Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2006

done J and K - CET Engineering Solved Paper-2006 Total Questions - 225

• question_answer1) Vector which   is   perpendicular   to \[a\,\,\cos \,\theta \,\,\hat{i}+b\,\sin \,\theta \,\,\hat{j}\] is
  A)
   \[b\,\sin \,\theta \,\hat{i}-a\,\cos \,\theta \,\hat{j}\]
  done clear
  B)
   \[\frac{1}{a}\,\sin \,\theta \,\hat{i}-a\,\cos \,\theta \,\hat{j}\]
  done clear
  C)
   \[5\hat{k}\]
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer2) Which of the following statements is true?
  A)
   When the coordinate axes are translated the component of a vector in a plane changes
  done clear
  B)
   When the coordinate axes are rotated through some angle components of the vector change but the vector's magnitude remains constant
  done clear
  C)
   Sum of \[\vec{a}\]and \[\vec{b}\] is \[\vec{R}\]. If the magnitude of \[\vec{a}\]alone is increased angle between \[\vec{b}\] and \[\vec{R}\] decreases
  done clear
  D)
   The cross product of \[3\,\,\hat{i}\] and \[4\,\,\hat{j}\] is 12
  done clear
  View Answer play_arrow

• question_answer3) From a balloon rising vertically upwards as \[5\text{ }m/s\]a stone is thrown up at 10 m/s relative to the balloon. Its velocity with respect to ground after \[2\text{ }s\]is (assume\[g=10\text{ }m/{{s}^{2}}\])
  A)
   zero         
  done clear
  B)
   \[5\text{ }m/s\]
  done clear
  C)
   \[10\text{ }m/s\]        
  done clear
  D)
   \[20\text{ }m/s\]
  done clear
  View Answer play_arrow

• question_answer4) Two bodies are projected from ground with equal speed \[20\text{ }m/s\]from the same position in the same vertical plane to have equal range but at different angles above the horizontal. If one of the angle is 30° the sum of their maximum heights is (assume\[g=10\text{ }m/{{s}^{2}}\])
  A)
   \[400\,\,m\]       
  done clear
  B)
   \[20\,\,m\]
  done clear
  C)
   \[30\,\,m\]         
  done clear
  D)
   \[40\,\,m\]
  done clear
  View Answer play_arrow

• question_answer5) Which of the following quantities measured from different inertial reference frames are same?
  A)
   Force        
  done clear
  B)
   Velocity
  done clear
  C)
   Displacement
  done clear
  D)
   Kinetic energy
  done clear
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• question_answer6) Two particles of equal mass are connected to a rope AB of negligible mass, such that one is at end A and the other dividing the length of the rope in the ratio \[1:2\] from B. The rope is rotated about end B in a horizontal plane. Ratio of the tensions in the smaller part to the other is (ignore effect of gravity)
  A)
   \[4:3\]         
  done clear
  B)
   \[1:4\]
  done clear
  C)
   \[1:2\]          
  done clear
  D)
   \[1:3\]
  done clear
  View Answer play_arrow

• question_answer7) Angle of banking for a vehicle speed of \[10\text{ }m/s\] for a radius of curvature \[10\text{ }m\]is (assume\[g=10\text{ }m/{{s}^{2}}\])
  A)
   \[{{30}^{o}}\]       
  done clear
  B)
   \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]
  done clear
  C)
   \[{{60}^{o}}\]          
  done clear
  D)
   \[{{45}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer8) A body of mass \[2\text{ }kg\]is projected at \[20\text{ }m/s\]at an angle \[{{60}^{o}}\] above the horizontal. Power due to the gravitational force at its highest point is
  A)
   \[200\text{ }W\]      
  done clear
  B)
   \[100\sqrt{3\,}W\]
  done clear
  C)
   \[50\,W\]        
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer9) A block of mass \[2\text{ }kg\]rests on a horizontal surface. If a horizontal force of \[5\text{ }N\]is applied on the block the frictional force on, it is \[({{\mu }_{k}}=0.4,\,\,{{\mu }_{s}}=0.5)\]
  A)
   \[5\,\,N\]           
  done clear
  B)
   \[10\,\,N\]
  done clear
  C)
   \[8\,\,N\]           
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer10) Three idential spheresof mass M each are placed at the comers of an equilateral triangle of side \[2m\]. Taking one of the comer as the origin, the position vector of the centre of mass is
  A)
   \[\sqrt{3}\,\,(\hat{i}-\hat{j})\]
  done clear
  B)
   \[\frac{i}{\sqrt{3}}+\hat{j}\]
  done clear
  C)
   \[\frac{\hat{i}+\hat{j}}{3}\]
  done clear
  D)
   \[\hat{i}+\frac{{\hat{j}}}{\sqrt{3}}\]
  done clear
  View Answer play_arrow

• question_answer11) A shell initially at rest explodes into two pieces of equal mass, the two pieces will
  A)
   move with different velocities in different Directions
  done clear
  B)
   move with the same velocity in opposite directions
  done clear
  C)
   move with the same velocity in the same direction
  done clear
  D)
   be at rest
  done clear
  View Answer play_arrow

• question_answer12) Impulse is
  A)
   a scalar
  done clear
  B)
   equal to change in the momentum of a body
  done clear
  C)
   equal to rate of change of momentum of a body
  done clear
  D)
   a force
  done clear
  View Answer play_arrow

• question_answer13) In a head on elastic collision of a very heavy body moving at V with a light body at rest, velocity of heavy body after collision is
  A)
   \[V\]
  done clear
  B)
   \[2\,V\]
  done clear
  C)
   zero          
  done clear
  D)
   \[\frac{V}{2}\]
  done clear
  View Answer play_arrow

• question_answer14) A T Joint is formed by  two identical rods A and B each of mass m and length L in the XY plane as shown. Its moment  of inertia about axis coinciding  with A is
  A)
   \[\frac{2\,m{{L}^{2}}}{3}\]
  done clear
  B)
   \[\frac{\,m{{L}^{2}}}{12}\]
  done clear
  C)
   \[\frac{\,m{{L}^{2}}}{6}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer15) A disc of moment of inertia \[5\text{ }kg-{{m}^{2}}\]is acted upon by a constant torque of\[40\text{ }Nm\]. Starting from rest the time taken by it to acquire an angular velocity of 24 rad/s is
  A)
   \[3\text{ }s\]           
  done clear
  B)
   \[\text{4 }s\]
  done clear
  C)
   \[2.5\,\,s\]         
  done clear
  D)
   \[120\,\,s\]
  done clear
  View Answer play_arrow

• question_answer16) If the angular momentum of a rotating body about a fixed axis is increased by\[10%\]. Its kinetic energy will be increased by
  A)
   \[10%\]        
  done clear
  B)
   \[20%\]
  done clear
  C)
   \[21%\]        
  done clear
  D)
   \[5%\]
  done clear
  View Answer play_arrow

• question_answer17) If the earth were to spin faster, acceleration due to gravity at the poles
  A)
   increases
  done clear
  B)
   decreases
  done clear
  C)
   remains the same
  done clear
  D)
   depends on how fast it spins
  done clear
  View Answer play_arrow

• question_answer18) The time period of an artificial satellite in a circular orbit is independent of
  A)
   the mass of the satellite
  done clear
  B)
   radius of the orbit
  done clear
  C)
   mass of the earth and radius of the earth
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer19) Angle of contact of a liquid with a solid depends on
  A)
   solid only
  done clear
  B)
   liquid only
  done clear
  C)
   both on solid and liquid
  done clear
  D)
   orientation of the solid surface in liquid
  done clear
  View Answer play_arrow

• question_answer20) If longitudinal strain for a wire is \[0.03\] and its Poisson's ratio is \[0.5,\] then its lateral strain is
  A)
   \[0.003\]         
  done clear
  B)
   \[0.0075\]
  done clear
  C)
   \[0.015\]         
  done clear
  D)
    \[0.4\]
  done clear
  View Answer play_arrow

• question_answer21) When the temperature increases, the viscosity of
  A)
   gas decreases and liquid increases
  done clear
  B)
   gas increases and liquid decreases
  done clear
  C)
   gas and liquid increases
  done clear
  D)
   gas and liquid decreases
  done clear
  View Answer play_arrow

• question_answer22) Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is p at a point where flow speed is v, the pressure at another point where the flow of speed is \[2\text{ }v,\]is (take density of water as p)
  A)
   \[p-\frac{3\,\rho {{v}^{2}}}{2}\]
  done clear
  B)
   \[p-\frac{\,\rho {{v}^{2}}}{2}\]
  done clear
  C)
   \[p-\frac{3\,\rho {{v}^{2}}}{4}\]
  done clear
  D)
   \[p-\rho {{v}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer23) Which of the following statements is true?
  A)
   Internal energy of a gas depends only on the state of the gas
  done clear
  B)
   In an isothermal process change in internal energy is maximum
  done clear
  C)
   Area under pressure, volume graph equals heat supplied in any process
  done clear
  D)
   Work done is state dependent but not path dependent                             
  done clear
  View Answer play_arrow

• question_answer24) A gas \[\left( \gamma =\frac{5}{3} \right),\] expands isobaric ally. The percentage, of heat supplied that increases thermal energy and that involved in doing work for expansion is
  A)
   \[40:60\]      
  done clear
  B)
   \[60:40\]
  done clear
  C)
   \[50:50\]      
  done clear
  D)
   \[25:30\]           
  done clear
  View Answer play_arrow

• question_answer25) A perfect black body is one whose emissive power is
  A)
   maximum    
  done clear
  B)
   zero
  done clear
  C)
   unity        
  done clear
  D)
   minimum
  done clear
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• question_answer26) A black body at a temperature T radiates  energy at E. If the temperature falls to \[\frac{T}{2},\] the radiated energy will be
  A)
   \[\frac{E}{4}\]
  done clear
  B)
   \[\frac{E}{2}\]
  done clear
  C)
   \[2E\]
  done clear
  D)
   \[\frac{E}{16}\]
  done clear
  View Answer play_arrow

• question_answer27) If the units of mass, length and time are doubled unit of angular momentum will be .
  A)
   doubled
  done clear
  B)
   tripled
  done clear
  C)
   quadrupled
  done clear
  D)
   8 times the original value
  done clear
  View Answer play_arrow

• question_answer28) Which of the following graphs shows variation of potential energy (U) with position x?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer29) Choose the correct statement
  A)
   Time period of a simple pendulum depends on amplitude
  done clear
  B)
   Time shown by a spring watch varies with acceleration due to gravity
  done clear
  C)
   In a simple pendulum time period varies linearly with the length of the pendulum
  done clear
  D)
   The graph between length of the pendulum and time period is a parabola
  done clear
  View Answer play_arrow

• question_answer30) Time period of a spring mass system is T. If this spring is cut into two parts whose lengths are in the ratio \[1:3\] and the same mass is attached to the longer part, the new time period will be
  A)
   \[\sqrt{\frac{3}{2}}T\]
  done clear
  B)
   \[\frac{T}{\sqrt{3}}\]
  done clear
  C)
   \[\frac{\sqrt{3}T}{2}\]
  done clear
  D)
   \[\sqrt{3}T\]
  done clear
  View Answer play_arrow

• question_answer31) Equation of progressive wave is \[y=A\,\sin \left( 10\,\pi x+11\pi t+\frac{\pi }{3} \right)\]
  A)
   its wavelength is \[2\text{ }units\]
  done clear
  B)
   it is travelling in the positive x-direction
  done clear
  C)
   wave velocity is \[1.5\text{ }units\]
  done clear
  D)
   time period of SHM is 1 s
  done clear
  View Answer play_arrow

• question_answer32) The phenomenon of sound propagation in air is
  A)
   isothermal process
  done clear
  B)
   isobaric process
  done clear
  C)
   adiabatic process
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer33) The second overtone of an open pipe is in resonance with the first overtone of a closed pipe of length \[2\,m\]. Length of the open pipe is
  A)
   \[4\,m\]          
  done clear
  B)
   \[2\,m\]
  done clear
  C)
   \[8\,m\]          
  done clear
  D)
   \[1\,m\]
  done clear
  View Answer play_arrow

• question_answer34) Choose the correct statement
  A)
   Beats are due to destructive interference
  done clear
  B)
   Maximum beat frequency audible to a human being is 20
  done clear
  C)
   Beats are as a result of Doppler?s effect
  done clear
  D)
   Beats are due to superposition of two waves of nearly equal frequencies
  done clear
  View Answer play_arrow

• question_answer35) A motor car is approaching towards a crossing with a velocity of\[72\text{ }km/h\]. The frequency of sound of its horn as heard by a policeman standing on the crossing is\[260\text{ }Hz\]. The frequency of horn is
  A)
   \[200\text{ }Hz\]       
  done clear
  B)
   \[244\text{ }Hz\]
  done clear
  C)
   \[150\text{ }Hz\]       
  done clear
  D)
   \[80\text{ }Hz\]
  done clear
  View Answer play_arrow

• question_answer36) Forces exerted by a uniform electric field on an electron having mass \[{{m}_{e}}\]  and proton of mass \[{{m}_{p}}\]are represented as \[{{F}_{e}}\] and \[{{F}_{p}}\] respectively are related as
  A)
   \[{{F}_{p}}={{F}_{e}}\]
  done clear
  B)
   \[\frac{{{F}_{e}}}{{{F}_{p}}}=\frac{{{m}_{e}}}{{{m}_{p}}}\]
  done clear
  C)
   \[\frac{{{F}_{e}}}{{{F}_{p}}}=\frac{{{m}_{p}}}{{{m}_{e}}}\]
  done clear
  D)
   \[\frac{{{F}_{e}}}{{{F}_{p}}}=\frac{m_{e}^{2}}{m_{p}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer37) Electric field strength due to a dipole at a point on the axial line of dipole is
  A)
   from positive charge to negative charge
  done clear
  B)
   from negative charge to positive charge
  done clear
  C)
   along the equatorial line
  done clear
  D)
   at an angle to axial line
  done clear
  View Answer play_arrow

• question_answer38) Potential and field strength at a certain distance from a point charge are \[600\text{ }V\]and\[200\text{ }N/C\]. Distance of the point from the charge is
  A)
   \[2\,m\]          
  done clear
  B)
   \[4\,m\]
  done clear
  C)
   \[8\,m\]           
  done clear
  D)
   \[3\,m\]
  done clear
  View Answer play_arrow

• question_answer39) Two identical spheres with charges \[4q,-2q\] kept some distance apart exert a force F on each other. If they are made to touch each other and replaced at their old positions, the force between them will be
  A)
   \[\frac{1}{9}F\]          
  done clear
  B)
   \[\frac{1}{8}F\]
  done clear
  C)
   \[\frac{9}{8}F\]
  done clear
  D)
   \[\frac{8}{9}F\]
  done clear
  View Answer play_arrow

• question_answer40) Two capacitors each of capacity \[2\mu F\] are connected in parallel. If they are connected to \[100\text{ }V\]battery, then energy stored in them is
  A)
   \[0.02\text{ }J\]        
  done clear
  B)
   \[0.04\text{ }J\]
  done clear
  C)
   \[0.01\text{ }J\]        
  done clear
  D)
   \[200\text{ }J\]
  done clear
  View Answer play_arrow

• question_answer41) Which factor is immaterial for the wire used in electric fuse?
  A)
   Length       
  done clear
  B)
   Radius
  done clear
  C)
   Material      
  done clear
  D)
   Current
  done clear
  View Answer play_arrow

• question_answer42) A battery of emf \[2\text{ }V\]and internal resistance  \[0.1\Omega \] is being charged by a current of \[~5\text{ }A\]. The potential difference between the terminals of the battery is
  A)
   \[2.5\text{ }V\]          
  done clear
  B)
   \[1.5\text{ }V\]
  done clear
  C)
   \[0.5V\]          
  done clear
  D)
   \[1\,\,V\]
  done clear
  View Answer play_arrow

• question_answer43) An electric bulb is rated at \[220\text{ }V,\] \[200\text{ }W;\] Power consumed by it when operated at \[110\text{ }V\]is
  A)
   \[25\text{ }W\]        
  done clear
  B)
   \[50\text{ }W\]
  done clear
  C)
   \[75\text{ }W\]         
  done clear
  D)
   \[90\text{ }W\]
  done clear
  View Answer play_arrow

• question_answer44) two cells having emf  \[4\text{ }V,\] \[2\text{ }V\]and internal resistances \[1\,\Omega ,\] \[1\,\,\Omega \] are connected as shown in figure below. Current through \[6\,\,\Omega \] resistance is
  A)
   \[\frac{1}{3}A\]
  done clear
  B)
   \[\frac{2}{3}A\]
  done clear
  C)
   \[1\,\,A\]
  done clear
  D)
   \[\frac{2}{9}\,\,A\]
  done clear
  View Answer play_arrow

• question_answer45) For a given thermocouple neutral temperature
  A)
   is a constant
  done clear
  B)
   depends on cold junction temperature
  done clear
  C)
   depends on inversion temperature
  done clear
  D)
   double that of cold junction temperature
  done clear
  View Answer play_arrow

• question_answer46) A charged particle enters a uniform magnetic field with a certain speed at right angles to it. In the magnetic field a change could occur in its
  A)
   kinetic energy
  done clear
  B)
   angular momentum
  done clear
  C)
   linear momentum
  done clear
  D)
   speed
  done clear
  View Answer play_arrow

• question_answer47) A coil having 500 turns of square shape each of side \[10\text{ }cm\]is placed normal to a magnetic field which is increasing at \[1\text{ }T/s\]. The induced emf is
  A)
   \[0.1\text{ }V\]        
  done clear
  B)
   \[0.5\,\,V\]    
  done clear
  C)
   \[1\,\,V\]          
  done clear
  D)
   \[-5\,\,V\]
  done clear
  View Answer play_arrow

• question_answer48) A galvanometer has a resistance \[50\,\,\Omega \]. A resistance of \[5\,\,\Omega \] is connected parallel to it. Fraction of the total current flowing through galvanometer is
  A)
   \[\frac{1}{10}\]
  done clear
  B)
   \[\frac{1}{11}\]
  done clear
  C)
   \[\frac{1}{50}\]
  done clear
  D)
   \[\frac{2}{15}\]
  done clear
  View Answer play_arrow

• question_answer49) A wire oriented in the east-west direction carries a current eastward. Direction of the magnetic field at a point to the south of the wire is
  A)
   vertically down
  done clear
  B)
   vertically up
  done clear
  C)
   north-east    
  done clear
  D)
   south-east
  done clear
  View Answer play_arrow

• question_answer50) An inductor is connected to an AC source, When compared to voltage, the current in the lead wires
  A)
   is ahead in phase by n
  done clear
  B)
   lags in phase by n
  done clear
  C)
   is ahead in phase by ?
  done clear
  D)
   lags in phase by ?
  done clear
  View Answer play_arrow

• question_answer51) Curie temperature is the one above which
  A)
   paramagnetic substance changes to ferromagnetic
  done clear
  B)
   paramagnetic changes to diamagnetic
  done clear
  C)
   diamagnetic changes to paramagnetic
  done clear
  D)
   ferromagnetic changes to paramagnetic
  done clear
  View Answer play_arrow

• question_answer52) Energy in a current carrying coil is stored in the form of
  A)
   electric field
  done clear
  B)
   magnetic field
  done clear
  C)
   heat
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer53) Graph of force per unit length between two long parallel currents carrying conductor and the distance between them is
  A)
   straight line
  done clear
  B)
   parabola
  done clear
  C)
   ellipse
  done clear
  D)
   rectangular hyperbola
  done clear
  View Answer play_arrow

• question_answer54) A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it from this position. The angle of rotation is
  A)
   \[{{60}^{o}}\]          
  done clear
  B)
   \[{{45}^{o}}\]
  done clear
  C)
   \[{{30}^{o}}\]          
  done clear
  D)
   \[{{75}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer55) A point source of light is kept below the surface of water in a pond
  A)
   light emerges from every point of the surface of the pond
  done clear
  B)
   no light is transmitted from the surface of the pond
  done clear
  C)
   all the light emitted by the source emerges from a circular region of the pond
  done clear
  D)
   some of the light emitted by the source emerges from a circular region of the pond
  done clear
  View Answer play_arrow

• question_answer56) If white light is used in Young's double slit experiment
  A)
   no interference pattern is formed
  done clear
  B)
   white fringes are formed
  done clear
  C)
   central bright fringe is white
  done clear
  D)
   central bright fringe is coloured
  done clear
  View Answer play_arrow

• question_answer57) Electromagnetic waves can be deflected by
  A)
   electric fields only
  done clear
  B)
   magnetic fields only
  done clear
  C)
   Both [a] and [b]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer58) Maximum lateral displacement of a ray of light incident on a slab of thickness t is
  A)
   \[\frac{t}{2}\]
  done clear
  B)
   \[\frac{t}{3}\]
  done clear
  C)
   \[\frac{t}{4}\]
  done clear
  D)
   \[t\]
  done clear
  View Answer play_arrow

• question_answer59) Mercury vapour lamp gives
  A)
   continuous spectrum
  done clear
  B)
   line spectrum
  done clear
  C)
   band spectrum
  done clear
  D)
   absorption spectrum
  done clear
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• question_answer60) Pick the correct statement from the following
  A)
   Primary rainbow is a virtual image and secondary rainbow is a real image
  done clear
  B)
   Primary rainbow is a real image and secondary rainbow is a virtual image
  done clear
  C)
   Both primary and secondary rainbows are virtual images
  done clear
  D)
   Both primary and secondary rainbows are real images
  done clear
  View Answer play_arrow

• question_answer61) The refractive index of water, glass and diamond are \[1.33,1.50,\text{ }2.40\]respectively. The refractive index of diamond relative to water and of glass relative to diamond, respectively are nearly
  A)
   \[1.80,0.625\]
  done clear
  B)
   \[0.554,\text{ }0.625\]
  done clear
  C)
   \[1.80,\text{ }1.6\]      
  done clear
  D)
   \[0.554,\text{ }1.6\]
  done clear
  View Answer play_arrow

• question_answer62) In the diffraction pattern of a single slit
  A)
   all bands are uniformly bright
  done clear
  B)
   all bands are uniformly wide
  done clear
  C)
   central band is narrower
  done clear
  D)
   central band is wider
  done clear
  View Answer play_arrow

• question_answer63) A radioactive substance has a half-life of four months. Three-fourth of the substance will decay in
  A)
   \[3\text{ }months\]   
  done clear
  B)
   \[4\text{ }months\]
  done clear
  C)
   \[~8\text{ }months\]  
  done clear
  D)
   \[\text{12 }months\]
  done clear
  View Answer play_arrow

• question_answer64) Electrons in the atom are held to the nucleus by        
  A)
   Coulomb's forces
  done clear
  B)
   nuclear forces
  done clear
  C)
   van der Waals' forces
  done clear
  D)
   gravitational forces
  done clear
  View Answer play_arrow

• question_answer65) Mass of the nucleons together in a heavy nucleus is
  A)
   greater than mass of nucleus
  done clear
  B)
   equal to mass of nucleus
  done clear
  C)
   same as mass of nucleus
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer66) Ratio of the radii of the nuclei with mass numbers 8 and 27 would be
  A)
   \[27/8\]        
  done clear
  B)
   \[8/27\]
  done clear
  C)
   \[2/3\]          
  done clear
  D)
   \[3/2\]
  done clear
  View Answer play_arrow

• question_answer67) Stopping potential required to reduce the photoelectric current to zero
  A)
   is directly proportional to the wavelength of the incident radiation
  done clear
  B)
   increases uniformly with wavelength of the incident radiation
  done clear
  C)
   is directly proportional to the frequency of the incident radiation
  done clear
  D)
   decreases uniformly with the frequency of the incident radiation
  done clear
  View Answer play_arrow

• question_answer68) The first member of the Ballmer?s series of the hydrogen has a wavelength \[\lambda ,\] the wavelength of the second member of its series is
  A)
   \[\frac{27}{20}\lambda \]
  done clear
  B)
   \[\frac{20}{27}\lambda \]
  done clear
  C)
   \[\frac{27}{20}\lambda \]         
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer69) The photoelectric threshold frequency of a metal is v. When light of frequency \[4v\] is incident on the metal. The maximum kinetic energy of the emitted photoelectrons is
  A)
   \[4\,\,hv\]         
  done clear
  B)
   \[3\,\,hv\]
  done clear
  C)
   \[5\,\,hv\]        
  done clear
  D)
   \[\frac{5}{2}\,\,hv\]
  done clear
  View Answer play_arrow

• question_answer70) The shortest wavelength in Lyman series is\[91.2\text{ }nm\]. The longest wavelength of the series   is                                  
  A)
   \[121.6\text{ }nm\]    
  done clear
  B)
   \[182.4\text{ }nm\]
  done clear
  C)
   \[243.4\text{ }nm\]    
  done clear
  D)
   \[364.8\text{ }nm\]
  done clear
  View Answer play_arrow

• question_answer71) Energy gap of a semiconductor is of the order of
  A)
   \[1\,\,eV\]         
  done clear
  B)
   \[10\,\,eV\]
  done clear
  C)
   \[0.1\text{ }eV\]        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer72) Majority charge carriers in p-type material are
  A)
   holes
  done clear
  B)
   electrons
  done clear
  C)
   Both  and
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer73) Resistance of a semiconductor
  A)
   increases with increase in temperature
  done clear
  B)
   decreases with increase in temperature
  done clear
  C)
   is not affected by change in temperature
  done clear
  D)
   increases for germanium and decreases for silicon
  done clear
  View Answer play_arrow

• question_answer74) Semiconductor material having fewer free electrons than pure germanium or silicon is
  A)
   p-type
  done clear
  B)
   n-type
  done clear
  C)
   Both [a] and [b]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer75) The concentrations of impurities in a transistor are
  A)
   equal for the emitter, base and collector regions
  done clear
  B)
   least for the emitter region
  done clear
  C)
   largest for the emitter region
  done clear
  D)
   least for the base region
  done clear
  View Answer play_arrow

• question_answer76) At \[\text{25}{{\,}^{\text{o}}}\text{C}\], the total pressure of an ideal solution obtained by mixing 3 moles of 'A? and 2 moles of 'B? is 184 Ton". What is the vapour pressure (in Torr) of pure 'B' at the same temperature? (vapour pressure of pure 'A? at \[25{{\,}^{o}}C,\] is 200 Torr)
  A)
   180          
  done clear
  B)
   160
  done clear
  C)
   16           
  done clear
  D)
   100
  done clear
  View Answer play_arrow

• question_answer77) Relative lowering of vapour pressure of a dilute solution is 0.2. What is the mole fraction of the non-volatile solute? 
  A)
   0.8            
  done clear
  B)
   0.5
  done clear
  C)
   0.3            
  done clear
  D)
   0.2
  done clear
  View Answer play_arrow

• question_answer78) Match the following            List ?A?                             List ?B? (1) \[PhC{{O}_{2}}C{{H}_{3}}\]               [A]\[2,4-\text{DNP}\] (2) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}C{{O}_{2}}H\]      [B] Arndt-Eistert synthesis (3)\[{{C}_{6}}{{H}_{5}}CHO\]                  [C] Hydrolysis Correct answer is
  A)
  \[1-A,\,2-B,\,3-C\]
  done clear
  B)
   \[1-B,\,2-C,\,3-A\]
  done clear
  C)
   \[1-C,\,2-B,\,3-A\]
  done clear
  D)
   \[1-B,\,2-A,\,3-C\]
  done clear
  View Answer play_arrow

• question_answer79) 2-pentanone and 3-methyl-2-butanone are a pair of....... isomers.
  A)
   functional     
  done clear
  B)
   chain
  done clear
  C)
   positional     
  done clear
  D)
   stereo
  done clear
  View Answer play_arrow

• question_answer80) What are the units of entropy?
  A)
  \[\text{cal K}\]         
  done clear
  B)
  \[\text{Cal}\,{{\text{K}}^{-1}}\]
  done clear
  C)
  \[\text{cm}\,{{\text{K}}^{-1}}\]       
  done clear
  D)
  \[\text{ }\!\!~\!\!\text{ cmK}\]
  done clear
  View Answer play_arrow

• question_answer81) Calculate \[\Delta H\](in Joules) for, C (graphite) \[\to C\](diamond), from the following data C(graphite)\[+\,{{O}_{2}}(g)\to C{{O}_{2}}(g);\] \[\Delta H=-393.5\,kJ\] C (diamond)\[+\,{{O}_{2}}(g)\to C{{O}_{2}}(g);\] \[\Delta H=-395.4\,kJ\]
  A)
  \[1,900\]        
  done clear
  B)
  \[~-788.9\times {{10}^{3}}\]
  done clear
  C)
  \[1,90,000\]    
  done clear
  D)
  \[~+\,788.9\times \,{{10}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer82) \[C{{H}_{2}}Br+\bar{O}H\xrightarrow{{}}C{{H}_{3}}OH+B{{r}^{-}}\]reaction proceeds by\[{{S}_{N}}2-\]mechanism. Its rate is dependent on the concentration of
  A)
  \[C{{H}_{3}}Br,\bar{O}H\]
  done clear
  B)
  \[C{{H}_{3}}Br\]only
  done clear
  C)
  \[~\bar{O}H\] only     
  done clear
  D)
  \[~C{{H}_{3}}Br,C{{H}_{3}}OH\]
  done clear
  View Answer play_arrow

• question_answer83) The end products in the Cannizaro reaction of benzaldehyde is
  A)
  \[~PhC{{O}_{2}}H,PhC{{H}_{2}}OH\]
  done clear
  B)
   \[~PhC{{O}_{2}}H,PhC{{H}_{2}}C{{O}_{2}}H\]
  done clear
  C)
  \[PhC{{H}_{2}}OH,PhCOC{{H}_{3}}\]
  done clear
  D)
   \[PhCO{{}_{2}}H,PhCOC{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer84) For a chemicalreaction, the free energy change \[(\Delta G)\] is negative. The reaction is
  A)
   a spontaneous reaction
  done clear
  B)
   an equilibrium reaction
  done clear
  C)
   a non-spontaneous reaction
  done clear
  D)
   characterised by\[{{r}_{f}}-{{r}_{b}}\] (where\[{{r}_{f}}\]and\[{{r}_{b}}\] are rates of forward and backward reactions respectively)
  done clear
  View Answer play_arrow

• question_answer85) In which of the following reactions, the heat liberated is known as "heat of combustion"?
  A)
   \[{{H}^{+}}(aq)+O{{H}^{-}}(aq)\to {{H}_{2}}O(l)+heat\]
  done clear
  B)
   \[C\text{(graphite)}+\frac{1}{2}{{O}_{2}}(g)\to CO(g)+\text{heat}\]
  done clear
  C)
   \[C{{H}_{4}}(g)+2{{O}_{2}}(g)\to C{{O}_{2}}(g)+2{{H}_{2}}O(l)+\,heat\]
  done clear
  D)
   \[{{H}_{2}}S{{O}_{4}}(aq)+{{H}_{2}}O(l)\to {{H}_{2}}S{{O}_{4}}(aq)+heat\]
  done clear
  View Answer play_arrow

• question_answer86) The number of chiral centres in \[(+)-\]glucose
  A)
   4              
  done clear
  B)
   3
  done clear
  C)
   2              
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer87) Aniline on oxidation with \[\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}\]and \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]gives
  A)
   benzoic acid
  done clear
  B)
  \[m-\] amino benzoic acid
  done clear
  C)
   Schiff?s base
  done clear
  D)
  \[~p-\] benzoquinone
  done clear
  View Answer play_arrow

• question_answer88) What are the units of equivalent conductivity of a solution?
  A)
   \[\text{mho c}{{\text{m}}^{-1}}\]
  done clear
  B)
   \[\text{ohm c}{{\text{m}}^{-1}}\text{ g equi}{{\text{v}}^{-1}}\]
  done clear
  C)
  \[\text{mho c}{{\text{m}}^{-2}}\text{ g equi}{{\text{v}}^{-1}}\]
  done clear
  D)
  \[\text{mho c}{{\text{m}}^{2}}\text{ g equi}{{\text{v}}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer89) What is the cell reaction occurring in Daniel cell (Galvanic cell)?
  A)
  \[Cu(s)+ZnS{{O}_{4}}(aq)\to CuS{{O}_{4}}(aq)+Zn(s)\]
  done clear
  B)
   \[Zn(s)+CuS{{O}_{4}}(aq)\to Cu(s)+ZnS{{O}_{4}}(aq)\]
  done clear
  C)
   \[Ni(s)+ZnS{{O}_{4}}(aq)\to NiS{{O}_{4}}(aq)+Zn(s)\]
  done clear
  D)
   \[2Na(s)+CdS{{O}_{4}}(aq)\to N{{a}_{2}}S{{O}_{4}}(aq)\]\[+\,Cd(s)\]
  done clear
  View Answer play_arrow

• question_answer90) \[n-\]propylamine yields a volatile compound X on warming with ale. alkali and chloroform. X has an offensive odour. The structure of X is
  A)
  \[~C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CN\]
  done clear
  B)
  \[~{{(C{{H}_{3}})}_{2}}CHCN\]
  done clear
  C)
  \[~C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}NC\]
  done clear
  D)
   \[{{(C{{H}_{3}})}_{2}}CHNC\]
  done clear
  View Answer play_arrow

• question_answer91) The molecular formula of benzonitrile is
  A)
  \[{{C}_{6}}{{H}_{5}}CN\]     
  done clear
  B)
  \[{{C}_{6}}{{H}_{5}}NC\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}CNO\]
  done clear
  D)
  \[{{C}_{6}}{{H}_{5}}NCO\]
  done clear
  View Answer play_arrow

• question_answer92) Which of the following statements (or equation) is correct?
  A)
   The units of cell emf are\[\text{V}\text{.c}{{\text{m}}^{-1}}\]
  done clear
  B)
   \[\Delta G=-\frac{nF}{{{E}_{cell}}}\]
  done clear
  C)
   In Galvanic cell, chemical energy is transformed into electrical energy
  done clear
  D)
   Oxidation state of Mn in potassium permanganate is + 6
  done clear
  View Answer play_arrow

• question_answer93) Which of the following metal can be obtained by the electrolysis of the aqueous solution of its salts?
  A)
   Cu          
  done clear
  B)
   Na
  done clear
  C)
   Mg         
  done clear
  D)
   K
  done clear
  View Answer play_arrow

• question_answer94) The magnetic moment (in BM) of \[\text{Z}{{\text{n}}^{\text{2+}}}\]ion according to spin-only formula is
  A)
   zero         
  done clear
  B)
   1.73
  done clear
  C)
   2.84         
  done clear
  D)
   3.87
  done clear
  View Answer play_arrow

• question_answer95) The 3d-block element that exhibits maximum number of oxidation states is
  A)
   Sc           
  done clear
  B)
   Ti
  done clear
  C)
   Mn          
  done clear
  D)
   Zn
  done clear
  View Answer play_arrow

• question_answer96) Which of the following molecule in its valence shell has three bond pairs of electrons and one lone pair of electrons?
  A)
  \[N{{H}_{3}}\]        
  done clear
  B)
  \[~{{H}_{2}}O\]
  done clear
  C)
  \[~B{{F}_{3}}\]           
  done clear
  D)
  \[~C{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer97) Which of the following set of properties belong to\[PC{{l}_{5}}\]?
  A)
  \[s{{p}^{3}},\] tetrahedral, 4 valence shell pairs of electrons
  done clear
  B)
   trigonal bipyramidal, 5 valence shell pairs of electrons
  done clear
  C)
  \[s{{p}^{3}}{{d}^{2}},\]octahedral, 6 valence shell pairs of electrons
  done clear
  D)
  \[s{{p}^{3}}d,\]square planar, 4 valence shell pairs of electrons
  done clear
  View Answer play_arrow

• question_answer98) The metal ion in complex \[\underset{\scriptscriptstyle-}{A}\]has BAN identical to the atomic number of krypton. \[\underset{\scriptscriptstyle-}{A}\]is (At. no. of\[Cr=24,\,Fe=26,\,Pd=46\])
  A)
  \[[Pd{{(N{{H}_{3}})}_{6}}]C{{l}_{4}}\]
  done clear
  B)
  \[[Cr{{(N{{H}_{3}})}_{5}}Cl]S{{O}_{4}}\]
  done clear
  C)
   \[N{{a}_{4}}[Fe{{(CN)}_{6}}]\]
  done clear
  D)
   \[{{K}_{3}}[Fe{{(CN)}_{6}}]\]
  done clear
  View Answer play_arrow

• question_answer99) The complex that does not give a precipitate wit\[\text{ }\!\!~\!\!\text{ AgN}{{\text{O}}_{\text{3}}}\]solution
  A)
   \[[Co{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]\]
  done clear
  B)
  \[[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}\]
  done clear
  C)
   \[\text{ }\!\![\!\!\text{ Ag(N}{{\text{H}}_{\text{3}}}{{\text{)}}_{\text{2}}}\text{ }\!\!]\!\!\text{ Cl}\]
  done clear
  D)
   \[[Cr{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl\]
  done clear
  View Answer play_arrow

• question_answer100) According to bond order concept, the correct order of stability of\[{{\text{O}}_{\text{2}}}\text{,O}_{\text{2}}^{\text{+}}\] and \[\text{O}_{2}^{-}\] is
  A)
  \[{{O}_{2}}>O_{2}^{+}>O_{2}^{-}\]
  done clear
  B)
  \[O_{2}^{-}>{{O}_{2}}>O_{2}^{+}\]
  done clear
  C)
   \[{{O}_{2}}>O_{2}^{-}>O_{2}^{+}\]
  done clear
  D)
   \[O_{2}^{+}>{{O}_{2}}<O_{2}^{-}\]
  done clear
  View Answer play_arrow

• question_answer101) Zero dipole moment is possessed by
  A)
  \[PC{{l}_{3}}\]         
  done clear
  B)
  \[~B{{F}_{3}}\]
  done clear
  C)
  \[Cl{{F}_{3}}\]         
  done clear
  D)
  \[~N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer102) The number of moles of ions given on complete ionisation of one mole of \[[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}\] is/are
  A)
   4            
  done clear
  B)
   3
  done clear
  C)
   2            
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer103) The coordination number in a/an........ complex may increase to 8.
  A)
   cobalt       
  done clear
  B)
   osmium
  done clear
  C)
   nickel         
  done clear
  D)
   iron
  done clear
  View Answer play_arrow

• question_answer104) The radius ratio \[\left( \frac{{{r}^{+}}}{{{r}^{-}}} \right)\] of an ionic solid\[({{A}^{+}}{{B}^{-}})\]is 0.69. What is the coordination number of\[{{B}^{-}}\]?
  A)
   6             
  done clear
  B)
   8
  done clear
  C)
   2 
  done clear
  D)
   10
  done clear
  View Answer play_arrow

• question_answer105) A, B and C are ideal gases. Their molecular weights are 2, 4 and 28 respectively. The ran of diffusion of these gases follow the order
  A)
  \[C>A>B\]    
  done clear
  B)
  \[~C>B>A\]
  done clear
  C)
  \[A=B=C\]     
  done clear
  D)
  \[~A>B>C\]        
  done clear
  View Answer play_arrow

• question_answer106) Among the following ions (hydrated), the colourless metal ion is
  A)
  \[C{{u}^{+}}\]
  done clear
  B)
  \[C{{u}^{2+}}\]
  done clear
  C)
   \[F{{e}^{2+}}\]
  done clear
  D)
   \[M{{n}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer107) German silver is an alloy of
  A)
  \[Cu,Zn\]       
  done clear
  B)
  \[~Cu,Ni,\,Zn\]
  done clear
  C)
  \[~Cu,Sn,Zn\]    
  done clear
  D)
  \[~Cu,Zn\]
  done clear
  View Answer play_arrow

• question_answer108) Which of the following Statements is not correct?
  A)
   The units of surface tension are dynes \[c{{m}^{-1}}\]
  done clear
  B)
   The units of viscosity coefficient of a liquid are "poise"
  done clear
  C)
   \[\text{CsCl}\]crystallizes in body centred cubic type of lattice                                
  done clear
  D)
   The coordination number of \[{{\text{S}}^{2-}}\]in ZnS is 6
  done clear
  View Answer play_arrow

• question_answer109) Which of the following is not a method of preparation of colloidal solution?
  A)
   Electrical dispersion
  done clear
  B)
   Peptization
  done clear
  C)
   Coagulation
  done clear
  D)
   Mechanical dispersion
  done clear
  View Answer play_arrow

• question_answer110) Pauling's equation for determining the electronegativity of an element, is
  A)
   \[{{X}_{A}}-{{X}_{B}}=0.208\sqrt{\Delta }\]
  done clear
  B)
   \[{{X}_{A}}+{{X}_{B}}=0.208\sqrt{\Delta }\]
  done clear
  C)
   \[{{X}_{A}}-{{X}_{B}}=0.208{{\Delta }^{2}}\]
  done clear
  D)
   \[{{X}_{A}}-{{X}_{B}}=\sqrt{\Delta }\] \[{{X}_{A}},{{X}_{B}}=\]electronegativity values of elements AandB \[\Delta =\]represents polarity of \[A-B\]bond
  done clear
  View Answer play_arrow

• question_answer111) The ionic radii\[(\overset{\text{o}}{\mathop{A}}\,)\]of \[{{C}^{4-}}\]and\[{{O}^{2-}}\]respectively are 2.60 and 1.40. The ionic radius of th6 isoelectronic ion \[{{N}^{3-}}\]would be
  A)
   2.6           
  done clear
  B)
   1.71
  done clear
  C)
   1.4           
  done clear
  D)
   0.95
  done clear
  View Answer play_arrow

• question_answer112) The gold numbers of some colloidal solution are given below Colloidal solution Gold number A                  0.01 B                  2.5 C                   20 The protective nature of these colloidal solutions follow the order
  A)
  \[~C>B>A\]     
  done clear
  B)
  \[~A>B>C\]
  done clear
  C)
  \[~A=B=C\]      
  done clear
  D)
  \[~B>A>C\]
  done clear
  View Answer play_arrow

• question_answer113) Which of the following reaction is an example for homogeneous catalysis?
  A)
  \[2{{H}_{2}}{{O}_{2}}(l)\xrightarrow{Mn{{O}_{2}}(s)}2{{H}_{2}}O(l)+{{O}_{2}}(g)\]
  done clear
  B)
   \[2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g)\]
  done clear
  C)
   \[2CO(g)+{{O}_{2}}(g)\xrightarrow{NO(g)}2C{{O}_{2}}(g)\]
  done clear
  D)
   \[{{H}_{2}}(g)+{{C}_{2}}{{H}_{4}}(g)\xrightarrow{Ni(s)}{{C}_{3}}{{H}_{6}}(g)\]
  done clear
  View Answer play_arrow

• question_answer114) Consider the following abbreviations for hydrated alkali ions \[X={{[Li{{({{H}_{2}}O)}_{n}}]}^{+}}\] \[X={{[K{{({{H}_{2}}O)}_{n}}]}^{+}}\] \[Z={{[Cs{{({{H}_{2}}O)}_{n}}]}^{+}}\] What is the correct order of size of these hydrated alkali ions?
  A)
  \[~X>Y>Z\]     
  done clear
  B)
  \[~Z>Y>X\]
  done clear
  C)
  \[~X=Y=Z\]     
  done clear
  D)
  \[~Z>X>Y\]
  done clear
  View Answer play_arrow

• question_answer115) What is the product formed when phosphorus trioxide is dissolved in water?
  A)
  \[~HP{{O}_{3}}\]       
  done clear
  B)
  \[~{{H}_{3}}P{{O}_{4}}\]
  done clear
  C)
  \[~{{H}_{3}}P{{O}_{3}}\]       
  done clear
  D)
  \[~HP{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer116) The molecular formula of dithionic acid is
  A)
  \[~{{H}_{2}}{{S}_{2}}{{O}_{4}}\]      
  done clear
  B)
  \[~{{H}_{2}}{{S}_{2}}{{O}_{6}}\]
  done clear
  C)
  \[~{{H}_{2}}{{S}_{2}}{{O}_{5}}\]       
  done clear
  D)
  \[{{H}_{2}}{{S}_{2}}{{O}_{7}}\]
  done clear
  View Answer play_arrow

• question_answer117) The bond dissociation energy of \[\text{C}{{\text{l}}_{\text{2}}}\text{, B}{{\text{r}}_{\text{2}}}\]and \[{{\text{I}}_{\text{2}}}\]follow the order
  A)
  \[~C{{l}_{2}}>{{I}_{2}}>B{{r}_{2}}\] 
  done clear
  B)
   \[{{I}_{2}}>B{{r}_{2}}>C{{l}_{2}}\]
  done clear
  C)
  \[{{I}_{2}}=C{{l}_{2}}=B{{r}_{2}}\]
  done clear
  D)
  \[C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer118) During the extraction of copper, the impurity \[(FeS)\]is removed as slag by mixing the contaminated copper ore with silica and coke. The molecular formula of slag is
  A)
  \[~FeSi{{O}_{3}}\]       
  done clear
  B)
  \[~F{{e}_{2}}{{O}_{3}}\]
  done clear
  C)
   \[FeSi\](solid)   
  done clear
  D)
  \[~FeSi\] (vapour)
  done clear
  View Answer play_arrow

• question_answer119) Which of the following is used as indelible ink?  
  A)
   Aqueous \[\text{CuS}{{\text{O}}_{\text{4}}}\]solution
  done clear
  B)
   Aqueous \[\text{AgN}{{\text{O}}_{\text{3}}}\]solution
  done clear
  C)
   Aqueous \[\text{NaCl}\]solution
  done clear
  D)
   Aqueous \[\text{NaOH}\]solution
  done clear
  View Answer play_arrow

• question_answer120) Which of the following ore is an ore of copper?
  A)
   Argentite     
  done clear
  B)
   Haematite
  done clear
  C)
   Malachite    
  done clear
  D)
   Calamine
  done clear
  View Answer play_arrow

• question_answer121) \[\text{KMn}{{\text{O}}_{\text{4}}}(mol\,wt.=158)\]oxidizes oxalic acid in acid medium to \[\text{C}{{\text{O}}_{\text{2}}}\]and water as follows \[5{{C}_{2}}O_{4}^{2-}+2MnO_{4}^{-}+16{{H}^{+}}\to 10C{{O}_{2}}+2M{{n}^{2+}}\]\[\text{+}\,\,\text{8}{{\text{H}}_{\text{2}}}\text{O}\] What is the equivalent weight of\[\text{KMn}{{\text{O}}_{\text{4}}}\]?
  A)
   158         
  done clear
  B)
   31.6
  done clear
  C)
   39.5         
  done clear
  D)
   79 
  done clear
  View Answer play_arrow

• question_answer122) Sodium bicarbonate on heating decomposes to form sodium carbonate, \[\text{C}{{\text{O}}_{\text{2}}}\]and water. If 0.2 moles of sodium bicarbonate is completely decomposed, how many moles of sodium carbonate is formed?
  A)
   0.1     
  done clear
  B)
   0.2
  done clear
  C)
   0.05          
  done clear
  D)
   0.025
  done clear
  View Answer play_arrow

• question_answer123) What is the energy (in eV) required to excite  the electron from\[n=1\]to\[n=2\]state in hydrogen atom? (\[n=\]principal quantum number)
  A)
   13.6         
  done clear
  B)
   3.4
  done clear
  C)
   17.0         
  done clear
  D)
   10.2
  done clear
  View Answer play_arrow

• question_answer124) According to aufbau principle, the correct order of energy of 3d, 4s and 4p orbitals is
  A)
  \[~4p<3d<4s\]  
  done clear
  B)
  \[~4s<4p<3d\]
  done clear
  C)
  \[~4s<3d<4p\]  
  done clear
  D)
  \[~3d<4s<4p\]
  done clear
  View Answer play_arrow

• question_answer125) \[n-\]pentane and 2-methylbutane are a pair of
  A)
   enantiomers
  done clear
  B)
   stereoisomers
  done clear
  C)
   diastereomers
  done clear
  D)
   constitutional isomers
  done clear
  View Answer play_arrow

• question_answer126)  Compound can exhibit
  A)
   geometrical isomerism
  done clear
  B)
   tautomerism
  done clear
  C)
   optical isomerism
  done clear
  D)
   geometrical and optical isomerism
  done clear
  View Answer play_arrow

• question_answer127) The activity of a radioactive nuclide is \[2\times {{10}^{7}}\] disintegrations per minute (dpm). After 23.03 min, its activity is reduced to\[2\times {{10}^{6}}\text{ dpm}\text{.}\] What is the average life (in min) of this nuclide?
  A)
   100          
  done clear
  B)
   10
  done clear
  C)
   1             
  done clear
  D)
   0.1
  done clear
  View Answer play_arrow

• question_answer128) What' is the correct order of velocity of alpha \[(\alpha ),\]beta \[(\beta )\]and gamma\[(\gamma )\]rays?
  A)
  \[\alpha >\,\beta >\gamma \]     
  done clear
  B)
  \[\alpha >\,\gamma >\beta \]
  done clear
  C)
   \[\gamma >\,\alpha >\beta \]     
  done clear
  D)
  \[\gamma >\beta >\alpha \]
  done clear
  View Answer play_arrow

• question_answer129) The isomers which are interconverted through rotation around a single bond are
  A)
   conformers   
  done clear
  B)
   diastereomers
  done clear
  C)
   enantiomers  
  done clear
  D)
   position isomers
  done clear
  View Answer play_arrow

• question_answer130) The major product in the reaction of 2-butyne with \[\text{Li/liq}\text{.N}{{\text{H}}_{\text{3}}}\]is
  A)
   
  done clear
  B)
   
  done clear
  C)
  \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\]
  done clear
  D)
  \[{{H}_{2}}C=CH-C{{H}_{2}}-C{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer131) What is X in the following nuclear reaction? \[_{11}N{{a}^{23}}+{{\,}_{0}}{{n}^{1}}\to {{\,}_{11}}N{{a}^{24}}+X\]
  A)
  \[{{\,}_{1}}{{H}^{1}}\]
  done clear
  B)
  \[{{\,}_{2}}H{{e}^{4}}\]
  done clear
  C)
   \[{{\,}_{1}}{{H}^{2}}\]
  done clear
  D)
   \[\gamma -\]ray (gamma ray)
  done clear
  View Answer play_arrow

• question_answer132) HA is a weak acid. The pH of 0.1 M HA solution is 2. What is the degree of dissociation \[(\alpha )\]of HA?
  A)
   0.5           
  done clear
  B)
   0.2
  done clear
  C)
   0.1           
  done clear
  D)
   0.301
  done clear
  View Answer play_arrow

• question_answer133) In the following reaction, A and B, respectively are \[A\xrightarrow{\text{HBr}}{{C}_{2}}{{H}_{5}}Br\xrightarrow{B}A\]
  A)
  \[{{C}_{2}}{{H}_{4}},alc\,KOH/\Delta \]
  done clear
  B)
  \[{{C}_{2}}{{H}_{5}}Cl,aq\,KOH/\Delta \]
  done clear
  C)
   \[C{{H}_{3}}OH,aq\,KOH/\Delta \]
  done clear
  D)
   \[{{C}_{2}}{{H}_{2}},PB{{r}_{3}}\]  
  done clear
  View Answer play_arrow

• question_answer134) The reagent(s) used in the preparation of aspirin from salicylic acid
  A)
   \[\text{SOC}{{\text{l}}_{\text{2}}}\text{,}\]pyridine
  done clear
  B)
  \[{{\text{(C}{{\text{H}}_{3}}\text{CO)}}_{2}}O,{{H}^{+}}\]
  done clear
  C)
   \[C{{H}_{3}}C{{O}_{2}}H,HCl\]
  done clear
  D)
  \[C{{H}_{3}}Cl,AlC{{l}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer135) The equilibrium reaction that is not influenced by volume change at constant temperature is
  A)
  \[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\]
  done clear
  B)
   \[{{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)\]
  done clear
  C)
   \[{{N}_{2}}{{O}_{4}}(g)2N{{O}_{2}}(g)\]
  done clear
  D)
   \[2NO(g)+{{O}_{2}}2N{{O}_{2}}(g)\]
  done clear
  View Answer play_arrow

• question_answer136) Consider the following solutions of equal concentrations \[A=N{{H}_{4}}Cl\]          \[B=C{{H}_{3}}COONa\] \[C=N{{H}_{2}}OH\]       \[D=C{{H}_{2}}COOH\] A buffer solution can be obtained by mixing equal volumes of                     
  A)
   C and D     
  done clear
  B)
   A and B      
  done clear
  C)
   A and C      
  done clear
  D)
   C and D      
  done clear
  View Answer play_arrow

• question_answer137) In the following reaction, X and Y respectively are \[{{C}_{2}}{{H}_{5}}OH\xrightarrow{KMn{{O}_{4}}/{{H}^{+}}}X\frac{Y}{{{H}_{2}}S{{O}_{4}}/\Delta }C{{H}_{3}}C{{O}_{2}}{{C}_{2}}{{H}_{5}}\]
  A)
   \[C{{H}_{3}}OH,{{C}_{2}}{{H}_{5}}OH\]
  done clear
  B)
  \[~C{{H}_{3}}CHO,C{{H}_{3}}OH\]
  done clear
  C)
  \[~C{{H}_{3}}C{{O}_{2}}H,\text{ }{{C}_{2}}{{H}_{5}}OH\]
  done clear
  D)
  \[~{{C}_{2}}{{H}_{4}},C{{H}_{3}}CO{{}_{2}}H\]
  done clear
  View Answer play_arrow

• question_answer138) The reaction conditions used for converting 1, 2-dibromopropane to propylene are
  A)
   \[KOH,alcohol/\Delta \]
  done clear
  B)
  \[KOH,\text{ }water/\Delta \]
  done clear
  C)
  \[~Zn,\text{ }alcohol/\Delta \]
  done clear
  D)
  \[~Na,\text{ }alcohol/\Delta \]
  done clear
  View Answer play_arrow

• question_answer139) Which of the following's a Lewis acid?
  A)
  \[AlC{{l}_{3}}\]
  done clear
  B)
  \[C{{l}^{-}}\]
  done clear
  C)
   \[CO\]
  done clear
  D)
  \[{{C}_{2}}{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer140) If "a" and\[''{{t}_{1/2}}''\] are initial concentration of reactant and half-life of a zero order reaction  respectively, which of the following is correct?
  A)
   \[{{t}_{1/2}}\propto \frac{1}{a}\]
  done clear
  B)
  \[{{t}_{1/2}}\propto a\]
  done clear
  C)
   \[{{t}_{1/2}}\propto \frac{1}{{{a}^{2}}}\]
  done clear
  D)
   \[{{t}_{1/2}}\propto {{a}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer141) All monosaccharides ....... Tollen's reagent.
  A)
   oxidises      
  done clear
  B)
   condense with
  done clear
  C)
   reduces       
  done clear
  D)
   add to
  done clear
  View Answer play_arrow

• question_answer142) The product formed in the reaction of glycine with benzoyl chloride \[\text{+ aq NaOH}\]is
  A)
  \[~PhCOC{{H}_{2}}N{{H}_{2}}\]
  done clear
  B)
  \[~PhC{{H}_{2}}N{{H}_{2}}\]
  done clear
  C)
  \[~PhCONHC{{H}_{3}}\]
  done clear
  D)
  \[~PhCONHC{{H}_{2}}C{{O}_{2}}H\]
  done clear
  View Answer play_arrow

• question_answer143) The rate constant of a reaction is found to be \[3\times {{10}^{-3}}\,mol\,{{L}^{-1}}\,{{\min }^{-1}}.\]The order of the reaction is
  A)
   zero          
  done clear
  B)
   1
  done clear
  C)
   2             
  done clear
  D)
   1.5  
  done clear
  View Answer play_arrow

• question_answer144) What is the two third life of a first order reaction having \[k=5.48\times {{10}^{-14}}{{s}^{-1}}\]
  A)
  \[2.01\times {{10}^{11}}s\]
  done clear
  B)
   \[2.01\times {{10}^{13}}s\]
  done clear
  C)
   \[8.08\times {{10}^{13}}\,s\]
  done clear
  D)
  \[16.04\times {{10}^{11}}\,s\]
  done clear
  View Answer play_arrow

• question_answer145) Which of the following solvents are aprotic? [A]\[N{{H}_{3}}\]         [B]\[S{{O}_{2}}\] [C] \[C{{H}_{3}}CN\] [D] \[C{{H}_{3}}C{{O}_{2}}H\]
  A)
   \[A,B,C\]
  done clear
  B)
   \[A,C,D\]
  done clear
  C)
   \[B,C\]
  done clear
  D)
   \[A,C\]
  done clear
  View Answer play_arrow

• question_answer146) Chlorobenzene is o, p -directing in electrophilic substitution reaction. The directing influence is explained by
  A)
   \[+\text{ }M\]of\[Ph\]    
  done clear
  B)
   \[+\,I\]of \[Cl\]
  done clear
  C)
   \[+\text{ }M\]of\[Cl\]    
  done clear
  D)
   \[-I\]of \[Ph\]
  done clear
  View Answer play_arrow

• question_answer147) 5 L of a solution contains\[\text{25}\,\text{mg}\] of \[\text{CaC}{{\text{O}}_{3}}.\]What is its concentration in ppm? (mol. wt. of \[\text{CaC}{{\text{O}}_{\text{3}}}\]is 100)
  A)
   25           
  done clear
  B)
   1
  done clear
  C)
   5           
  done clear
  D)
   2500
  done clear
  View Answer play_arrow

• question_answer148) Observe the following abbrevations \[{{\pi }_{obs}}=\]observed colligative property \[{{\pi }_{cal}}=\]theoretical colligative property  assuming normal behaviour of solute. van't Hoff factor \[(i)\]is given by
  A)
  \[i={{\pi }_{obs}}\times {{\pi }_{cal}}\]
  done clear
  B)
  \[i={{\pi }_{obs}}+{{\pi }_{cal}}\]
  done clear
  C)
   \[i={{\pi }_{obs}}-{{\pi }_{cal}}\]
  done clear
  D)
   \[i=\frac{{{\pi }_{obs}}}{{{\pi }_{cal}}}\]
  done clear
  View Answer play_arrow

• question_answer149) The correct order for homolytic bond dissociation energies (\[\Delta H\]in kcal/mol) for \[C{{H}_{4}}(A),{{C}_{2}}{{H}_{6}}(B)\]and\[C{{H}_{3}}Br(C),\]under  identical experimental conditions
  A)
  \[C>B>A\]    
  done clear
  B)
  \[B>C>A\]
  done clear
  C)
  \[~C>A>B\]    
  done clear
  D)
  \[~A>B>C\]
  done clear
  View Answer play_arrow

• question_answer150) \[RX+{{I}^{-}}\xrightarrow{{}}R-I+X\]is an example of....... reaction.
  A)
   nucleophilic addition
  done clear
  B)
   nucleophilic substitution
  done clear
  C)
   electrophilic addition
  done clear
  D)
   elimination
  done clear
  View Answer play_arrow

• question_answer151) If \[a{{x}^{3}}+b{{x}^{2}}+ex+d=0\]has a repeated root \[\alpha ,\]  then a is also a root of
  A)
   \[3a{{x}^{2}}+2bx+d=0\]
  done clear
  B)
   \[a{{x}^{2}}+b\,x+c=0\]
  done clear
  C)
   \[3a{{x}^{2}}+2bx+c=0\]
  done clear
  D)
   \[6ax+2b=0\]
  done clear
  View Answer play_arrow

• question_answer152) If the roots of \[{{x}^{3}}-3{{x}^{2}}-6x+8=0\]  are in arithmetic progression, then the roots of the equation are
  A)
   \[3,4,5\]        
  done clear
  B)
   \[4,7,10\]
  done clear
  C)
   \[-2,1,4\]       
  done clear
  D)
   \[1,4,7\]
  done clear
  View Answer play_arrow

• question_answer153) If \[\alpha ,\beta ,\gamma \]  are the roots of the cubic equation \[{{x}^{3}}-{{x}^{2}}+x-1=0,\]then \[{{\alpha }^{-3}}+{{\beta }^{-3}}+{{\gamma }^{-3}}\] is equal to
  A)
   \[1\]             
  done clear
  B)
   \[2\]
  done clear
  C)
   \[3\]             
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer154) If \[\alpha ,\beta ,\gamma \] are the roots of \[{{x}^{3}}+bx+c=0,\]then \[{{\alpha }^{2}}\beta +\alpha {{\beta }^{2}}+{{\beta }^{2}}\gamma +{{\gamma }^{2}}\alpha +\gamma {{\alpha }^{2}}\]  is equal to
  A)
   \[c\]             
  done clear
  B)
   \[-c\]
  done clear
  C)
   \[-3c\]           
  done clear
  D)
   \[3c\]
  done clear
  View Answer play_arrow

• question_answer155) \[\underset{x\to \infty }{\mathop{\lim }}\,(\sqrt{x+\sqrt{x}}-\sqrt{x})\]
  A)
   \[-1/2\]         
  done clear
  B)
   \[1/2\]
  done clear
  C)
   \[1\]             
  done clear
  D)
   \[0\]
  done clear
  View Answer play_arrow

• question_answer156) \[\underset{x\to 1}{\mathop{\lim }}\,\frac{2{{x}^{2}}+x-3}{3{{x}^{2}}+2x-2}\]is equal to
  A)
   \[1\]
  done clear
  B)
   \[2\]
  done clear
  C)
   \[-1\]
  done clear
  D)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer157) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\sin }^{-1}}x-x}{{{x}^{3}}\,\cos x}\]is equal to
  A)
   \[1/2\]           
  done clear
  B)
   \[1/3\]
  done clear
  C)
   \[1/6\]
  done clear
  D)
   \[1/12\]
  done clear
  View Answer play_arrow

• question_answer158) If \[f:R\to R\] given by \[f(x)=\left\{ \begin{matrix}    2\,\cos x, & if & x\le -\frac{\pi }{2}  \\    a\,\sin \,x+b, & if & -\frac{\pi }{2}<x<\frac{\pi }{2}  \\    1+{{\cos }^{2}}x, & if & x\ge \frac{\pi }{2}  \\ \end{matrix} \right.\] is a continuous function on R, then (a, b) is equal to
  A)
   \[(1/2,\,1/2)\]
  done clear
  B)
   \[(0,-1)\]
  done clear
  C)
   \[(0,2)\]
  done clear
  D)
   \[(1,0)\]
  done clear
  View Answer play_arrow

• question_answer159) \[\frac{d}{dx}\left\{ \begin{align}   & {{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)+{{\tan }^{-1}}\left( \frac{3x-{{x}^{2}}}{1-3{{x}^{2}}} \right) \\  & -{{\tan }^{-1}}\left( \frac{4x-4{{x}^{2}}}{1-6{{x}^{2}}+{{x}^{4}}} \right) \\ \end{align} \right\}\]equal to
  A)
   \[\frac{1}{\sqrt{1-{{x}^{2}}}}\]
  done clear
  B)
   \[-\frac{1}{\sqrt{1-{{x}^{2}}}}\]
  done clear
  C)
   \[\frac{1}{1+{{x}^{2}}}\]
  done clear
  D)
   \[-\frac{1}{1+{{x}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer160) If \[2{{x}^{2}}-3xy+{{y}^{2}}+x-2y-8=0,\]then \[\frac{dy}{dx}\] is equal to
  A)
   \[\frac{3y-4x-1}{2y-3x-2}\]   
  done clear
  B)
   \[\frac{3y+4x-1}{2y+3x+2}\]
  done clear
  C)
   \[\frac{3y+4x+1}{2y-3x+2}\]
  done clear
  D)
   \[\frac{3y+4x+1}{2y-3x-2}\]
  done clear
  View Answer play_arrow

• question_answer161) The equation of the tangent at \[(1,5)\] to the curve \[y=5{{x}^{4}}\] is
  A)
   \[20x-y=15\] 
  done clear
  B)
   \[x+20y=101\]
  done clear
  C)
   \[20x+y=15\]  
  done clear
  D)
   \[x-20y=101\]
  done clear
  View Answer play_arrow

• question_answer162) The length of the sub tangent at any point \[({{x}_{1}},\,{{y}_{1}})\] on the curve \[y={{a}^{x}},\]\[(a>0)\] is
  A)
   \[2\,\,\log \,a\]        
  done clear
  B)
   \[1/\,\,\log \,a\]
  done clear
  C)
   \[\log \,a\]          
  done clear
  D)
   \[{{a}^{{{2}_{{{x}_{1}}}}}}\log \,a\]
  done clear
  View Answer play_arrow

• question_answer163) The set \[\{{{x}^{3}}-12x:-3\le x\le 3\}\] is equal to
  A)
   \[\{x:-16\le x\le 16\}\]
  done clear
  B)
   \[\{x:-12\le x\le 12\}\]
  done clear
  C)
   \[\{x:-9\le x\le 9\}\]
  done clear
  D)
   \[\{x:0\le x\le 10\}\]
  done clear
  View Answer play_arrow

• question_answer164) The set of all local maxima for \[y=\cos \,\,x\]is
  A)
   \[\{n\pi :n\in I\}\]   
  done clear
  B)
   \[\{2n\pi :n\in I\}\]
  done clear
  C)
   \[\{n\pi /2:n\in I\}\] 
  done clear
  D)
   \[\{n\pi /3:n\in I\}\]
  done clear
  View Answer play_arrow

• question_answer165) The absolute maximum of \[{{x}^{40}}-{{x}^{20}}\]on the interval \[[0,1]\] is
  A)
   \[-1/4\]
  done clear
  B)
   \[0\]
  done clear
  C)
   \[1/4\]          
  done clear
  D)
   \[1/2\]
  done clear
  View Answer play_arrow

• question_answer166) \[\int_{-2}^{2}{(x-|x|)}\,\,dx\] is equal to
  A)
   \[0\]               
  done clear
  B)
   \[2\]
  done clear
  C)
   \[4\]               
  done clear
  D)
   \[-4\]
  done clear
  View Answer play_arrow

• question_answer167) If \[\int{\frac{dx}{x\,\log \,x}}=f(x)+\] constant,  then \[f(x)\] is equal to
  A)
   \[1/\,\log \,x\]        
  done clear
  B)
   \[\log \,x\]
  done clear
  C)
   \[\log \,\,\log \,x\]
  done clear
  D)
   \[x/\,\log \,x\]
  done clear
  View Answer play_arrow

• question_answer168) If \[\int{\text{cosec x}\,\text{dx =f(x)+}}\] constant, then \[f(x)\] is equal to         
  A)
   \[\tan \,x/2\]       
  done clear
  B)
   \[\log \,|\tan \,(x/2)|\]
  done clear
  C)
   \[\log |\sin \,x|\]     
  done clear
  D)
   \[\log |cos\,x|\]
  done clear
  View Answer play_arrow

• question_answer169) \[{{I}_{n}}=\int{{{\tan }^{n}}x}\,\,dx\] for \[n\ge 2,\] then \[{{I}_{n}}+{{I}_{n-2}}\] is equal to
  A)
   \[{{\tan }^{n\,}}x+c\]
  done clear
  B)
   \[\frac{({{\tan }^{n-1}}x)}{n-1}+c\]
  done clear
  C)
   \[\frac{{{\tan }^{n}}x}{n}+c\]
  done clear
  D)
   \[n\,\,{{\tan }^{n}}x+c\]
  done clear
  View Answer play_arrow

• question_answer170) \[\int_{0}^{\pi /2}{x\,\sin \,x}\,\,dx\]is equal to
  A)
   \[0\]
  done clear
  B)
   \[1\]
  done clear
  C)
   \[-1\]
  done clear
  D)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer171) The area (in square unit) of the region bounded by the y-axis and the curve \[2x={{y}^{2}}-1\]is
  A)
   \[1/3\]           
  done clear
  B)
   \[2/3\]
  done clear
  C)
   \[1\]              
  done clear
  D)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer172) The solution of the differential equation \[({{x}^{2}}+{{y}^{2}})dx=2xy\,\,dy\]is
  A)
   \[{{x}^{2}}+{{y}^{2}}=cy\]
  done clear
  B)
   \[c({{x}^{2}}-{{y}^{2}})=x\]
  done clear
  C)
   \[{{x}^{2}}-{{y}^{2}}=cy\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}=cx\] (here c is an arbitrary constant)
  done clear
  View Answer play_arrow

• question_answer173) A number n is chosen at random from the set \[\{11,12,13,.....30\}.\]The probability that n is neither divisible by 3 nor divisible by 5 is   
  A)
   \[7/20\]           
  done clear
  B)
   \[9/20\]              
  done clear
  C)
   \[11/20\]           
  done clear
  D)
   \[13/20\]           
  done clear
  View Answer play_arrow

• question_answer174) The probability that a number n chosen at random from 1 to 30, to satisfy \[n+(50/n)>27\]is
  A)
   \[7/30\]         
  done clear
  B)
   \[3/10\]
  done clear
  C)
   \[3/5\]           
  done clear
  D)
   \[1/5\]
  done clear
  View Answer play_arrow

• question_answer175) If a random variable X has the distribution given below, then the value of c is

  \[x=k\]	\[-2\]	\[-1\]	\[0\]	\[1\]	\[2\]	\[3\]
  \[P(X=k)\]	\[\frac{1}{10}\]	\[\frac{1}{10}\]	\[2c\]	\[\frac{3}{10}\]	\[\frac{1}{5}\]	\[c\]

  A)
   \[1/5\]           
  done clear
  B)
   \[2/5\]
  done clear
  C)
   \[1/10\]          
  done clear
  D)
   \[3/10\]
  done clear
  View Answer play_arrow

• question_answer176) A random variable X can attain only the value 1, 2, 3, 4, 5 with respective probabilities k, 2k, 3k, 2k, k. If m is the mean of the probability  distribution, then (k, m) is equal to
  A)
   \[(3,\,1/9)\]       
  done clear
  B)
   \[(\,1/9,3)\]
  done clear
  C)
   \[(\,1/8,4)\]        
  done clear
  D)
   \[(\,1,3)\]
  done clear
  View Answer play_arrow

• question_answer177) If \[f(x)=\lambda {{e}^{-ax}}\,\,(a>0)\] for  \[0\le x<\infty \] is a probability density, then 'k is equal to
  A)
   \[a\]              
  done clear
  B)
   \[{{a}^{2}}\]
  done clear
  C)
   \[1/a\]           
  done clear
  D)
   \[{{a}^{2}}\]                  
  done clear
  View Answer play_arrow

• question_answer178) Two unbiased dice are thrown simultaneously-   The probability to get a sum more than 8 is 
  A)
   \[5/36\]          
  done clear
  B)
   \[5/18\]              
  done clear
  C)
   \[5/12\]         
  done clear
  D)
   \[2/9\]              
  done clear
  View Answer play_arrow

• question_answer179) The moment generating function of a random variable X is
  A)
   \[E({{e}^{-1X}})\]      
  done clear
  B)
   \[E({{e}^{itX}})\]
  done clear
  C)
   \[E({{e}^{tX}})\]                
  done clear
  D)
   \[E({{e}^{-it\,X}})\]
  done clear
  View Answer play_arrow

• question_answer180) It \[\sigma \] is the standard deviation of a random variable X, then the standard deviation of the random variable \[aX+b,\]where \[a,\text{ }b\in R\]is
  A)
   \[a\sigma +b\]        
  done clear
  B)
   \[|a|\sigma \]
  done clear
  C)
   \[|a|\sigma +b\]
  done clear
  D)
   \[{{a}^{2}}\sigma \]
  done clear
  View Answer play_arrow

• question_answer181) If A and B are two sets, then \[A-(A-B)\]is equal to
  A)
   \[B\]             
  done clear
  B)
   \[A\cup B\]
  done clear
  C)
   \[A\cap B\]         
  done clear
  D)
   \[B-A\]
  done clear
  View Answer play_arrow

• question_answer182) For any real number y the greatest integers not exceeding y is denoted by [y]. If \[f:R\to R\] is defined by \[f(x)=[2x]-2[x]\] for \[x\in R,\] then the range of f is
  A)
   \[\{x\in R:x>0\}\]
  done clear
  B)
   \[\{x\in R:x\le 0\}\]
  done clear
  C)
   \[\{x\in R:0\le x\le 1\}\]
  done clear
  D)
   \[\{0,\,1\}\]
  done clear
  View Answer play_arrow

• question_answer183) The argument of \[\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\] is
  A)
   \[2\pi /3\]                                 
  done clear
  B)
   \[\pi /3\]
  done clear
  C)
   \[-\pi /3\]          
  done clear
  D)
   \[-2\pi /3\]
  done clear
  View Answer play_arrow

• question_answer184) If \[S=\left\{ z\in C:\arg \left( \frac{z-2}{z+2} \right)=\frac{\pi }{3} \right\},\]  then S is
  A)
   an ellipse      
  done clear
  B)
   a straight line.
  done clear
  C)
   a circle        
  done clear
  D)
   a parabola      
  done clear
  View Answer play_arrow

• question_answer185) If \[ac\ne 0\] and \[\alpha ,\beta \] are the roots of the equation \[a{{x}^{2}}+bx+c=0,\]then the quadratic equation with \[1/\alpha \] and \[1/\beta \] as its root is
  A)
   \[{{x}^{2}}/a+x/b+1/c=0\]
  done clear
  B)
   \[c{{x}^{2}}+bx+a=0\]            
  done clear
  C)
   \[b{{x}^{2}}+cx+a=0\]
  done clear
  D)
   \[a{{x}^{2}}+cx+b=0\]
  done clear
  View Answer play_arrow

• question_answer186) If \[\left\{ {{a}_{n}} \right\}_{n}^{x}\] is a sequence with \[{{a}_{0}}=p\] and \[{{a}_{n}}-{{a}_{n-1}}=r{{a}_{n-1}}\] for \[n\ge 1,\] then the terms of the sequence are in
  A)
   an arithmetic progression
  done clear
  B)
   a geometric progression
  done clear
  C)
   a harmonic progression
  done clear
  D)
   an arithmetico-geometric progression
  done clear
  View Answer play_arrow

• question_answer187) The coefficient of \[{{x}^{-17}}\]in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\]is
  A)
   \[^{15}{{C}_{11}}\]
  done clear
  B)
   \[^{15}{{C}_{12}}\]
  done clear
  C)
   \[^{-15}{{C}_{11}}\]
  done clear
  D)
   \[^{-15}{{C}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer188) The term independent of x in the expansion of \[{{\left( {{x}^{3}}+\frac{2}{{{x}^{2}}} \right)}^{15}}\] is
  A)
   \[{{T}_{7}}\]
  done clear
  B)
   \[{{T}_{8}}\]
  done clear
  C)
   \[{{T}_{9}}\]
  done clear
  D)
   \[{{T}_{10}}\]
  done clear
  View Answer play_arrow

• question_answer189) The ortho centre of the \[\Delta \,OAB,\]where O is the origin,\[A(6,0)\] and \[B(3,\,3\sqrt{3})\] is
  A)
   \[(9/2,\,\sqrt{3}/2)\]    
  done clear
  B)
   \[(3,\,\sqrt{3})\]
  done clear
  C)
   \[(\,\sqrt{3},3)\]      
  done clear
  D)
   \[(3,-\sqrt{3})\]
  done clear
  View Answer play_arrow

• question_answer190) The distance between the pair of parallel lines given by \[{{x}^{2}}-1005x+2006=0\]is
  A)
   \[1001\]        
  done clear
  B)
   \[1000\]
  done clear
  C)
   \[1005\]         
  done clear
  D)
   \[2006\]
  done clear
  View Answer play_arrow

• question_answer191) The radical axis of the coaxial system of circles with limiting points \[(1,2)\] and \[(-2,1)\] is
  A)
   \[x+3y=0\]     
  done clear
  B)
   \[3x+y=0\]
  done clear
  C)
   \[2x+3y=0\]    
  done clear
  D)
   \[3x+2y=0\]
  done clear
  View Answer play_arrow

• question_answer192) The equation of the circle that can be inscribed in the square OABC, where O is the origin \[A(-2,0),\,B(-2,2)\] and \[C(0,2)\] is
  A)
    \[{{x}^{2}}+{{y}^{2}}+2x-2y=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}+2x-2y+1=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+2x-2y-1=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}-2x+2y+1=0\]
  done clear
  View Answer play_arrow

• question_answer193) The   curve   with   parametric   equation \[x={{e}^{t}}+{{e}^{-t}}\] and \[y={{e}^{t}}-{{e}^{-t}}\] is
  A)
   a circle        
  done clear
  B)
   an ellipse
  done clear
  C)
   a hyperbola    
  done clear
  D)
   a parabola
  done clear
  View Answer play_arrow

• question_answer194) If \[(-1,\,2\sqrt{2})\] is one of extremity of a focal chord of the parabola \[{{y}^{2}}=-8x,\] then the other extremity is
  A)
   \[(-1,-\sqrt{2})\]    
  done clear
  B)
   \[(2\sqrt{2},-1)\]
  done clear
  C)
   \[(-4,4\sqrt{2})\]    
  done clear
  D)
   \[(4,4\sqrt{2})\]
  done clear
  View Answer play_arrow

• question_answer195) The equation of the pair of straight lines perpendicular to the pair \[2{{x}^{2}}+3xy+2{{y}^{2}}+10x+5y=0\] and passing through the origin is
  A)
   \[2{{x}^{2}}+5xy+2{{y}^{2}}=0\]
  done clear
  B)
   \[2{{x}^{2}}-3xy+2{{y}^{2}}=0\]
  done clear
  C)
   \[2{{x}^{2}}+3xy+{{y}^{2}}=0\]
  done clear
  D)
   \[2{{x}^{2}}-5xy+2{{y}^{2}}=0\]
  done clear
  View Answer play_arrow

• question_answer196) If two angles of a triangle are \[{{45}^{o}}\] and \[{{\tan }^{-1}}(2),\] then the third angle is        
  A)
   \[{{60}^{o}}\]    
  done clear
  B)
   \[{{75}^{o}}\]
  done clear
  C)
   \[{{\tan }^{-1}}3\]
  done clear
  D)
   \[{{90}^{o}}\]                       
  done clear
  View Answer play_arrow

• question_answer197) \[\frac{\tan A}{1+\sec A}+\frac{1+\sec A}{\tan A}\]is equal to
  A)
   \[2\text{ }sin\text{ }A\]        
  done clear
  B)
   \[2\text{ }cos\text{ }A\]
  done clear
  C)
   \[2\text{ }cosec\text{ }A\]      
  done clear
  D)
   \[2\text{ }sec\text{ }A\]
  done clear
  View Answer play_arrow

• question_answer198) If \[\sin \theta +\cos \theta =h,\] then the quadratic equation having \[\sin \theta \] and \[\cos \theta \] as its roots is
  A)
   \[{{x}^{2}}-hx+({{h}^{2}}-1)=0\]
  done clear
  B)
   \[2{{x}^{2}}-2hx+({{h}^{2}}-1)=0\]
  done clear
  C)
   \[{{x}^{2}}-hx+2({{h}^{2}}-1)=0\]
  done clear
  D)
   \[{{x}^{2}}-2hx+({{h}^{2}}-1)=0\]
  done clear
  View Answer play_arrow

• question_answer199) In a triangle, if \[{{r}_{1}}+{{r}_{3}}=k\,\,{{\cos }^{2}}\,B/2,\]then k is equal to
  A)
   \[R\]           
  done clear
  B)
   \[2R\]
  done clear
  C)
   \[3R\]           
  done clear
  D)
   \[4R\]
  done clear
  View Answer play_arrow

• question_answer200) If \[\tan (k+1)\theta =\tan \theta ,\] then \[\theta \] belongs to the set
  A)
   \[\{n\pi :n\in I\}\]    
  done clear
  B)
   \[\{n\pi /2:n\in I\}\]
  done clear
  C)
   \[\{n\pi /k:n\in I\}\]  
  done clear
  D)
   \[\{n\pi /2k:n\in I\}\]
  done clear
  View Answer play_arrow

• question_answer201) \[{{\tan }^{-1}}\left( \frac{3x-{{x}^{3}}}{1-3{{x}^{2}}} \right)-{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)\] is equal to
  A)
   \[0\]
  done clear
  B)
   \[1\]
  done clear
  C)
   \[{{\tan }^{-1}}(x)\]
  done clear
  D)
   \[{{\tan }^{-1}}(2x)\]
  done clear
  View Answer play_arrow

• question_answer202) If    \[sin\text{ }A:sin\text{ }B:sin\text{ }C=3:4:5,\]    then \[cos\text{ }A:cos\text{ }B\]is equal to
  A)
   \[4:3\]          
  done clear
  B)
   \[5:3\]
  done clear
  C)
   \[3:4\]          
  done clear
  D)
   \[3:5\]
  done clear
  View Answer play_arrow

• question_answer203) If A is a matrix such that \[{{A}^{2}}=A+I,\]where I is the unit matrix, then \[{{A}^{5}}\]is equal to
  A)
   \[5A+I\]        
  done clear
  B)
   5A + 21
  done clear
  C)
   \[5A+3I\]       
  done clear
  D)
   \[5A+4I\]
  done clear
  View Answer play_arrow

• question_answer204) The inverse of \[\left[ \begin{matrix}    0 & 0 & 2  \\    0 & 2 & 0  \\    2 & 0 & 0  \\ \end{matrix} \right]\] is
  A)
   \[\left[ \begin{matrix}    2 & 0 & 0  \\    0 & 2 & 0  \\    0 & 0 & 2  \\ \end{matrix} \right]\]
  done clear
  B)
   \[\left[ \begin{matrix}    \frac{1}{2} & 0 & 0  \\    0 & \frac{1}{2} & 0  \\    0 & 0 & \frac{1}{2}  \\ \end{matrix} \right]\]
  done clear
  C)
   \[\left[ \begin{matrix}    0 & 0 & 2  \\    0 & 2 & 0  \\    2 & 0 & 0  \\ \end{matrix} \right]\]
  done clear
  D)
   \[\left[ \begin{matrix}    0 & 0 & \frac{1}{2}  \\    0 & \frac{1}{2} & 0  \\    \frac{1}{2} & 0 & 0  \\ \end{matrix} \right]\]
  done clear
  View Answer play_arrow

• question_answer205) \[\left| \begin{matrix}    1 & 2 & 3  \\    {{1}^{3}} & {{2}^{3}} & {{3}^{3}}  \\    {{1}^{5}} & {{2}^{5}} & {{3}^{5}}  \\ \end{matrix} \right|\] equal to         
  A)
   \[1!\,\,2\,\,1\,\,\,3\]
  done clear
  B)
   \[1\,\,!\,\,\,3\,\,!\,\,\,5\,\,!\]
  done clear
  C)
   \[6\,\,!\]
  done clear
  D)
   \[9\,\,!\]     
  done clear
  View Answer play_arrow

• question_answer206) \[\left| \begin{matrix}    a & b & a+b  \\    b & a+b & a  \\    a+b & a & b  \\ \end{matrix} \right|\] is equal to         
  A)
   \[{{a}^{3}}+{{b}^{3}}\]
  done clear
  B)
   \[-({{a}^{3}}+{{b}^{3}})\]
  done clear
  C)
   \[2\,({{a}^{3}}+{{b}^{3}})\]
  done clear
  D)
   \[-2\,({{a}^{3}}+{{b}^{3}})\]
  done clear
  View Answer play_arrow

• question_answer207) If \[A\left[ \begin{matrix}    a & b & 0  \\    -b & a & 0  \\    0 & 0 & 1  \\ \end{matrix} \right],\] where \[{{a}^{2}}+{{b}^{2}}=1,\] then adj  is equal to                      
  A)
   \[{{A}^{-1}}\]           
  done clear
  B)
   \[{{A}^{T}}\]
  done clear
  C)
   \[A\]             
  done clear
  D)
   \[-A\] (Here, \[{{A}^{T}}\] is the transpose of A) 
  done clear
  View Answer play_arrow

• question_answer208) If A is a non-singular matrix such that \[{{A}^{3}}=A+I,\] then the inverse of \[B={{A}^{6}}-{{A}^{5}}\]is
  A)
   \[A\]            
  done clear
  B)
   \[{{A}^{-1}}\]
  done clear
  C)
   \[-A\]           
  done clear
  D)
   \[-{{A}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer209) The value of \[\lambda \] such that \[x+3y+\lambda z=0,\]\[2x+4y-z=0,\,\,\,\,\,\,\,x+5y-2z=0\]has a non-trivial solution is                    
  A)
   \[-1\]             
  done clear
  B)
   \[0\]
  done clear
  C)
   \[1\]             
  done clear
  D)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer210) If \[A=\left[ \begin{matrix}    0 & -3 & -4/3  \\    3 & 0 & -1/4  \\    4/3 & 1/4 & 0  \\ \end{matrix} \right],\] then det \[(A+{{A}^{T}})\] is equal to                                 
  A)
   \[0\]              
  done clear
  B)
   \[1\]
  done clear
  C)
   \[2\]             
  done clear
  D)
   \[3\]
  done clear
  View Answer play_arrow

• question_answer211) If the position vector of A with respect to O is \[3\hat{i}-2\hat{j}+4\hat{k}\]and \[\overrightarrow{AB}=3\hat{i}-\hat{j}+\hat{k},\] then the position vector of B with respect to 0 is
  A)
   \[-\hat{j}+3\hat{k}\]     
  done clear
  B)
   \[6\hat{i}-3\hat{j}+5\hat{k}\]
  done clear
  C)
   \[\hat{j}-3\hat{k}\]      
  done clear
  D)
   \[\hat{i}-3\hat{j}+5\hat{k}\]
  done clear
  View Answer play_arrow

• question_answer212) If \[|\vec{a}|=|\vec{b}|=|\vec{a}-\vec{b}|=1,\] then \[|\vec{a}+\vec{b}|\]is equal to
  A)
   \[1\]             
  done clear
  B)
   \[2\]
  done clear
  C)
   \[\sqrt{2}\]            
  done clear
  D)
   \[\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer213) If the vectors \[2\hat{i}-3\hat{j}+4\hat{k},\,\,\hat{i}+2\hat{j}-\hat{k}\] and \[\lambda \hat{i}-\hat{j}+2\hat{k}\]are coplanar, then X is equal to
  A)
   \[0\]
  done clear
  B)
   \[5/8\]
  done clear
  C)
   \[8/5\]
  done clear
  D)
   \[1\]
  done clear
  View Answer play_arrow

• question_answer214) If \[\vec{a}=2\hat{i}+2\hat{j}+\hat{k},\,\vec{a}.\vec{b}=14\] and \[\vec{a}\times \vec{b}=3\hat{i}+\hat{j}-8\hat{k},\] then \[\vec{b}\] equals
  A)
   \[\hat{i}+5\hat{j}+2\hat{k}\]
  done clear
  B)
   \[\hat{i}-2\hat{j}+16\hat{k}\]
  done clear
  C)
   \[5\hat{i}+\hat{j}+2\hat{k}\]
  done clear
  D)
   \[5\hat{i}-\hat{j}+2\hat{k}\]
  done clear
  View Answer play_arrow

• question_answer215) If \[\vec{a},\vec{b},\vec{c}\] are non-coplanar vectors and \[(\vec{a}-\lambda \vec{b}).(\vec{b}-2\vec{c})\times (\vec{c}+2\vec{a})=0,\] then \[\lambda \] is equal to
  A)
   \[1\]
  done clear
  B)
   \[1/4\]
  done clear
  C)
   \[0\]
  done clear
  D)
   \[-1/4\]
  done clear
  View Answer play_arrow

• question_answer216) If \[\vec{a},\vec{b},\vec{c}\] are non-coplanar and  \[[\vec{a}+\vec{b}\,\,\,\vec{b}+\vec{c}\,\,\,\,\vec{c}+\vec{a}]=k[\vec{a}\vec{b}\vec{c}],\]then k is equal to
  A)
   \[0\]
  done clear
  B)
   \[1\]
  done clear
  C)
   \[2\]
  done clear
  D)
    \[3\]
  done clear
  View Answer play_arrow

• question_answer217) If \[\vec{a}+2\vec{b}+2\vec{c}=\vec{0}\] and \[(\vec{a}\times \vec{b})+(\vec{b}\times \vec{c})+(\vec{c}\times \vec{a})=\lambda (\vec{b}\times \vec{c}),\] then \[\lambda \] is equal to
  A)
   \[4\]
  done clear
  B)
   \[7\]
  done clear
  C)
   \[8\]
  done clear
  D)
   \[9\]
  done clear
  View Answer play_arrow

• question_answer218) The line segment adjoining the points A , B makes projection 1,4,3 on X,Y,Z axis respectively. Then the direction cosines of AB are
  A)
   \[1,4,3\]
  done clear
  B)
   \[1/\sqrt{26},\,\,4/\sqrt{26},\,\,3/\sqrt{26}\]
  done clear
  C)
   \[-1/\sqrt{26},\,\,4/\sqrt{26},\,\,3/\sqrt{26}\]
  done clear
  D)
   \[1/\sqrt{26},-\,\,4/\sqrt{26},\,\,3/\sqrt{26}\]
  done clear
  View Answer play_arrow

• question_answer219) The length of the projection of the line segment joining \[(3,-1,0)\] and \[(-3,5,\sqrt{2})\] on a line with direction cosines \[1/2,\,\,1/2,\,\,1/\sqrt{2}\] is
  A)
   \[1\]                                           
  done clear
  B)
   \[2\]
  done clear
  C)
   \[3\]
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer220) The line perpendicular to the plane s\[2x-y+5z=4\] passing through the point \[(-1,0,1)\] is
  A)
   \[\frac{x+1}{2}=-y=\frac{z-1}{-5}\]
  done clear
  B)
   \[\frac{x+1}{2}=-y=\frac{z-1}{-5}\]
  done clear
  C)
   \[\frac{x+1}{2}=-y=\frac{z-1}{5}\]
  done clear
  D)
   \[\frac{x+1}{2}=y=\frac{z-1}{5}\]
  done clear
  View Answer play_arrow

• question_answer221) The shortest distance between the lines \[\frac{x-2}{3}=\frac{y+3}{4}=\frac{z-1}{5}\] and \[\frac{x-5}{1}=\frac{y-1}{2}=\frac{z-6}{3}\] is
  A)
   \[3\]
  done clear
  B)
   \[2\]
  done clear
  C)
   \[1\]
  done clear
  D)
   \[0\]
  done clear
  View Answer play_arrow

• question_answer222) Angle between the line \[\frac{x+1}{1}=\frac{y}{2}=\frac{z-1}{1}\] and a normal to the plane \[x-y+z=0\] is
  A)
   \[{{0}^{o}}\]
  done clear
  B)
   \[{{30}^{o}}\]
  done clear
  C)
   \[{{45}^{o}}\]
  done clear
  D)
   \[{{90}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer223) A point on x-axis which is equidistant from both the points \[(1,\,2,3)\] and \[(3,5,-2)\] is
  A)
   \[(-6,0,0)\]
  done clear
  B)
   \[(5,0,0)\]
  done clear
  C)
   \[(-5,0,0)\]
  done clear
  D)
   \[(6,0,0)\]
  done clear
  View Answer play_arrow

• question_answer224) Foot of the perpendicular from \[(-2,1,4)\] to a plane is  \[(3,1,2)\], then the equation of the plane is
  A)
   \[4x-2y=11\]
  done clear
  B)
   \[5x-2y=10\]
  done clear
  C)
   \[5x-2z=11\]
  done clear
  D)
   \[5x+2z=11\]
  done clear
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• question_answer225) If \[\theta \] is  the angle between the planes \[2x-y+z-1=0\] and \[x-2y+z+2=0,\] then \[\cos \,\theta \] is equal to
  A)
   \[2/3\]
  done clear
  B)
   \[3/4\]
  done clear
  C)
   \[4/5\]
  done clear
  D)
   \[5/6\]s
  done clear
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