Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010

done CET - Karnataka Engineering Solved Paper-2010 Total Questions - 179

• question_answer1)  All capacitors used in the diagram are identical and each is of capacitance C. Then the effective capacitance between the point A and B is
  A)
  1.5 C
  done clear
  B)
  6 C
  done clear
  C)
  C
  done clear
  D)
  3 C
  done clear
  View Answer play_arrow

• question_answer2)  Two identical conducting balls A and B have positive charges \[{{q}_{1}}\] and \[{{q}_{2}}\] respectively but \[{{q}_{1}}\ne {{q}_{2}}.\] The balls are brought together so that they touch each other and then kept in their original positions. The force between them is
  A)
  less than that before the balls touched
  done clear
  B)
  greater than that before the balls touched
  done clear
  C)
  same as that before the balls touched
  done clear
  D)
  zero
  done clear
  View Answer play_arrow

• question_answer3)    Red light of wavelength 625 nm is incident normally on an optical diffraction grating with \[2\times {{10}^{5}}\] lines/m. Including central principal maxima, how many maxima may be observed on a screen which is far from the grating?  
  A)
  15
  done clear
  B)
  17
  done clear
  C)
  8
  done clear
  D)
  16
  done clear
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• question_answer4)  A battery of emf E has an internal resistance r. A variable resistance R is connected to the terminals of the battery. A current; is drawn from the battery. V is the terminal potential difference. If R alone is gradually reduced to zero, which of the following best describes \[i\]and V?
  A)
  \[i\]approaches zero, V approaches E
  done clear
  B)
  \[i\] approaches \[\frac{E}{r}\], V approaches zero
  done clear
  C)
  \[i\] approaches \[\frac{E}{r}\], V approaches E
  done clear
  D)
  \[i\] approaches infinity, V approaches E
  done clear
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• question_answer5)  Three voltmeters A, B and C having resistances R, 1.5R and 3 R respectively are used in a circuit as shown. When a potential difference is applied between X and Y, the readings of the voltmeters are \[{{V}_{1}},\text{ }{{V}_{2}}\], and \[{{V}_{3}}\]respectively. Then
  A)
  \[{{V}_{1}}={{V}_{2}}={{V}_{3}}\]
  done clear
  B)
  \[{{V}_{1}}<{{V}_{2}}={{V}_{3}}\]
  done clear
  C)
  \[{{V}_{1}}>{{V}_{2}}>{{V}_{3}}\]
  done clear
  D)
  \[{{V}_{1}}>{{V}_{2}}={{V}_{3}}\]
  done clear
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• question_answer6)  A point object O is placed in front of a glass rod having spherical end of radius of curvature 30 cm. The image would be formed at
  A)
  30 cm left           
  done clear
  B)
  infinity
  done clear
  C)
  1 cm to the right              
  done clear
  D)
  18 cm to the left
  done clear
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• question_answer7)  A, B and C are the parallel sided transparent media of refractive indices \[{{n}_{1}},{{n}_{2}}\] and \[{{n}_{3}}\]respectively. They are arranged as shown in the figure. A ray is incident at an angle \[i\] on the surface of separation of A and B which is as shown in the figure. After the refraction into the medium B, the ray grazes the surface of separation of the madia B and C. Then, \[\sin i\] equals to
  A)
  \[\frac{{{n}_{3}}}{{{n}_{1}}}\]                                    
  done clear
  B)
  \[\frac{{{n}_{1}}}{{{n}_{3}}}\]
  done clear
  C)
  \[\frac{{{n}_{2}}}{{{n}_{3}}}\]                                   
  done clear
  D)
  \[\frac{{{n}_{1}}}{{{n}_{2}}}\]
  done clear
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• question_answer8)  A boat has green light of wavelength \[\lambda =500\,nm\] on the mast. What wavelength would be measured and what colour would be observed for this light as seen by a diver submerged in water by the side of the boat? Given, \[{{n}_{w}}=\frac{4}{3}\].
  A)
  Green of wavelength 376 nm
  done clear
  B)
  Red of wavelength 665 nm
  done clear
  C)
  Green of wavelength 500 nm
  done clear
  D)
  Blue of wavelength 376 nm
  done clear
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• question_answer9)  Two beams of red and violet colours are made to pass separately through a prism of \[A={{60}^{o}}\]. In the minimum deviation position, the angle of refraction inside the prism will be
  A)
  greater for red colour
  done clear
  B)
  equal but not \[{{30}^{o}}\] for both the colours
  done clear
  C)
  greater for violet colour
  done clear
  D)
  \[{{30}^{o}}\] for both the colours
  done clear
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• question_answer10)  A plano-convex lens is made of refractive index of 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is
  A)
  400 cm
  done clear
  B)
    200 cm
  done clear
  C)
    100 cm                 
  done clear
  D)
    50 cm
  done clear
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• question_answer11)  Two simple harmonic motions are represented by \[{{y}_{1}}=5[\sin 2\pi t+\sqrt{3}\cos 2\pi t]\]and \[{{y}_{2}}=5\sin \left( 2\pi t+\frac{\pi }{4} \right)\] The ratio of their amplitudes is
  A)
  \[1:1\]                                  
  done clear
  B)
  \[2:1\]
  done clear
  C)
  \[1:3\]                                  
  done clear
  D)
  \[\sqrt{3}:1\]
  done clear
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• question_answer12)  A bat flies at a steady speed of \[4\text{ }m{{s}^{-1}}\] emitting a sound of \[f=90\times {{10}^{3}}Hz\]. It is flying horizontally towards a vertical wall. The frequency of the reflected sound as detected by the bat will be (take velocity of sound in air is \[330\text{ }m{{s}^{-1}}\])
  A)
  \[88.1\times {{10}^{3}}Hz\]        
  done clear
  B)
  \[87.1\times {{10}^{3}}Hz\]
  done clear
  C)
  \[92.1\times {{10}^{3}}Hz\]        
  done clear
  D)
  \[89.1\times {{10}^{3}}Hz\]
  done clear
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• question_answer13)  A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is
  A)
  2
  done clear
  B)
  6
  done clear
  C)
  8
  done clear
  D)
  7
  done clear
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• question_answer14)  A uniform wire of length L, diameter D and density \[\rho \] is stretched under a tension T. The correct relation between, its fundamental frequency \[f\], the length L and the diameter D is
  A)
  \[f\propto \frac{1}{LD}\]                             
  done clear
  B)
  \[f\propto \frac{1}{L\sqrt{D}}\]
  done clear
  C)
  \[f\propto \frac{1}{{{D}^{2}}}\]                
  done clear
  D)
  \[f\propto \frac{1}{L{{D}^{2}}}\]
  done clear
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• question_answer15)  Two small spheres of masses \[{{M}_{1}}\] and \[{{M}_{2}}\]are suspended by weightless insulating threads of lengths \[{{L}_{1}}\] and \[{{L}_{2}}\]. The spheres carry charges \[{{Q}_{1}}\] and \[{{Q}_{2}}\] respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\] as shown. Which one of the following conditions is essential, if \[{{\theta }_{1}}={{\theta }_{2}}\]?
  A)
  \[{{M}_{1}}\ne {{M}_{2}},\] but \[{{Q}_{1}}={{Q}_{2}}\]
  done clear
  B)
  \[{{M}_{1}}={{M}_{2}}\]
  done clear
  C)
  \[{{Q}_{1}}={{Q}_{2}}\]                
  done clear
  D)
  \[{{L}_{1}}={{L}_{2}}\]
  done clear
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• question_answer16)  The wavelength of the light used in Young's double slit experiment is \[\lambda \]. The intensity at a point on the screen is \[I\], where the path difference is \[\frac{\lambda }{6}\]. If \[{{I}_{0}}\] denotes the maximum intensity, then the ratio of \[I\] and \[{{I}_{0}}\] is
  A)
  0.866                                    
  done clear
  B)
  0.5
  done clear
  C)
  0.707                                    
  done clear
  D)
  0.75
  done clear
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• question_answer17)  What is the minimum thickness of a thin film required for constructive interference in the reflected light from it? Given, the refractive index of the film = 1.5, wavelength of the light incident on the film = 600 nm.
  A)
  100 nm                                
  done clear
  B)
  300 nm
  done clear
  C)
  50 nm                                   
  done clear
  D)
  200 nm
  done clear
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• question_answer18)  There is a uniform electric field of intensity E which is as shown. How many labelled points have the same electric potential as the fully shaded point?  
  A)
  2
  done clear
  B)
  3
  done clear
  C)
  8
  done clear
  D)
  11
  done clear
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• question_answer19)  Critical angle for certain medium is \[si{{n}^{-1}}(0.6)\]. The polarizing angle of that medium is
  A)
  \[ta{{n}^{-1}}[1.5]\]                       
  done clear
  B)
  \[{{\sin }^{-1}}[0.8]\]
  done clear
  C)
  \[{{\tan }^{-1}}[1.6667]\]             
  done clear
  D)
  \[{{\tan }^{-1}}[0.6667]\]
  done clear
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• question_answer20)  The speed of electromagnetic wave in vacuum depends upon the source of radiation
  A)
  increases as we move from \[\gamma \]-rays to radio waves
  done clear
  B)
  decreases as we move from \[\gamma \]-rays to radio waves
  done clear
  C)
  is same for all of them
  done clear
  D)
  None of the above
  done clear
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• question_answer21)  The moment of inertia of a circular disc of radius 2 m and mass 1 kg about an axis passing through the centre of mass but perpendicular to the plane of the disc is\[2\text{ }kg\text{ }{{m}^{2}}\]. Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is (see the given figure).
  A)
  \[8\text{ }kg\text{ }{{m}^{2}}\]                
  done clear
  B)
  \[4\text{ }kg\text{ }{{m}^{2}}\]
  done clear
  C)
  \[10\text{ }kg\text{ }{{m}^{2}}\]                              
  done clear
  D)
  \[6\text{ }kg\text{ }{{m}^{2}}\]
  done clear
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• question_answer22)  An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of earth. Which of the following could explain this?
  A)
  Both the mass and radius of the planet are half as that of earth
  done clear
  B)
  Radius of the planet is half as that of earth, but the mass is the same as that of earth
  done clear
  C)
  Both the mass and radius of the planet are twice as that of earth
  done clear
  D)
  Mass of the planet is half as that of earth, but radius is same as that of earth
  done clear
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• question_answer23)  Which of the following substances has the highest elasticity?
  A)
  Sponge                                
  done clear
  B)
  Steel
  done clear
  C)
  Rubber                                
  done clear
  D)
  Copper
  done clear
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• question_answer24)  Three liquids of equal masses are taken in three identical cubical vessels A, B and C. Their densities are \[{{\rho }_{A}},{{\rho }_{B}}\] and \[{{\rho }_{C}}\]respectively but \[{{\rho }_{A}}<{{\rho }_{B}}<{{\rho }_{C}}.\] The force exerted by the liquid on the base of the cubical vessel is
  A)
  maximum in vessel C
  done clear
  B)
  minimum in vessel C
  done clear
  C)
  the same in all the vessels
  done clear
  D)
  maximum in vessel A
  done clear
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• question_answer25)  Water is in streamline flows along a horizontal pipe with non-uniform cross-section. At a point in the pipe where the area of cross section is \[10\text{ }c{{m}^{2}}\], the velocity of water is \[1\text{ }m{{s}^{-1}}\] and the pressure is 2000 Pa. The pressure at another point where the cross sectional area is \[5\text{ }c{{m}^{2}}\] is
  A)
  4000 Pa                
  done clear
  B)
  2000 Pa
  done clear
  C)
  1000 Pa                
  done clear
  D)
  500 Pa
  done clear
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• question_answer26)  In the circuit given here, the points A, B and C are 70 V, zero, 10 V respectively. Then
  A)
  the point D will be at a potential of 60 V
  done clear
  B)
  the point D will be at a potential of 20 V
  done clear
  C)
  currents in the paths AD, DB and DC are in the ratio of \[1:2:3\]
  done clear
  D)
   currents in the paths AB, DB and DC are in the ratio of \[3:2:1\]
  done clear
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• question_answer27)  \[{{B}_{1}},{{B}_{2}}\] and \[{{B}_{3}}\] are the three identical bulbs connected to a battery of steady emf with key K closed. What happens to the brightness of the bulbs \[{{B}_{1}}\] and \[{{B}_{2}}\] when the key is opened?
  A)
  Brightness of the bulb \[{{B}_{1}}\] increases and that of \[{{B}_{2}}\] decreases
  done clear
  B)
  Brightness of the bulbs \[{{B}_{1}}\] and \[{{B}_{2}}\]increase
  done clear
  C)
  Brightness of the bulb \[{{B}_{1}}\] decreases and \[{{B}_{2}}\]increases
  done clear
  D)
  Brightness of the bulbs \[{{B}_{1}}\] and \[{{B}_{2}}\]decrease
  done clear
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• question_answer28)  Magnetic field at the centre of a circular coil of radius R due to \[i\] flowing through it is B. The magnetic field at a point along the axis at distance R from the centre is
  A)
  \[\frac{B}{2}\]                                  
  done clear
  B)
  \[\frac{B}{4}\]
  done clear
  C)
  \[\frac{B}{\sqrt{8}}\]                     
  done clear
  D)
  \[\sqrt{8}B\]
  done clear
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• question_answer29)  Two thick wires and two thin wires, all of same material and same length, form a square in three different ways P, Q and R as shown in the figure. With correct connections shown, the magnetic field due to the current flow, at the centre of the loop will be zero in case of
  A)
  Q and R                               
  done clear
  B)
  P only
  done clear
  C)
  P and Q               
  done clear
  D)
  P and R
  done clear
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• question_answer30)  There is a uniform magnetic field directed perpendicular and into the plane of the paper. An irregular shaped conducting loop is slowly changing into a circular loop in the plane of the paper. Then
  A)
  current is induced in the loop in the anticlockwise direction
  done clear
  B)
  current is induced in the loop in the clockwise direction
  done clear
  C)
  AC is induced in the loop
  done clear
  D)
  no current is induced in the loop
  done clear
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• question_answer31)  The dimensions of resistance are same as those of..... .where h is the Planck's constant, e is the charge.
  A)
  \[\frac{{{h}^{2}}}{{{e}^{2}}}\]                                    
  done clear
  B)
  \[\frac{{{h}^{2}}}{e}\]
  done clear
  C)
  \[\frac{h}{{{e}^{2}}}\]                                   
  done clear
  D)
  \[\frac{h}{e}\]
  done clear
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• question_answer32)  A train is moving slowly on a straight track with a constant speed of \[2\text{ }m{{s}^{-1}}\]. A passenger in that train starts walking at a steady speed of \[2\text{ }m{{s}^{-1}}\] to the back of the train in the opposite direction of the motion of the train. So to an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to be
  A)
  \[4\,m{{s}^{-1}}\]
  done clear
  B)
  \[2\,m{{s}^{-1}}\]
  done clear
  C)
  \[2\,m{{s}^{-1}}\] in the opposite direction of the train
  done clear
  D)
  zero
  done clear
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• question_answer33)  A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right as shown relative to its initial position with respect to the table, the ball
  A)
  Both (1) and (2)               
  done clear
  B)
  only (3)
  done clear
  C)
  only (1)                
  done clear
  D)
  only (2)                
  done clear
  View Answer play_arrow

• question_answer34)  A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
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• question_answer35)  If the linear momentum of a body is increased by 50%, then the kinetic energy of that body increases by
  A)
  100%                                    
  done clear
  B)
  125%
  done clear
  C)
  225%                                    
  done clear
  D)
  25%
  done clear
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• question_answer36)  The temperature of a gas contained in a closed vessel of constant volume increases by \[{{1}^{o}}C\] when the pressure of the gas is increased by 1%. The initial temperature of the gas is
  A)
  100 K                                    
  done clear
  B)
  \[{{273}^{o}}C\]
  done clear
  C)
  \[{{100}^{o}}C\]               
  done clear
  D)
  200 K
  done clear
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• question_answer37)  A motorboat covers a given distance in 6 h moving downstream on a river. It covers the same distance in 10 h moving upstream. The time it takes to cover the same distance in still water is
  A)
  9 h                                         
  done clear
  B)
  7.5 h
  done clear
  C)
  6.5 h                                     
  done clear
  D)
  8 h
  done clear
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• question_answer38)  Two slabs are of the thicknesses \[{{d}_{1}}\] and \[{{d}_{2}}\]. Their thermal conductivities are \[{{K}_{1}}\] and \[{{K}_{2}}\] respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\]. Assume \[{{\theta }_{1}}>{{\theta }_{2}}\]. The temperature \[\theta \] of their common junction is
  A)
    \[\frac{{{K}_{1}}{{\theta }_{1}}+{{K}_{2}}{{\theta }_{2}}}{{{\theta }_{1}}+{{\theta }_{2}}}\]                           
  done clear
  B)
    \[\frac{{{K}_{1}}{{\theta }_{1}}{{d}_{1}}+{{K}_{2}}{{\theta }_{2}}{{d}_{2}}}{{{K}_{1}}{{d}_{2}}+{{K}_{2}}{{d}_{1}}}\]
  done clear
  C)
    \[\frac{{{K}_{1}}{{\theta }_{1}}{{d}_{2}}+{{K}_{2}}{{\theta }_{2}}{{d}_{1}}}{{{K}_{1}}{{d}_{2}}+{{K}_{2}}{{d}_{1}}}\]               
  done clear
  D)
    \[\frac{{{K}_{1}}{{\theta }_{1}}+{{K}_{2}}{{\theta }_{2}}}{{{K}_{1}}+{{K}_{2}}}\]
  done clear
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• question_answer39)  Hot water cools from \[{{60}^{o}}C\] to \[{{50}^{o}}C\] in the first 10 min and to \[{{42}^{o}}C\] in the next 10 min. Then the temperature of the surroundings is
  A)
  \[{{20}^{o}}C\]                 
  done clear
  B)
  \[{{30}^{o}}C\]
  done clear
  C)
  \[{{15}^{o}}C\]                                 
  done clear
  D)
  \[{{10}^{o}}C\]
  done clear
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• question_answer40)  The efficiency of Carnot's heat heat engine is 0.5 when the temperature of the source is \[{{T}_{1}}\]that of sink is \[{{T}_{2}}\]. The efficiency of source. Carnot's heat engine is also 0.5. The temperatures of source and second engine are respectively
  A)
  \[2{{T}_{1}},2{{T}_{2}}\]                               
  done clear
  B)
  \[2{{T}_{1}},\frac{{{T}_{2}}}{2}\]
  done clear
  C)
  \[{{T}_{1}}+5,\,{{T}_{2}}-5\]       
  done clear
  D)
  \[{{T}_{1}}+10,\,{{T}_{2}}-10\]  
  done clear
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• question_answer41)  A current \[i\] is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre of the loop is \[\frac{{{\mu }_{0}}i}{R}\] times
  A)
    \[\frac{5}{16},\] but out of the plane of the paper
  done clear
  B)
    \[\frac{5}{16},\] but into the plane of the paper
  done clear
  C)
    \[\frac{7}{16},\] but out of the plane of the paper
  done clear
  D)
    \[\frac{7}{16},\] but into the plane of the paper
  done clear
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• question_answer42)  An ideal choke draws a current of 8 A when connected to an AC supply of 100 V, 50 Hz. A pure resistor draws a current of 10 A when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the AC source of 150 V, 40 Hz. The current in the circuit becomes
  A)
    \[\frac{15}{\sqrt{2}}A\]                                
  done clear
  B)
    8 A
  done clear
  C)
    18 A                                      
  done clear
  D)
    10 A
  done clear
  View Answer play_arrow

• question_answer43)  The spectrum of an oil flame is an example for
  A)
  line emission spectrum
  done clear
  B)
  continuous emission spectrum
  done clear
  C)
  line absorption spectrum
  done clear
  D)
  band emission spectrum
  done clear
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• question_answer44)  According to Einstein's photoelectric equation, the graph of KE of the photoelectron emitted from the metal versus the frequency of the incident radiation gives a straight line graph, whose slope
  A)
  depends on the intensity of the incident radiation
  done clear
  B)
  depends on the nature of the metal and also on the intensity of incident radiation
  done clear
  C)
  is same for all metals and independent of the intensity of the incident radiation
  done clear
  D)
  depends on the nature of the metal
  done clear
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• question_answer45)  An electron is moving in an orbit of a hydrogen atom from which there can be a maximum of six transition. An electron is moving in an orbit of another hydrogen atom from which there can be a maximum of three transition. The ratio of the velocities of the electron in these two orbits is
  A)
  \[\frac{1}{2}\]                                   
  done clear
  B)
  \[\frac{2}{1}\]
  done clear
  C)
  \[\frac{5}{4}\]                                   
  done clear
  D)
  \[\frac{3}{4}\]
  done clear
  View Answer play_arrow

• question_answer46)  \[{{v}_{1}}\] is the frequency of the series limit of Lyman series, \[{{v}_{2}}\] is the frequency of the first line of Lyman series and \[{{v}_{3}}\] is the frequency of the series limit of the Balmer series. Then
  A)
  \[{{v}_{1}}-{{v}_{2}}={{v}_{3}}\]                               
  done clear
  B)
  \[{{v}_{1}}={{v}_{2}}-{{v}_{3}}\]
  done clear
  C)
  \[\frac{1}{{{v}_{1}}}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{3}}}\]      
  done clear
  D)
  \[\frac{1}{{{v}_{1}}}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{3}}}\]
  done clear
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• question_answer47)  Assume the graph of specific binding energy versus mass number is as shown in the figure. Using this graph, select the correct choice from the following.
  A)
    Fusion of two nuclei of mass number lying in the range of \[100<A<200\] will release energy
  done clear
  B)
    Fusion of two nuclei of mass number lying in the range of \[51<A<100\] will release energy
  done clear
  C)
    Fusion of two nuclei of mass number lying in the range of \[1<A<50\] will release energy
  done clear
  D)
  Fission of the nucleus of mass number lying in the rang of \[100<A<200\] will release energy when broken into two fragments
  done clear
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• question_answer48)  Pick out the correct statement from the following.
  A)
  Energy released per unit mass of the reactant is less in case of fusion reaction
  done clear
  B)
  Packing fraction may be positive or may be negative
  done clear
  C)
  \[P{{u}^{239}}\] is not suitable for a fission reaction
  done clear
  D)
  For stable nucleus, the specific binding energy is low
  done clear
  View Answer play_arrow

• question_answer49)  A radioactive sample \[{{S}_{1}}\] having the activity \[{{A}_{1}}\] has twice the number of nuclei as another sample \[{{S}_{2}}\] of activity \[{{A}_{2}}\]. If \[{{A}_{2}}=2{{A}_{1}}\], then the ratio of half-life of \[{{S}_{1}}\] to the half-life of \[{{S}_{2}}\] is
  A)
  4
  done clear
  B)
  2
  done clear
  C)
  0.25
  done clear
  D)
  0.75
  done clear
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• question_answer50)  When a neutron is disintegrated to give a \[\beta \]-particle,
  A)
  a neutrino alone is emitted
  done clear
  B)
  a proton and neutrino are emitted
  done clear
  C)
  a proton alone is emitted
  done clear
  D)
  a proton and an antineutrino are emitted
  done clear
  View Answer play_arrow

• question_answer51)  The forbidden energy gap in Ge is 0.72 eV, Given, \[hc=12400\text{ }eV-\overset{o}{\mathop{A}}\,\]. The maximum wavelength of radiation that will generate electron hole pair is
  A)
  \[172220\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  B)
    \[172.2\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]  
  done clear
  C)
  \[17222\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  D)
  \[1722\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  View Answer play_arrow

• question_answer52)  In a p-n junction diode not connected to any circuit
  A)
  the potential is the same everywhere
  done clear
  B)
  the p-type side has a higher potential than the n-type side
  done clear
  C)
  there is an electric field at the junction  directed from the n-type side to p-type side
  done clear
  D)
  there is an electric field at the junction directed from the p-type side to n-type side
  done clear
  View Answer play_arrow

• question_answer53)  In a given direction, the intensities of the scattered light by a scattering substance for two beams of light are in the ratio of \[256:81\]. The ratio of the frequency of the first beam to the frequency of the second beam is
  A)
  \[64:127\]                           
  done clear
  B)
  \[1:2\]
  done clear
  C)
  \[64:27\]                             
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer54)  Identify the logic operation performed by the circuit given here.
  A)
  OR                                         
  done clear
  B)
  NOR
  done clear
  C)
  NOT                                      
  done clear
  D)
  NAND
  done clear
  View Answer play_arrow

• question_answer55)  The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is ...... (radius of the first orbit of hydrogen atom\[=0.53\overset{o}{\mathop{A}}\,\]).
  A)
  \[1.67\overset{o}{\mathop{A}}\,\]                         
  done clear
  B)
  \[3.33\overset{o}{\mathop{A}}\,\]
  done clear
  C)
  \[1.06\overset{o}{\mathop{A}}\,\]                         
  done clear
  D)
  \[0.53\overset{o}{\mathop{A}}\,\]
  done clear
  View Answer play_arrow

• question_answer56)  PQ and RS are long parallel conductors   separated by certain distance. M is the midpoint between them (see the figure). The net magnetic field at M is B. Now, the current 2 A is switched off. The field at M now becomes
  A)
  2 B                                         
  done clear
  B)
  B
  done clear
  C)
  \[\frac{B}{2}\]
  done clear
  D)
  35
  done clear
  View Answer play_arrow

• question_answer57)  An electron enters the space between the plates of a charged capacitor as shown. The charge density on the plate is \[\sigma \]. Electric intensity in the space between the plates is A uniform magnetic field B also exists in the space perpendicular to the direction of E. The electron moves perpendicular to both \[\overrightarrow{E}\] and \[\overrightarrow{B}\] without any change in direction. The time taken by the electron to travel a distance l in the space is
  A)
  \[\frac{\sigma l}{{{\varepsilon }_{0}}B}\]                              
  done clear
  B)
  \[\frac{\sigma B}{{{\varepsilon }_{0}}l}\]
  done clear
  C)
  \[\frac{{{\varepsilon }_{0}}lB}{\sigma B}\]                           
  done clear
  D)
  \[\frac{{{\varepsilon }_{0}}l}{\sigma B}\]
  done clear
  View Answer play_arrow

• question_answer58)  In a series resonant R-L-C circuit, the voltage across R is 100 V and the value of \[R=1000\,\Omega \]. The capacitance of the capacitor is \[2\times {{10}^{-6}}F\]; angular frequency of AC is \[200\text{ }rad\text{ }{{s}^{-1}}\]. Then the potential difference across the inductance coil is
  A)
  100 V                                    
  done clear
  B)
  40 V
  done clear
  C)
  250 V                                    
  done clear
  D)
  400 V
  done clear
  View Answer play_arrow

• question_answer59)  A capacitor and an inductance coil are connected in separate AC circuits with a bulb glowing in both the circuits. The bulb glows more brightly when
  A)
  an iron rod is introduced into the inductance coil
  done clear
  B)
  the number of turns in the inductance coil is increased
  done clear
  C)
  separation between the plates of the capacitor is increased
  done clear
  D)
  a dielectric is introduced into the gap between the plates of the capacitor
  done clear
  View Answer play_arrow

• question_answer60)  A charge +Q is moving upwards vertically. It enters a magnetic field directed to north. The force on the charge will be towards
  A)
  north                                    
  done clear
  B)
  south
  done clear
  C)
  east                                      
  done clear
  D)
  west
  done clear
  View Answer play_arrow

• question_answer61)  In the electrolytic refining of zinc
  A)
  graphite is at the anode
  done clear
  B)
  the impure metal is at the cathode
  done clear
  C)
  the metal ion get reduced at the anode
  done clear
  D)
  acidified zinc sulphate is the electrolyte
  done clear
  View Answer play_arrow

• question_answer62)  The wave number of the spectral line in the emission spectrum of hydrogen will be equal to \[\frac{8}{9}\] times the Rydberg's constant if the electron jumps from
  A)
  \[n=3\] to \[n=1\]           
  done clear
  B)
  \[n=10\] to \[n=1\]
  done clear
  C)
  \[n=9\] to \[n=1\]           
  done clear
  D)
  \[n=2\] to \[n=1\]
  done clear
  View Answer play_arrow

• question_answer63)  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)
  \[K_{1}^{2}=\frac{1}{{{K}_{2}}}\]             
  done clear
  B)
  \[2{{K}_{1}}=K_{2}^{2}\]
  done clear
  C)
  \[{{K}_{2}}=\frac{2}{K_{1}^{2}}\]                             
  done clear
  D)
  \[K_{2}^{2}=\frac{1}{{{K}_{1}}}\]
  done clear
  View Answer play_arrow

• question_answer64)  Enthalpy of vaporization of benzene is \[+\,\,35.3\,kJ\,\,mo{{l}^{-1}}\] at its boiling point, \[{{80}^{o}}C\]. The entropy change in the transition of the vapour to liquid at its boiling point in \[[J{{K}^{-1}}mo{{l}^{-1}}]\] is
  A)
  -441                                      
  done clear
  B)
  -100
  done clear
  C)
  +441                                     
  done clear
  D)
  +100
  done clear
  View Answer play_arrow

• question_answer65)  Which one of the following conversions involve change in both hybridisation and shape?
  A)
    \[C{{H}_{4}}\xrightarrow{{}}{{C}_{2}}{{H}_{6}}\]               
  done clear
  B)
    \[N{{H}_{3}}\xrightarrow{{}}NH_{4}^{+}\]
  done clear
  C)
    \[B{{F}_{3}}\xrightarrow{{}}BF_{4}^{-}\]              
  done clear
  D)
    \[{{H}_{2}}O\xrightarrow{{}}{{H}_{3}}{{O}^{+}}\]
  done clear
  View Answer play_arrow

• question_answer66)  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_answer67)  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 entropy change is negative
  done clear
  B)
  Equilibrium constant is greater than one
  done clear
  C)
  The reaction should be instantaneous
  done clear
  D)
  The reaction is thermodynamically not feasible
  done clear
  View Answer play_arrow

• question_answer68)  Out of the compounds below the vapour pressure of at a particular temperature is
  A)
  higher than that of
  done clear
  B)
  lower than that of
  done clear
  C)
  higher or lower than, depending on the size of the vessel
  done clear
  D)
  same as that of 
  done clear
  View Answer play_arrow

• question_answer69)  The amount of heat evolved when \[500\text{ }c{{m}^{3}}\] of \[0.1\text{ }M\,HCl\] is mixed with \[200\text{ }c{{m}^{3}}\] of \[0.2\text{ }NaOH\] is
  A)
  2.292 kJ               
  done clear
  B)
  1.292kJ
  done clear
  C)
  0.292 kJ                               
  done clear
  D)
  3.392 kJ
  done clear
  View Answer play_arrow

• question_answer70)  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_answer71)  The set of quantum numbers for the outermost electron for copper in its ground state is
  A)
  \[4,\,\,1,\,\,1,+\frac{1}{2}\]        
  done clear
  B)
  \[3,\,\,2,\,\,2,+\frac{1}{2}\]
  done clear
  C)
  \[4,\,\,0,\,\,0,+\frac{1}{2}\]        
  done clear
  D)
  \[4,\,\,2,\,\,2,+\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer72)  Peroxide ion ......
  A)
  (ii) and (iii)          
  done clear
  B)
  (i), (ii) and (iv)
  done clear
  C)
  (i), (ii) and (iii)  
  done clear
  D)
  (i) and (iv)
  done clear
  View Answer play_arrow

• question_answer73)  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)
  The heat of hydrogenation of benzene is less than the theoretical value
  done clear
  D)
  The bond angle between the carbon-carbon bonds is \[{{120}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer74)  A mixture of \[CaC{{l}_{2}}\] and \[NaCl\] weighing 4.44 g is treated with sodium carbonate solution to precipitate all the \[C{{a}^{2+}}\] 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 (atomic mass of \[Ca=40\]) is
  A)
  75                                          
  done clear
  B)
  30.6
  done clear
  C)
  25                                          
  done clear
  D)
  69.4
  done clear
  View Answer play_arrow

• question_answer75)  For one mole of an ideal gas, increasing the temperature from \[{{10}^{o}}C\] to \[{{20}^{o}}C\]
  A)
  increases the average kinetic energy by two times
  done clear
  B)
  increases the rms velocity by \[\sqrt{2}\] times
  done clear
  C)
  increases the rms velocity by two times
  done clear
  D)
  increases both the average kinetic energy and rms velocity, but not significantly
  done clear
  View Answer play_arrow

• question_answer76)  Generally, the first ionization energy increases along a period. But there are some exceptions. One which is not an exception is
  A)
  N and O               
  done clear
  B)
  Na and Mg
  done clear
  C)
  Mg and Al           
  done clear
  D)
  Be and B
  done clear
  View Answer play_arrow

• question_answer77)  \[50\,\,c{{m}^{3}}\] of \[0.2\text{ }N\,HCl\] is titrated against \[0.1\text{ }N\,NaOH\] solution. The titration is discontinued after adding \[50\,\,c{{m}^{3}}\] of \[NaOH\]. The remaining titration is completed by adding \[0.5\text{ }N\,KOH\]. 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)
  \[25\,\,c{{m}^{3}}\]                       
  done clear
  D)
  \[10.5\,\,c{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer78)  In which one of the following, does the given amount of chlorine exert the least pressure in a vessel of capacity \[1\,\,d{{m}^{3}}\] at 273 K?
  A)
  0.0355 g
  done clear
  B)
  0.071 g
  done clear
  C)
  \[6.023\times {{20}^{21}}\]molecules
  done clear
  D)
  0.02 mol
  done clear
  View Answer play_arrow

• question_answer79)  Based on the first law of thermodynamics, which one of the following is correct?
  A)
  For an isochoric process \[=\Delta E=-q\]
  done clear
  B)
  For an adiabatic process \[=\Delta E=-w\]
  done clear
  C)
  For an isothermal process \[=q=+w\]
  done clear
  D)
  For a cyclic process \[q=-w\]
  done clear
  View Answer play_arrow

• question_answer80)  For alkali metals, which one of the following trends is incorrect?
  A)
  Hydration energy: \[Li>Na>K>Rb\]
  done clear
  B)
  Ionization energy: \[Li>Na>K>Rb\]
  done clear
  C)
  Density: \[Li<Na<K<Rb\]
  done clear
  D)
  Atomic size: \[Li<Na<K<Rb\]
  done clear
  View Answer play_arrow

• question_answer81)  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 in the zinc layer is approximately
  A)
  89
  done clear
  B)
  91
  done clear
  C)
  97
  done clear
  D)
  94
  done clear
  View Answer play_arrow

• question_answer82)  One mole of an organic compound A with the formula \[{{C}_{3}}{{H}_{8}}O\] reacts completely with two moles of HI to form X and Y. When Y is boiled with aqueous alkali it forms Z. Z answers the iodoform test. The compound A is
  A)
  propan-2-ol       
  done clear
  B)
  propan-1-ol
  done clear
  C)
  ethoxyethane                  
  done clear
  D)
  methoxyethane
  done clear
  View Answer play_arrow

• question_answer83)    The IUPAC name of \[{{K}_{2}}[Ni{{(CN)}_{4}}]\] is  
  A)
  potassium tetracyanonickelate (II)
  done clear
  B)
  potassium tetracyanatonickelate (III)
  done clear
  C)
  potassium tetracyanatonickelate (II)
  done clear
  D)
  potassium tetracyanonickelate (III)
  done clear
  View Answer play_arrow

• question_answer84)  The spin only magnetic moment of \[M{{n}^{4+}}\] ion is nearly
  A)
  3 BM                                     
  done clear
  B)
  6 BM
  done clear
  C)
  4 BM                                     
  done clear
  D)
  5 BM
  done clear
  View Answer play_arrow

• question_answer85)  In Kjeldahl’s method, ammonia from 5 g of food neutralizes \[30\,c{{m}^{3}}\] of 0.1 N acid. The percentage of nitrogen in the food is
  A)
  8.4
  done clear
  B)
    8.4
  done clear
  C)
    16.8                                       
  done clear
  D)
    1.68
  done clear
  View Answer play_arrow

• question_answer86)  Carbon can reduce ferric oxide to iron at a temperature above 983 K because
  A)
  carbon monoxide formed is thermodynamically less stable than ferric oxide
  done clear
  B)
  carbon has a higher affinity towards oxidation than iron
  done clear
  C)
  free energy change for the formation of carbon dioxide is less negative than that for ferric oxide
  done clear
  D)
  iron has a higher affinity towards oxygen than carbon
  done clear
  View Answer play_arrow

• question_answer87)  An oxygen containing organic compound upon oxidation forms a carboxylic acid as the only organic product with its molecular mass higher by 14 units. The organic compound is
  A)
  an aldehyde
  done clear
  B)
  a primary alcohol
  done clear
  C)
  a secondary alcohol
  done clear
  D)
  acetone
  done clear
  View Answer play_arrow

• question_answer88)  The compound obtained when acetaldehyde reacts with dilute aqueous sodium hydroxide exhibits
  A)
  geometrical isomerism
  done clear
  B)
  optical isomerism
  done clear
  C)
  neither optical nor geometrical isomerism
  done clear
  D)
  both optical and geometrical isomerism
  done clear
  View Answer play_arrow

• question_answer89)  The activation energy for a reaction at the temperature TK was found to be\[2.303\text{ }RT\text{ }J\text{ }mo{{l}^{-1}}\]. The ratio of the rate constant to Arrhenius factor is
  A)
  \[{{10}^{-1}}\]                                  
  done clear
  B)
  \[{{10}^{-2}}\]
  done clear
  C)
  \[2\times {{10}^{-3}}\]                  
  done clear
  D)
  \[2\times {{10}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer90)  A dibromo derivative of an alkane reacts with sodium metal to form an alicyclic hydrocarbon. The derivative is
  A)
  1,1-dibromopropane
  done clear
  B)
  2, 2-dibromobutane
  done clear
  C)
  1, 2-dibromoethane
  done clear
  D)
  1, 4-dibromobutane
  done clear
  View Answer play_arrow

• question_answer91)  Time required for 100 per cent completion of a zero order reaction is
  A)
  \[\frac{2k}{a}\]                                
  done clear
  B)
  \[\frac{a}{2k}\]
  done clear
  C)
  \[\frac{a}{k}\]                                   
  done clear
  D)
  \[ak\]
  done clear
  View Answer play_arrow

• question_answer92)  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)
  11
  done clear
  C)
  9
  done clear
  D)
  12
  done clear
  View Answer play_arrow

• question_answer93)  Which one of the following is wrongly matched?
  A)
  \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\]       - Square planar
  done clear
  B)
  \[[Ni{{(CO)}_{4}}]\]                         - Neutral ligand
  done clear
  C)
  \[[Fe{{(C{{N}_{6}})}^{3-}}]\]                       - \[s{{p}^{3}}{{d}^{2}}\]
  done clear
  D)
  \[{{[Co{{(en)}_{3}}]}^{3+}}\]      - Follows EAN rule
  done clear
  View Answer play_arrow

• question_answer94)  Which one of the following conformations of cyclohexane is the least stable?
  A)
  Half-chair            
  done clear
  B)
  Boat
  done clear
  C)
  Twisted-boat                    
  done clear
  D)
  Chair
  done clear
  View Answer play_arrow

• question_answer95)  Which one of the following is a molecular crystal?
  A)
  Rock salt             
  done clear
  B)
  Quartz
  done clear
  C)
  Dry ice                                 
  done clear
  D)
  Diamond
  done clear
  View Answer play_arrow

• question_answer96)  A buffer solution contains 0.1 mole of sodium acetate in \[1000\,\,c{{m}^{3}}\] 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 equal to
  A)
  \[p{{K}_{a}}-\log \,2\]                   
  done clear
  B)
  \[p{{K}_{a}}\]
  done clear
  C)
  \[p{{K}_{a}}+\,2\]                           
  done clear
  D)
  \[p{{K}_{a}}+\log \,2\]
  done clear
  View Answer play_arrow

• question_answer97)  Which one of the following has the most nucleophilic nitrogen?
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer98)  Chloroacetic acid is a stronger acid than acetic acid. This can be explained using
  A)
  -M effect            
  done clear
  B)
  -I effect
  done clear
  C)
  + M effect          
  done clear
  D)
  +I effect
  done clear
  View Answer play_arrow

• question_answer99)  The correct sequence of reactions to convert p-nitrophenol into quinol involves
  A)
  reduction, diazotization and hydrolysis
  done clear
  B)
  hydrolysis, diazotization and reduction
  done clear
  C)
  hydrolysis, reduction and diazotization
  done clear
  D)
  diazotization, reduction and hydrolysis
  done clear
  View Answer play_arrow

• question_answer100)  \[C{{H}_{3}}C{{H}_{2}}Br\xrightarrow[\Delta ]{aq.\,KOH}a=\xrightarrow[\Delta ]{KMn{{O}_{4}}/{{H}^{+}}}\]\[B\xrightarrow[\Delta ]{N{{H}_{3}}}C\xrightarrow[alkali]{B{{r}_{2}}}D,'D'\] is
  A)
  \[C{{H}_{3}}Br\]                               
  done clear
  B)
  \[C{{H}_{3}}COON{{H}_{2}}\]
  done clear
  C)
  \[C{{H}_{3}}N{{H}_{2}}\]                              
  done clear
  D)
  \[CHB{{r}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer101)  The letter ‘D’ in D-glucose signifies
  A)
  configuration at all chiral carbons
  done clear
  B)
  dextrorotatory
  done clear
  C)
  that it is a monosaccharide
  done clear
  D)
  configuration at a particular chiral carbon
  done clear
  View Answer play_arrow

• question_answer102)  Reaction of methyl bromide with aqueous sodium hydroxide involves
  A)
  racemization
  done clear
  B)
  \[{{S}_{N}}1\] mechanism
  done clear
  C)
  retention of configuration
  done clear
  D)
  \[{{S}_{N}}2\] mechanism
  done clear
  View Answer play_arrow

• question_answer103)  9.65 C of electric current is passed through fused anhydrous magnesium chloride. The magnesium metal thus, obtained is completely converted into a Grignard reagent. The number of moles of the 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_answer104)  Which one of the following does not involve coagulation?
  A)
  Formation of delta regions
  done clear
  B)
  Peptization
  done clear
  C)
  Treatment of drinking water by potash alum
  done clear
  D)
  Clotting of blood by the use of ferric chloride
  done clear
  View Answer play_arrow

• question_answer105)    In alkaline medium, alanine exists predominantly as  
  A)
    anion                                    
  done clear
  B)
      Zwitterion  
  done clear
  C)
    cation                                   
  done clear
  D)
    covalent form
  done clear
  View Answer play_arrow

• question_answer106)  The standard emf of galvanic cell involving 3 moles of electrons in its redox reaction is 0.59 V. The equilibrium constant for the reaction of the cell is
  A)
    \[{{10}^{25}}\]                                  
  done clear
  B)
    \[{{10}^{20}}\]
  done clear
  C)
    \[{{10}^{15}}\]                                  
  done clear
  D)
    \[{{10}^{30}}\]
  done clear
  View Answer play_arrow

• question_answer107)    Benzaldehyde and acetone can be best distinguished using  
  A)
    Fehling's solution
  done clear
  B)
    Sodium hydroxide solution
  done clear
  C)
    2, 4-DNP
  done clear
  D)
    Tollen's reagent
  done clear
  View Answer play_arrow

• question_answer108)    Which one of the following statements is true?  
  A)
    Saponification of oil yields a diol
  done clear
  B)
    Drying of oil involves hydrolysis
  done clear
  C)
    Addition of antioxidant to oil minimizes rancidity
  done clear
  D)
    Refining of oil involves hydrogenation
  done clear
  View Answer play_arrow

• question_answer109)    The following data is obtained during the first order thermal decomposition of \[2A(g)\xrightarrow{{}}B(g)+C(s)\]at constant volume and temperature.  

  S.N.	Time	Total pressure in Pascal
  1.	At the end of 10 min	300
  2.	After completion	200

    The rate constant in \[{{\min }^{-1}}\] is  
  A)
    0.0693                                  
  done clear
  B)
    6.93
  done clear
  C)
    0.00693                
  done clear
  D)
      69.3  
  done clear
  View Answer play_arrow

• question_answer110)  Phenol \[\xrightarrow{X}\] forms a tribromo derivative. ‘’X’’ is
  A)
  bromine in benzene
  done clear
  B)
  bromine in water
  done clear
  C)
  potassium bromide solution
  done clear
  D)
  bromine in carbon tetrachloride at \[{{0}^{o}}C\]
  done clear
  View Answer play_arrow

• question_answer111)  The correct sequence of steps involved in the mechanism of Cannizaro’s reaction is
  A)
  nucleophilic attack, transfer of \[{{H}^{-}}\]and transfer of \[{{H}^{+}}\]
  done clear
  B)
  transfer of \[{{H}^{-}}\], transfer of \[{{H}^{+}}\] and nucleophilic attack
  done clear
  C)
  transfer if \[{{H}^{+}}\] nucleophilic attack and transfer of \[{{H}^{-}}\]
  done clear
  D)
  electrophilic attack by \[O{{H}^{-}}\], transfer of\[{{H}^{+}}\] and transfer of \[{{H}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer112)  Which one of the following is an example for homogeneous catalysis?
  A)
  Manufacture of sulphuric acid by Contact process
  done clear
  B)
  Manufacture of ammonia by Habeas process
  done clear
  C)
  Hydrolysis of sucrose in presence of dilute hydrochloric acid
  done clear
  D)
  Hydrogenation of oil
  done clear
  View Answer play_arrow

• question_answer113)  The empirical formula of a non-electrolyte is \[C{{H}_{2}}O\]. A solution containing 6 g of the compound exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The molecular formula of the compound is
  A)
    \[{{C}_{2}}{{H}_{4}}{{O}_{2}}\]                  
  done clear
  B)
    \[{{C}_{3}}{{H}_{6}}{{O}_{3}}\]
  done clear
  C)
    \[{{C}_{5}}{{H}_{10}}{{O}_{5}}\]               
  done clear
  D)
    \[{{C}_{4}}{{H}_{8}}{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer114)    A white crystalline salt A reacts with dilute \[HCl\] to liberate a suffocating gas B and also forms a yellow precipitate. The gas B turns potassium dichromate acidified with dilute \[{{H}_{2}}S{{O}_{4}}\] to a green coloured solution C. A, B and C are respectively  
  A)
  \[N{{a}_{2}}S{{O}_{3}},\,S{{O}_{2}}\,\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]
  done clear
  B)
  \[N{{a}_{2}}{{S}_{2}}{{O}_{3}},\,S{{O}_{2}}\,\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]
  done clear
  C)
  \[N{{a}_{2}}S,\,\,S{{O}_{2}},\,\,\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]
  done clear
  D)
  \[N{{a}_{2}}S{{O}_{4}},\,\,S{{O}_{2}},\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer115)  Molecules of a noble gas do not possess vibrational energy because a noble gas
  A)
  is monoatomic
  done clear
  B)
  is chemically inert
  done clear
  C)
  has completely filled shells
  done clear
  D)
  is diamagnetic
  done clear
  View Answer play_arrow

• question_answer116)  \[1\,\,d{{m}^{3}}\] solution containing \[{{10}^{-5}}\] moles each of \[C{{l}^{-}}\] ions and \[CrO_{4}^{2-}\] ions is treated with \[{{10}^{-4}}\] moles of silver nitrate. Which one of the following observations is made? \[[{{K}_{sp}}A{{g}_{2}}Cr{{O}_{4}}=4\times {{10}^{-12}}]\]
  A)
  Precipitation does not occur
  done clear
  B)
  Silver chromate gets precipitated first
  done clear
  C)
  Silver chloride gets precipitated first
  done clear
  D)
  Both silver chromate and silver chloride start precipitating simultaneously
  done clear
  View Answer play_arrow

• question_answer117)  pH value of which one of the following is not equal to one?
  A)
  \[0.1\text{ }M\text{ }HN{{O}_{3}}\]
  done clear
  B)
  \[0.05\text{ }M\text{ }{{H}_{2}}S{{O}_{4}}\]
  done clear
  C)
  \[0.1\text{ }M\text{ }C{{H}_{3}}COOH\]
  done clear
  D)
  \[50\,\,c{{m}^{3}}\]of \[0.4\,\,M\]\[HCl+50\,\,c{{m}^{3}}\]of \[0.2\,M\,NaOH\]
  done clear
  View Answer play_arrow

• question_answer118)    \[{{E}_{1}},\,{{E}_{2}},{{E}_{3}}\] are the emf values of the three galvanic cells respectively.      

  (i) \[Zn|Zn_{1M}^{2+}||Cu_{0.1M}^{2+}|Cu\]

  (ii) \[Zn|Zn_{1M}^{2+}||Cu_{1M}^{2+}|Cu\]

  (iii) \[Zn|Zn_{0.1\,M}^{2+}||Cu_{1M}^{2+}|Cu\]

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

• question_answer119)    The IUPAC name of is  
  A)
    2-methyl-3-bromohexanal
  done clear
  B)
    - 3-bromo-2-methylbutanal
  done clear
  C)
    2-methyl-3-bromobutanal
  done clear
  D)
    3-bromo-2-methylpentanal
  done clear
  View Answer play_arrow

• question_answer120)  Which one of the following forms propane nitrile as the major product?
  A)
  Ethyl bromide + alcoholic \[KCN\]
  done clear
  B)
  Propyl bromide + alcoholic \[KCN\]
  done clear
  C)
  Propyl bromide + alcoholic \[AgCN\]
  done clear
  D)
  Ethyl bromide + alcoholic \[AgCN\]
  done clear
  View Answer play_arrow

• question_answer121)  If then \[{{A}^{2}}+xA+I=0\]  for \[(x,y)\] is
  A)
    \[(-4,1)\]                             
  done clear
  B)
    \[(-1,3)\]
  done clear
  C)
    \[(4,-1)\]                             
  done clear
  D)
    \[(1,3)\]
  done clear
  View Answer play_arrow

• question_answer122)  The constant term of the polynomial is
  A)
  0
  done clear
  B)
  2
  done clear
  C)
  -1
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer123)  If \[\vec{a},\vec{b}\] and \[\vec{c}\] are non-zero coplanar vectors, then \[[2\vec{a}-\vec{b}3\vec{b}-\vec{c}4\vec{c}-\vec{a}]\] is
  A)
  \[25\]                                   
  done clear
  B)
  \[0\]
  done clear
  C)
  \[27\]                                   
  done clear
  D)
  \[9\]
  done clear
  View Answer play_arrow

• question_answer124)  A space vector makes the angles \[{{150}^{o}}\] and \[{{60}^{o}}\] with the positive direction of x-and y-axes. The angle made by the vector with the positive direction z-axis is
  A)
  \[{{90}^{o}}\]                                    
  done clear
  B)
  \[{{60}^{o}}\]
  done clear
  C)
  \[{{180}^{o}}\]                                 
  done clear
  D)
  \[{{120}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer125)  If \[\vec{a},\vec{b}\]and \[\vec{c}\] are unit vectors, such that \[\vec{a}+\vec{b}+\vec{c}=\vec{0},\]then  \[3\vec{a}.\vec{b}+2\,\vec{b}.\vec{c}+\vec{c}.\vec{a}\]
  A)
  -1
  done clear
  B)
  1
  done clear
  C)
  -3
  done clear
  D)
  3
  done clear
  View Answer play_arrow

• question_answer126)  If \[a>b>c,\] \[{{\sec }^{-1}}\frac{a+b}{a-b}=2{{\sin }^{-1}}x,\] then x is
  A)
  \[-\sqrt{\frac{b}{a+b}}\]                              
  done clear
  B)
  \[\sqrt{\frac{b}{a+b}}\]
  done clear
  C)
  \[-\sqrt{\frac{a}{a+b}}\]                              
  done clear
  D)
  \[\sqrt{\frac{a}{a+b}}\]
  done clear
  View Answer play_arrow

• question_answer127)  If \[x\ne n\pi ,\] \[x\ne (2n+1)\frac{\pi }{2},\] \[n\in Z,\] then \[\frac{{{\sin }^{-1}}(\cos x)+{{\cos }^{-1}}(\sin x)}{{{\tan }^{-1}}(\cot x)+{{\cot }^{-1}}(\tan x)}\] is
  A)
  \[\frac{\pi }{2}\]                                              
  done clear
  B)
  \[\frac{\pi }{6}\]
  done clear
  C)
  \[\frac{\pi }{4}\]                                              
  done clear
  D)
  \[\frac{\pi }{3}\]
  done clear
  View Answer play_arrow

• question_answer128)  The general solution \[1+{{\sin }^{2}}3\sin x.\cos x,\tan x\ne \frac{1}{2},\]is
  A)
  \[2n\pi +\frac{\pi }{4},n\in Z\]
  done clear
  B)
  \[2n\pi -\frac{\pi }{4},n\in Z\]
  done clear
  C)
  \[n\pi -\frac{\pi }{4},n\in Z\]
  done clear
  D)
  \[n\pi +\frac{\pi }{4},n\in Z\]
  done clear
  View Answer play_arrow

• question_answer129)  The least positive integer n, for which \[\frac{{{(1+i)}^{n}}}{{{(1-i)}^{n-2}}}\] is positive, is
  A)
  3
  done clear
  B)
  4
  done clear
  C)
  1
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer130)  If \[x+iy={{(-1+i\sqrt{3})}^{2010}},\] then x is
  A)
  \[-{{2}^{2010}}\]                              
  done clear
  B)
  \[{{2}^{2010}}\]
  done clear
  C)
  \[1\]                                     
  done clear
  D)
  \[-1\]
  done clear
  View Answer play_arrow

• question_answer131)  \[(\sin \theta +\cos \theta )\,(\tan \theta +cot\theta )\] is equal to
  A)
  \[\sin \theta \,\cos \theta \]
  done clear
  B)
  \[1\]
  done clear
  C)
  \[\sec \theta +\text{cosec}\theta \]
  done clear
  D)
  \[\sec \theta \,\,\text{cosec}\theta \]
  done clear
  View Answer play_arrow

• question_answer132)  This sides of a triangle are \[6+2\sqrt{3},4\sqrt{3}\] and \[\sqrt{24}.\] the tangent of the smallest angle of the triangle is
  A)
  \[\frac{1}{\sqrt{3}}\]                                     
  done clear
  B)
  \[\sqrt{2}-1\]
  done clear
  C)
  \[\sqrt{3}\]                                        
  done clear
  D)
  \[1\]
  done clear
  View Answer play_arrow

• question_answer133)  A simple graph contains 24 edges. Degree of each vertex is 3. The number of vertices is
  A)
  8
  done clear
  B)
  12
  done clear
  C)
  21
  done clear
  D)
  16
  done clear
  View Answer play_arrow

• question_answer134)  \[\underset{x\to \infty }{\mathop{\lim }}\,\,n\,\sin \frac{2\pi }{3n}.\cos \frac{2\pi }{3n}\] is
  A)
  \[\frac{\pi }{6}\]                                              
  done clear
  B)
  \[\frac{2\pi }{3}\]
  done clear
  C)
  \[1\]                                     
  done clear
  D)
  \[\frac{\pi }{3}\]
  done clear
  View Answer play_arrow

• question_answer135)  The function \[f(x)=[x],\]  where [x] denotes the greatest integer not greater than x, is
  A)
  continuous for all non-integral values of x
  done clear
  B)
  continuous only at positive integral values of x
  done clear
  C)
  continuous for all real values of x
  done clear
  D)
  continuous only at rational values of x
  done clear
  View Answer play_arrow

• question_answer136)  The greatest value of x satisfying \[~21=385\](mod x) and \[587=167\] (mod x) is
  A)
  \[156\]                                 
  done clear
  B)
  \[32\]
  done clear
  C)
  \[28\]                                   
  done clear
  D)
  \[56\]
  done clear
  View Answer play_arrow

• question_answer137)  The number \[({{49}^{2}}-4)({{49}^{3}}-49)\] is divisible by
  A)
  \[7!\]                                    
  done clear
  B)
  \[9!\]
  done clear
  C)
  \[6!\]                                    
  done clear
  D)
  \[5!\]
  done clear
  View Answer play_arrow

• question_answer138)  The least positive integer x satisfying\[{{2}^{2010}}\equiv 3x\](mod 5) is
  A)
  3
  done clear
  B)
  4
  done clear
  C)
  1
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer139)  If A and B are two square matrices of the same order such that \[AB=B\]and \[BA=A,\] then \[{{A}^{2}}+{{B}^{2}}\]is always equal to
  A)
  \[I\]                                      
  done clear
  B)
  \[A+B\]
  done clear
  C)
  \[2AB\]                                
  done clear
  D)
  \[2BA\]
  done clear
  View Answer play_arrow

• question_answer140)  If A is a \[3\times 3\] non-singular matrix and if \[|A|=3,\]then \[|{{(2A)}^{-1}}|\] is
  A)
  \[24\]                                   
  done clear
  B)
  \[3\]
  done clear
  C)
  \[\frac{1}{3}\]                                   
  done clear
  D)
  \[\frac{1}{24}\]
  done clear
  View Answer play_arrow

• question_answer141)  If   \[a,-a,\] b   are   the   roots   of \[{{x}^{3}}-5{{x}^{2}}-x+5=0,\]  then b is a root of
  A)
  \[{{x}^{2}}+3x-20=0\]
  done clear
  B)
  \[{{x}^{2}}-5x+10=0\]
  done clear
  C)
  \[{{x}^{2}}-3x-10=0\]
  done clear
  D)
    \[{{x}^{2}}+5x-30=0\]  
  done clear
  View Answer play_arrow

• question_answer142)  In the binomial expansion of \[{{(1+x)}^{15}},\] the coefficients of \[{{x}^{r}}\] and \[{{x}^{r+3}}\] are equal. Then, r is
  A)
  \[8\]                                     
  done clear
  B)
  \[7\]
  done clear
  C)
  \[4\]                                     
  done clear
  D)
  \[6\]
  done clear
  View Answer play_arrow

• question_answer143)  The   nth   term   of   the   series \[1+3+7+13+21+.....\] is 9901. The value of n is
  A)
  \[100\]                                 
  done clear
  B)
  \[90\]
  done clear
  C)
  \[900\]                                 
  done clear
  D)
  \[99\]
  done clear
  View Answer play_arrow

• question_answer144)  If \[\frac{1}{(3-5x)(2+3x)}=\frac{A}{3-5x}+\frac{B}{2+3x},\]  then \[A:B\] is
  A)
  \[2:3\]                                  
  done clear
  B)
  \[5:3\]
  done clear
  C)
  \[3:5\]                                  
  done clear
  D)
  \[3:2\]
  done clear
  View Answer play_arrow

• question_answer145)  If \[\hat{i},\hat{j},\hat{k}\] are unit vectors along the positive direction of x, y and z-axes, then a false statement in the following is
  A)
  \[\Sigma \hat{i}\times (\hat{j}+\hat{k})=\vec{0}\]
  done clear
  B)
  \[\Sigma \hat{i}\times (\hat{j}\times \hat{k})=\vec{0}\]
  done clear
  C)
  \[\Sigma \,\hat{i}.(\hat{j}\times \hat{k})=\vec{0}\]
  done clear
  D)
  \[\Sigma \,\hat{i}.(\hat{j}+\hat{k})=\vec{0}\]
  done clear
  View Answer play_arrow

• question_answer146)  In P(X), the power set of a non-empty set X, an binary operation * is defined by\[A\,*\,B=A\cup B,\forall A,B\in P(x)\] under *, a true statement is
  A)
  identity law is not satisfied
  done clear
  B)
  inverse law is not satisfied
  done clear
  C)
  commutative law is not satisfied
  done clear
  D)
  associative law is not satisfied
  done clear
  View Answer play_arrow

• question_answer147)  The inverse of 2010 in the group \[{{Q}^{+}}\] of all positive rational under the binary operation * defined by \[a*b=\frac{ab}{2010},\forall \,a,b\in {{Q}^{+}},\] is
  A)
  \[2009\]                              
  done clear
  B)
  \[2011\]
  done clear
  C)
  \[1\]                                     
  done clear
  D)
  \[2010\]
  done clear
  View Answer play_arrow

• question_answer148)  If the three function \[f(x),g(x)\] and \[h(x)\] are such that \[h(x)=f(x).g(x)\] and \[f'(x).g'(x)=c\] where c is constant, then
  A)
  \[h'=(x).h''(x)\]
  done clear
  B)
  \[\frac{h(x)}{h''(x)}\]
  done clear
  C)
  \[\frac{h''(x)}{h(x)}\]
  done clear
  D)
  \[\frac{h(x)}{h'(x)}\]
  done clear
  View Answer play_arrow

• question_answer149)  The derivative of \[{{e}^{ax}}\,\,\cos \,bx\]with respect x is \[r{{e}^{ax}}\,\,\cos \,bx\,\,{{\tan }^{-1}}\frac{b}{a}.\] When \[a>0,b>0,\]then value of r, is
  A)
  \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
  done clear
  B)
  \[\frac{1}{\sqrt{ab}}\]
  done clear
  C)
  \[ab\]
  done clear
  D)
  \[a+b\]
  done clear
  View Answer play_arrow

• question_answer150)  The chord of the circle \[{{x}^{2}}+{{y}^{2}}-4x=0\] which is bisected at \[(1,0)\] is perpendicular to the line
  A)
  \[y=x\]
  done clear
  B)
  \[x+y=0\]
  done clear
  C)
  \[x=1\]
  done clear
  D)
  \[y=1\]        
  done clear
  View Answer play_arrow

• question_answer151)  In \[\Delta ABC,\]if \[a=2,b={{\tan }^{-1}}\frac{1}{2}\] and \[C={{\tan }^{-1}}\frac{1}{3},\] then (A, b) equals
  A)
  \[\frac{3\pi }{4},\frac{2}{\sqrt{5}}\]
  done clear
  B)
  \[\frac{\pi }{4},\frac{2\sqrt{2}}{\sqrt{5}}\]
  done clear
  C)
  \[\frac{3\pi }{4},\frac{2\sqrt{2}}{\sqrt{5}}\]
  done clear
  D)
  \[\frac{\pi }{4},\frac{2}{\sqrt{5}}\]
  done clear
  View Answer play_arrow

• question_answer152)  The straight line \[2x+3y-k=0,\] \[k>0\] cuts the x and y-axes at A and B. The area of \[\Delta OAB,\], where 0 is the origin, is \[12\text{ }sq\]unit.    The equation of the circle having AB as diameter is
  A)
  \[{{x}^{2}}+{{y}^{2}}-6x-4y=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}+4x-6y=0\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}-6x+4y=0\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}-4x-6y=0\]
  done clear
  View Answer play_arrow

• question_answer153)  Let \[P(x,y)\] be the mid point of the line joining \[(1,0)\] to a point on the curve Then, locus of P is symmetrical about
  A)
    \[y-axis\]
  done clear
  B)
    \[x-axis\]
  done clear
  C)
    \[x=1\]
  done clear
  D)
    \[y=1\]
  done clear
  View Answer play_arrow

• question_answer154)  The function \[f(x)=|x-2|+x\] is
  A)
  differentiable at both \[x=2\] and \[x=0\]
  done clear
  B)
  differentiable at \[x=2\] but not at \[x=0\]
  done clear
  C)
  continuous at \[x=2\]but not at \[x=0\]
  done clear
  D)
  continuous at both \[x=2\] and \[x=0\]
  done clear
  View Answer play_arrow

• question_answer155)  Let R be an equivalence relation defined on a set containing 6 elements. The minimum number or ordered pairs that R should contain is
  A)
  \[12\]                                   
  done clear
  B)
  \[6\]    
  done clear
  C)
  \[64\]                                   
  done clear
  D)
  \[36\]
  done clear
  View Answer play_arrow

• question_answer156)  The line joining \[A(2,-7)\] and \[B(6,5)\] is divided into 4 equal parts by the points P, Q and R such that\[AQ=RP=QB\]. The mid-point of PR is
  A)
  \[(4,12)\]                            
  done clear
  B)
  \[(-8,1)\]
  done clear
  C)
  \[(4,-1)\]                             
  done clear
  D)
  \[(8,-2)\]
  done clear
  View Answer play_arrow

• question_answer157)  Let \[P\equiv (-1,0),\] \[Q\equiv (0,0)\] and \[R=(3,3)\] be three points. The equation of the bisector of the angle PQR is
  A)
  \[x-\sqrt{3}y=0\]    
  done clear
  B)
  \[\sqrt{3}x-y=0\]
  done clear
  C)
  \[x+\sqrt{3}y=0\]    
  done clear
  D)
  \[\sqrt{3}x+y=0\]
  done clear
  View Answer play_arrow

• question_answer158)  If m is the slope of one of the lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0,\]then \[{{(h+bm)}^{2}}\] is equal to
  A)
  \[{{(a+b)}^{2}}\]
  done clear
  B)
  \[{{(a-b)}^{2}}\]
  done clear
  C)
  \[{{h}^{2}}+ab\]
  done clear
  D)
  \[{{h}^{2}}-ab\]
  done clear
  View Answer play_arrow

• question_answer159)  \[\cos {{12}^{o}}\,\cot {{102}^{o}}+\cot {{102}^{o}}\,\cot {{66}^{o}}\]\[+\cot {{66}^{o}}\,\cot {{12}^{o}}\] is
  A)
  \[-2\]                                    
  done clear
  B)
  \[1\]
  done clear
  C)
  \[-1\]                                    
  done clear
  D)
  \[2\]
  done clear
  View Answer play_arrow

• question_answer160)  A wire of length \[20\text{ }cm\]is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is
  A)
  \[20\text{ }sq\text{ }cm\]       
  done clear
  B)
  \[25\text{ }sq\text{ }cm\]
  done clear
  C)
  \[10\,\,sq\,\,cm\]       
  done clear
  D)
  \[30\,\,sq\,\,cm\]
  done clear
  View Answer play_arrow

• question_answer161)  Two circles centred at \[(2,3)\] and \[(5,6)\] intersect each other. If the radii are equal, the equation of the common chord is
  A)
  \[x+y+1=0\]
  done clear
  B)
  \[x-y+1=0\]
  done clear
  C)
  \[x+y-8=0\]
  done clear
  D)
  \[x-y-8=0\]
  done clear
  View Answer play_arrow

• question_answer162)  Equation of the circle centred at \[(4,3)\] touching the circle \[{{x}^{2}}+{{y}^{2}}=1\]externally, is
  A)
  \[{{x}^{2}}+{{y}^{2}}-8x-6y+9=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}+8x+6y+9=0\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}+8x-6y+9=0\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}-8x6y+9=0\]
  done clear
  View Answer play_arrow

• question_answer163)  The points \[(1,0),\] \[(0,1),\] \[(0,0)\]  and \[(2k,3k),k\ne 0\]  are concyclic, if k is
  A)
  \[\frac{1}{5}\]                                   
  done clear
  B)
  \[-\frac{1}{5}\]
  done clear
  C)
  \[-\frac{5}{13}\]                                               
  done clear
  D)
  \[\frac{5}{13}\]
  done clear
  View Answer play_arrow

• question_answer164)  The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola \[{{x}^{2}}=-\text{ }8y\] is
  A)
  \[x=2\]                                
  done clear
  B)
  \[x=-2\]
  done clear
  C)
  \[y=2\]                                
  done clear
  D)
  \[y=-2\]
  done clear
  View Answer play_arrow

• question_answer165)  The condition for the line \[y=mx+c\]to be a normal to the parabola \[{{y}^{2}}=4ax\] is
  A)
  \[c=-2am-a{{m}^{3}}\]
  done clear
  B)
  \[c=-\frac{a}{m}\]
  done clear
  C)
  \[c=\frac{a}{m}\]
  done clear
  D)
  \[c=2am+a{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer166)  The eccentric angle of the point \[(2,\sqrt{3})\]  lying on \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{4}=1\] is
  A)
  \[\frac{\pi }{4}\]                                              
  done clear
  B)
  \[\frac{\pi }{2}\]
  done clear
  C)
  \[\frac{\pi }{3}\]                                              
  done clear
  D)
  \[\frac{\pi }{6}\]
  done clear
  View Answer play_arrow

• question_answer167)  The distance of the focus of \[{{x}^{2}}-{{y}^{2}}=4,\]form the directrix which is nearer to it, is
  A)
  \[4\sqrt{2}\]                                      
  done clear
  B)
  \[8\sqrt{2}\]
  done clear
  C)
  \[2\sqrt{2}\]                                      
  done clear
  D)
  \[\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer168)  If \[\int{f(x)\,\sin x.\cos x\,dx}\]\[=\frac{1}{2({{b}^{2}}-{{a}^{2}})}\log f(x)+c,\]where c is the constant of integration, then \[f(x)\] is
  A)
  \[\frac{2}{ab\,\,\cos \,\,2x}\]
  done clear
  B)
  \[\frac{2}{({{b}^{2}}-{{a}^{2}})\,\cos \,2x}\]
  done clear
  C)
  \[\frac{2}{ab\,\sin \,2x}\]
  done clear
  D)
  \[\frac{2}{({{b}^{2}}-{{a}^{2}})\,\sin \,2x}\]
  done clear
  View Answer play_arrow

• question_answer169)  If  \[\int{\frac{\sqrt{x}}{x(x+1)}}\,dx=k\,{{\tan }^{-1}}m,\]then \[(k,m)\] is
  A)
  \[(2,x)\]                              
  done clear
  B)
  \[(1,x)\]
  done clear
  C)
  \[(1,\sqrt{x})\]                 
  done clear
  D)
  \[(2,\sqrt{x})\]
  done clear
  View Answer play_arrow

• question_answer170)  \[\int_{0}^{\pi /4}{\frac{\sin \,x+\cos x}{3+\sin 2x}}dx\] is
  A)
  \[\frac{1}{4}\log 3\]
  done clear
  B)
  \[\log 3\]
  done clear
  C)
  \[\frac{1}{2\log \,3}\]
  done clear
  D)
  \[2\log 3\]
  done clear
  View Answer play_arrow

• question_answer171)  \[\int_{0}^{1}{x{{(1-x)}^{3/2}}}dx\] is
  A)
  \[-\frac{2}{35}\]                               
  done clear
  B)
  \[\frac{4}{35}\]
  done clear
  C)
    \[\frac{24}{35}\]                                                
  done clear
  D)
  \[-\frac{8}{35}\]
  done clear
  View Answer play_arrow

• question_answer172)  The area bounded by the curve \[y=\left\{ \begin{matrix}    {{x}^{2}}, & x<0  \\    x, & x\ge 0  \\ \end{matrix} \right.\] and the line \[y=4,\] is
  A)
  \[\frac{32}{3}\]                                
  done clear
  B)
  \[\frac{8}{3}\]
  done clear
  C)
  \[\frac{40}{3}\]                                
  done clear
  D)
  \[\frac{16}{3}\]
  done clear
  View Answer play_arrow

• question_answer173)  The order and degree of the differential equation   \[y=\frac{dp}{dx}x=\sqrt{{{a}^{2}}{{p}^{2}}+{{b}^{2}}},\]where  \[p=\frac{dy}{dx}\] (here a and b are arbitrary constants) respectively are
  A)
  \[2,2\]                                  
  done clear
  B)
  \[1,1\]
  done clear
  C)
  \[1,2\]                                  
  done clear
  D)
  \[2,1\]
  done clear
  View Answer play_arrow

• question_answer174)  The general solution of the differential equation \[2x\frac{dy}{dx}-y=3\] is a family of
  A)
  hyperbolas      
  done clear
  B)
  parabolas
  done clear
  C)
  straight lines   
  done clear
  D)
  circles
  done clear
  View Answer play_arrow

• question_answer175)  If \[x=a\,{{\cos }^{3}}\theta \]and \[y=a\,{{\sin }^{3}}\,\theta ,\] then \[\frac{dy}{dx}\] is
  A)
  \[\sqrt[3]{\frac{y}{x}}\]                                
  done clear
  B)
  \[\sqrt[3]{\frac{x}{y}}\]
  done clear
  C)
  \[-\sqrt[3]{\frac{x}{y}}\]                              
  done clear
  D)
  \[-\sqrt[3]{\frac{y}{x}}\]
  done clear
  View Answer play_arrow

• question_answer176)  If \[y={{\tan }^{-1}}\sqrt{{{x}^{2}}-1},\]  then the ratio \[\frac{{{d}^{2}}y}{d{{x}^{2}}}:\frac{dy}{dx}\] is
  A)
  \[\frac{x({{x}^{2}}-1)}{1+2{{x}^{2}}}\]
  done clear
  B)
  \[\frac{1-2{{x}^{2}}}{x({{x}^{2}}-1)}\]
  done clear
  C)
    \[\frac{1+2{{x}^{2}}}{x({{x}^{2}}+1)}\]  
  done clear
  D)
  \[\frac{x({{x}^{2}}+1)}{1-2{{x}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer177)  P is the point of contact of the tangent form the origin to the curve\[y=lo{{g}_{e}}\text{ }x\]. The length of the perpendicular drawn form the origin to the normal at P is
  A)
  \[\frac{1}{2e}\]                                
  done clear
  B)
  \[\frac{1}{e}\]
  done clear
  C)
  \[2\sqrt{{{e}^{2}}+1}\]                 
  done clear
  D)
  \[\sqrt{{{e}^{2}}+1}\]
  done clear
  View Answer play_arrow

• question_answer178)  For the curve \[4{{x}^{5}}=5{{y}^{4}},\] the ratio of the    cube of the subtangent at a point on the curve the square of the subnormal at the same point is
  A)
  \[\frac{{{4}^{4}}}{5}\]                                    
  done clear
  B)
  \[\frac{{{5}^{4}}}{4}\]
  done clear
  C)
  \[\frac{{{4}^{4}}}{{{5}^{4}}}\]                                     
  done clear
  D)
  \[{{\left( \frac{5}{4} \right)}^{4}}\]
  done clear
  View Answer play_arrow

• question_answer179)  The set of real values of x for which \[f(x)=\frac{x}{\log \,x}\]is increasing, is
  A)
  \[\{x:x\ge e\}\]
  done clear
  B)
  empty
  done clear
  C)
  \[\{x:x<e\}\]
  done clear
  D)
  \[\{1\}\]
  done clear
  View Answer play_arrow