
  B)
   \[143\times {{10}^{-3}}\]
  done clear
  C)
   \[143\times {{10}^{-2}}\]
  done clear
  D)
   \[287\times {{10}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer93) The following data were obtained during the first order decomposition of \[2A\,(g)\to B\,(g)+C\,(s)\] at a constant volume and at a particular temperature

  S.no.	Time	Total pressure in Pascal
  1.	At the end of 10 min	300
  2.	After completion	200

  The rate constant in \[mi{{n}^{-1}}\] is
  A)
   0.0693                                 
  done clear
  B)
   69.3
  done clear
  C)
   6.93                                      
  done clear
  D)
   \[6.93\times {{10}^{-4}}\]
  done clear
  View Answer play_arrow

• question_answer94) The time required for 100% completion of a zero order reaction is
  A)
   \[ak\]                                  
  done clear
  B)
   \[\frac{a}{2k}\]
  done clear
  C)
   \[\frac{a}{k}\]                                  
  done clear
  D)
   \[\frac{2k}{a}\]
  done clear
  View Answer play_arrow

• question_answer95) The activation energy of a reaction at a given temperature is found to be \[2.303\text{ }RT\text{ }J\text{ }mo{{l}^{-1}}\]. The ratio of rate constant to the Arrhenius factor is
  A)
   0.01                                      
  done clear
  B)
   0.1
  done clear
  C)
   0.02                                      
  done clear
  D)
   0.001
  done clear
  View Answer play_arrow

• question_answer96) pH value of which one of the following is not equal to one?
  A)
   \[0.1M\,C{{H}_{3}}COOH\]
  done clear
  B)
   \[0.1\text{ }M\text{ }HN{{O}_{3}}\]
  done clear
  C)
   \[0.05M\,{{H}_{2}}S{{O}_{4}}\]
  done clear
  D)
   \[50\text{ }c{{m}^{3}}\,0.4\text{ }M\,HCl+50\text{ }c{{m}^{3}}\text{ }0.2\text{ }M\text{ }NaOH\]
  done clear
  View Answer play_arrow

• question_answer97) A buffer solution contains 0.1 mole of sodium acetate dissolved in \[1000\text{ }c{{m}^{3}}\] of 0.1 M acetic acid. To the above buffer solution, 0.1 mole of Sodium acetate is further added and dissolved. The pH of the resulting buffer is
  A)
   \[p{{K}_{a}}\]                                  
  done clear
  B)
   \[p{{K}_{a}}+2\]
  done clear
  C)
   \[p{{K}_{a}}-\log \,2\]                  
  done clear
  D)
   \[p{{K}_{a}}+\log \,2\]
  done clear
  View Answer play_arrow

• question_answer98) \[{{H}_{2}}S\] is passed into one \[n{{m}^{3}}\] of a solution containing 0.1 mole of \[Z{{n}^{2+}}\] and 0.01 mole of \[C{{u}^{2+}}\] till the sulphide ion concentration reaches to \[8.1\times {{10}^{-19}}\] moles. Which one of the following statements is true? [\[{{K}_{sp}}\] of \[ZnS\] and \[CuS\] are \[3\times {{10}^{-22}}\] and\[8\times {{10}^{-36}}\] respectively.]
  A)
   Only \[ZnS\] precipitates
  done clear
  B)
   Both \[CuS\] and \[ZnS\] precipitate
  done clear
  C)
   Only \[CuS\] precipitates
  done clear
  D)
   No precipitation occurs
  done clear
  View Answer play_arrow

• question_answer99) \[{{E}_{1}},\,{{E}_{2}}\] and \[{{E}_{3}}\] are the emfs of the following three galvanic cells respectively.

  (i) \[Zn\,(s)|Z{{n}^{2+}}(0.1\,M)||C{{u}^{2+}}(1M)|(Cu\,(s)\]

  (ii) \[Zn\,(s)|Z{{n}^{2+}}(1\,M)||C{{u}^{2+}}(1M)|(Cu\,(s)\]

  (iii) \[Zn\,(s)|Z{{n}^{2+}}(1\,M)||C{{u}^{2+}}(0.1\,M)|(Cu\,(s)\]

  Which one of the following is true?
  A)
   \[{{E}_{2}}>{{E}_{1}}>{{E}_{3}}\]             
  done clear
  B)
   \[{{E}_{1}}>{{E}_{2}}>{{E}_{3}}\]
  done clear
  C)
   \[{{E}_{3}}>{{E}_{1}}>{{E}_{2}}\]                             
  done clear
  D)
   \[{{E}_{3}}>{{E}_{2}}>{{E}_{1}}\]
  done clear
  View Answer play_arrow

• question_answer100) 0.023 g of sodium metal is reacted with\[100\text{ }c{{m}^{3}}\] of water. The pH of the resulting solution is
  A)
   10                                         
  done clear
  B)
   8
  done clear
  C)
   9                                            
  done clear
  D)
   12
  done clear
  View Answer play_arrow

• question_answer101) The standard emf of a galvanic cell involving 2 moles of electrons in its redox reaction is 0.59 V. The equilibrium constant for the redox reaction of the cell is
  A)
   1020                                     
  done clear
  B)
   105
  done clear
  C)
   10                                         
  done clear
  D)
   1010
  done clear
  View Answer play_arrow

• question_answer102) 9.65 C of electric current is passed through fused alhydrous \[MgC{{l}_{2}}\]. The magnesium metal thus obtained is completely converted into a Grignard reagent. The number of moles of Grignard reagent obtained is
  A)
   \[5\times {{10}^{-4}}\]                                 
  done clear
  B)
   \[1\times {{10}^{-4}}\]
  done clear
  C)
   \[5\times {{10}^{-5}}\]                                 
  done clear
  D)
   \[1\times {{10}^{-5}}\]
  done clear
  View Answer play_arrow

• question_answer103) The empirical formula of a non-electrolyte is\[C{{H}_{2}}O\]. A solution containing 3 g of the compound exerts the same osmotic pressure as that of 0.05 M glucose solution. The molecular formula of the compound is
  A)
   \[C{{H}_{2}}O\]                               
  done clear
  B)
   \[{{C}_{2}}{{H}_{4}}{{O}_{2}}\]
  done clear
  C)
   \[{{C}_{4}}{{H}_{8}}{{O}_{4}}\]                 
  done clear
  D)
   \[{{C}_{3}}{{H}_{6}}{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer104) Which one of the following is a covalent crystal?
  A)
   Rock salt            
  done clear
  B)
   Ice
  done clear
  C)
   Quartz                                
  done clear
  D)
   Dry ice
  done clear
  View Answer play_arrow

• question_answer105) Which one of the following does not involve coagulation?
  A)
   Clotting of blood by the use of ferric chloride
  done clear
  B)
   Formation of delta region
  done clear
  C)
   Treatment of drinking water by potash alum
  done clear
  D)
   Peptization
  done clear
  View Answer play_arrow

• question_answer106) A solution of two liquids boils at a temperature more than the boiling point of either of them. Hence, the binary solution shows
  A)
   negative deviation from Raoult?s law
  done clear
  B)
   positive deviation from Raoult?s law
  done clear
  C)
   no deviation from Raoult?s law
  done clear
  D)
   positive or negative deviation from Raoult?s law depending upon the composition
  done clear
  View Answer play_arrow

• question_answer107) Which one of the nitrogen atoms in\[{{H}_{2}}\underset{I}{\mathop{N}}\,-\underset{II}{\mathop{N}}\,H-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-\underset{III}{\mathop{N}}\,{{H}_{2}}\] is the most nudeophilic?
  A)
   III
  done clear
  B)
   I
  done clear
  C)
   II
  done clear
  D)
   All three nitrogen atoms are equally strong nudeophilic centres
  done clear
  View Answer play_arrow

• question_answer108) The maximum number of possible optical isomers in l-bromo-2-methyl cyclobutane is
  A)
   4                                            
  done clear
  B)
   2
  done clear
  C)
   8                                            
  done clear
  D)
   16
  done clear
  View Answer play_arrow

• question_answer109) Which one of the following is the most energetic conformation of cyclohexane?
  A)
   Boat                                     
  done clear
  B)
   Twisted boat
  done clear
  C)
   Chair                                    
  done clear
  D)
   Half chair
  done clear
  View Answer play_arrow

• question_answer110) Which one of the following is an intermediate in the reaction of benzene with \[C{{H}_{3}}Cl\] in the presence of anhydrous \[AlC{{l}_{3}}\]?
  A)
   \[C{{l}^{-}}\]                                     
  done clear
  B)
   \[CH_{3}^{-}\]
  done clear
  C)
   \[CH_{3}^{+}\]                                
  done clear
  D)
    
  done clear
  View Answer play_arrow

• question_answer111) Which one of the following is not true for the hydrolysis of t-butyl bromide with aqueous\[NaOH\]?
  A)
   Reaction occurs through the \[{{S}_{{{N}^{1}}}}\]mechanism
  done clear
  B)
   The intermediate formed is a carbocation
  done clear
  C)
   Rate of the reaction doubles when the concentration of alkali is doubled
  done clear
  D)
   Rate of the reaction doubles when the concentration of r-butyl bromide is doubled
  done clear
  View Answer play_arrow

• question_answer112) Following is the substitution reaction in which \[-CN\] replaces \[-Cl\]. \[R-Cl+\underset{(alcoholic)}{\mathop{KCN}}\,\xrightarrow[\Delta ]{}R-CN+KCl\] To obtain propanenitrile, \[R-Cl\] should be
  A)
   chloroethane                   
  done clear
  B)
   1-chloropropane
  done clear
  C)
   chloromethane               
  done clear
  D)
   2-chloropropane
  done clear
  View Answer play_arrow

• question_answer113) The conversion of m-nitrophenol to resorcinol involves respectively
  A)
   hydrolysis, diazotization and reduction
  done clear
  B)
   diazotization, reduction and hydrolysis
  done clear
  C)
   hydrolysis, reduction and diazotization
  done clear
  D)
   reduction, diazotization and hydrolysis
  done clear
  View Answer play_arrow

• question_answer114) Formic acid is a stronger acid than acetic acid. This can be explained using
  A)
   +M effect          
  done clear
  B)
   \[-I\]effect
  done clear
  C)
   \[+I\]effect                      
  done clear
  D)
   -M effect
  done clear
  View Answer play_arrow

• question_answer115) The reagent with which both acetaldehyde and acetone react is
  A)
   Fehling's solution           
  done clear
  B)
   \[{{I}_{2}}/NaOH\]
  done clear
  C)
   Tollen's reagent              
  done clear
  D)
   carbonic acid
  done clear
  View Answer play_arrow

• question_answer116) Which of the following gives an aldehyde on dry distillation?
  A)
   Calcium formate + calcium acetate
  done clear
  B)
   Calcium acetate 4- calcium benzoate
  done clear
  C)
   Calcium acetate
  done clear
  D)
   Calcium benzoate
  done clear
  View Answer play_arrow

• question_answer117) \[\alpha \]-maltose consists of
  A)
   one \[\alpha \]-D-glucopyranose unit and one \[\beta \] -D-glucopyranose unit with 1-2 glycosidic linkage
  done clear
  B)
   two \[\alpha \]-D-glucopyranose units with 1-2 glycosidic linkage
  done clear
  C)
   two \[\beta \]-D-glucopyranose units with 1-4 glycosidic linkage
  done clear
  D)
   two \[\alpha \]-D-glucopyranose units with 1-4 glycosidic linkage
  done clear
  View Answer play_arrow

• question_answer118) Which one of the following does not correctly match with each other?
  A)
   Silk-polyamide                
  done clear
  B)
   Lipase-enzyme
  done clear
  C)
   Butter-fat          
  done clear
  D)
   Oxytocin-enzyme
  done clear
  View Answer play_arrow

• question_answer119) In an alkaline medium, glycine predominantly exists as/in a/an
  A)
   cation                                  
  done clear
  B)
   anion
  done clear
  C)
   Zwitterion         
  done clear
  D)
   covalent form
  done clear
  View Answer play_arrow

• question_answer120) The IUPAC name of  is
  A)
   but-3-enoic acid             
  done clear
  B)
   but-1-enoic acid
  done clear
  C)
   pent-4-enoic acid           
  done clear
  D)
   prop-2-enoic acid
  done clear
  View Answer play_arrow

• question_answer121) If \[\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log a}{a-b},\]then the value of \[{{x}^{b+c}},{{y}^{c+a}},{{z}^{a+b}}\]is
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   0                                            
  done clear
  D)
   -1
  done clear
  View Answer play_arrow

• question_answer122) The sum of the first \[n\]terms of \[\frac{{{1}^{2}}}{1}+\frac{{{1}^{2}}+{{2}^{2}}}{1+2}+\frac{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}{1+2+3}+....\]is
  A)
   \[\frac{{{n}^{2}}-2n}{3}\]                            
  done clear
  B)
  \[\frac{2{{n}^{2}}+n}{3}\]a
  done clear
  C)
  \[\frac{n(n+2)}{3}\]                       
  done clear
  D)
   \[\frac{2{{n}^{2}}-n}{3}\]
  done clear
  View Answer play_arrow

• question_answer123) If \[n\]is an odd positive integer and \[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{n}}=\sum\limits_{r=0}^{3n}{{{a}_{r}}{{x}^{r}}},\]then \[{{a}_{0}}-{{a}_{1}}+{{a}_{2}}-{{a}_{3}}+...-{{a}_{3n}}\]is equal to
  A)
   \[{{4}^{n}}\]                                     
  done clear
  B)
   1
  done clear
  C)
   -1                                          
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer124) If rth and \[(r+1)th\]terms in the expansion of \[{{(p+q)}^{n}}\]are equal, then \[\frac{(n+1)q}{r(p+q)}\]is
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   \[\frac{1}{4}\]                                  
  done clear
  D)
   \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer125) If \[\alpha ,\beta \]and \[\gamma \]are roots of \[{{x}^{3}}-2x+1=0,\]then the value of \[\sum{\left( \frac{1}{\alpha +\beta -\gamma } \right)}\]is
  A)
   \[-\frac{1}{2}\]                                
  done clear
  B)
   \[-1\]
  done clear
  C)
   0                                            
  done clear
  D)
   \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer126) Define a relation R on \[A=\{1,2,3,4\}\]as \[xRy\]if \[x\]divides \[y.R\]is
  A)
   reflexive and transitive
  done clear
  B)
   reflexive and symmetric
  done clear
  C)
   symmetric and transitive
  done clear
  D)
   equivalence
  done clear
  View Answer play_arrow

• question_answer127) The negation of \[p\to (\tilde{\ }p\vee q)\]is
  A)
  \[p\vee (p\vee \tilde{\ }q)\]      
  done clear
  B)
  \[p\to \tilde{\ }(p\vee q)\]
  done clear
  C)
  \[p\to q\]                           
  done clear
  D)
  \[p\wedge \tilde{\ }q\]
  done clear
  View Answer play_arrow

• question_answer128) In Any \[\Delta ABC,\]the simplified form of \[\frac{\cos 2A}{{{a}^{2}}}-\frac{\cos 2B}{{{b}^{2}}}\]is
  A)
   \[{{a}^{2}}-{{b}^{2}}\]                  
  done clear
  B)
   \[\frac{1}{{{a}^{2}}-{{b}^{2}}}\]
  done clear
  C)
  \[\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}\]                              
  done clear
  D)
  \[{{a}^{2}}+{{b}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer129) . Angles of elevation of the top of a tower from three point (collinear) A, Band C on a road leading to the foot of the tower are \[{{30}^{o}},{{45}^{o}}\]and \[{{60}^{o}}\]respectively. The ration of AB to BC is
  A)
  \[\sqrt{3}:1\]                    
  done clear
  B)
  \[\sqrt{3}:2\]
  done clear
  C)
   \[1:2\]                                 
  done clear
  D)
  \[2:\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer130) The value of \[\sin \,{{10}^{o}}.\sin \,{{30}^{o}}.\sin \,{{50}^{o}}.\sin \,{{70}^{o}}\]is
  A)
   \[\frac{1}{8}\]                                  
  done clear
  B)
   \[\frac{3}{16}\]
  done clear
  C)
   \[\frac{\sqrt{3}}{16}\]                                  
  done clear
  D)
   \[\frac{1}{16}\]
  done clear
  View Answer play_arrow

• question_answer131) Locus of a point which moves such that its distance from the line \[x-y=0\]is
  A)
  \[{{x}^{2}}+4xy-{{y}^{2}}=0\]
  done clear
  B)
  \[2{{x}^{2}}-4xy+{{y}^{2}}=0\]
  done clear
  C)
  \[{{x}^{2}}-4xy+{{y}^{2}}=0\]
  done clear
  D)
  \[{{x}^{2}}-4xy-{{y}^{2}}=0\]
  done clear
  View Answer play_arrow

• question_answer132) The points \[A(1,2),B(2,4)\]and \[C\,(4,8)\]form\[a/an\]
  A)
   isosceles triangles
  done clear
  B)
   equilateral triangle
  done clear
  C)
   straight line
  done clear
  D)
   right angled triangle
  done clear
  View Answer play_arrow

• question_answer133) If lines represented by \[x+3y-6=0,\]\[2x+y-4=0\]and \[kx-3y+1=0\]are concurrent, then the value of \[k\]is
  A)
  \[\frac{6}{19}\]                                
  done clear
  B)
  \[\frac{19}{6}\]
  done clear
  C)
   \[-\frac{19}{6}\]                              
  done clear
  D)
   \[-\frac{6}{19}\]
  done clear
  View Answer play_arrow

• question_answer134) \[\underset{x\to a}{\mathop{\lim }}\,\left[ \frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}} \right]\]is equal to
  A)
   \[\frac{2}{3}\]                                  
  done clear
  B)
  \[\frac{2}{\sqrt{3}}\]
  done clear
  C)
   \[\frac{3\sqrt{3}}{2}\]                  
  done clear
  D)
   \[\frac{2}{3\sqrt{3}}\]
  done clear
  View Answer play_arrow

• question_answer135) If \[f(x)=\left\{ \begin{matrix}    \frac{\log x}{x-1}, & if\,x\ne 1  \\    \,\,k\,\,\,\,\,\,\,\,\,\,\,, & if\,x=1  \\ \end{matrix} \right.\]is continuous at \[x=1,\]then the value of k is
  A)
   0                                            
  done clear
  B)
   -1
  done clear
  C)
   1                                            
  done clear
  D)
   e
  done clear
  View Answer play_arrow

• question_answer136) If \[A=\left[ \begin{matrix}    \cos \theta  & \sin \theta   \\    -\sin \theta  & \cos \theta   \\ \end{matrix} \right],\]then A.A? is
  A)
   I                                             
  done clear
  B)
   A
  done clear
  C)
   \[-A\]                                  
  done clear
  D)
   \[{{A}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer137) If \[\left[ \begin{matrix}    1 & 2 & -1  \\    1 & x-2 & 1  \\    x & 1 & 1  \\ \end{matrix} \right]\]is singular, then the value of \[x\]is
  A)
   2                                            
  done clear
  B)
   3
  done clear
  C)
   1                                            
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer138) If A and B are symmetric matrices of the same order, then which one of the following is not true?
  A)
   A + B is symmetric
  done clear
  B)
   A - B is symmetric
  done clear
  C)
   AB + BA is symmetric
  done clear
  D)
   AB - BA is symmetric
  done clear
  View Answer play_arrow

• question_answer139)  If \[\omega \]is an imaginary cube root o unity, then the value of \[\left[ \begin{matrix}    1 & {{\omega }^{2}} & 1-{{\omega }^{4}}  \\    \omega  & 1 & 1+{{\omega }^{5}}  \\    1 & \omega  & {{\omega }^{2}}  \\ \end{matrix} \right]\]is
  A)
   \[-4\]                                   
  done clear
  B)
  \[{{\omega }^{2}}-4\]
  done clear
  C)
  \[{{\omega }^{2}}\]                                        
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer140) If a, b and c are unit vectors such tat \[a+b+c=0,\]then angle between a and b is
  A)
   \[\frac{\pi }{2}\]                                             
  done clear
  B)
   \[\frac{\pi }{3}\]
  done clear
  C)
   \[\frac{2\pi }{3}\]                                           
  done clear
  D)
   \[\pi \]
  done clear
  View Answer play_arrow

• question_answer141) If a, b and c are non-coplanar, then the value of \[a.\left\{ \frac{b\times c}{3b.(c\times a)} \right\}-b\left\{ \frac{c\times a}{2c.(a\times b)} \right\}\]is
  A)
   \[-\frac{1}{2}\]                                
  done clear
  B)
   \[-\frac{1}{3}\]
  done clear
  C)
   \[-\frac{1}{6}\]                                
  done clear
  D)
   \[\frac{1}{6}\]
  done clear
  View Answer play_arrow

• question_answer142) If \[2i+3j,i+j+k\]and \[\lambda i+4j+2k\]taken in an order are coterminous edges of a parallelepiped of volume 2 cu units, then value of \[\lambda \]is
  A)
  \[-4\]                                    
  done clear
  B)
   2
  done clear
  C)
   3                                            
  done clear
  D)
   4                            
  done clear
  View Answer play_arrow

• question_answer143) A unit vector perpendicular to both \[i+j+k\]and \[2i+j+3k\]is
  A)
   \[(2i-j-k)\sqrt{6}\]                         
  done clear
  B)
   \[\frac{(2i-j-k)}{\sqrt{6}}\]
  done clear
  C)
  \[2i+j+k\]                           
  done clear
  D)
   \[\frac{3i+j-2k}{\sqrt{6}}\]         
  done clear
  View Answer play_arrow

• question_answer144) The digit in the unit?s place of \[{{7}^{171}}+(177)!\]is
  A)
   3                                            
  done clear
  B)
   2
  done clear
  C)
   1                                            
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer145) The sum of all positive divisors of 242 except 1and itself is
  A)
   156                                       
  done clear
  B)
   242
  done clear
  C)
   342                                       
  done clear
  D)
   399
  done clear
  View Answer play_arrow

• question_answer146) On the set of all non-zero reals, an operation is defined as \[a*b=\frac{3ab}{2}.\]in this group, a solution of \[({{2}^{*}}x)*{{3}^{-1}}={{4}^{-1}}\]is
  A)
   6                                            
  done clear
  B)
   1            
  done clear
  C)
   1/6                                       
  done clear
  D)
   3/2
  done clear
  View Answer play_arrow

• question_answer147) \[G=\left\{ \left[ \begin{matrix}    x & x  \\    x & x  \\ \end{matrix} \right],x\,\text{is}\,\text{a}\,\text{non}-\text{zero}\,\text{real}\,\text{number} \right\}\]is a group with respect to matrix multiplication. In this group, the inverse of \[\left[ \begin{matrix}    \frac{1}{3} & \frac{1}{3}  \\    \frac{1}{3} & \frac{1}{3}  \\ \end{matrix} \right]\]is
  A)
  \[\left[ \begin{matrix}    4/3 & 4/3  \\    4/3 & 4/3  \\ \end{matrix} \right]\]   
  done clear
  B)
   \[\left[ \begin{matrix}    3/4 & 3/4  \\    3/4 & 3/4  \\ \end{matrix} \right]\]
  done clear
  C)
   \[\left[ \begin{matrix}    3 & 3  \\    3 & 3  \\ \end{matrix} \right]\]                   
  done clear
  D)
   \[\left[ \begin{matrix}    1 & 1  \\    1 & 1  \\ \end{matrix} \right]\]
  done clear
  View Answer play_arrow

• question_answer148) If \[2{{x}^{2}}+2{{y}^{2}}+4x+5y+1=0\]and \[3{{x}^{2}}+3{{y}^{2}}+6x-7y+3k=0\]are orthogonal, then value of k is
  A)
  \[\frac{12}{17}\]                                              
  done clear
  B)
  \[\frac{12}{17}\]
  done clear
  C)
   \[-\frac{12}{17}\]                           
  done clear
  D)
  \[-\frac{17}{12}\]            
  done clear
  View Answer play_arrow

• question_answer149) The total number of common tangents of  \[{{x}^{2}}+{{y}^{2}}-6x-8y+9=0\]and \[{{x}^{2}}+{{y}^{2}}=1\]is
  A)
   4                                            
  done clear
  B)
   2
  done clear
  C)
   3                                            
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer150) The centre of a circle which cuts \[{{x}^{2}}+{{y}^{2}}-1=0,\]\[{{x}^{2}}+{{y}^{2}}-3y+2=0\]and \[{{x}^{2}}+\]\[{{y}^{2}}+x+y-3=0\]orthogonally is
  A)
  \[\left( \frac{1}{7},\frac{9}{7} \right)\]                   
  done clear
  B)
  \[\left( -\frac{1}{7},-\frac{9}{7} \right)\]
  done clear
  C)
  \[\left( \frac{1}{7},-\frac{9}{7} \right)\]                 
  done clear
  D)
   \[\left( -\frac{1}{7},\frac{9}{7} \right)\]
  done clear
  View Answer play_arrow

• question_answer151) The length of the latusrectum of \[3{{x}^{2}}-4y+6x-3=0\]is
  A)
  \[\frac{3}{4}\]                                   
  done clear
  B)
  \[\frac{4}{3}\]
  done clear
  C)
   2                                            
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer152) The sum of the reciprocals of focal distances of a focal PQ of \[{{y}^{2}}=4ax\]is
  A)
  \[\frac{1}{a}\]                                   
  done clear
  B)
   a
  done clear
  C)
   \[2a\]                                  
  done clear
  D)
  \[\frac{1}{2a}\]
  done clear
  View Answer play_arrow

• question_answer153) If the foci of \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{4}=1\]and \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{9}=1\]coincide, then the value of a is
  A)
  \[\sqrt{3}\]                                        
  done clear
  B)
   \[\frac{1}{\sqrt{3}}\]
  done clear
  C)
   2                                            
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer154) The equation of a hyperbola whose asymptotes are \[3x\pm 5y=0\]and vertices are \[(\pm 5,0)\]is
  A)
  \[3{{x}^{2}}-5{{y}^{2}}=25\]       
  done clear
  B)
  \[5{{x}^{2}}-3{{y}^{2}}=225\]
  done clear
  C)
  \[25{{x}^{2}}-9{{y}^{2}}=225\]   
  done clear
  D)
  \[9{{x}^{2}}-25{{y}^{2}}=225\]
  done clear
  View Answer play_arrow

• question_answer155) The domain of \[f(x)={{\sin }^{-1}}\left[ {{\log }_{2}}\left( \frac{x}{2} \right) \right]\]is
  A)
  \[0\le x\le 1\]                   
  done clear
  B)
  \[0\le x\le 4\]
  done clear
  C)
  \[1\le x\le 4\]                   
  done clear
  D)
  \[4\le x\le 6\]
  done clear
  View Answer play_arrow

• question_answer156) If \[{{\tan }^{-1}}x=\frac{\pi }{4}-{{\tan }^{-1}}\left( \frac{1}{3} \right),\]then \[x\]is
  A)
  \[\frac{1}{3}\]                                   
  done clear
  B)
  \[\frac{1}{2}\]
  done clear
  C)
   \[\frac{1}{4}\]                                  
  done clear
  D)
   \[\frac{1}{6}\]
  done clear
  View Answer play_arrow

• question_answer157) A value of \[\theta \]satisfying \[\sin 5\theta -\sin 3\theta +\sin \theta =0,\]such that \[0<\theta <\frac{\pi }{2}\]is
  A)
  \[\frac{\pi }{12}\]                                            
  done clear
  B)
  \[\frac{\pi }{6}\]
  done clear
  C)
   \[\frac{\pi }{4}\]                                             
  done clear
  D)
   \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer158) The value of \[\left| \frac{1+i\sqrt{3}}{{{\left( 1+\frac{1}{i+1} \right)}^{2}}} \right|\]is
  A)
   20                                         
  done clear
  B)
   9
  done clear
  C)
  \[\frac{5}{4}\]                                   
  done clear
  D)
   \[\frac{4}{5}\]
  done clear
  View Answer play_arrow

• question_answer159) If\[\omega \]is an imaginary cube root of unity, then the value of \[(1-\omega +{{\omega }^{2}}).(1-{{\omega }^{2}}+{{\omega }^{4}}).(1-{{\omega }^{4}}+{{\omega }^{8}})....\](\[2n\]factors) is
  A)
  \[{{2}^{2n}}\]                                    
  done clear
  B)
  \[{{2}^{n}}\]
  done clear
  C)
   1                                            
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer160) If \[P(x,y)\]denotes \[z=x+iy\]in Argand?s plane and \[\left| \frac{z-1}{z+2i} \right|=1,\]then the locus of P is a/an
  A)
   hyperbola                         
  done clear
  B)
   ellipse
  done clear
  C)
   circle    
  done clear
  D)
   straight line      
  done clear
  View Answer play_arrow

• question_answer161) If \[\sqrt{r}=a{{e}^{\theta \cot \alpha }}\]where a and \[\alpha \]are real numbers, then \[\frac{{{d}^{2}}r}{d{{\theta }^{2}}}-4r{{\cot }^{2}}\alpha \]is
  A)
   r                                            
  done clear
  B)
   \[\frac{1}{r}\]
  done clear
  C)
   1                                            
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer162) The derivative of \[{{\tan }^{-1}}\left[ \frac{\sin x}{1+\cos x} \right]\]with respect to \[{{\tan }^{-1}}\left[ \frac{\cos x}{1+\sin x} \right]\]is
  A)
   2                                            
  done clear
  B)
   -1
  done clear
  C)
   0                                            
  done clear
  D)
   -2
  done clear
  View Answer play_arrow

• question_answer163) \[\frac{d}{dx}\left[ {{\cos }^{2}}\left( {{\cot }^{-1}}\sqrt{\frac{2+x}{2-x}} \right) \right]\]is
  A)
  \[\frac{1}{4}\]                                   
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[-\frac{1}{2}\]                                
  done clear
  D)
   \[-\frac{3}{4}\]
  done clear
  View Answer play_arrow

• question_answer164) If \[f(x)=\frac{{{\sin }^{2}}x}{1+\cot x}+\frac{{{\cos }^{2}}x}{1+\tan x},\]then \[f'\left( \frac{\pi }{4} \right)\]is
  A)
  \[\sqrt{3}\]                                        
  done clear
  B)
   \[\frac{1}{\sqrt{3}}\]
  done clear
  C)
   0                                            
  done clear
  D)
   \[-\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer165) If \[{{\cos }^{-1}}\left( \frac{y}{b} \right)=n\log \left( \frac{x}{n} \right),\]then
  A)
  \[x{{y}_{1}}=n\sqrt{{{b}^{2}}-{{y}^{2}}}\]
  done clear
  B)
  \[x{{y}_{1}}+n\sqrt{{{b}^{2}}-{{y}^{2}}}=0\]
  done clear
  C)
  \[{{y}_{1}}=x\sqrt{{{b}^{2}}-{{y}^{2}}}\]
  done clear
  D)
  \[x{{y}_{1}}-\sqrt{{{b}^{2}}-{{y}^{2}}}=0\]
  done clear
  View Answer play_arrow

• question_answer166) Area of a triangle formed by tangent and normal to the curve \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{v}^{2}}}=1\]at \[P\left( \frac{a}{\sqrt{2}},\frac{b}{\sqrt{2}} \right)\]with the x-axis is
  A)
   4ab                                       
  done clear
  B)
  \[\frac{ab\sqrt{{{a}^{2}}+{{b}^{2}}}}{4}\]
  done clear
  C)
  \[\frac{ab\sqrt{{{a}^{2}}-{{b}^{2}}}}{4}\]                              
  done clear
  D)
  \[\frac{b({{a}^{2}}+{{b}^{2}})}{4a}\]
  done clear
  View Answer play_arrow

• question_answer167) The angle between\[{{y}^{2}}=4x\]and \[{{x}^{2}}+{{y}^{2}}=12\]at a point of their intersection is
  A)
  \[{{\tan }^{-1}}\sqrt{2}\]                              
  done clear
  B)
  \[{{\tan }^{-1}}2\]
  done clear
  C)
  \[{{\tan }^{-1}}2\sqrt{2}\]                           
  done clear
  D)
   \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer168) A sphere increase its volume at the rate of \[\pi cc/s.\]The rate at which its surface area increases when the radius is 1 cm is
  A)
  \[2\pi \,sq\,cm/s\]                         
  done clear
  B)
  \[\pi \,sq\,cm/s\]
  done clear
  C)
  \[\frac{3\pi }{2}sq\,cm/s\]                          
  done clear
  D)
  \[\frac{\pi }{2}sq\,cm/s\]
  done clear
  View Answer play_arrow

• question_answer169) The value of \[\int_{0}^{4}{|x-1|}\,dx\]is
  A)
   \[\frac{5}{2}\]                                  
  done clear
  B)
   5
  done clear
  C)
   4                                            
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer170) If \[{{I}_{n}}-\int_{0}^{\pi /4}{{{\tan }^{n}}x\,dx,}\]where \[n\]is a positive integer, then\[{{I}_{10}}+{{I}_{8}}\]is
  A)
   \[\frac{1}{9}\]                                  
  done clear
  B)
   \[\frac{1}{8}\]
  done clear
  C)
   \[\frac{1}{7}\]                                  
  done clear
  D)
   9
  done clear
  View Answer play_arrow

• question_answer171) \[\int_{{}}^{{}}{{{e}^{x}}\left[ \frac{\sin x+\cos x}{1-{{\sin }^{2}}x} \right]}\,dx\]is
  A)
  \[({{e}^{x}}.\cos ecx)+C\]           
  done clear
  B)
  \[{{e}^{x}}\cot x+C\]
  done clear
  C)
  \[({{e}^{x}}.\sec x)+C\]
  done clear
  D)
   \[{{e}^{x}}\tan x+C\]
  done clear
  View Answer play_arrow

• question_answer172) When \[x>0,\]then \[\int_{{}}^{{}}{{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)dx}\]is
  A)
  \[2[x{{\tan }^{-1}}x-\log (1+{{x}^{2}})]+C\]
  done clear
  B)
  \[2[x{{\tan }^{-1}}x+\log (1+{{x}^{2}})]+C\]
  done clear
  C)
  \[2x{{\tan }^{-1}}x+\log (1+{{x}^{2}})+C\]
  done clear
  D)
  \[2x{{\tan }^{-1}}x-\log (1+{{x}^{2}})+C\]
  done clear
  View Answer play_arrow

• question_answer173) If the area between \[y=m{{x}^{2}}\]and \[x=m{{y}^{2}}(m>0)\]is \[1/4\,sq\]units, then the value of m is
  A)
  \[\pm \,3\sqrt{2}\]                         
  done clear
  B)
  \[\pm \,\frac{2}{\sqrt{3}}\]
  done clear
  C)
   \[\sqrt{2}\]                                       
  done clear
  D)
   \[\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer174) If \[m\]and \[n\] are degree and order of \[{{(1+y_{1}^{2})}^{2/3}}={{y}_{2}},\]then the value of \[\frac{m+n}{m-n}\]is
  A)
   3                                            
  done clear
  B)
   4
  done clear
  C)
   5                                            
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer175) The general solution of \[{{\left( \frac{dy}{dx} \right)}^{2}}=1-{{x}^{2}}-{{y}^{2}}+{{x}^{2}}{{y}^{2}}\]is
  A)
  \[2{{\sin }^{-1}}y=x\sqrt{1-{{x}^{2}}}+{{\sin }^{-1}}x+C\]
  done clear
  B)
  \[{{\cos }^{-1}}y=x{{\cos }^{-1}}x+C\]
  done clear
  C)
  \[{{\sin }^{-1}}y=\frac{1}{2}{{\sin }^{-1}}x+C\]
  done clear
  D)
  \[2{{\sin }^{-1}}y=x\sqrt{1-{{y}^{2}}}+C\]
  done clear
  View Answer play_arrow

• question_answer176) If\[x\cos \alpha +y\sin \alpha =4\]is tangent to\[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{9}=1,\]then the value of \[\alpha \]is
  A)
  \[{{\tan }^{-1}}(3/7)\]                   
  done clear
  B)
  \[{{\tan }^{-1}}(\sqrt{3}/7)\]
  done clear
  C)
  \[{{\tan }^{-1}}(7/3)\]                   
  done clear
  D)
  \[{{\tan }^{-1}}(3/\sqrt{7})\]
  done clear
  View Answer play_arrow

• question_answer177) If P is a point on \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]with foci S and s?, then the maximum value of \[\Delta SPS'\]is
  A)
   ab                                         
  done clear
  B)
  \[ab{{e}^{2}}\]
  done clear
  C)
   \[abc\]                                
  done clear
  D)
   ab/e
  done clear
  View Answer play_arrow

• question_answer178) In Argand?s plane, the point corresponding to \[\frac{(1-i\sqrt{3})(1+i)}{(\sqrt{3}+i)}\]lies in
  A)
   quadrant I                         
  done clear
  B)
   quadrant II
  done clear
  C)
   quadrant III                      
  done clear
  D)
   quadrant IV
  done clear
  View Answer play_arrow

• question_answer179) If \[y=\sin x.\sin 2x.\sin 3x...\sin n\,x,\]then y? is
  A)
  \[\sum\limits_{k=1}^{n}{k\,\tan \,k\,x}\]                            
  done clear
  B)
  \[y.\sum\limits_{k=1}^{n}{k\,\cot \,kx}\]
  done clear
  C)
   \[y.\sum\limits_{k=1}^{n}{k\,\tan \,kn}\]                           
  done clear
  D)
  \[\sum\limits_{k=1}^{n}{\cot kx}\]
  done clear
  View Answer play_arrow

• question_answer180) \[\left| \begin{matrix}    \sin \alpha  & \cos \alpha  & \sin (\alpha +\delta )  \\    \sin \beta  & \cos \beta  & \sin (\beta +\delta )  \\    \sin \gamma  & \cos \gamma  & \sin (\gamma +\delta )  \\ \end{matrix} \right|\] is equal to
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   \[1+\sin \alpha \sin \beta \sin \gamma \]
  done clear
  D)
   \[1-(sin\alpha -sin\beta )(sin\beta -sin\gamma )\]\[(sin\gamma -sin\alpha )\]
  done clear
  View Answer play_arrow