Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

done Rajasthan PET Solved Paper-2003 Total Questions - 300

• question_answer1) A stretched string of length\[l,\]fixed at both ends can sustain stationary waves of wavelength  given by
  A)
   \[\lambda =\frac{{{n}^{2}}}{2l}\]
  done clear
  B)
   \[\lambda =\frac{{{I}^{2}}}{2n}\]
  done clear
  C)
   \[\lambda =\frac{2l}{n}\]
  done clear
  D)
   \[\lambda =2\ln \]
  done clear
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• question_answer2) Moment of inertia of a thin circular ring of mass M and radius R about any diameter is
  A)
   \[M{{R}^{2}}\]           
  done clear
  B)
   \[2M{{R}^{2}}\]
  done clear
  C)
   \[\frac{M{{R}^{2}}}{2}\]
  done clear
  D)
   \[\frac{M{{R}^{2}}}{4}\]
  done clear
  View Answer play_arrow

• question_answer3) A particle moves with constant speed in circular path. During the motion its
  A)
   velocity is constant
  done clear
  B)
   acceleration is constant
  done clear
  C)
   radial acceleration towards the inside
  done clear
  D)
   radial acceleration towards the outside
  done clear
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• question_answer4) A stone thrown upward with a speed u from the top of the tower, reaches the ground with velocity 3u. The height of the tower is
  A)
   \[\frac{8{{u}^{2}}}{g}\]
  done clear
  B)
   \[\frac{3{{u}^{2}}}{g}\]
  done clear
  C)
   \[\frac{4{{u}^{2}}}{g}\]
  done clear
  D)
   \[\frac{5{{u}^{2}}}{g}\]
  done clear
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• question_answer5) Which one of the following is scalar?
  A)
   Electric potential
  done clear
  B)
   Momentum
  done clear
  C)
   Velocity         
  done clear
  D)
   Force
  done clear
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• question_answer6) Dimensions of torque are
  A)
   \[[M{{L}^{2}}{{T}^{-1}}]\]          
  done clear
  B)
   \[[M{{L}^{2}}{{T}^{-2}}]\]
  done clear
  C)
   \[[ML{{T}^{-2}}]\]           
  done clear
  D)
   \[[M{{L}^{-1}}{{T}^{-1}}]\]
  done clear
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• question_answer7) If total torque of the system is zero, then the total angular momentum of the system will be constant at
  A)
   direction
  done clear
  B)
   both direction and magnitude
  done clear
  C)
   magnitude
  done clear
  D)
   None of the above
  done clear
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• question_answer8) The angular velocity of earth rotating about its own axis is
  A)
  \[\frac{2\pi }{60\,\times \,60\,\times \,2\pi }rad/s\]
  done clear
  B)
  \[\frac{2\pi }{60\,\times \,60}rad/s\]
  done clear
  C)
  \[\frac{2\pi }{60}rad/s\]
  done clear
  D)
  \[\frac{2\pi }{365\,\times \,24\,\times \,60\,\times \,60}rad/s\]
  done clear
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• question_answer9) The equation of progressive wave is\[y=a\text{ }sin(200\] \[(200tx),\]where\[x\]is in metre and\[x\]is in second. The velocity of wave will be
  A)
   200 m/s         
  done clear
  B)
   100 m/s
  done clear
  C)
   50 m/s          
  done clear
  D)
   None of these
  done clear
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• question_answer10) According to Newton's third law, which of the following statements is true?
  A)
   Both forces are acted upon one body
  done clear
  B)
   Both forces are acted upon the different bodies
  done clear
  C)
   Directions and magnitudes of both forces are same
  done clear
  D)
   Both forces have different magnitudes and opposite directions
  done clear
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• question_answer11) If \[\overrightarrow{F}=5\widehat{i}+3\widehat{j},\,\overrightarrow{r}=2\widehat{i}-\widehat{j},\], then work done by the system will be
  A)
   \[-7\text{ }J\]           
  done clear
  B)
   7 J
  done clear
  C)
   10 J          
  done clear
  D)
   \[-10\text{ }J\]
  done clear
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• question_answer12) If n is a number and u is unit of physical quantity then which of the following is correct for measurement nu?
  A)
   \[n\propto u\]
  done clear
  B)
   \[n\propto \frac{1}{u}\]
  done clear
  C)
   No relation between n and u
  done clear
  D)
   None of the above
  done clear
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• question_answer13) The force F is exterted one end of wire when second end is tight, the extension of wire is\[x,\]then
  A)
   \[F\propto x\]            
  done clear
  B)
   \[F\propto {{x}^{2}}\]
  done clear
  C)
   \[F\propto {{x}^{3}}\]          
  done clear
  D)
   \[F\propto {{x}^{4}}\]
  done clear
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• question_answer14) If the length and radius of wire are doubled then Young's modulus of the wire will be
  A)
   doubled         
  done clear
  B)
   half
  done clear
  C)
   constant         
  done clear
  D)
   None of these
  done clear
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• question_answer15) What is the formula of escape velocity?
  A)
   \[\sqrt{g{{R}_{e}}}\]             
  done clear
  B)
  \[~2g{{R}_{e}}\]
  done clear
  C)
   \[\sqrt{2g{{R}_{e}}}\]           
  done clear
  D)
   None of these
  done clear
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• question_answer16) What is the true of following in an elastic collision?
  A)
   The kinetic energy will be conservative
  done clear
  B)
   The momentum will be conservative
  done clear
  C)
   Both kinetic energy and momentum will be conservative
  done clear
  D)
   None of the above
  done clear
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• question_answer17) If the speed of particle became twice, then which of the following quantities will be doubled?
  A)
   Length           
  done clear
  B)
   Kinetic energy
  done clear
  C)
   Momentum      
  done clear
  D)
   Acceleration
  done clear
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• question_answer18) If in the lift, the body of mass 5 kg is suspended to spring balance, the lift moves downward with acceleration\[10\text{ }m/{{s}^{2}},\]then the reading of spring balance is
  A)
   more than 5 kg-wt
  done clear
  B)
   less than 5 kg-wt
  done clear
  C)
   5 kg-wt
  done clear
  D)
   zero
  done clear
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• question_answer19) The ratio of fraction of displacement of mass with which of the following quantities is constant if its motion is simple harmonic?
  A)
   Velocity         
  done clear
  B)
   Acceleration
  done clear
  C)
   Time period      
  done clear
  D)
   Mass
  done clear
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• question_answer20) If the maximum acceleration of motion of a particle is\[16\text{ }m/{{s}^{2}},\]and the maximum velocity is 24 m/s, then amplitude of the particle will be
  A)
   36 m            
  done clear
  B)
   20 m
  done clear
  C)
   16 m            
  done clear
  D)
   None of these
  done clear
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• question_answer21) Two wires A and B are made from the same material. The ratio of lengths and diameters respectively are 1:2 and 2:1. If these are stretched by a force, then the ratio of these expansion of lengths will be
  A)
   2 : 1             
  done clear
  B)
   1 : 4
  done clear
  C)
   1 : 8          
  done clear
  D)
   8 : 1
  done clear
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• question_answer22) If gravitational potential at the surface of is zero, then gravitational potential at infinity will be
  A)
   \[{{W}_{2}}>{{W}_{1}}>{{W}_{3}}\]
  done clear
  B)
   \[{{W}_{2}}>{{W}_{3}}>{{W}_{1}}\]
  done clear
  C)
   \[{{W}_{1}}>{{W}_{2}}>{{W}_{3}}\]
  done clear
  D)
   \[{{W}_{1}}>{{W}_{3}}>{{W}_{2}}\]
  done clear
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• question_answer23) Starting with the same initial conditions, an ideal gas expands from volumes\[{{V}_{1}}\]to\[{{V}_{2}}\]three different ways, the work done by the gas is \[{{W}_{1}}\] if the process is purely isothermal, \[{{W}_{2}}\] if purely isobaric and W3 if purely adiabatic, then
  A)
   \[{{W}_{2}}>{{W}_{1}}>{{W}_{3}}\]  
  done clear
  B)
   \[{{W}_{2}}>{{W}_{3}}>{{W}_{1}}\]
  done clear
  C)
   \[{{W}_{1}}>{{W}_{2}}>{{W}_{3}}\]
  done clear
  D)
   \[{{W}_{1}}>{{W}_{3}}>{{W}_{2}}\]
  done clear
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• question_answer24) The gas is expanded in such a way so that its pressure and volume laws follow\[p{{V}^{2}}=\]constant. In this process, the gas will become                               
  A)
   hot                                     
  done clear
  B)
   cold                                  
  done clear
  C)
   nor hot neither cold     
  done clear
  D)
   first hot after that cold                 
  done clear
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• question_answer25) The time period of simple pendulum depends on
  A)
   length          
  done clear
  B)
   mass           
  done clear
  C)
   momentum      
  done clear
  D)
   density      
  done clear
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• question_answer26) The stored uniform energy in a spring which is displaced by distance x is               
  A)
   \[k/x\]
  done clear
  B)
   \[\frac{1}{2}\,k/{{x}^{2}}\]
  done clear
  C)
   \[k/{{x}^{2}}\]                 
  done clear
  D)
   \[2k/{{x}^{2}}\]
  done clear
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• question_answer27) A particle of mass 0.10 kg is executing simple harmonic motion at the rate of 20 oscillation/\[{{s}^{2}}\] and its amplitude is 0.05 m. Its energy at equilibrium position will be
  A)
   2 J               
  done clear
  B)
   4 J            
  done clear
  C)
   1 J               
  done clear
  D)
   zero
  done clear
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• question_answer28) When any rigid body is in rotational motion about any axis then what is the same for all particles?                                 
  A)
   Angular velocity  
  done clear
  B)
   Linear velocity
  done clear
  C)
   Radius           
  done clear
  D)
   Linear acceleration
  done clear
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• question_answer29) The coefficients of thermal conductivities of copper, murcury and glass respectively are\[{{K}_{c}},{{K}_{m}}\] and\[{{K}_{g}}\]such that\[{{K}_{c}}>\text{ }{{K}_{m}}>\text{ }{{K}_{g}}\]. If the same quantity of heat flows per second per unit area of each and corresponding temperature gradients are\[{{X}_{c}},{{X}_{m}}\]and\[{{X}_{g}},\]then
  A)
  \[{{X}_{c}}=\text{ }{{X}_{m}}=\text{ }{{X}_{g}}\] 
  done clear
  B)
   \[{{X}_{c}}>{{X}_{m}}>\text{ }{{X}_{g}}\]
  done clear
  C)
   \[{{X}_{c}}<{{X}_{m}}<\text{ }{{X}_{g}}\]  
  done clear
  D)
   \[{{X}_{m}}<{{X}_{c}}<\text{ }{{X}_{g}}\]
  done clear
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• question_answer30) The emitted energy from any body depends on
  A)
   temperature     
  done clear
  B)
   nature of matter
  done clear
  C)
   area            
  done clear
  D)
   None of these
  done clear
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• question_answer31) What is the absorptive power of ideal black body?
  A)
   0                 
  done clear
  B)
   1
  done clear
  C)
   \[\infty \]               
  done clear
  D)
   None of these
  done clear
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• question_answer32) The initial coordinates of any system are p and V. If a gas \[\left( \gamma =\frac{5}{3} \right)\]is compressed to \[\frac{1}{8}\] of its original volume, then the pressure of the gas will be
  A)
   p                
  done clear
  B)
   16p
  done clear
  C)
   4p               
  done clear
  D)
   32 p
  done clear
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• question_answer33) Which of the following relationships between p and T for adiabatic process is true?
  A)
   \[{{p}^{1-\gamma }}+{{T}^{\gamma }}\] = constant
  done clear
  B)
   \[{{p}^{\gamma }}+{{T}^{1-\gamma }}\] = constant
  done clear
  C)
   \[p{{T}^{1-\gamma }}T\]= constant
  done clear
  D)
   \[{{p}^{1-\gamma }}T\]= constant
  done clear
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• question_answer34) The energy related per degree of freedom of one molecule is
  A)
   \[\frac{3}{2}kT\]            
  done clear
  B)
   \[\frac{1}{2}kT\]
  done clear
  C)
   \[\frac{3}{2}RT\]               
  done clear
  D)
   \[\frac{1}{2}RT\]
  done clear
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• question_answer35) Absolute temperature is that temperature at which
  A)
   molecular motion of all particles becomes zero
  done clear
  B)
   molecules move randomly
  done clear
  C)
   gas's atoms change to liquid
  done clear
  D)
   None of the above
  done clear
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• question_answer36) If the surface tension of liquid is\[5\times {{10}^{-2}}N/m\] and weight of liquid column is\[6.28\times {{10}^{-4}}N,\]then radius of capillary is
  A)
   \[2\times {{10}^{-3}}m\]       
  done clear
  B)
   \[2.5\times {{10}^{-3}}m\]
  done clear
  C)
   \[2\times {{10}^{-4}}\]      
  done clear
  D)
   \[4\times {{10}^{-3}}m\]
  done clear
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• question_answer37) When the liquid does not wet the sides of a solid, then angle of contact is
  A)
   obtuse           
  done clear
  B)
   acute
  done clear
  C)
   \[90{}^\circ \]              
  done clear
  D)
   zero
  done clear
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• question_answer38) A tuning fork is placed on the table. It produces maximum sound due to
  A)
   beat             
  done clear
  B)
   resonance
  done clear
  C)
   interference      
  done clear
  D)
   stationary waves
  done clear
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• question_answer39) A body cools down from\[61{}^\circ C\]to\[59{}^\circ C\]in 4 min. If the temperature of atmosphere is\[30{}^\circ C,\]then the time taken to cool it from\[51{}^\circ C\]to\[49{}^\circ C\]will be
  A)
   4 min           
  done clear
  B)
   2 min
  done clear
  C)
   6 min           
  done clear
  D)
   8 min
  done clear
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• question_answer40) Temperature is a measurement of degree of coldness or hotness of an object. The definition is based on
  A)
   Zeroth law of thermodynamics
  done clear
  B)
   First law of thermodynamics
  done clear
  C)
   Second law of thermodynamics
  done clear
  D)
   Newton's law of cooling
  done clear
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• question_answer41) The correct relation between isothermal gradient and adiabatic gradient is
  A)
   adiabatic gradient\[=\gamma \times \] isothermal gradient
  done clear
  B)
   isothermal gradient\[=\gamma \times \] adiabatic gradient
  done clear
  C)
   adiabatic gradient\[={{\gamma }^{2}}\times \] isothermal gradient
  done clear
  D)
   isothermal   gradient\[={{\gamma }^{2}}\times \]adiabatic gradient
  done clear
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• question_answer42) If root mean square velocity for hydrogen gas is 318 m/s and density is\[8.99\times {{10}^{-5}}kg/{{m}^{3}}\]then the pressure of gas will be
  A)
   3 atm           
  done clear
  B)
   1 atm
  done clear
  C)
   2 atm           
  done clear
  D)
   None of these
  done clear
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• question_answer43) \[pV/kT\] represents
  A)
   number of molecules
  done clear
  B)
   number of moles
  done clear
  C)
   universal gas constant
  done clear
  D)
   None of the above
  done clear
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• question_answer44) The spherical shape of rain drop is due to
  A)
   surface tension   
  done clear
  B)
   viscosity
  done clear
  C)
   elasticity         
  done clear
  D)
   gravity
  done clear
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• question_answer45) The excess of pressure inside a soap bubble than that of the outer pressure is
  A)
   \[\frac{4T}{r}\]
  done clear
  B)
   \[\frac{2T}{r}\]  
  done clear
  C)
   \[\frac{8T}{r}\]
  done clear
  D)
   None of these
  done clear
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• question_answer46) There is an electric field E in\[x-\]direction. If the work done on moving a charge 0.2 C through a distance of 2 m along a line making an angle \[60{}^\circ \] with the\[x-\]axis is 4.0, what is the value of E?
  A)
   \[\sqrt{3}\]N/C          
  done clear
  B)
   4N/C
  done clear
  C)
   5 N/C           
  done clear
  D)
   None of these
  done clear
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• question_answer47) An electron is accelerated from a potential difference of\[{{10}^{4}}V\]at distance 5 cm. The force on electron will be
  A)
   \[3.2\,\times \,{{10}^{-14}}N\]
  done clear
  B)
   \[4N\]
  done clear
  C)
   \[3.2\,\times \,{{10}^{-12}}N\]
  done clear
  D)
   None of these
  done clear
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• question_answer48) A point charge\[+q\]is placed at the centre of a cube. The electric flux emerging from the cube
  A)
   \[\frac{q}{{{\varepsilon }_{0}}}\]
  done clear
  B)
   \[\frac{q}{2{{\varepsilon }_{0}}}\]
  done clear
  C)
   \[\frac{q}{6{{\varepsilon }_{0}}}\]
  done clear
  D)
   \[\frac{q}{3{{\varepsilon }_{0}}}\]
  done clear
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• question_answer49) To cool a liquid rapidly, cooling system should be used
  A)
   in middle        
  done clear
  B)
   on head
  done clear
  C)
   any point        
  done clear
  D)
   None of these
  done clear
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• question_answer50) A stone is shot straight upward with a speed of 20 m/s from a tower 200 m high. The speed with which it strikes the ground is approximately
  A)
   60 m/s           
  done clear
  B)
   65 m/s
  done clear
  C)
   70 m/s
  done clear
  D)
   75 m/s
  done clear
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• question_answer51) When light ray goes from air to water, then its quality that remains unchanged is
  A)
   frequency       
  done clear
  B)
   wavelength
  done clear
  C)
   speed            
  done clear
  D)
   None of these
  done clear
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• question_answer52) Sources are in phase when
  A)
   first phase is constant with the time
  done clear
  B)
   first phase changes with the time
  done clear
  C)
   first phase  is  constant with the displacement
  done clear
  D)
   None of the above
  done clear
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• question_answer53) Find the fundamental frequency of a closed pipe, if the length of pipe is 1 m. (speed of sound in air = 320 m/s)
  A)
   320 Hz          
  done clear
  B)
   160 Hz
  done clear
  C)
   80 Hz           
  done clear
  D)
   40 Hz
  done clear
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• question_answer54) The musical interval between two tones of frequencies 400 Hz and 200 Hz is
  A)
   2               
  done clear
  B)
   200
  done clear
  C)
   1               
  done clear
  D)
   None of these
  done clear
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• question_answer55) Two pulses in a stretched string whose centres are initially 8 cm apart are moving towards each other as shown in the figure. The speed of each pulse is 2 cm/s. After 2s, the total energy of the pulses will be
  A)
   zero
  done clear
  B)
   purely kinetic
  done clear
  C)
   purely potential
  done clear
  D)
   partly kinetic and partly potential
  done clear
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• question_answer56) Two charges of\[3\times {{10}^{-9}}\]and\[{{10}^{-9}}C\]are placed at a distance 5 cm. The force of attraction between them is                    
  A)
   \[1.08\times {{10}^{5}}N\]
  done clear
  B)
   \[1.08\times {{10}^{-6}}N\]
  done clear
  C)
   \[1.08\times {{10}^{-5}}N\]
  done clear
  D)
   None of these   
  done clear
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• question_answer57) If in diffraction by single slit, the width of slit is equal to wavelength of light, then what happened at the screen?              
  A)
   Image of slit       
  done clear
  B)
   Diffraction band
  done clear
  C)
   Equal illuminate  
  done clear
  D)
   Unequal illuminate
  done clear
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• question_answer58) Two positive point charges 12\[\mu \]C are 8\[\mu \]C are placed at a distance work done to bring closer 4 cm will be
  A)
   5.8 J             
  done clear
  B)
   5.8 eV         
  done clear
  C)
   13 J             
  done clear
  D)
   13 eV            
  done clear
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• question_answer59) The object at distance of 20 cm is placed in front of convex lens of focal length 10 cm, where will be image formed?          
  A)
   10 cm            
  done clear
  B)
   20 cm        
  done clear
  C)
   5 cm           
  done clear
  D)
   25 cm        
  done clear
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• question_answer60) The equivalent resistance between points P and Q of an infinite network of resistance each of 2\[\Omega \] connected as shown in figure
  A)
   3.23\[\Omega \]            
  done clear
  B)
   4.23\[\Omega \]
  done clear
  C)
   6.32\[\Omega \]            
  done clear
  D)
   infinite
  done clear
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• question_answer61) Two tuning forks of frequencies 256 and 258 Hz produce 5 beats/s with the third tuning fork. The frequency of third tuning fork will be
  A)
   120 Hz          
  done clear
  B)
   115 Hz
  done clear
  C)
   105 Hz          
  done clear
  D)
   95 Hz
  done clear
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• question_answer62) The equation of wave is\[y=5\text{ }sin\text{ }n\text{ }(t+4)\]. The amplitude and time period will be
  A)
   5 cm, 2s        
  done clear
  B)
   5 cm, \[\frac{1}{2}\]s
  done clear
  C)
   5 cm, 4s        
  done clear
  D)
   5 cm, \[\frac{1}{4}\]s
  done clear
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• question_answer63) If\[R=25\text{ }\Omega ,\text{ }Z=5\,\Omega \]then coefficient of power will be
  A)
   \[\frac{1}{2}\]                   
  done clear
  B)
   2
  done clear
  C)
   1                   
  done clear
  D)
   zero
  done clear
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• question_answer64) The formula of impedance for circuit R-L is
  A)
   \[\sqrt{{{R}^{2}}+\frac{1}{{{\omega }^{2}}{{L}^{2}}}}R\]
  done clear
  B)
   \[{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}\]
  done clear
  C)
   \[\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}\]
  done clear
  D)
   \[\sqrt{{{\omega }^{2}}{{L}^{2}}+\frac{1}{{{R}^{2}}}}\,\]
  done clear
  View Answer play_arrow

• question_answer65) Loss of power m R-L circuit is
  A)
   \[\frac{{{V}^{2}}}{({{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}R\]
  done clear
  B)
  \[\frac{{{V}^{2}}}{\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}}\]
  done clear
  C)
   \[\frac{{{V}^{2}}}{R}\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer66) The phase difference in R-C circuit will be
  A)
   \[\phi ={{\tan }^{-1}}\left( \frac{1}{\omega CR} \right)\]
  done clear
  B)
   \[\phi ={{\tan }^{-1}}\left( \frac{\omega }{RC} \right)\]
  done clear
  C)
   \[\phi ={{\tan }^{-1}}\left( \frac{RC}{\omega } \right)\]
  done clear
  D)
   \[\phi ={{\tan }^{-1}}\sqrt{\frac{\omega }{RC}}\]
  done clear
  View Answer play_arrow

• question_answer67) The electric field gets induced by changing magnetic force lines passing through a conductor. This can be understood by which law?
  A)
   Faraday's law    
  done clear
  B)
   Ampere's law
  done clear
  C)
   Lenz's law      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer68) In a transformer,\[{{e}_{p}}=110\text{ }V\]and\[{{e}_{s}}=440\text{ }V,\]then its round ratio will be
  A)
   4 : 1             
  done clear
  B)
   1 : 4
  done clear
  C)
   1 : 3             
  done clear
  D)
   1 : 2
  done clear
  View Answer play_arrow

• question_answer69) The intensity of magnetic field at centre of circular coil is
  A)
   \[\frac{{{\mu }_{0}}I}{2R}\]
  done clear
  B)
   \[\frac{{{\mu }_{0}}NI{{R}^{2}}}{2{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}\]
  done clear
  C)
   \[\frac{{{\mu }_{0}}I}{4R}\]
  done clear
  D)
   \[\frac{{{\mu }_{0}}I}{8R}\]
  done clear
  View Answer play_arrow

• question_answer70) In a potentiometer experiment two cells of emf? s \[{{E}_{1}}\]and\[{{E}_{2}}\]are used in series and in conjunction and the balancing length is found to be 58 cm of the wire. If the polarity of\[{{E}_{2}}\]is reversed, then the balancing length becomes 29 cm. The ratio \[\frac{{{E}_{1}}}{{{E}_{2}}}\]of the emf of the two cells is
  A)
   1 : 1             
  done clear
  B)
   2 : 1
  done clear
  C)
   3 : 1             
  done clear
  D)
   4 : 1
  done clear
  View Answer play_arrow

• question_answer71) Power dissipated in pure inductive circuit will be
  A)
   \[\frac{{{V}^{2}}}{({{R}^{2}}+{{\omega }^{2}}{{L}^{2}})}R\]
  done clear
  B)
   zero
  done clear
  C)
   \[\frac{{{V}^{2}}}{{{L}^{2}}}R\]
  done clear
  D)
   \[\frac{{{V}^{2}}}{{{Z}^{2}}}R\]
  done clear
  View Answer play_arrow

• question_answer72) An AC circuit has voltage\[V=5\text{ }sin\text{ }10t,\]if\[R=1\,\Omega \]and\[L=0.1\text{ }H,\]then what is the phase difference between current and voltage?
  A)
   \[\frac{\pi }{4}\]             
  done clear
  B)
   \[0\]
  done clear
  C)
   \[\frac{\pi }{2}\]             
  done clear
  D)
   \[\infty \]
  done clear
  View Answer play_arrow

• question_answer73) In R-L-C circuit,\[R=100\text{ }\Omega ,\text{ }L=1\text{ }H,\text{ }C=10\mu F\] and \[\omega \]= 314 rad /s, then find the value of impedance.
  A)
   100 \[\Omega \]            
  done clear
  B)
   272.6 \[\Omega \]
  done clear
  C)
   217.2 \[\Omega \]          
  done clear
  D)
   205.5\[\Omega \]
  done clear
  View Answer play_arrow

• question_answer74) In circuit, when the current changes to 8A from 2A in 2 s, then the value of emf becomes 2 V. The inductance of the circuit is
  A)
   \[\frac{4}{3}H\]
  done clear
  B)
   \[\frac{2}{3}H\]
  done clear
  C)
   \[\frac{1}{3}H\]
  done clear
  D)
   \[\sqrt{\frac{2}{3}}\,H\]
  done clear
  View Answer play_arrow

• question_answer75) Generator generates electric current. In actual, it is a source of
  A)
   inducted force    
  done clear
  B)
   emf
  done clear
  C)
   electric force     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer76) Lenz's law is accordance on
  A)
   conservation of energy
  done clear
  B)
   conservation of charge
  done clear
  C)
   conservation of momentum
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer77) When the current flows from the conductor, then force above of magnetic field is
  A)
   in circular form around the wire
  done clear
  B)
   near the wire and parallel to wire
  done clear
  C)
   near the wire and perpendicular to wire
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer78) In the following figure, a coil of radius 2 cm is shown along with a coil of radius 7 cm present at   its centre. Each coil has 100 round and big coil has 5 A current. What should be the current in small coil so that total magnetic field at centre is 2 mT?
  A)
   1.44 A            
  done clear
  B)
   0.793 A
  done clear
  C)
   2.88 A            
  done clear
  D)
   3.4 A
  done clear
  View Answer play_arrow

• question_answer79) If amplification factor and mutual conductance are 20 and\[{{10}^{-3}}\]mho respectively, then plate resistance will be
  A)
   20 k\[\Omega \]           
  done clear
  B)
  \[10\,k\Omega \]
  done clear
  C)
   \[20\times {{10}^{-3}}\Omega \]       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer80) On the basis which of the following a nucleus can be explained?
  A)
   By nuclear liquid drop model
  done clear
  B)
   By Thomson model
  done clear
  C)
   By Rutherford model
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer81) If the radius of nucleus is\[{{10}^{-15}}m,\]the uncertainty in momentum of nuclear particle will be
  A)
   \[\frac{6.62\,\times \,{{10}^{-19}}}{4\pi }\]      
  done clear
  B)
   \[6.62\,\times \,{{10}^{-29}}\]
  done clear
  C)
   \[6.62\,\times \,{{10}^{-39}}\]      
  done clear
  D)
   \[6.62\,\times \,{{10}^{-49}}\]
  done clear
  View Answer play_arrow

• question_answer82) If de-Broglie wavelength and accelerated potential difference are 6000\[\overset{o}{\mathop{\text{A}}}\,\]and 9000 V respectively, then value of \[\frac{h}{e}\] will be
  A)
   \[1.9\times {{10}^{-10}}\]       
  done clear
  B)
   \[18\,\times \,{{10}^{-19}}\]
  done clear
  C)
   \[8.2\,\times \,{{10}^{-20}}\]
  done clear
  D)
   \[18\,\times \,{{10}^{-20}}\]
  done clear
  View Answer play_arrow

• question_answer83) Photoelectric effect will occur if
  A)
   \[v<{{v}_{0}}\]           
  done clear
  B)
   \[v\ge {{v}_{0}}\]
  done clear
  C)
   \[v>2{{v}_{0}}\]          
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer84) Increasing the principle quantum number, the energy gap between consequence energy state
  A)
   increases        
  done clear
  B)
   decreases
  done clear
  C)
   remains unchange
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer85) First law of Kirchhoff is accordance on
  A)
   conservation of charge
  done clear
  B)
   conservation of energy
  done clear
  C)
   conservation of momentum
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer86) Three capacitors of equal capacitances 3 \[\mu \]F each are connected in a circuit. Then their maximum and minimum capacities will be
  A)
   \[9\mu F,1\mu F\]          
  done clear
  B)
   \[8\mu F,2\mu F\]
  done clear
  C)
   \[9\mu F,0\mu F\]          
  done clear
  D)
   \[3\mu F,2\mu F\]
  done clear
  View Answer play_arrow

• question_answer87) For non-conductors, the forbidden energy gap is
  A)
   5 eV            
  done clear
  B)
   1.1 eV
  done clear
  C)
   20 eV           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer88) Change of AC to DC is called
  A)
   rectification      
  done clear
  B)
   polarization
  done clear
  C)
   amplification     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer89) Write the resolving powers of\[\alpha ,\beta \]and\[\gamma \]to ascending order.
  A)
   \[\alpha ,\beta ,\gamma \]              
  done clear
  B)
   \[\gamma ,\beta ,\alpha \]
  done clear
  C)
   \[\beta ,\alpha ,\gamma \]             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer90) Diffraction of electron beam is proved by
  A)
   Davisson-Germer
  done clear
  B)
   Berg
  done clear
  C)
   Newton          
  done clear
  D)
   Einsteen
  done clear
  View Answer play_arrow

• question_answer91) On the basis of which photoelectric effect is  explained?
  A)
   Relativity theory
  done clear
  B)
   The electromagnetic waves of light
  done clear
  C)
   Energy spectrum of atoms
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer92) Which of the following atoms or ions has minimum radius?
  A)
   H
  done clear
  B)
   \[{{H}^{+}}\]
  done clear
  C)
   \[L{{i}^{++}}\]
  done clear
  D)
   Deuteron
  done clear
  View Answer play_arrow

• question_answer93) The value of resistance R will be
  A)
   10\[\Omega \]
  done clear
  B)
   15\[\Omega \]
  done clear
  C)
   20\[\Omega \]
  done clear
  D)
   25\[\Omega \]
  done clear
  View Answer play_arrow

• question_answer94) What will be .the stored energy in capacitor of R-C
  A)
   \[\frac{CV}{2}\]
  done clear
  B)
   \[\frac{C{{V}^{2}}}{2}\]
  done clear
  C)
   \[\frac{{{q}^{2}}}{C}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer95) The valancy of carbon atom is
  A)
   1                
  done clear
  B)
   2
  done clear
  C)
   3                
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer96) What is valancy of impurity added for donar atoms?
  A)
   Pentavalent       
  done clear
  B)
   Trivalent        
  done clear
  C)
   Tertravalent      
  done clear
  D)
   None of these     
  done clear
  View Answer play_arrow

• question_answer97) In LC-R circuit,\[R=300\Omega ,\text{ }L=0.9\text{ }H,\text{ }C=\]\[2\mu F\]and \[\omega =1000\]rad/s, the impedance of circuit is
  A)
   1300\[\Omega \]             
  done clear
  B)
   900\[\Omega \]
  done clear
  C)
   500\[\Omega \]         
  done clear
  D)
   400\[\Omega \]
  done clear
  View Answer play_arrow

• question_answer98) What should be the capacity of capacitor of R-C circuit, in which the value of resistance is 10\[\Omega \] to become the value of time constant 10? 
  A)
   \[10\mu F\]
  done clear
  B)
   \[100\mu F\]
  done clear
  C)
   \[1000\mu F\]
  done clear
  D)
   \[10,000\mu F\]
  done clear
  View Answer play_arrow

• question_answer99) The energy needed to remove the one electron from neutral helium atom is 24.6 eV. Then the energy needed to remove both the electrons from neutral helium atom is             
  A)
   79.0 eV          
  done clear
  B)
   51.8 eV
  done clear
  C)
   49.2 eV          
  done clear
  D)
   38.2 eV
  done clear
  View Answer play_arrow

• question_answer100) Two same light cathode gets the light of frequencies\[{{f}_{1}}\]and\[{{f}_{2}}\]. If the velocities of emitted photo electrons are \[{{v}_{1}}\] and \[{{v}_{2}}\] then
  A)
   \[{{v}^{2}}_{1}-v\frac{2}{2}=\frac{2h}{m}({{f}_{1}}-{{f}_{2}})\]
  done clear
  B)
   \[{{v}_{1}}+{{v}_{2}}={{\left[ \frac{2h}{m}({{f}_{1}}+{{f}_{2}}) \right]}^{2}}\]
  done clear
  C)
   \[{{v}^{2}}_{1}+{{v}^{2}}_{2}=\frac{2h}{m}({{f}_{1}}+{{f}_{2}})\]
  done clear
  D)
   \[{{v}_{1}}-{{v}_{2}}={{\left[ \frac{2h}{m}({{f}_{1}}-{{f}_{2}} \right]}^{1/2}}\]
  done clear
  View Answer play_arrow

• question_answer101) For the salt of weak acid and weak base, the value of\[{{K}_{b}}\]will be
  A)
   \[{{K}_{b}}=\frac{{{K}_{w}}}{{{K}_{a}}}\]
  done clear
  B)
   \[{{K}_{h}}=\frac{{{K}_{w}}}{{{K}_{b}}}\]
  done clear
  C)
   \[{{K}_{h}}=\frac{{{K}_{w}}}{{{K}_{a}}.{{K}_{b}}}\]
  done clear
  D)
   Hydrolysis does not take place
  done clear
  View Answer play_arrow

• question_answer102) Formation of cyanohydrin from\[C{{H}_{3}}COC{{H}_{3}}\]is called
  A)
   electrophilic substitution
  done clear
  B)
   nucleophilic substitution
  done clear
  C)
   nucleophilic addition
  done clear
  D)
   electrophilic substitution
  done clear
  View Answer play_arrow

• question_answer103) Bond energy of\[C-H\]bond in ethane, ethane and ethyne is
  A)
   equal in three    
  done clear
  B)
   more in ethane
  done clear
  C)
   more in ethene   
  done clear
  D)
   more in ethyne
  done clear
  View Answer play_arrow

• question_answer104) \[C{{H}_{3}}-CH=C{{H}_{2}}+HBr\xrightarrow[{}]{{}}A;\] compound A is
  A)
   \[\underset{\begin{smallmatrix}  | \\  Br \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,-CH=C{{H}_{2}}\]
  done clear
  B)
   \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}Br\]
  done clear
  C)
   \[C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  Br \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{3}}\]
  done clear
  D)
   \[\underset{\begin{smallmatrix}  | \\  Br \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,-C{{H}_{2}}-\underset{\begin{smallmatrix}  | \\  Br \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\]
  done clear
  View Answer play_arrow

• question_answer105) Which of the following is represented by prefix word 'alkali' used for alkali metals?
  A)
   Ash of plants     
  done clear
  B)
   Lusture of silver
  done clear
  C)
   Metallic nature   
  done clear
  D)
   Reactive metal
  done clear
  View Answer play_arrow

• question_answer106) The product is obtained on reaction of urea with ammonia
  A)
   barbituric acid   
  done clear
  B)
   semicarbazide
  done clear
  C)
   methylol urea    
  done clear
  D)
   acetamide
  done clear
  View Answer play_arrow

• question_answer107) Structure of ammonia is
  A)
   pyramidal
  done clear
  B)
   tetrahederal
  done clear
  C)
   trigonal
  done clear
  D)
   trigonal bipyramidal
  done clear
  View Answer play_arrow

• question_answer108) The decreasing order of reactivity of alkyl halide is
  A)
   \[RI>RCl>RBr\]
  done clear
  B)
   \[RCl>RI>RBr\]
  done clear
  C)
   \[RCl>RBr>RI\]
  done clear
  D)
   \[RI>RBr>RCl\]
  done clear
  View Answer play_arrow

• question_answer109) If the pH value of\[HCl\]solution is 4 then its molar concentration will
  A)
   4 M             
  done clear
  B)
   0.0001 M
  done clear
  C)
   0.4 M            
  done clear
  D)
   10 M
  done clear
  View Answer play_arrow

• question_answer110) The product is formed on the condensation of phenol with phthalic anhydride
  A)
   methyl orange    
  done clear
  B)
   phenol red
  done clear
  C)
   salicylic acid     
  done clear
  D)
   phenolphthalein
  done clear
  View Answer play_arrow

• question_answer111) 23 g sodium metal reacts from methyl alcohol to give
  A)
   1 mol\[{{H}_{2}}\]        
  done clear
  B)
   2 mol\[{{H}_{2}}\]
  done clear
  C)
   \[\frac{1}{2}\] mol\[{{H}_{2}}\]        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer112) Nitration of benzene is
  A)
   electrophilic addition
  done clear
  B)
   electrophilic substitution
  done clear
  C)
   nucleophilic addition
  done clear
  D)
   nucleophilic substitution
  done clear
  View Answer play_arrow

• question_answer113) Which of the following has maximum magnetic moment?
  A)
   \[3{{d}^{5}}\]            
  done clear
  B)
   \[3{{d}^{2}}\]
  done clear
  C)
   \[3{{d}^{9}}\]            
  done clear
  D)
   \[3{{d}^{7}}\]
  done clear
  View Answer play_arrow

• question_answer114) The correct order of atomic and ionic size of iodine is
  A)
   \[I>{{I}^{-}}>{{I}^{+}}\]
  done clear
  B)
   \[{{I}^{-}}>I>{{I}^{+}}\]
  done clear
  C)
   \[I>{{I}^{+}}>{{I}^{-}}\]
  done clear
  D)
   \[{{I}^{+}}>I>{{I}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer115) Number of\[\sigma \]and\[\pi \]bonds in l-butene-3-yne
  A)
   \[5\sigma ,5\pi \]           
  done clear
  B)
   \[7\sigma ,3\pi \]
  done clear
  C)
   \[8\sigma ,6\pi \]           
  done clear
  D)
   \[6\sigma ,4\pi \]
  done clear
  View Answer play_arrow

• question_answer116) Which of the following salt does not give brown gas on heating?
  A)
   \[LiN{{O}_{3}}\]
  done clear
  B)
   \[KN{{O}_{3}}\]
  done clear
  C)
   \[Pb{{(N{{O}_{3}})}_{2}}\]
  done clear
  D)
   \[AgN{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer117) 2-chloropropane reacts with sodium in presence of ether to form
  A)
   n-hexane
  done clear
  B)
   n-hexene
  done clear
  C)
   \[C{{H}_{3}}-CH=C{{H}_{2}}\]
  done clear
  D)
   \[C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,=C{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer118) \[{{C}_{6}}{{H}_{6}}+C{{H}_{3}}-\underset{\begin{smallmatrix}  || \\  O \end{smallmatrix}}{\mathop{C}}\,-Cl\xrightarrow[{}]{{}}A;\]Product A is
  A)
   benzophenone   
  done clear
  B)
   benzoyl chloride
  done clear
  C)
   acetophenone    
  done clear
  D)
   toluene
  done clear
  View Answer play_arrow

• question_answer119) Which group is/are present in picric acid?
  A)
   \[-OH\]
  done clear
  B)
   \[N{{O}_{2}}\]
  done clear
  C)
   \[-OH\] and\[-N{{O}_{2}}\]
  done clear
  D)
   \[-COOH\]and\[-N{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer120) Number of\[C-C\]and\[C-H\]bonds in 4-methyl-2-pentyne will be
  A)
   4, 10            
  done clear
  B)
   5, 10
  done clear
  C)
   4, 9             
  done clear
  D)
   5, 9
  done clear
  View Answer play_arrow

• question_answer121)         The oxidation state of iron is zero in which of the following compound?
  A)
   \[FeS{{O}_{4}}\]
  done clear
  B)
   \[Fe{{(CO)}_{4}}\]
  done clear
  C)
   \[{{[Fe{{(CN)}_{6}}]}^{4-}}\]
  done clear
  D)
   \[FeC{{l}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer122) Which of the following overlapping does not give\[\pi -\]bond in a molecule AB? (z-axis is the axis of molecule)
  A)
   \[{{p}_{x}}-{{p}_{x}}\]
  done clear
  B)
   \[{{p}_{y}}-{{p}_{xy}}\]
  done clear
  C)
   \[{{p}_{y}}-s\]
  done clear
  D)
   \[{{p}_{y}}-{{p}_{y}}\]
  done clear
  View Answer play_arrow

• question_answer123) Which of the following equilibrium does not affect from change in pressure?
  A)
   \[2N{{O}_{2}}(g){{N}_{2}}{{O}_{4}}(g)\]
  done clear
  B)
   \[2HI(g){{H}_{2}}(g)+{{I}_{2}}(g)\]
  done clear
  C)
   \[2{{O}_{3}}(g)3{{O}_{2}}(g)\]
  done clear
  D)
   \[PC{{l}_{5}}(g)PC{{l}_{3}}(g)+C{{l}_{2}}(g)\]
  done clear
  View Answer play_arrow

• question_answer124) The concentration of a acidic solution is 0.1 M and degree of dissociation is 1%. The dissociation constant of acid will be
  A)
   \[1.01\times {{10}^{-5}}\]
  done clear
  B)
   \[1.01\times {{10}^{-3}}\]
  done clear
  C)
   \[1.01\times {{10}^{3}}\]
  done clear
  D)
   \[1.01\times {{10}^{5}}\]
  done clear
  View Answer play_arrow

• question_answer125) Number of elements in s-block are
  A)
   more from elements of p-block
  done clear
  B)
   less from elements of d-block
  done clear
  C)
   more from elements of d-block
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer126) On doubling the concentration of A and B in reaction\[A+BAB,\]the equilibrium constant will be
  A)
   unchanged      
  done clear
  B)
   halved
  done clear
  C)
   doubled         
  done clear
  D)
   four times
  done clear
  View Answer play_arrow

• question_answer127) The compound is not used in redox titration
  A)
   \[KMn{{O}_{4}}\]
  done clear
  B)
   \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]
  done clear
  C)
   \[{{(COOH)}_{2}}\]        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer128) Which of the following does not used as primary standard in redox titration?
  A)
  \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]          
  done clear
  B)
   \[KMn{{O}_{4}}\]
  done clear
  C)
   \[{{(COOH)}_{2}}\]         
  done clear
  D)
   Mohr's salt
  done clear
  View Answer play_arrow

• question_answer129) The solubility product of a metal sulphide MS is\[7\times {{10}^{-24}}mo{{l}^{2}}{{L}^{-2}}\]. The solubility of MS will be
  A)
   \[7\times {{10}^{-24}}mo{{l}^{2}}{{L}^{2}}\]
  done clear
  B)
   \[2.65\times {{10}^{-12}}mol\,{{L}^{-1}}\]
  done clear
  C)
   \[1.32\times {{10}^{-12}}mol\,{{L}^{-1}}\]
  done clear
  D)
   \[14\times {{10}^{-24}}mo{{l}^{3}}{{L}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer130) Which ion has the maximum hydration energy?
  A)
   \[M{{g}^{2+}}\]
  done clear
  B)
   \[B{{a}^{2+}}\]
  done clear
  C)
   \[C{{a}^{2+}}\]
  done clear
  D)
   \[S{{r}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer131) What will form on reduction of\[{{P}_{2}}{{O}_{5}}\]from acetic acid?
  A)
   Acetic anhydride
  done clear
  B)
   Acetyl chloride
  done clear
  C)
   Acetic ester      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer132) Possible number of isomers of alkane\[{{C}_{5}}{{H}_{12}}\]will be
  A)
   4               
  done clear
  B)
   3
  done clear
  C)
   5               
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer133) Molecular formula of chrornyl chloride is
  A)
   \[Cr{{O}_{2}}C{{l}_{2}}\]
  done clear
  B)
   \[Cr{{O}_{2}}Cl\]
  done clear
  C)
   \[CrOC{{l}_{2}}\]
  done clear
  D)
   \[{{(CrOCl)}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer134) Phenol reacts with dil.\[HN{{O}_{3}}\]to give
  A)
   o-nitrophenol
  done clear
  B)
   p-nitrophenol
  done clear
  C)
   o- and p-nitrophenol
  done clear
  D)
   picric acid
  done clear
  View Answer play_arrow

• question_answer135) Which of the following compound is obtained from ozonolysis of benzene?
  A)
   Benzene triozonide
  done clear
  B)
   Glyoxal
  done clear
  C)
   Ethane dial      
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer136) Oxidation state of iron and sulphur in copper pyrite are respectively
  A)
   + 2 and -2       
  done clear
  B)
   + 2 and - 4
  done clear
  C)
   + 3 and -4       
  done clear
  D)
   + 3 and - 6
  done clear
  View Answer play_arrow

• question_answer137) What will obtain on distillation of acetic acid with\[PC{{l}_{3}}\]?
  A)
   Acetic anhydride
  done clear
  B)
   Chloroacetic acid
  done clear
  C)
   Acetyl chloride   
  done clear
  D)
   Ethyl acetate
  done clear
  View Answer play_arrow

• question_answer138) Strongest acid is
  A)
   \[C{{l}_{2}}CH.CHOOH\]
  done clear
  B)
   \[C{{H}_{3}}COOH\]
  done clear
  C)
   \[CC{{l}_{3}}COOH\]
  done clear
  D)
   \[ClC{{H}_{2}}.COOH\]
  done clear
  View Answer play_arrow

• question_answer139) The gas is released in fermentation reaction
  A)
   \[{{O}_{2}}\]              
  done clear
  B)
   \[C{{O}_{2}}\]
  done clear
  C)
   \[{{N}_{2}}\]              
  done clear
  D)
   \[S\]
  done clear
  View Answer play_arrow

• question_answer140) Which of the following molecule of compound will be linear structure?
  A)
  \[C{{O}_{2}}\]            
  done clear
  B)
  \[S{{O}_{2}}\]
  done clear
  C)
   \[{{H}_{2}}O\]            
  done clear
  D)
  \[C{{H}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer141) Which of the following ion is colourless?
  A)
   \[C{{u}^{+}}\]
  done clear
  B)
   \[C{{u}^{2+}}\]
  done clear
  C)
   \[C{{u}^{3+}}\]
  done clear
  D)
   \[F{{e}^{3+}}\]
  done clear
  View Answer play_arrow

• question_answer142) The colour of iodine solution disappears on reaction with which of the following compound?
  A)
   \[{{C}_{2}}{{H}_{4}}\]
  done clear
  B)
   \[{{C}_{2}}{{H}_{6}}\]
  done clear
  C)
   \[CC{{l}_{4}}\]
  done clear
  D)
   \[CHC{{l}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer143) \[PC{{l}_{5}}\]is used in the
  A)
   synthesis of \[C{{H}_{3}}COCl\]
  done clear
  B)
   synthesis of \[{{C}_{6}}{{H}_{5}}OH\]
  done clear
  C)
   synthesis of \[{{C}_{2}}{{H}_{5}}-O-{{C}_{2}}{{H}_{5}}\]
  done clear
  D)
   synthesis of \[C{{H}_{3}}COOH\]
  done clear
  View Answer play_arrow

• question_answer144) It is cleared by the a-particle scattering experiment of Rutherford. That
  A)
  \[\alpha -\]particle is heavier than electron
  done clear
  B)
  \[\alpha -\]particle is positively charged
  done clear
  C)
   mostly part of atom is hollow
  done clear
  D)
  \[\alpha -\]particle moves with high velocity
  done clear
  View Answer play_arrow

• question_answer145) Which of the following compound has maximum covalent character?
  A)
   \[NaF\]
  done clear
  B)
   \[CaC{{l}_{2}}\]
  done clear
  C)
   \[BeB{{r}_{2}}\]
  done clear
  D)
   \[KI\]
  done clear
  View Answer play_arrow

• question_answer146) The suitable indicator in the titration of strong acid and weak base is
  A)
   methyl orange   
  done clear
  B)
   bromothymol blue
  done clear
  C)
   phenol red      
  done clear
  D)
   phenolphthalein
  done clear
  View Answer play_arrow

• question_answer147) The product is formed on the reaction of ethylene bromide with Zn
  A)
   alkane          
  done clear
  B)
   alkene
  done clear
  C)
  alkyne          
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer148) Which of the following is formed on the hydrolysis of product, formed by the reaction of\[C{{H}_{3}}CHO\]and\[C{{H}_{3}}MgBr\]?
  A)
   Primary alcohol  
  done clear
  B)
   Secondary alcohol
  done clear
  C)
   Tertiary alcohol  
  done clear
  D)
   Ketone
  done clear
  View Answer play_arrow

• question_answer149) Bond angle is\[s{{p}^{2}}\]hybridization is
  A)
  \[180{}^\circ \]             
  done clear
  B)
   \[120{}^\circ \]
  done clear
  C)
   \[90{}^\circ \]             
  done clear
  D)
   \[109{}^\circ 45'\]
  done clear
  View Answer play_arrow

• question_answer150) Scientist who discovered the positron?
  A)
   Pauling          
  done clear
  B)
   Anderson
  done clear
  C)
   Yukava          
  done clear
  D)
   Sanger
  done clear
  View Answer play_arrow

• question_answer151) Number of electrons are required for the complete reduction of one molecule of \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]
  A)
   3               
  done clear
  B)
   4
  done clear
  C)
   5               
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer152) Which of the following pair has same oxidation number of sulphur and chromium?
  A)
   \[SO_{3}^{2-},CrO_{4}^{2-}\]
  done clear
  B)
   \[S{{O}_{3}},CrO_{4}^{2-}\]
  done clear
  C)
   \[S{{O}_{2}},CrO_{4}^{2-}\]
  done clear
  D)
   \[S{{O}_{2}},C{{r}_{2}}O_{7}^{2-}\]
  done clear
  View Answer play_arrow

• question_answer153) Which of the following gives haloform reaction?
  A)
   Acetaldehyde    
  done clear
  B)
   Propionaldehyde
  done clear
  C)
   iso-butyraldehyde
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer154) The percentage of nitrogen will equal in oximes of which of the following compound pairs?
  A)
   Acetone and acetaldehyde
  done clear
  B)
   Acetone and propionaldehyde
  done clear
  C)
   Aqetone and acraldehyde
  done clear
  D)
   Acetaldehyde and acraldehyde
  done clear
  View Answer play_arrow

• question_answer155) The highest atomic number radioactive element in p-block elements is
  A)
   Pb              
  done clear
  B)
   Te
  done clear
  C)
   Rn              
  done clear
  D)
   Po
  done clear
  View Answer play_arrow

• question_answer156) Which of the following reagent evolves nitrogen on reaction with ethyl amine?
  A)
   Nitrosyl chloride 
  done clear
  B)
   Acetyl chloride
  done clear
  C)
   Carbon disulphide
  done clear
  D)
   Benzoyl chloride
  done clear
  View Answer play_arrow

• question_answer157) The density of ice is less than water because
  A)
   ice floats on water
  done clear
  B)
   the structure of ice is three dimensional with porous
  done clear
  C)
   H-bond does not present in ice
  done clear
  D)
   water is a polar solvent
  done clear
  View Answer play_arrow

• question_answer158) The value of energy will increase in sub energy level because
  A)
   on increasing the value of principal quantum number
  done clear
  B)
   on increasing the value of azimuthal quantum number
  done clear
  C)
   on increasing the value of both principal quantum number and azimuthal quantum number
  done clear
  D)
   on increasing the value of spin quantum Number
  done clear
  View Answer play_arrow

• question_answer159) The density of Na is higher than K because
  A)
   ionization potential of Na is greater than K
  done clear
  B)
   size of Na is smaller than K
  done clear
  C)
   atomic weight of K is greater than Na
  done clear
  D)
   only eight electrons are present in third shell of K
  done clear
  View Answer play_arrow

• question_answer160) Same magnetic moment ions are
  A)
   \[C{{u}^{+}},F{{e}^{3+}}\]
  done clear
  B)
   \[M{{n}^{2+}},F{{e}^{3+}}\]
  done clear
  C)
   \[C{{u}^{2+}},F{{e}^{2+}}\]
  done clear
  D)
   \[M{{n}^{2+}},T{{i}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer161) The set of oxidation of nitrogen in ammonium nitrate is
  A)
   \[-3,+3\]             
  done clear
  B)
   \[-1,+1\]
  done clear
  C)
   \[+1,-1\]             
  done clear
  D)
   \[-3,+5\]
  done clear
  View Answer play_arrow

• question_answer162) At\[300{}^\circ C,\]the vapour density of\[PC{{l}_{5}}\]is 60. At this temperature, its dissociation percentage will be
  A)
   73                
  done clear
  B)
   77
  done clear
  C)
   83                
  done clear
  D)
   87
  done clear
  View Answer play_arrow

• question_answer163) The degree of dissociation of A is\[\alpha \]in equilibrium reaction\[A\xrightarrow[{}]{{}}2B+C\]. If one mole of A is taken initially then total .number of moles will in equilibrium.
  A)
   \[1-\alpha \]             
  done clear
  B)
   \[1+\alpha \]
  done clear
  C)
   \[1-2\alpha \]
  done clear
  D)
   \[1+2\alpha \]
  done clear
  View Answer play_arrow

• question_answer164) Which of the following compounds will form mesitylene on distillation with cone.\[{{H}_{2}}S{{O}_{4}}\]?
  A)
   Acetaldehyde    
  done clear
  B)
   Acetone
  done clear
  C)
   Acetophenone   
  done clear
  D)
   Acetyl chlorine
  done clear
  View Answer play_arrow

• question_answer165) Generally, alkenes and alkynes show the following type of reaction
  A)
   nucleophilic addition
  done clear
  B)
   electrophilic addition
  done clear
  C)
   free radical substitution
  done clear
  D)
   electrophilic substitution
  done clear
  View Answer play_arrow

• question_answer166) Which of the following is not a polymer?
  A)
   Teflon           
  done clear
  B)
   Nylon
  done clear
  C)
   Orion           
  done clear
  D)
   Phorone
  done clear
  View Answer play_arrow

• question_answer167) The formula of wavelength of spectral lines for hydrogen atom is
  A)
   \[\frac{1}{\lambda }=R\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\]
  done clear
  B)
   \[\frac{1}{\lambda }=R\left( \frac{1}{n_{2}^{2}}-\frac{1}{n_{1}^{2}} \right)\]
  done clear
  C)
   \[\frac{1}{\lambda }=R{{\left( \frac{1}{{{n}_{1}}}-\frac{1}{{{n}_{2}}} \right)}^{2}}\]
  done clear
  D)
   \[\frac{1}{\lambda }=R{{\left( \frac{1}{{{n}_{2}}}-\frac{1}{{{n}_{1}}} \right)}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer168) Power alcohol is
  A)
   absolute alcohol\[+C{{H}_{3}}OH\]
  done clear
  B)
   absolute alcohol\[+{{C}_{6}}{{H}_{5}}OH\]
  done clear
  C)
   absolute alcohol + petrol 4- benzene
  done clear
  D)
   absolute alcohol \[+C{{H}_{3}}COOH\]
  done clear
  View Answer play_arrow

• question_answer169) \[C{{H}_{3}}C{{H}_{2}}OH\]and\[C{{H}_{3}}-O-C{{H}_{3}}\]are
  A)
   positive isomers
  done clear
  B)
   functional isomers
  done clear
  C)
   chain isomers
  done clear
  D)
   geometrical isomers
  done clear
  View Answer play_arrow

• question_answer170) Alkaline\[KMn{{O}_{4}}\]solution is called
  A)
   Tollen's reagent  
  done clear
  B)
   Baeyer's reagent
  done clear
  C)
   Benedict's solution
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer171) The bond angle and bond length in benzene are respectively
  A)
  \[120{}^\circ \]and 1.34\[\overset{o}{\mathop{\text{A}}}\,\] 
  done clear
  B)
  \[120{}^\circ \]and 1.39\[\overset{o}{\mathop{\text{A}}}\,\]
  done clear
  C)
   \[180{}^\circ \]and 1.33\[\overset{o}{\mathop{\text{A}}}\,\]  
  done clear
  D)
  \[120{}^\circ \]and 1.54\[\overset{o}{\mathop{\text{A}}}\,\]
  done clear
  View Answer play_arrow

• question_answer172) \[{{(C{{H}_{3}}CO)}_{2}}O+HCl\xrightarrow[{}]{{}}X+C{{H}_{3}}COH;\] compound X is
  A)
  \[C{{H}_{3}}Cl\]         
  done clear
  B)
   \[C{{H}_{3}}COCl\]
  done clear
  C)
   \[C{{H}_{3}}COC{{H}_{3}}\]      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer173) The main product of the reaction of \[C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\]with nitrous acid is
  A)
  \[C{{H}_{3}}CN\]          
  done clear
  B)
   \[C{{H}_{3}}ONO\]
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}OH\]     
  done clear
  D)
   \[C{{H}_{3}}-N=O\]
  done clear
  View Answer play_arrow

• question_answer174) \[RX+2Na+BX\xrightarrow[{}]{{}}R-R+2NaX\] This reaction is known as
  A)
   Wurtz reaction
  done clear
  B)
   Williamson's synthesis
  done clear
  C)
   Kolbe's electrolysis
  done clear
  D)
   Sabatier-Sendern's reaction
  done clear
  View Answer play_arrow

• question_answer175) In froth floatation method of ore concentration, ore particles rise to the surface because
  A)
   they are light
  done clear
  B)
   these are insoluble
  done clear
  C)
   their surface do not wet with water easily
  done clear
  D)
   these contain electric charge
  done clear
  View Answer play_arrow

• question_answer176) The number of k electrons present in aromatic ring are
  A)
   \[(4+2)n\]          
  done clear
  B)
   \[(4+2n)\]
  done clear
  C)
   \[(4n+2)\]           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer177) \[C{{H}_{3}}C{{H}_{2}}I+NaOR\to C{{H}_{3}}C{{H}_{2}}R+NaI\] This reaction is
  A)
   Wurtz reaction
  done clear
  B)
   Williamson's synthesis
  done clear
  C)
   Wittig reaction
  done clear
  D)
   Curtius reaction
  done clear
  View Answer play_arrow

• question_answer178) Absolute alcohol can obtained from rectified spirit by the process of
  A)
   Steam distillation
  done clear
  B)
   Fractional distillation
  done clear
  C)
   Azeotropic distillation
  done clear
  D)
   Hydrolysis
  done clear
  View Answer play_arrow

• question_answer179) The product of the reaction of benzene with\[CO+HCl\]in the presence of anhydrous\[AlC{{l}_{3}}\]is
  A)
   benzoyl chloride 
  done clear
  B)
   benzal chloride
  done clear
  C)
   chlorobenzene   
  done clear
  D)
   benzaldehyde
  done clear
  View Answer play_arrow

• question_answer180) The suitable indicator for the titration of \[N{{H}_{4}}OH\]and\[HCl\]is
  A)
   phenolphthalein 
  done clear
  B)
   methyl orange
  done clear
  C)
   bromothymol blue
  done clear
  D)
   litmus paper
  done clear
  View Answer play_arrow

• question_answer181) Which of the following is not Lewis acid?
  A)
   \[FeC{{l}_{3}}\]            
  done clear
  B)
   \[BC{{l}_{3}}\]
  done clear
  C)
   \[AlC{{l}_{3}}\]            
  done clear
  D)
   \[N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer182) Which of the following metal can displace Cu from copper sulphate solution?
  A)
   Fe              
  done clear
  B)
   Ag
  done clear
  C)
   Au              
  done clear
  D)
   Pt
  done clear
  View Answer play_arrow

• question_answer183) Which enzyme is used for the conversion of starch into maltose?
  A)
   Zymase          
  done clear
  B)
   Invertase
  done clear
  C)
   Maltase          
  done clear
  D)
   Diastase
  done clear
  View Answer play_arrow

• question_answer184) Which of the following is used in the extraction of copper?
  A)
   \[C{{u}_{2}}S\]
  done clear
  B)
   Pyrite
  done clear
  C)
   Silver argentocyanide
  done clear
  D)
   \[CuFe{{S}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer185) The product of the reaction of ethanol with ethyl magnesium iodide is
  A)
   \[C{{H}_{3}}-C{{H}_{3}}\]
  done clear
  B)
   \[C{{H}_{3}}C{{H}_{2}}-C{{H}_{2}}C{{H}_{3}}\]
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}-O-C{{H}_{2}}C{{H}_{3}}\]
  done clear
  D)
   \[C{{H}_{3}}COC{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer186) Which of the following element has the maximum tendency of loose the electron?
  A)
   Be              
  done clear
  B)
   B
  done clear
  C)
   Mg             
  done clear
  D)
   Rb
  done clear
  View Answer play_arrow

• question_answer187) Which of the following is formed on the hydrolysis of the product, formed by the reaction of acetone with methyl magnesium iodide?
  A)
   Primary alcohol  
  done clear
  B)
   Secondary alcohol
  done clear
  C)
   Tertiary alcohol  
  done clear
  D)
   Carboxylic acid
  done clear
  View Answer play_arrow

• question_answer188) Which complex forms on adding sodium cyanide solution in\[A{{g}_{2}}S,\]in the cyanide method of silver extraction?
  A)
   \[N{{a}_{2}}[Ag{{(CN)}_{2}}]\]
  done clear
  B)
   \[Na[Ag{{(CN)}_{2}}]\]
  done clear
  C)
   \[NaAgCN\]
  done clear
  D)
   \[Na[Ag{{(CN)}_{4}}]\]
  done clear
  View Answer play_arrow

• question_answer189) Benzene was discovered by
  A)
   Faraday         
  done clear
  B)
   Prisetly
  done clear
  C)
   Kekule          
  done clear
  D)
   Hofmann
  done clear
  View Answer play_arrow

• question_answer190) Which substance is used in the preparation of absolute alcohol from rectified spirit?
  A)
   \[Ca{{(OH)}_{2}}\]         
  done clear
  B)
   \[CaO\]
  done clear
  C)
   Anhydrous \[CaC{{l}_{2}}\]
  done clear
  D)
   Wire of Na
  done clear
  View Answer play_arrow

• question_answer191) Benzenediazonium chloride reacts with phenol to give
  A)
   \[{{C}_{6}}{{H}_{5}}-NH-{{C}_{6}}{{H}_{5}}\]
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}-NH=N-{{C}_{6}}{{H}_{5}}\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix}  \downarrow  \\  O \end{smallmatrix}}{\mathop{N}}\,=N-{{C}_{6}}{{H}_{5}}\]
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer192) The first ionization potentials of nitrogen and oxygen are respectively
  A)
   14.6 eV, 13.6 eV  
  done clear
  B)
   13.6 eV, 14.6 eV
  done clear
  C)
   13.6 eV, 13.6 eV  
  done clear
  D)
   14.6 eV, 14.6 eV
  done clear
  View Answer play_arrow

• question_answer193) Which of the following compound forms 3-hydroxy butanal on reaction with dil. alkali?
  A)
   \[C{{H}_{3}}CHO\]                      
  done clear
  B)
   \[HCHO\]
  done clear
  C)
   \[C{{H}_{3}}CHO+C{{H}_{3}}COC{{H}_{3}}\]
  done clear
  D)
   \[C{{H}_{3}}COC{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer194) The product of the reaction of ethylidene chloride with zinc dust is
  A)
   \[C{{H}_{2}}=C{{H}_{2}}\]
  done clear
  B)
   \[CH\equiv CH\]
  done clear
  C)
   \[C{{H}_{3}}-CH=CH-C{{H}_{3}}\]
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}-CH=C{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer195) Which of the following pair shows the paramagnetic character?
  A)
  \[FeS{{O}_{4}}\]and\[NiC{{l}_{2}}\]
  done clear
  B)
  \[ZnC{{l}_{2}}\]and\[FeS{{O}_{4}}\]
  done clear
  C)
  \[MgC{{l}_{2}}\]and\[NiC{{l}_{4}}\]
  done clear
  D)
  \[KCl\]and\[ZnC{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer196) The quantum number which shows the orientation of electron cloud in the presence of external magnetic field?
  A)
   Principal quantum number
  done clear
  B)
   Azimuthal quantum number
  done clear
  C)
   Magnetic quantum number
  done clear
  D)
   Spin quantum number
  done clear
  View Answer play_arrow

• question_answer197) Oxidation number of\[Mn\]in\[MnO_{4}^{-}\]is
  A)
   +5                 
  done clear
  B)
   + 6
  done clear
  C)
   +7                 
  done clear
  D)
   + 4
  done clear
  View Answer play_arrow

• question_answer198) Which of the following salt gives anionic hydrolysis?
  A)
   \[NaCl\]            
  done clear
  B)
   \[NaCN\]
  done clear
  C)
   \[N{{H}_{4}}Cl\]         
  done clear
  D)
   \[CuS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer199) Which of the following compounds will form chloropicrin on reaction with cone.\[HN{{O}_{3}}\]?
  A)
   \[CC{{l}_{4}}\]            
  done clear
  B)
   \[C{{H}_{2}}C{{l}_{2}}\]
  done clear
  C)
   \[CHC{{l}_{3}}\]          
  done clear
  D)
   \[C{{H}_{3}}Cl\]
  done clear
  View Answer play_arrow

• question_answer200) \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}\xrightarrow[{}]{Zn+NaOH}\] Product The product of reaction is
  A)
   \[{{C}_{6}}{{H}_{5}}-NH-NH-{{C}_{6}}{{H}_{5}}\]
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}-N=N-{{C}_{6}}{{H}_{5}}\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}-\underset{\downarrow }{\mathop{N}}\,={{C}_{6}}{{H}_{5}}\]
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer201) If the base of an equilateral triangle is\[x+y=2\]and vertex,\[(2,-1)\]is, then length of each side is equal to
  A)
   \[\sqrt{\frac{2}{3}}\]
  done clear
  B)
   \[\sqrt{\frac{3}{2}}\]
  done clear
  C)
   \[\frac{3}{\sqrt{2}}\]
  done clear
  D)
   \[\frac{2}{3}\]
  done clear
  View Answer play_arrow

• question_answer202) Minimum number of zeros in an upper triangular matrix is
  A)
   \[\frac{n(n+1)}{2}\]
  done clear
  B)
   \[\frac{n(n-1)}{2}\]
  done clear
  C)
   \[\frac{2n(n-1)}{2}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer203) \[\left| \begin{matrix}    {{1}^{2}} & {{2}^{2}} & {{3}^{2}}  \\    {{2}^{2}} & {{3}^{2}} & {{4}^{2}}  \\    {{3}^{2}} & {{4}^{2}} & {{5}^{2}}  \\ \end{matrix} \right|\]is equal to
  A)
   8                 
  done clear
  B)
   \[-8\]
  done clear
  C)
   400               
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer204) For any complex number z, minimum value of\[|z|+|z-1|\]is equal to
  A)
   1              
  done clear
  B)
   0
  done clear
  C)
   1/2             
  done clear
  D)
   3/2
  done clear
  View Answer play_arrow

• question_answer205) \[\left| \begin{matrix}    1/a & {{a}^{2}} & bc  \\    1/b & {{b}^{2}} & ca  \\    1/c & {{c}^{2}} & ab  \\ \end{matrix} \right|\]is equal to
  A)
   \[abc\]
  done clear
  B)
   0
  done clear
  C)
   1
  done clear
  D)
   \[a+b+c\]
  done clear
  View Answer play_arrow

• question_answer206) lf\[^{n}{{C}_{3}}{{+}^{n}}{{C}_{4}}{{>}^{n+1}}{{C}_{3}},\]then
  A)
   \[n>7\]             
  done clear
  B)
   \[n<6\]
  done clear
  C)
   \[n>6\]             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer207) If \[{{x}^{2}}+{{y}^{2}}=t-\frac{1}{t},{{x}^{4}}+{{y}^{4}}={{t}^{2}}+\frac{1}{{{t}^{2}}},\]then\[\frac{dy}{dx}\]is equal to
  A)
   \[\frac{1}{x{{y}^{3}}}\]
  done clear
  B)
   \[\frac{1}{{{x}^{3}}y}\]
  done clear
  C)
   \[-\frac{1}{x{{y}^{3}}}\]
  done clear
  D)
   \[-\frac{1}{{{x}^{3}}y}\]
  done clear
  View Answer play_arrow

• question_answer208) \[\hat{i}\times (\hat{j}\times \hat{k})+\hat{j}\times (\hat{k}\times \hat{i})+\hat{k}(\hat{i}\times \hat{j})\]is equal to
  A)
   1               
  done clear
  B)
   0
  done clear
  C)
   3                
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer209) The area of a rectangle of given perimeter is minimum, if the ratio of its length to width is
  A)
   1:1             
  done clear
  B)
   2:1
  done clear
  C)
   4:3            
  done clear
  D)
   3:2
  done clear
  View Answer play_arrow

• question_answer210) If AB = A, BA = B for any two square matrices A and B, then\[{{A}^{2}}\]is equal to
  A)
   A               
  done clear
  B)
   B
  done clear
  C)
   AB              
  done clear
  D)
   \[{{B}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer211) If\[z=x+iy,\]then \[z\overline{z}+2(z+\overrightarrow{z})+c=0\]will define a
  A)
   circle             
  done clear
  B)
   straight line
  done clear
  C)
   parabola          
  done clear
  D)
   point
  done clear
  View Answer play_arrow

• question_answer212) If\[(3,\lambda )\]and (5,6) are the conjugate points of \[{{x}^{2}}+{{y}^{2}}=3,\]then \[\lambda \]is equal to
  A)
   2              
  done clear
  B)
   \[-2\]
  done clear
  C)
   1              
  done clear
  D)
   \[-1\]
  done clear
  View Answer play_arrow

• question_answer213) The argument of\[{{\left( \frac{1+\cos \theta +i\sin \theta }{1+\cos \theta -i\sin \theta } \right)}^{n}}\]is
  A)
   \[n\theta \]
  done clear
  B)
   \[\frac{n\theta }{2}\]
  done clear
  C)
   \[-\frac{n\theta }{2}\]
  done clear
  D)
   \[-n\theta \]
  done clear
  View Answer play_arrow

• question_answer214) The figure made by the lines\[ax\pm by\pm c=0\]is
  A)
   rectangle        
  done clear
  B)
   square
  done clear
  C)
   rhombus        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer215) If focal chord of a parabola\[{{y}^{2}}=4ax\]intercepted at b and k, then k is equal to
  A)
   \[\frac{ab}{b-a}\]
  done clear
  B)
   \[\frac{b}{b-a}\]
  done clear
  C)
   \[\frac{a}{b-a}\]
  done clear
  D)
   \[\frac{ba}{a-b}\]
  done clear
  View Answer play_arrow

• question_answer216) If\[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0\]and\[|\overrightarrow{a}|=5,|\overrightarrow{b}|=3,|\overrightarrow{c}|=7,\]then angle between a and b is
  A)
   \[\frac{\pi }{6}\]
  done clear
  B)
   \[\frac{\pi }{4}\]
  done clear
  C)
   \[\frac{\pi }{3}\]
  done clear
  D)
   \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer217) If a coin is tossed n times, then the probability that head comes odd number of times is
  A)
   \[\frac{1}{2}\]
  done clear
  B)
   \[\frac{1}{{{2}^{n}}}\]
  done clear
  C)
   \[\frac{1}{{{2}^{n-1}}}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer218) \[\int{\sqrt{1+\sec x}}dx\]is equal to
  A)
   \[2{{\sin }^{-1}}(\sqrt{2}\sin x)+c\]
  done clear
  B)
   \[-2{{\sin }^{-1}}\left( \sqrt{2}\sin \frac{x}{2} \right)+c\]
  done clear
  C)
   \[2{{\sin }^{-1}}\left( \sqrt{2}\sin \frac{x}{2} \right)+c\]
  done clear
  D)
   \[\frac{1}{2}{{\sin }^{-1}}(\sqrt{2}\sin x)+c\]
  done clear
  View Answer play_arrow

• question_answer219) \[\int{\cos (\log x)dx}\]is equal to
  A)
   \[\frac{x}{2}[\sin (\log x)-\cos (\log x)]+c\]
  done clear
  B)
   \[\frac{x}{2}[\sin (\log x)+\cos (\log x)]+c\]
  done clear
  C)
   \[\frac{1}{2}[\sin (\log x)-\cos (\log x)]+c\]
  done clear
  D)
   \[\frac{1}{2}[\sin (\log x)+\cos (\log x)]+c\]
  done clear
  View Answer play_arrow

• question_answer220) The value of\[|{{z}_{1}}+{{z}_{2}}{{|}^{2}}+|{{z}_{1}}-{{z}_{2}}{{|}^{2}}\]is
  A)
   \[\frac{1}{2}[|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}]\]
  done clear
  B)
   \[2[|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}]\]
  done clear
  C)
   \[2[|{{z}_{1}}{{|}^{2}}-|{{z}_{2}}{{|}^{2}}]\]
  done clear
  D)
   \[\frac{1}{2}[|{{z}_{1}}{{|}^{2}}-|{{z}_{2}}{{|}^{2}}]\]
  done clear
  View Answer play_arrow

• question_answer221) If 5th term and 11th term of a harmonic progression are\[\frac{1}{45}\]and\[\frac{1}{69}\]respectively, then 16th term is
  A)
   \[\frac{1}{89}\]
  done clear
  B)
   \[\frac{1}{85}\]
  done clear
  C)
   \[\frac{1}{81}\]
  done clear
  D)
   \[\frac{1}{77}\]
  done clear
  View Answer play_arrow

• question_answer222) The geometric mean of the roots of the equation\[{{x}^{2}}-18x+9=0\]is
  A)
   \[9\sqrt{2}\]
  done clear
  B)
   \[9\]
  done clear
  C)
   \[\frac{1}{81}\]
  done clear
  D)
   \[\frac{1}{77}\]
  done clear
  View Answer play_arrow

• question_answer223) If the roots of the equation \[{{x}^{2}}-8x+{{a}^{2}}-60=0\]are real, then the value of\[a\]is
  A)
   \[-2<a<8\]         
  done clear
  B)
   \[-2<a<8\]
  done clear
  C)
   \[-2<a<8\]
  done clear
  D)
   \[2<a<8\]
  done clear
  View Answer play_arrow

• question_answer224) The equation of common tangent to the circle \[{{x}^{2}}+{{y}^{2}}=2\]and the parabola\[{{y}^{2}}=8x\]is
  A)
   \[y=x+1\]         
  done clear
  B)
   \[y=x+2\]
  done clear
  C)
   \[y=x-2\]         
  done clear
  D)
   \[y=-x+2\]
  done clear
  View Answer play_arrow

• question_answer225) The angle between the tangents drawn from the origin to the circle\[{{(x-7)}^{2}}+{{(y+1)}^{2}}=25\]is
  A)
   \[\frac{\pi }{3}\]
  done clear
  B)
   \[\frac{\pi }{6}\]
  done clear
  C)
   \[\frac{\pi }{2}\]
  done clear
  D)
   \[\frac{\pi }{8}\]
  done clear
  View Answer play_arrow

• question_answer226) \[{{\left( \frac{\sqrt{3}+i}{2} \right)}^{6}}+{{\left( \frac{i-\sqrt{3}}{2} \right)}^{6}}\]is equal to
  A)
   0              
  done clear
  B)
   \[-1\]
  done clear
  C)
   2              
  done clear
  D)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer227) If\[A=\left[ \begin{matrix}    3 & 2  \\    1 & -4  \\ \end{matrix} \right],\]then A (adj A) is equal to
  A)
   \[-14I\]
  done clear
  B)
   \[-10I\]
  done clear
  C)
   \[8I\]
  done clear
  D)
   \[-\frac{1}{14}I\]
  done clear
  View Answer play_arrow

• question_answer228) Maximum value of\[\frac{\log x}{x}\]is.
  A)
   e               
  done clear
  B)
   1
  done clear
  C)
   2e              
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer229) If the line\[lx+my=1\]is the tangent to the circle\[{{x}^{2}}+{{y}^{2}}={{r}^{2}},\]then locus of\[(l,m)\]is
  A)
   \[{{x}^{2}}+{{y}^{2}}=1\]
  done clear
  B)
   \[{{r}^{2}}({{x}^{2}}+{{y}^{2}})=1\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}=2{{r}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer230) \[\frac{d}{dx}{{\cosh }^{-1}}(\sec x)\]is equal to
  A)
   \[sin\text{ }x\]             
  done clear
  B)
   \[sec\text{ }x\]
  done clear
  C)
   \[tan\text{ }x\]             
  done clear
  D)
   \[cosec\text{ }x\]
  done clear
  View Answer play_arrow

• question_answer231) If\[\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k},\overrightarrow{b}=\hat{j}+\hat{k}\]and\[\overrightarrow{c}=\hat{i}-\hat{k}\]and \[\overrightarrow{a}+\overrightarrow{b}\]and\[\overrightarrow{b}+\overrightarrow{c}\]are the diagonals of a parallelogram, then it's vector area is equal to
  A)
   \[\hat{i}+\hat{j}+\hat{k}\]         
  done clear
  B)
   \[-\hat{i}+\hat{j}+\hat{k}\]
  done clear
  C)
   \[\hat{i}-\hat{j}+\hat{k}\]        
  done clear
  D)
   \[\hat{i}+\hat{j}-\hat{k}\]
  done clear
  View Answer play_arrow

• question_answer232) If\[\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c},\]then\[\overrightarrow{a}(\overrightarrow{b}\times \overrightarrow{c})\]is equal to
  A)
   \[\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})\]
  done clear
  B)
   \[2\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})\]
  done clear
  C)
   \[\overrightarrow{b}.(\overrightarrow{a}+\overrightarrow{c})\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer233) \[\int_{0}^{1}{\sqrt{\frac{1-x}{1+x}}}dx\]is equal to
  A)
   \[\frac{\pi }{2}-1\]
  done clear
  B)
   \[\frac{\pi }{2}+1\]
  done clear
  C)
   \[\frac{\pi }{2}\]
  done clear
  D)
   \[\pi +1\]
  done clear
  View Answer play_arrow

• question_answer234) If\[\alpha \]and\[\beta \]are the roots of the equationx\[{{x}^{2}}-(1+{{n}^{2}})x+\frac{1}{2}(1+{{n}^{2}}+{{n}^{4}})=0\]then\[{{\alpha }^{2}}+{{\beta }^{2}}\]is equal to
  A)
   \[{{n}^{2}}+2\]            
  done clear
  B)
   \[-{{n}^{2}}\]
  done clear
  C)
   \[{{n}^{2}}\]                  
  done clear
  D)
   \[2{{n}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer235) If\[{{(1+x)}^{n}}{{=}^{n}}{{C}_{0}}{{+}^{n}}{{C}_{1}}x{{+}^{n}}{{C}_{2}}{{x}^{2}}+....{{+}^{n}}{{C}_{n}}{{x}^{n}},\]then the value of \[\frac{^{n}{{C}_{1}}}{^{n}{{C}_{0}}}+2.\frac{^{n}{{C}_{2}}}{^{n}{{C}_{1}}}+3.\frac{^{n}{{C}_{3}}}{^{n}{{C}_{2}}}+....+n.\frac{^{n}{{C}_{n}}}{^{n}{{C}_{n-1}}}\]is
  A)
   \[\frac{n(n+1)}{2}\]
  done clear
  B)
   \[\frac{(n+1)}{n!}\]
  done clear
  C)
   \[\frac{n({{n}^{2}}+1)}{2}\]
  done clear
  D)
   \[n\frac{(n+1)}{2}\]
  done clear
  View Answer play_arrow

• question_answer236) \[\frac{1-2i}{2+i}+\frac{4-i}{3+2i}\]is equal to
  A)
   \[-\frac{24}{13}+\frac{10}{13}i\]
  done clear
  B)
   \[\frac{24}{13}-\frac{10}{13}i\]
  done clear
  C)
   \[\frac{10}{13}-\frac{24}{13}i\]
  done clear
  D)
   \[\frac{10}{13}+\frac{24}{13}i\]
  done clear
  View Answer play_arrow

• question_answer237) If\[\omega \]is the cube root of unity, then the value of \[\left| \begin{matrix}    1 & \omega  & {{\omega }^{2}}  \\    \omega  & {{\omega }^{2}} & 1  \\    {{\omega }^{2}} & 1 & \omega   \\ \end{matrix} \right|\]is equal to
  A)
   1                   
  done clear
  B)
   0
  done clear
  C)
   \[\omega \]                    
  done clear
  D)
   \[{{\omega }^{2}}+1\]
  done clear
  View Answer play_arrow

• question_answer238) If \[z=\frac{(1-i)(2+i)}{3+i},\]then\[|z|\]is equal to
  A)
   \[-1\]             
  done clear
  B)
   1
  done clear
  C)
   \[1/2\]             
  done clear
  D)
   \[-1/2\]
  done clear
  View Answer play_arrow

• question_answer239) In the expansion of\[{{\left( 2{{x}^{4}}-\frac{1}{{{x}^{7}}} \right)}^{11}},\]the term independent of \[x\]is
  A)
   330             
  done clear
  B)
   42240
  done clear
  C)
   114050          
  done clear
  D)
   \[-32190\]
  done clear
  View Answer play_arrow

• question_answer240) The equation of radical axis of the circles \[2{{x}^{2}}+2{{y}^{2}}-7x=0\]and\[{{x}^{2}}+{{y}^{2}}-4y-7=0\]is
  A)
   \[7x+8y+14=0\]  
  done clear
  B)
   \[7x-8y-14=0\]
  done clear
  C)
   \[7x-8y+14=0\]  
  done clear
  D)
   \[8x-7y+14=0\]
  done clear
  View Answer play_arrow

• question_answer241) If\[f(\theta )=\tan \theta ,\]then the value of\[\frac{f(\theta )-f(\phi )}{1+f(\theta )f(\phi )}\]is
  A)
   \[f(\theta )+f(\phi )\]
  done clear
  B)
   \[f(\theta -\phi )\]
  done clear
  C)
   \[f\left( \frac{\theta }{\phi } \right)\]
  done clear
  D)
   \[\theta -\phi \]
  done clear
  View Answer play_arrow

• question_answer242) If\[A=\left[ \begin{matrix}    2 & 14  \\    0 & 3  \\ \end{matrix} \right]\]and\[B=\left[ \begin{matrix}    1 & 2  \\    0 & 5  \\ \end{matrix} \right],\]then\[4A-3B\]is equal to
  A)
   \[\left[ \begin{matrix}    7 & 14  \\    0 & 7  \\ \end{matrix} \right]\]
  done clear
  B)
   \[\left[ \begin{matrix}    5 & 10  \\    0 & -3  \\ \end{matrix} \right]\]
  done clear
  C)
   \[\left[ \begin{matrix}    -5 & -10  \\    0 & 3  \\ \end{matrix} \right]\]
  done clear
  D)
   \[\left[ \begin{matrix}    1 & 2  \\    0 & 2  \\ \end{matrix} \right]\]
  done clear
  View Answer play_arrow

• question_answer243) If two vertices of a triangle are (6, 4) and (2,6) and centroid is (4,6), then the third vertex is
  A)
   (4, 8)              
  done clear
  B)
   (8, 4)
  done clear
  C)
   (6, 4)               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer244) \[\frac{d}{dx}({{\sec }^{-1}}x)\]is equal to
  A)
   \[\frac{1}{x\sqrt{1-{{x}^{2}}}}\]           
  done clear
  B)
    \[\frac{1}{x\sqrt{1+x}}\]
  done clear
  C)
   \[\frac{1}{x\sqrt{{{x}^{2}}-1}}\]
  done clear
  D)
   \[\frac{1}{x\sqrt{x-1}}\]
  done clear
  View Answer play_arrow

• question_answer245) Differential coefficient of\[{{\sin }^{-1}}x\]with respect to \[{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]is
  A)
   \[\frac{2}{\sqrt{1-{{x}^{2}}}}\]
  done clear
  B)
   \[\frac{1}{\sqrt{1-{{x}^{2}}}}\]
  done clear
  C)
   \[-\frac{1}{\sqrt{1+{{x}^{2}}}}\]             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer246) \[\int{{{\cos }^{3}}xdx}\]is equal to
  A)
   \[{{\sin }^{3}}x+c\]
  done clear
  B)
   \[\frac{\sin 3x}{3}+\frac{\sin x}{2}+c\]
  done clear
  C)
   \[\frac{\sin 3x}{12}+\frac{3}{4}\sin x+c\]
  done clear
  D)
   \[\frac{\sin 3x}{4}+3\sin x+c\]
  done clear
  View Answer play_arrow

• question_answer247) \[\frac{d}{dx}{{(\sin x)}^{\tan x}}\]is equal to
  A)
   \[{{(\sin x)}^{\tan x}}[1+{{\sec }^{2}}x\log \sin x]\]
  done clear
  B)
   \[{{(\sin x)}^{\tan x}}[1-{{\sec }^{2}}x\log \sin x]\]
  done clear
  C)
   \[{{(\tan x)}^{\sin x}}[\log {{\sec }^{2}}x\log \sin x]\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer248) When two dices are thrown together, then the probability that sum of the digits is seven, is
  A)
   \[\frac{5}{36}\]
  done clear
  B)
   \[\frac{1}{12}\]
  done clear
  C)
   \[\frac{1}{6}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer249) A card is drawn from a pack of cards. The probability that this card is diamond or ace, is
  A)
   \[\frac{4}{13}\]
  done clear
  B)
   \[\frac{17}{52}\]
  done clear
  C)
   \[\frac{1}{52}\]
  done clear
  D)
   \[\frac{1}{13}\]
  done clear
  View Answer play_arrow

• question_answer250) The value of the determinant\[\left| \begin{matrix}    a+ib & c+ib  \\    c-id & a-ib  \\ \end{matrix} \right|\]is
  A)
   \[(a+b)(c-d)\]
  done clear
  B)
   \[({{a}^{2}}+{{b}^{2}})({{c}^{2}}-{{d}^{2}})\]
  done clear
  C)
   \[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}-{{d}^{2}}\]
  done clear
  D)
   \[{{a}^{2}}-{{b}^{2}}+{{c}^{2}}-{{d}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer251) The value of\[\left| \begin{matrix}    43 & 1 & 6  \\    35 & 7 & 4  \\    17 & 3 & 2  \\ \end{matrix} \right|\]is
  A)
   150             
  done clear
  B)
   0
  done clear
  C)
   \[-110\]            
  done clear
  D)
   \[-6\]
  done clear
  View Answer play_arrow

• question_answer252) If roots of the equation\[{{x}^{2}}-ax+b=0\]are a and\[\beta \]and\[{{V}_{n}}={{\alpha }^{n}}+{{\beta }^{n}},\]then
  A)
   \[{{V}_{n+1}}=\alpha {{V}_{n}}-b{{V}_{n-1}}\]
  done clear
  B)
   \[{{V}_{n+1}}=b{{V}_{n}}+a{{V}_{n-1}}\]
  done clear
  C)
   \[{{V}_{n+1}}=b{{V}_{n}}-a{{V}_{n-1}}\]
  done clear
  D)
   \[{{V}_{n+1}}=b{{V}_{n}}+b{{V}_{n-1}}\]
  done clear
  View Answer play_arrow

• question_answer253) If arithmetic mean and harmonic mean of two numbers be 27 and 12, then their geometric mean is equal to
  A)
   36             
  done clear
  B)
   24
  done clear
  C)
   18             
  done clear
  D)
   9
  done clear
  View Answer play_arrow

• question_answer254) Real part of\[(\alpha +i\beta )\]is
  A)
   \[cosh\text{ }\alpha \text{ }cos\text{ }\beta \]      
  done clear
  B)
   \[cos\text{ }\alpha \text{ }cos\text{ }\beta \]
  done clear
  C)
   \[cos\text{ }\alpha \text{ }cosh\text{ }\beta \]      
  done clear
  D)
   \[sin\text{ }\alpha \text{ }sinh\text{ }\beta \]
  done clear
  View Answer play_arrow

• question_answer255) If A be a square matrix and\[A+{{A}^{T}}\]is a symmetric matrix, then\[A-{{A}^{T}}\]is
  A)
   a unit matrix
  done clear
  B)
   a symmetric matrix
  done clear
  C)
   a skew-symmetric matrix
  done clear
  D)
   a zero matrix
  done clear
  View Answer play_arrow

• question_answer256) If\[\alpha \]and\[\beta \]be the roots of the equation \[{{x}^{2}}-2x+4=0,\]then the value of\[{{\alpha }^{n}}+{{\beta }^{n}}\]is
  A)
   \[{{2}^{n-1}}\cos \left( \frac{n\pi }{3} \right)\]
  done clear
  B)
   \[i{{2}^{n-1}}\sin \left( \frac{n\pi }{3} \right)\]
  done clear
  C)
   \[{{2}^{n+1}}\cos \left( \frac{n\pi }{3} \right)\]
  done clear
  D)
   \[i{{2}^{n+1}}\sin \left( \frac{n\pi }{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer257) If the normal to any curve is parallel to\[x-\]axis, then the true statement is
  A)
   \[\frac{dy}{dx}=0\]
  done clear
  B)
   \[\frac{dx}{dy}=0\]
  done clear
  C)
   \[\frac{dy}{dx}=1\]
  done clear
  D)
   \[\frac{dx}{dy}=-1\]
  done clear
  View Answer play_arrow

• question_answer258) Differential coefficient of\[{{x}^{3}}\]with respect to\[{{x}^{2}}\]
  A)
   \[\frac{3{{x}^{2}}}{2}\]
  done clear
  B)
   \[\frac{3x}{2}\]
  done clear
  C)
   \[\frac{3}{2}x\]
  done clear
  D)
   \[\frac{3}{2x}\]
  done clear
  View Answer play_arrow

• question_answer259) If A and B are two events, then\[P\left( \frac{\overline{A}}{B} \right)\]is equal to
  A)
   \[1-P\left( \frac{A}{B} \right)\]
  done clear
  B)
   \[\frac{1-P(AB)}{P(B)}\]
  done clear
  C)
   \[\frac{1-P(A+B)}{P(\overline{B})}\]
  done clear
  D)
   \[\frac{P(\overline{A})}{P(\overline{B})}\]
  done clear
  View Answer play_arrow

• question_answer260) \[\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})\]is equal to
  A)
   \[(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c}+(\overrightarrow{a}.\overrightarrow{c})\overrightarrow{b}\]
  done clear
  B)
   \[(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c}-(\overrightarrow{a}.\overrightarrow{c})\overrightarrow{b}\]
  done clear
  C)
   \[(\overrightarrow{a}.\overrightarrow{c})\overrightarrow{b}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c}\]
  done clear
  D)
   \[(\overrightarrow{a}.\overrightarrow{c})\overrightarrow{b}+(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c}\]
  done clear
  View Answer play_arrow

• question_answer261) For any two events A and B, which of the following is true?
  A)
   \[P(A\cap B)\ge P(A)+P(B)-1\]
  done clear
  B)
   \[P(A\cap B)\le P(A)+P(B)-1\]
  done clear
  C)
   \[P(A\cap B)\ge P(A)+P(B)\]
  done clear
  D)
   \[P(A\cap B)\le P(A)+P(B)\]
  done clear
  View Answer play_arrow

• question_answer262) \[P\left( \frac{\overline{A}}{A\cup B} \right)\]is equal to
  A)
   \[\frac{P(\overline{B})}{P(A\cup B)}\]
  done clear
  B)
   \[\frac{P(\overline{A})}{P(A\cup B)}\]
  done clear
  C)
   \[\frac{P(\overline{A}\cap B)}{P(A\cup B)}\]
  done clear
  D)
   \[\frac{P(A)}{P(A\cup B)}\]
  done clear
  View Answer play_arrow

• question_answer263) If the vectors\[2\hat{i}+\hat{j}-\hat{k}\]and\[\hat{i}-4\hat{j}+\lambda \hat{k}\]are perpendicular to each other, then\[\lambda \]is equal to
  A)
   0               
  done clear
  B)
   \[-1\]
  done clear
  C)
   \[-2\]             
  done clear
  D)
   \[-3\]
  done clear
  View Answer play_arrow

• question_answer264) If\[f(a-x)=f(x),\]then\[\int_{0}^{a}{x}f(x)dx\]is equal to
  A)
   \[a\int_{0}^{a}{f(x)dx}\]
  done clear
  B)
   \[\frac{a}{2}\int_{0}^{a}{f(x)dx}\]
  done clear
  C)
   \[\int_{0}^{a}{f(x)dx}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer265) If\[A=\left[ \begin{matrix}    i & 0  \\    0 & i  \\ \end{matrix} \right]\]and\[B=\left[ \begin{matrix}    0 & -i  \\    -i & 0  \\ \end{matrix} \right],\]then \[(A+B)(A-B)\]is equal to
  A)
   2A              
  done clear
  B)
   2B
  done clear
  C)
   \[2I\]              
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer266) If\[{{x}^{y}}={{e}^{x-y}},\]then\[\frac{dy}{dx}\] is equal to
  A)
   \[\frac{\log x}{{{(1+\log x)}^{2}}}\]
  done clear
  B)
   \[\frac{y-x}{x(1+\log x)}\]
  done clear
  C)
   \[\frac{x-y}{1+\log \,\,x}\]
  done clear
  D)
   \[\frac{y-x}{x(1+log\,\,x)}\]
  done clear
  View Answer play_arrow

• question_answer267) If intercept on made by a line on the axes are a and b and its distance from the origin is p, then
  A)
   \[\frac{1}{{{p}^{2}}}={{a}^{2}}+{{b}^{2}}\]
  done clear
  B)
   \[{{p}^{2}}={{a}^{2}}+{{b}^{2}}\]
  done clear
  C)
   \[{{p}^{2}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}\]
  done clear
  D)
   \[\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer268) If the circle\[{{x}^{2}}+{{y}^{2}}+2ax+8y+16=0\]touches the\[x-\]axis, then a is equal to
  A)
   ±16             
  done clear
  B)
   ± 8
  done clear
  C)
   ± 1              
  done clear
  D)
   ± 4
  done clear
  View Answer play_arrow

• question_answer269) The true statement is
  A)
   \[cos{{h}^{2}}x+sin{{h}^{2}}x=1\]
  done clear
  B)
   \[cos{{h}^{2}}x-sin{{h}^{2}}x=cos{{h}^{2}}x\]
  done clear
  C)
   \[1+tan{{h}^{2}}x=sec{{h}^{2}}x\]
  done clear
  D)
   \[cos{{h}^{2}}x-sin{{h}^{2}}x=1\]
  done clear
  View Answer play_arrow

• question_answer270) If the points (1,2),\[(-1,x)\]and (2,3) are collinear, then\[x\]is equal to
  A)
   1                
  done clear
  B)
   2
  done clear
  C)
   0                
  done clear
  D)
   \[-1\]
  done clear
  View Answer play_arrow

• question_answer271) A hits an aim four times out of 5 trials, B hits three times out of 4 trials and C hits two times out of 3 trials. The probability that only two hits the target is
  A)
   \[\frac{5}{12}\]
  done clear
  B)
   \[\frac{5}{6}\]
  done clear
  C)
   \[\frac{25}{60}\]
  done clear
  D)
   \[\frac{26}{60}\]
  done clear
  View Answer play_arrow

• question_answer272) A card is drawn from a pack of cards. The probability that this card is an ace or a queen is
  A)
   \[\frac{4}{13}\]
  done clear
  B)
   \[\frac{17}{52}\]
  done clear
  C)
   \[\frac{3}{13}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer273) The probability of occuring 1 or 6 when a dice is thrown, is
  A)
   \[\frac{1}{6}\]
  done clear
  B)
   \[\frac{1}{36}\]
  done clear
  C)
   \[\frac{2}{3}\]
  done clear
  D)
   \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer274) Which one is not true from the following?
  A)
   \[{{(A+B)}^{T}}={{A}^{T}}+{{B}^{T}}\]
  done clear
  B)
   \[{{({{A}^{T}})}^{T}}=A\]
  done clear
  C)
   \[{{(KA)}^{T}}=K{{A}^{T}}\]
  done clear
  D)
   \[{{(AB)}^{T}}={{A}^{T}}{{B}^{T}}\]
  done clear
  View Answer play_arrow

• question_answer275) If\[{{z}_{1}}\]and\[{{z}_{2}}\]are any two complex numbers, then true relation is
  A)
   \[|{{z}_{1}}+{{z}_{2}}|\le |{{z}_{1}}|-|{{z}_{2}}|\]
  done clear
  B)
   \[|{{z}_{1}}-{{z}_{2}}|\ge |{{z}_{1}}|+|{{z}_{2}}|\]
  done clear
  C)
   \[|{{z}_{1}}+{{z}_{2}}|\ge |{{z}_{1}}|+|{{z}_{2}}|\]
  done clear
  D)
   \[|{{z}_{1}}-{{z}_{2}}|\le |{{z}_{1}}|+|{{z}_{2}}|\]
  done clear
  View Answer play_arrow

• question_answer276) The equation of parabola which has the vertex at origin and axis is\[x-\]axis and also passes through the point (4,3), is
  A)
   \[9{{y}^{2}}=4x\]
  done clear
  B)
   \[9{{y}^{2}}=-4x\]
  done clear
  C)
   \[4{{y}^{2}}=-9x\]
  done clear
  D)
   \[4{{y}^{2}}=9x\]
  done clear
  View Answer play_arrow

• question_answer277) If\[3{{y}^{2}}-4{{x}^{2}}=0,\]then\[\frac{{{d}^{2}}y}{d{{x}^{2}}}\]is equal to
  A)
   \[\frac{{{y}^{3}}}{2{{y}^{2}}-4{{x}^{2}}}\]
  done clear
  B)
   \[\frac{2{{y}^{2}}-4{{x}^{2}}}{{{y}^{3}}}\]
  done clear
  C)
   \[\frac{4y-8x}{{{y}^{3}}}\]
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer278) The equation of that circle which passes through the origin and cut the axes\[x\]and y of length 6 and 8 on respectively, is
  A)
   \[{{x}^{2}}+{{y}^{2}}\pm 6x\pm 8y=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}\pm 8x\pm 6y=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}\pm 12x\pm 16y=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}\pm 16x\pm 12y=0\]
  done clear
  View Answer play_arrow

• question_answer279) The equation of directrix of the parabola \[{{y}^{2}}=-12x\]is
  A)
   \[x+3=0\]           
  done clear
  B)
   \[x=3\]
  done clear
  C)
   \[y+3=0\]           
  done clear
  D)
   \[y-3=0\]
  done clear
  View Answer play_arrow

• question_answer280) \[\int{\frac{x\,dx}{1+\cos x}}\]is equal to
  A)
   \[x\tan \frac{x}{2}+2\log \cos \frac{x}{2}+c\]
  done clear
  B)
   \[x\tan \frac{x}{2}-\log \cos \frac{x}{2}+c\]
  done clear
  C)
   \[2\left\{ x\tan \frac{x}{2}+\log \cos \frac{x}{2} \right\}+c\]
  done clear
  D)
   \[x\tan \frac{x}{2}-\log \cos \frac{x}{2}+c\]
  done clear
  View Answer play_arrow

• question_answer281) If\[x=a\text{ }cos\text{ }t,\text{ }y=b\text{ }sin\text{ }t,\]then\[\frac{dy}{dx}\]is equal to
  A)
   \[-\frac{b}{a}\tan t\]
  done clear
  B)
   \[-\frac{b}{a}\cot t\]
  done clear
  C)
   \[-\frac{a}{b}\cot t\]
  done clear
  D)
   \[-\frac{a}{b}\tan t\]
  done clear
  View Answer play_arrow

• question_answer282) If\[y=\frac{1}{(t+2)(t+1)},\]then\[\frac{dy}{dx}\]is equal to
  A)
   \[-\frac{1}{{{(t+1)}^{2}}}+\frac{1}{{{(t+2)}^{2}}}\]
  done clear
  B)
   \[\frac{1}{{{(t+1)}^{2}}}+\frac{1}{{{(t+2)}^{2}}}\]
  done clear
  C)
   \[-\frac{1}{{{(t+1)}^{2}}}-\frac{1}{{{(t+2)}^{2}}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer283) The equation of tangents at that point where the curve\[y={{x}^{2}}-3x+2\]cut the\[x-\]axis, is
  A)
   \[x+y-1=0,x-y-2=0\]
  done clear
  B)
   \[x-y-1=0,\text{ }x-y=0\]
  done clear
  C)
   \[x-y+2=0,x-y-1=0\]
  done clear
  D)
   \[x+y=0,\text{ }x-y=0\]
  done clear
  View Answer play_arrow

• question_answer284) \[\int_{0}^{a}{\sqrt{\frac{a}{a-x}}}dx\]is equal to
  A)
   \[4a\]                
  done clear
  B)
   \[-4a\]
  done clear
  C)
   \[2a\]                
  done clear
  D)
   \[a\]
  done clear
  View Answer play_arrow

• question_answer285) \[\int{\frac{2dx}{{{x}^{2}}-1}}\] is equal to
  A)
   \[\frac{1}{2}\log \frac{x-1}{x+1}+c\]
  done clear
  B)
   \[\log \frac{x-1}{x+1}+c\]
  done clear
  C)
   \[\frac{1}{2}\log \frac{x+1}{x-1}+c\]
  done clear
  D)
   \[\log \frac{x+1}{x-1}+c\]
  done clear
  View Answer play_arrow

• question_answer286) Two cards are drawn one by one from a pack of 52 cards. The probability that these axes, is
  A)
   \[\frac{1}{26}\]
  done clear
  B)
   \[\frac{1}{221}\]
  done clear
  C)
   \[\frac{2}{21}\]              
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer287) If there are 4 copper coins and 3 silver coins in a purse while 6 copper coins and 2 silver coins in an another purse a coin is taken randomly from any one of the purse, the probability that this is of copper coin is
  A)
   \[\frac{4}{7}\]
  done clear
  B)
   \[\frac{3}{4}\]
  done clear
  C)
   \[\frac{2}{7}\]
  done clear
  D)
   \[\frac{37}{56}\]
  done clear
  View Answer play_arrow

• question_answer288) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}\]is equal to
  A)
   \[-1\]                
  done clear
  B)
   \[1/2\]
  done clear
  C)
   2                  
  done clear
  D)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer289) The order of a matrix A is\[P\times Q\]and that of B is\[R\times S,\]then for\[A-B,\]the values of P and Q are
  A)
   \[P=Q\]            
  done clear
  B)
   \[P=Q,R=S\]
  done clear
  C)
   \[P=R,\text{ }Q=S\]      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer290) If\[f(x)=\frac{x}{\sqrt{1+{{x}^{2}}}},\]then\[fofof(x)\]is equal to
  A)
   \[\frac{x}{\sqrt{1+3{{x}^{2}}}}\]
  done clear
  B)
   \[\frac{x}{\sqrt{1+{{x}^{2}}}}\]
  done clear
  C)
   \[\frac{x}{\sqrt{1+2{{x}^{2}}}}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer291) Argument of\[\left( \frac{1-i\sqrt{3}}{1+i\sqrt{3}} \right)\]is
  A)
   \[60{}^\circ \]             
  done clear
  B)
   \[120{}^\circ \]
  done clear
  C)
   \[-120{}^\circ \]            
  done clear
  D)
   \[-135{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer292) If\[^{n-1}{{C}_{3}}{{+}^{n-1}}{{C}_{4}}{{>}^{n}}{{C}_{3}},\]then n is equal to
  A)
   4                   
  done clear
  B)
   6
  done clear
  C)
   8                   
  done clear
  D)
   7
  done clear
  View Answer play_arrow

• question_answer293) Which one of the following is an even function?
  A)
   \[f(x)=\frac{{{a}^{x}}+{{a}^{-x}}}{{{a}^{x}}-{{a}^{-x}}}\]
  done clear
  B)
   \[f(x)=\frac{{{a}^{x}}+1}{{{a}^{x}}-1}\]
  done clear
  C)
   \[f(x)=x\frac{{{a}^{x}}-1}{{{a}^{x}}+1}\]
  done clear
  D)
   \[f(x)={{\log }_{e}}(x+\sqrt{{{x}^{2}}+1})\]
  done clear
  View Answer play_arrow

• question_answer294) Locus of the centroid of the triangle with vertices\[(a\text{ }cos\text{ }t,a\text{ }sin\text{ }t),(b\text{ }sin\text{ }t,-b\text{ }cos\text{ }t)\] and (1,0), where t is a parameter, is
  A)
   \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]
  done clear
  B)
   \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]
  done clear
  C)
   \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]
  done clear
  D)
   \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer295) If sum of squares of the roots of the equation \[{{x}^{2}}-(a-2)x-(a+1)=0\]is minimum, then the value of a is
  A)
   0               
  done clear
  B)
   2
  done clear
  C)
   \[-1\]              
  done clear
  D)
   \[1\]
  done clear
  View Answer play_arrow

• question_answer296) If\[{{A}^{T}}\]is the transpose matrix of the matrix A, then \[A{{A}^{T}}\]is
  A)
   symmetric matrix
  done clear
  B)
   inverse matrix
  done clear
  C)
   skew-symmetric matrix
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer297) If\[y=f(x)=\frac{ax+b}{cx-a},\]then\[x\]is equal to
  A)
   \[\frac{1}{f(x)}\]
  done clear
  B)
   \[\frac{1}{f(y)}\]
  done clear
  C)
   \[yf(x)\]
  done clear
  D)
   \[f(y)\]
  done clear
  View Answer play_arrow

• question_answer298) Domain of the function\[f(x)=\sqrt{2-2x-{{x}^{2}}}\]is
  A)
   \[-\sqrt{3}\le x\le \sqrt{3}\]
  done clear
  B)
   \[-1-\sqrt{3}\le x\le -1+\sqrt{3}\]
  done clear
  C)
   \[-2\le x\le 2\]
  done clear
  D)
   \[-2+\sqrt{3}\le x\le -2-\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer299) Equation   of  tangent   to  the   ellipse \[{{x}^{2}}+16{{y}^{2}}=16\]which makes an angle of\[60{}^\circ \]with\[x-\]axis, is
  A)
   \[\sqrt{3}x-y+7=0\]   
  done clear
  B)
   \[\sqrt{3}x-y-7=0\]
  done clear
  C)
   \[\sqrt{3}x-y\pm 7=0\]   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer300) Intersection points of the circles\[{{x}^{2}}+{{y}^{2}}=25\] and \[{{x}^{2}}+{{y}^{2}}-8x+7=0,\]are
  A)
   (4, 3) and \[(4,-3)\]
  done clear
  B)
  \[(4,-3)\]and\[(-4,-3)\]
  done clear
  C)
  \[(-4,3)\]and (4, 3)
  done clear
  D)
   (4, 3) and (3, 4)
  done clear
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