Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2009

done JCECE Engineering Solved Paper-2009 Total Questions - 150

• question_answer1) The twinkling effect of star light is due to
  A)
   total internal reflection
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  B)
   high dense matter of star
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  C)
   constant burning of hydrogen in the star
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  D)
   the fluctuating apparent position of the star being slightly different from the actual position of the star
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• question_answer2) The width of the diffraction band varies
  A)
   inversely as the wavelength
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  B)
   directly as the width of the slit
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  C)
   directly as the distance between the slit and the screen
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  D)
   inversely as the size of the source from which the slit is illuminated
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• question_answer3) An unpolarised beam of intensity \[{{I}_{0}}\] is incident on a pair of Nichols making an angle of \[{{60}^{o}}\] with each other. The intensity of light emerging from the pair is
  A)
  \[{{I}_{0}}\]                                       
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  B)
  \[\frac{{{I}_{0}}}{2}\]
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  C)
  \[\frac{{{I}_{0}}}{4}\]                                     
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  D)
  \[\frac{{{I}_{0}}}{8}\]
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• question_answer4) When a low flying aircraft passes over head, we sometimes notice a slight shaking of the picture on our TV screen. This is due to
  A)
   diffraction of the signal received from the antenna
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  B)
   interference of the direct signal received by the antenna with the weak signal reflected by the passing aircraft
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  C)
   change of magnetic flux occurring due to the passage of aircraft
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  D)
   vibration created by the, passage of aircraft,
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• question_answer5) A beam of light of wavelength \[600\,\,nm\] from a distant source falls on a single slit \[1\,\,mm\] wide and the resulting diffraction pattern is observed on a screen \[2\,\,m\] away. The distance between the first dark fringes on either side of the central bright fringe is
  A)
  \[1.2\,\,cm\]                     
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  B)
  \[1.2\,\,mm\]
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  C)
  \[2.4\,\,cm\]                     
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  D)
  \[2.4\,\,mm\]
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• question_answer6) The physical quantity having the dimensions \[[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]\]is
  A)
   resistance
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  B)
   resistivity
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  C)
   electrical conductivity
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  D)
   electromotive force
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• question_answer7) A battery of emf \[10\,\,V\] and internal resistance \[3\Omega \] is connected to a resistor. The current in the circuit is\[0.5\,\,A\] The terminal voltage of the battery when the circuit is closed is
  A)
  \[10\,\,V\]                                         
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  B)
  \[0\,\,V\]
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  C)
  \[1.5\,\,V\]                        
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  D)
  \[8.5\,\,V\]
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• question_answer8) A galvanometer coil has a resistance of \[15\Omega \] and gives full scale deflection for a current of\[4\,\,mA\]. To convert it to an am metal of range \[0\] to\[6\,\,A\]
  A)
   \[10\,\,m\Omega \] resistance is to be connected in parallel to the galvanometer
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  B)
   \[10\,\,m\Omega \] resistance is to be connected in series with the galvanometer
  done clear
  C)
   \[0.1\,\,\Omega \] resistance is to be connected in parallel to the galvanometer
  done clear
  D)
   \[0.1\,\,\Omega \] resistance is to be connected in series with the galvanometer
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• question_answer9) The electron drift speed is small and the charge of the electron is also small but still, we obtain large current in a conductor. This is due to
  A)
   the conducting property of the conductor
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  B)
   the resistance of the conductor is small
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  C)
   the electron number density of the conductor is small
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  D)
   the electron number density of the conductor is enormous
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• question_answer10) A straight wire of mass \[200\,\,g\] and length \[1.5\,\,m\] carries a current of\[2\,\,A\]. It is suspended in mid- air by a uniform horizontal magnetic field\[B\]. The magnitude of \[B\] (in tesla) is (assume\[g=9.8\,\,m{{s}^{-2}})\]
  A)
  \[2\]                                     
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  B)
  \[1.5\]
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  C)
  \[0.55\]                               
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  D)
  \[0.65\]
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• question_answer11) A Gaussian sphere encloses an electric dipole within it. The total flux across the sphere is
  A)
   zero
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  B)
   half that due to a single charge
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  C)
   double that due to a single charge
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  D)
   dependent on the position of the dipole
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• question_answer12) A parallel plate air capacitor has a capacitance\[C\]. When it is half filled with a dielectric of dielectric constant\[5\], the percentage increase in the capacitance will be
  A)
  \[400%\]                             
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  B)
  \[66.6%\]
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  C)
  \[33.3%\]                            
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  D)
  \[200%\]
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• question_answer13) A comb run through one's dry hair attracts small bits of paper. This is due to
  A)
   comb is a good conductor
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  B)
   paper is a good conductor
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  C)
   the atoms is the paper get polarised by the charged comb
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  D)
   the comb possesses magnetic properties
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• question_answer14) The specific charge of a proton is\[9.6\times {{10}^{7}}C\,\,k{{g}^{-1}}\]. The specific charge of an alpha particle will be
  A)
  \[9.6\times {{10}^{7}}C\,\,k{{g}^{-1}}\] 
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  B)
  \[19.2\times {{10}^{7}}C\,\,k{{g}^{-1}}\]
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  C)
  \[4.8\times {{10}^{7}}C\,\,k{{g}^{-1}}\] 
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  D)
  \[2.4\times {{10}^{7}}C\,\,k{{g}^{-1}}\]
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• question_answer15) When light of wavelength \[300\,\,nm\] falls on a photoelectric emitter, photoelectrons are liberated. For another emitter, light of wavelength \[600\,\,nm\] is sufficient for liberating photoelectrons. The ratio of the work function of the two emitters is
  A)
  \[1:2\]                                  
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  B)
  \[2:1\]
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  C)
  \[4:1\]                                  
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  D)
  \[1:4\]
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• question_answer16) White light is passed through a dilute solution of potassium permanganate. The spectrum produced by the emergent light is
  A)
   band emission spectrum
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  B)
   line emission spectrum
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  C)
   band absorption spectrum
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  D)
    line absorption spectrum
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• question_answer17) If  \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] are the wavelengths of the first members of the Lyman and Paschen series respectively, then \[{{\lambda }_{1}}:{{\lambda }_{2}}\] is
  A)
  \[1:3\]                                  
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  B)
  \[1:30\]
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  C)
  \[7:50\]               
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  D)
  \[7:108\]
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• question_answer18) Activity of a radioactive sample decreases to \[{{(1/3)}^{rd}}\] of its original value in \[3\] days. Then, in \[9\] days its activity will become
  A)
  \[(1/27)\] of the original value
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  B)
  \[(1/9)\] of the original value
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  C)
  \[(1/18)\] of the original value
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  D)
  \[(1/3)\]of the original value
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• question_answer19) The working of which of the following is similar to that of a slide projector?
  A)
   Electron microscope
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  B)
   Scanning electron microscope
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  C)
   Transmission electron microscope
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  D)
    Atomic force microscope
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• question_answer20) In a transistor the collector current is always less than the emitter current because
  A)
   collector side is reverse biased and the emitter side is forward biased
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  B)
   a few electrons are lost in the base and only remaining ones reach the collector
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  C)
   collector being reverse biased, attracts less electrons
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  D)
   collector side is forward biased and emitter side is reverse biased
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• question_answer21) A transparent cube of \[0.21\,\,m\] edge contains a small air bubble. Its apparent distance when viewed through one face of the cube is \[0.10\,\,m\] and when viewed from the opposite face is\[0.04\,\,m\]. The actual distance of the bubble from the second face of the cube is
  A)
  \[0.06\,\,m\]                     
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  B)
  \[0.17\,\,m\]
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  C)
  \[0.05\,\,m\]                     
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  D)
  \[0.04\,\,m\]
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• question_answer22) To a fish under water, viewing obliquely a fisherman standing on the bank of a lake, the man looks
  A)
   taller than what he actually is
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  B)
   shorter that what he actually is
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  C)
   the same height as he actually is
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  D)
   depends on the obliquity
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• question_answer23) If white light is used in the Newton's rings experiment, the colour observed in the reflected light is complementary to that observed in the transmitted light through the same point. This is due to
  A)
   \[{{90}^{o}}\] change of phase in one of the reflected waves
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  B)
   \[{{180}^{o}}\] change of phase in one of the reflected waves
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  C)
   \[{{145}^{o}}\] change of phase in one of the reflected waves
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  D)
   \[{{45}^{o}}\] change of phase in one the reflected waves
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• question_answer24) A satellite in a circular orbit of radius \[R\] has a period of\[4\,\,h\]. Another satellite with orbital radius \[3R\] around the same planet will have a period (in hours)
  A)
  \[16\]                                   
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  B)
  \[4\]
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  C)
  \[4\sqrt{27}\]                   
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  D)
  \[4\sqrt{8}\]
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• question_answer25) The freezer in a refrigerator is located at the top section so that
  A)
   the entire chamber of the refrigerator is cooled quickly due to convection
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  B)
   the motor is not heated
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  C)
   the heat gained from the environment is high
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  D)
    the heat gained from the environment is low
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• question_answer26) A monoatomic gas is suddenly compressed to \[{{(1/8)}^{th}}\] of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be\[5/3)\]
  A)
  \[32\]                                   
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  B)
  \[40/3\]
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  C)
  \[24/5\]                               
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  D)
  \[8\]
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• question_answer27) A Carnot engine takes heat from a reservoir at \[{{627}^{o}}C\] and rejects heat to a sink at\[{{27}^{o}}C\]. Its efficiency will be
  A)
  \[3/5\]                                 
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  B)
  \[1/3\]
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  C)
  \[2/3\]                                 
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  D)
  \[200/209\]
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• question_answer28) A \[30\,\,V,\,\,90\,\,W\] lamp is to be operated on a \[120\,\,V\]\[DC\] line. For proper glow, a resistor, of\[...\Omega \] should be connected in series with the lamp.
  A)
  \[40\]                                   
  done clear
  B)
  \[10\]
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  C)
  \[20\]                                   
  done clear
  D)
  \[30\]
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• question_answer29) A tuning fork \[A\] produces \[4\] beats/s with another tuning fork \[B\] of frequency\[320\,\,Hz\]. On filing one of the prongs of \[A,\,\,4\] beats/s are again heard when sounded with the same fork\[B\]. Then, the frequency of the fork \[A\] before filing is
  A)
  \[328\,\,Hz\]                     
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  B)
  \[316\,\,Hz\]
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  C)
  \[324\,\,Hz\]                     
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  D)
  \[320\,\,Hz\]
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• question_answer30) The sprinkling of water reduces slightly the temperature of a closed room because
  A)
   temperature of water is less than that of the room
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  B)
   specific heat of water is high
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  C)
   water has large latent heat of vaporisation
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  D)
   water is a bad conductor of heat
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• question_answer31) The equation of a simple harmonic wave is given by\[y=5\sin \frac{\pi }{2}(100t-x)\], where \[x\] and \[y\] are in metre and time is in second. The period of the wave in second will be
  A)
  \[0.04\]                               
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  B)
  \[0.01\]
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  C)
  \[1\]                                     
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  D)
  \[5\]
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• question_answer32) The loudness and pitch of a sound note depends on
  A)
   intensity and frequency
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  B)
   frequency and number of harmonics
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  C)
   intensity and velocity
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  D)
    frequency and velocity
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• question_answer33) For ordinary terrestrial experiments, the observer in an inertial frame in the following cases is
  A)
   a child revolving in a giant wheel
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  B)
   a driver in a sports car moving with a constant high speed of \[200\,\,km{{h}^{-1}}\] on a straight rod
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  C)
   the pilot of an aeroplane which is taking off
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  D)
   a cyclist negotiating a sharp curve
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• question_answer34) A rectangular vessel when full of water, takes \[10\,\,\min \] to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water?
  A)
  \[9\,\,\min \]                    
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  B)
  \[7\,\,\min \]
  done clear
  C)
  \[5\,\,\min \]                    
  done clear
  D)
  \[3\,\,\min \]
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• question_answer35) If there were no gravity, which of the following will not be there for a fluid?
  A)
   Viscosity
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  B)
   Surface tension
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  C)
   Pressure
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  D)
    Archimedes' upward thrust
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• question_answer36) In a \[LCR\] series circuit, the potential difference between the terminals of the inductance is\[60\,\,V\], between the terminals of the capacitor is\[30\,\,V\] and that across the resistance is\[40\,\,V\]. Then, supply voltage will be equal to
  A)
  \[50\,\,V\]
  done clear
  B)
  \[70\,\,V\]
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  C)
  \[130\,\,V\]                       
  done clear
  D)
   \[10\,\,V\]
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• question_answer37) When deuterium and helium are subjected to an accelerating field simultaneously then
  A)
   both acquire same energy
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  B)
   deuterium accelerates faster
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  C)
   helium accelerates faster
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  D)
   neither of them is accelerated
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• question_answer38) A solenoid \[1.5\,\,m\] long and \[0.4\,\,cm\] in diameter possesses \[10\] turns per \[cm\] length. A current of \[5\,\,A\] falls through it. The magnetic field at the axis inside the solenoid is
  A)
  \[2\pi \times {{10}^{-3}}T\]                         
  done clear
  B)
  \[2\pi \times {{10}^{-5}}T\]
  done clear
  C)
  \[4\pi \times {{10}^{-2}}T\]                         
  done clear
  D)
  \[4\pi \times {{10}^{-3}}T\]
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• question_answer39) A wire \[PQR\] is bent as shown in figure and is placed in a region of uniform magnetic field\[B\]. The length of \[PQ=QR=l\,\,A\] current \[l\] ampere flows through the wire as shown. The magnitude of the force on \[PQ\] and \[QR\] will be
  A)
  \[BIl,\,\,0\]                        
  done clear
  B)
  \[BIl,\,\,0\]
  done clear
  C)
  \[0,\,\,BIl\]                        
  done clear
  D)
  \[0,\,\,0\]
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• question_answer40) A choke is preferred to a resistance for limiting current in \[AC\] circuit because
  A)
   choke is cheap
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  B)
   there is no wastage of power
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  C)
   choke is compact in size
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  D)
   choke is a good absorber of heat
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• question_answer41) If \[{{r}_{1}}\] and \[{{r}_{2}}\] are the radii of the atomic nuclei of mass numbers 64 and 125 respectively, then the ratio \[({{r}_{1}}/{{r}_{2}})\] is
  A)
  \[\frac{64}{125}\]                                            
  done clear
  B)
  \[\sqrt{\frac{64}{125}}\]
  done clear
  C)
  \[\frac{5}{4}\]                                   
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  D)
  \[\frac{4}{5}\]
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• question_answer42) A motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver \[n-\]times the water through the same pipe in the same time the power of the motor must be increased as follows
  A)
  \[n-\]times                        
  done clear
  B)
  \[{{n}^{2}}-\]times
  done clear
  C)
  \[{{n}^{3}}-\]times                         
  done clear
  D)
  \[{{n}^{4}}-\]times
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• question_answer43) For a system to follow the law of conservation of linear momentum during a collision, the condition is (i) total external force acting on the system is zero. (ii) total external force acting on the system is finite and time of collision is negligible. (iii) total internal force acting on the system is zero.
  A)
   (i) only
  done clear
  B)
   (ii) only
  done clear
  C)
   (iii) only
  done clear
  D)
   (i) or (ii)
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• question_answer44) An air bubble of radius \[1\,\,cm\] rises from the bottom portion through a liquid of density \[1.5\,\,g/cc\] at a constant speed of\[0.25\,\,cm\,\,{{s}^{-1}}\]. If the density of air is neglected, the coefficient of viscosity of the liquid is approximately, (In\[Pa)\]
  A)
  \[13000\]                            
  done clear
  B)
  \[1300\]
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  C)
  \[130\]                                 
  done clear
  D)
  \[13\]
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• question_answer45) A given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be \[0.75\] of its initial pressure. The ratio of the specific heats of the gas is approximately
  A)
  \[1.2\]                                  
  done clear
  B)
  \[1.41\]
  done clear
  C)
  \[1.67\]                               
  done clear
  D)
  \[1.83\]
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• question_answer46) Two solid spheres \[A\] and \[B\] made of the same material have radii \[{{r}_{A}}\] and \[{{r}_{B}}\] respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature \[A\] and \[B\] is
  A)
  \[\frac{{{r}_{A}}}{{{r}_{B}}}\]                                     
  done clear
  B)
  \[\frac{{{r}_{B}}}{{{r}_{A}}}\]
  done clear
  C)
  \[\frac{r_{A}^{2}}{r_{B}^{2}}\]                                  
  done clear
  D)
  \[\frac{r_{B}^{2}}{r_{A}^{2}}\]
  done clear
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• question_answer47) The effect due to uniform magnetic field on a freely suspended magnetic needle is as follows
  A)
   both torque and net force are present
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  B)
   torque is present but no net force
  done clear
  C)
   both torque and net force are absent
  done clear
  D)
   net force is present but not torque
  done clear
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• question_answer48) When a positively charged particle enters a uniform magnetic field with uniform velocity, its trajectory can be (i) a straight line (ii) a circle (iii) a helix
  A)
   (i) only
  done clear
  B)
   (i) or (ii)
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  C)
   (i) or (iii)
  done clear
  D)
   any one of (i), (ii) and (iii)
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• question_answer49) An oil drop having a mass \[4.8\times {{10}^{-10}}g\] and charge \[24\times {{10}^{-18}}C\] stands still between two charged horizontal plates separated by a distance of\[1\,\,cm\]. If now the polarity of the plates is changed, instantaneous acceleration of the drop is\[(g=10\,\,m{{s}^{-2}})\]
  A)
  \[5\,\,m{{s}^{-2}}\]                        
  done clear
  B)
  \[10\,\,m{{s}^{-2}}\]
  done clear
  C)
  \[15\,\,m{{s}^{-2}}\]                      
  done clear
  D)
  \[20\,\,m{{s}^{-2}}\]
  done clear
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• question_answer50) A free neutron decays spontaneously into
  A)
   a proton, an electron and anti-neutrino
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  B)
   a proton, an electron and a neutrino
  done clear
  C)
   a proton and electron
  done clear
  D)
   a proton, and electron, a neutrino and an anti-neutrino
  done clear
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• question_answer51) What is the correct order of spin only magnetic moment (in\[BM)\]of\[M{{n}^{2+}},\,\,\,C{{r}^{2+}}\]and\[{{V}^{2+}}\]?
  A)
  \[M{{n}^{2+}}>{{V}^{2+}}>C{{r}^{2+}}\]               
  done clear
  B)
  \[{{V}^{2+}}>C{{r}^{2+}}>M{{n}^{2+}}\]
  done clear
  C)
  \[M{{n}^{2+}}>C{{r}^{2+}}>{{V}^{2+}}\]               
  done clear
  D)
   \[C{{r}^{2+}}>{{V}^{2+}}>M{{n}^{2+}}\]
  done clear
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• question_answer52) Which of the following is used for making optical instruments?
  A)
  \[Si{{O}_{2}}\]                                  
  done clear
  B)
  \[Si\]
  done clear
  C)
   \[Si{{H}_{4}}\]                 
  done clear
  D)
   \[SiC\]
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• question_answer53) Which of the following is not correct?
  A)
  \[3{{O}_{2}}\underset{\text{discharge}}{\overset{\text{Silent}\,\,\text{electric}}{\longleftrightarrow}}2{{O}_{3}};\,\,\Delta H=-284.5\,\,kJ\]
  done clear
  B)
   Ozone undergoes addition reaction with unsaturated carbon compounds
  done clear
  C)
    Sodium thio sulphate reacts with \[{{I}_{2}}\] to form sodium tetrathionate and sodium iodide
  done clear
  D)
    Ozone oxidises lead sulphide to lead sulphate
  done clear
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• question_answer54) Which of the following reactions can produce aniline as main product?
  A)
  \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}+Zn/KOH\]
  done clear
  B)
  \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}+Zn/N{{H}_{4}}Cl\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}+LiAl{{H}_{4}}\]
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}+Zn/HCl\]
  done clear
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• question_answer55) Which of the following reagents when heated with ethyl chloride, forms ethylene?
  A)
   Aqueous\[KOH\]
  done clear
  B)
   \[Zn/HCl\]
  done clear
  C)
    Alcoholic\[KOH\]
  done clear
  D)
   \[HI\]
  done clear
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• question_answer56) The energy of a photon is\[3\times {{10}^{-12}}erg\]. What is its wavelength in\[nm\]?       \[(h=6.62\times {{10}^{-27}}erg-s;\,\,c=3\times {{10}^{10}}cm/s)\]
  A)
  \[66.2\]                               
  done clear
  B)
  \[1324\]
  done clear
  C)
   \[66.2\]                                              
  done clear
  D)
   \[6.62\]
  done clear
  View Answer play_arrow

• question_answer57) What is the time (in sec) required for depositing all the Silver present in \[125\,\,mL\] of \[1\,\,M\,\,AgN{{O}_{3}}\] solution by passing a current of\[241.25\,\,A\]?                 \[(1F=96500\,\,C)\]
  A)
  \[10\]                                   
  done clear
  B)
  \[50\]
  done clear
  C)
   \[1000\]                             
  done clear
  D)
   \[100\]
  done clear
  View Answer play_arrow

• question_answer58) The disperse phase, dispersion medium and nature of colloidal solution (lyophilic or lyophobic) of ?gold sol? respectively, are
  A)
   solid, solid, lyophobic
  done clear
  B)
   liquid, liquid, lyophobic
  done clear
  C)
    solid, liquid, lyophobic
  done clear
  D)
    solid, liquid, lyophilic
  done clear
  View Answer play_arrow

• question_answer59) The rate constant of a first order reaction at \[{{27}^{o}}C\] is \[{{10}^{-3}}{{\min }^{-1}}\]. The temperature coefficient of this reaction is\[2\]. What is the rate constant (in\[{{\min }^{-1}})\]  at \[{{17}^{o}}C\] for this reaction?
  A)
  \[{{10}^{-3}}\]                                  
  done clear
  B)
  \[5\times {{10}^{-4}}\]
  done clear
  C)
   \[2\times {{10}^{-3}}\]                 
  done clear
  D)
   \[{{10}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer60) A solution of an acid has\[[{{H}^{+}}]=2\times {{10}^{-5}}\]. Find out the concentration of \[O{{H}^{-}}\] ions.
  A)
  \[5\times {{10}^{-10}}N\]
  done clear
  B)
  \[4\times {{10}^{-10}}N\] 
  done clear
  C)
   \[2\times {{10}^{-5}}N\]
  done clear
  D)
   \[9\times {{10}^{-4}}N\]
  done clear
  View Answer play_arrow

• question_answer61) Which of the following is added to chloroform to slow down its aerial oxidation in presence of light?
  A)
   Carbonyl chloride
  done clear
  B)
   Ethyl alcohol
  done clear
  C)
   Sodium hydroxide
  done clear
  D)
    Nitric acid
  done clear
  View Answer play_arrow

• question_answer62) Which of the products is formed when acetone is reacted with barium hydroxide solution?
  A)
  \[C{{H}_{3}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]
  done clear
  B)
  \[C{{H}_{3}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]
  done clear
  C)
   \[C{{H}_{3}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]
  done clear
  D)
   \[C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix}  OH \\  | \end{smallmatrix}}{\mathop{C}}}\,-\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix}  OH \\  | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer63) When acetaldehyde is heated with Fehling solution, a red precipitate is formed. Which of the following is that?
  A)
  \[C{{u}_{2}}O\]                
  done clear
  B)
  \[Cu\]
  done clear
  C)
   \[CuO\]                              
  done clear
  D)
   \[CuS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer64) What is the correct order of occurrence \[(%\] by weight) in air of\[Ne,\,\,\,Ar\]and\[Kr\]?
  A)
  \[Ne>Ar>Kr\]   
  done clear
  B)
  \[Ar>Ne>Kr\]
  done clear
  C)
  \[Ar>Kr>Ne\]   
  done clear
  D)
  \[Ne>Kr>Ar\]
  done clear
  View Answer play_arrow

• question_answer65) Which of the following compounds when heated with \[CO\] at \[{{150}^{o}}C\] and \[500\,\,atm\] pressure in presence of \[B{{F}_{3}}\] forms ethyl propionate?
  A)
  \[{{C}_{2}}{{H}_{5}}OH\]                              
  done clear
  B)
  \[C{{H}_{3}}OC{{H}_{3}}\]
  done clear
  C)
  \[{{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}\]                             
  done clear
  D)
   \[C{{H}_{3}}O{{C}_{2}}{{H}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer66) Identify the reaction for which\[\Delta H\ne \Delta E\].
  A)
  \[S(\text{rhombic})+{{O}_{2}}(g)\xrightarrow{{}}S{{O}_{2}}(g)\]
  done clear
  B)
  \[{{N}_{2}}(g)+{{O}_{2}}(g)\xrightarrow{{}}2NO(g)\]
  done clear
  C)
   \[{{H}_{2}}(g)+C{{l}_{2}}(g)\xrightarrow{{}}2HCl(g)\]
  done clear
  D)
  \[CO(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}C{{O}_{2}}(g)\]
  done clear
  View Answer play_arrow

• question_answer67) Hydrolysis of \[N{{O}_{3}}\] gives \[N{{H}_{3}}\] and\[X\]. Which of the following is\[X\]?
  A)
  \[HClO\]                              
  done clear
  B)
  \[HCl{{O}_{3}}\]
  done clear
  C)
   \[HOCl\]                             
  done clear
  D)
   \[HCl{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer68) What are the metal ions present in carnallite?
  A)
  \[Mg,\,\,K\]                      
  done clear
  B)
  \[Al,\,\,Na\]
  done clear
  C)
  \[Na,\,\,Mg\]                   
  done clear
  D)
   \[Zn,\,\,Mg\]
  done clear
  View Answer play_arrow

• question_answer69) Ethyl chloride reacts with sodium ethoxide to form a compound\[A\]. Which of the following reactions also yields\[A?\]
  A)
  \[{{C}_{2}}{{H}_{5}}Cl,\,\,KOH(alc.),\,\,\Delta \]
  done clear
  B)
  \[2{{C}_{2}}{{H}_{5}}OH,\,\,conc.{{H}_{2}}S{{O}_{4}},\,\,{{140}^{o}}C\]
  done clear
  C)
   \[{{C}_{2}}{{H}_{5}}Cl,\,\,Mg\](dry ether)
  done clear
  D)
   \[{{C}_{2}}{{H}_{2}}dil.\,\,{{H}_{2}}S{{O}_{4}},\,\,HgS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer70) The number of sigma and \[pi(\pi )\] bonds present in benzene respectively are
  A)
  \[12,\,\,6\]                         
  done clear
  B)
  \[6,\,\,6\]
  done clear
  C)
   \[6,\,\,12\]                        
  done clear
  D)
   \[12,\,\,3\]
  done clear
  View Answer play_arrow

• question_answer71) Edge length of a cube is \[400\,\,pm\], its body diagonal would be
  A)
  \[566\,\,pm\]                   
  done clear
  B)
  \[600\,\,pm\]
  done clear
  C)
   \[500\,\,pm\]                  
  done clear
  D)
   \[693\,\,pm\]
  done clear
  View Answer play_arrow

• question_answer72) The number of \[\alpha -\]particles emitted by\[_{84}R{{a}^{218}}{{\xrightarrow{{}}}_{82}}P{{b}^{206}}\]
  A)
  \[3\]                                     
  done clear
  B)
  \[4\]
  done clear
  C)
   \[6\]                                    
  done clear
  D)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer73) The \[IUPAC\] name of the following compound is\[C{{H}_{3}}-\underset{\begin{smallmatrix}  | \\  {{C}_{6}}{{H}_{5}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}-C{{H}_{3}}\]
  A)
   \[2-\]cyclohexylbutane
  done clear
  B)
   \[\sec -\]butylbenzene
  done clear
  C)
    \[3-\]cyclohexylbutane
  done clear
  D)
    \[2-\]phenylbutane
  done clear
  View Answer play_arrow

• question_answer74) The reaction of primary amine with chloroform and ethanolic solution of \[KOH\] is called
  A)
   Hermann's reaction
  done clear
  B)
   Reimer-Tiemann's reaction
  done clear
  C)
   Carbylamine reaction
  done clear
  D)
    Kolbe's reaction
  done clear
  View Answer play_arrow

• question_answer75) \[0.01\]mole of a non-electrolyte is dissolved in \[10\,\,g\] of water. The molality of the solution is
  A)
  \[0.1\,\,m\]                       
  done clear
  B)
   \[0.5\,\,m\]
  done clear
  C)
   \[1.0\,\,m\]                      
  done clear
  D)
   \[0.18\,\,m\]
  done clear
  View Answer play_arrow

• question_answer76) Atoms with same atomic number and different mass numbers are called
  A)
   isobars                
  done clear
  B)
   isomers
  done clear
  C)
    isotones                            
  done clear
  D)
    isotopes
  done clear
  View Answer play_arrow

• question_answer77) The shape of the orbital with the value of\[l=2\] and \[m=0\]is
  A)
   spherical
  done clear
  B)
   dumb-bell
  done clear
  C)
    trigonal planar
  done clear
  D)
    square-planar
  done clear
  View Answer play_arrow

• question_answer78) In the following, the element with the highest ionisation energy is
  A)
  \[[Ne]3{{s}^{2}}3{{p}^{1}}\]                       
  done clear
  B)
  \[[Ne]3{{s}^{2}}3{{p}^{3}}\]
  done clear
  C)
   \[[Ne]3{{s}^{2}}3{{p}^{2}}\]                      
  done clear
  D)
   \[[Ne]3{{s}^{2}}3{{p}^{4}}\]
  done clear
  View Answer play_arrow

• question_answer79) In the conversion of \[B{{r}_{2}}\] to\[BrO_{3}^{-}\], the oxidation number of \[Br\] changes from
  A)
   zero to\[+5\]                   
  done clear
  B)
   \[+1\]to\[+5\]
  done clear
  C)
    zero to\[-3\]                   
  done clear
  D)
  \[+2\]to\[+5\]
  done clear
  View Answer play_arrow

• question_answer80) Among the alkali metals cesium is the most reactive because
  A)
   its incomplete shell is nearest to the nucleus
  done clear
  B)
   it has a single electron in-the valence shell
  done clear
  C)
    it is the heaviest alkali metal
  done clear
  D)
    the outermost electron is more loosely bound than the outermost electron of the other alkali metals
  done clear
  View Answer play_arrow

• question_answer81) Which of the following represents the Lewis structure of \[{{N}_{3}}\] molecule?
  A)
  \[_{\text{X}}^{\text{X}}N\equiv N_{\text{X}}^{\text{X}}\]                         
  done clear
  B)
  \[_{\text{X}}^{\text{X}}\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,\equiv \overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}\]
  done clear
  C)
   \[_{\text{X}}^{\text{X}}\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}-\underset{\text{X}\,\,\text{X}}{\mathop{\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}}}\,\]                               
  done clear
  D)
   \[\underset{\text{X}\,\,\text{X}}{\mathop{_{\text{X}}^{\text{X}}\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,}}\,_{\text{X}}^{\text{X}}-\underset{\text{X}\,\,\text{X}}{\mathop{\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}}}\,\]
  done clear
  View Answer play_arrow

• question_answer82) Hydrogen bond is strongest in
  A)
  \[S-H\cdot \cdot \cdot O\]                         
  done clear
  B)
  \[O-H\cdot \cdot \cdot S\]
  done clear
  C)
   \[F-H\cdot \cdot \cdot F\]                         
  done clear
  D)
   \[O-H\cdot \cdot \cdot N\]
  done clear
  View Answer play_arrow

• question_answer83) The density of a gas is \[1.964\,\,d{{m}^{-3}}\] at \[273\,\,K\]and\[76\,\,cm\]\[Hg\]. The gas is
  A)
  \[C{{H}_{4}}\]                                   
  done clear
  B)
  \[{{C}_{2}}{{H}_{6}}\]
  done clear
  C)
   \[C{{O}_{2}}\]                                  
  done clear
  D)
   \[Xe\]
  done clear
  View Answer play_arrow

• question_answer84) The shape of \[PC{{l}_{3}}\] molecule is
  A)
   trigonal bipyramidal
  done clear
  B)
   tetrahedral
  done clear
  C)
    pyramidal
  done clear
  D)
    square planar
  done clear
  View Answer play_arrow

• question_answer85) The concentration of a reactant \[X\] decreases from \[0.1\,\,M\] to \[0.005\,\,M\] in\[40\,\,\min \]. If the reaction follows first order kinetics, the rate of the reaction when the concentration of \[X\] is \[0.01\,\,M\] will be
  A)
  \[1.73\times {{10}^{-4}}M\,\,{{\min }^{-1}}\]
  done clear
  B)
  \[3.47\times {{10}^{-4}}M\,\,{{\min }^{-1}}\]
  done clear
  C)
   \[3.47\times {{10}^{-5}}M\,\,{{\min }^{-1}}\]
  done clear
  D)
   \[7.5\times {{10}^{-4}}M\,\,{{\min }^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer86) Which of the following does not conduct electricity?
  A)
   Fused\[NaCl\]                 
  done clear
  B)
   Solid\[NaCl\]
  done clear
  C)
    Brine solution                 
  done clear
  D)
    Copper
  done clear
  View Answer play_arrow

• question_answer87) Solubility product of a salt \[AB\] is \[1\times {{10}^{-8}}{{M}^{2}}\] in a solution in which the concentration of \[{{A}^{+}}\] ions is\[{{10}^{-3}}M\]. The salt will precipitate when the concentration of \[{{B}^{-}}\] ions is kept
  A)
   between\[{{10}^{-8}}M\]to\[{{10}^{-7}}M\]
  done clear
  B)
   between\[{{10}^{-7}}M\]to\[{{10}^{-8}}M\]
  done clear
  C)
   \[>{{10}^{-5}}M\]
  done clear
  D)
   \[<{{10}^{-8}}M\]
  done clear
  View Answer play_arrow

• question_answer88) The \[pH\] of \[{{10}^{-8}}M\,\,HCl\] Solution is
  A)
  \[8\]
  done clear
  B)
    more than\[8\]
  done clear
  C)
    between \[6\] and \[7\]
  done clear
  D)
    slightly more than\[7\]
  done clear
  View Answer play_arrow

• question_answer89) For a reaction to be spontaneous, at all temperatures
  A)
   \[\Delta G\] and \[\Delta H\] should be negative
  done clear
  B)
    \[\Delta G\] and \[\Delta H\] should be positive
  done clear
  C)
   \[\Delta G=\Delta S=0\]
  done clear
  D)
  \[\Delta H<\Delta G\]
  done clear
  View Answer play_arrow

• question_answer90) Which of the following electrolytes will have maximum flocculation value for\[Fe{{(OH)}_{3}}\]sol?
  A)
  \[NaCl\]                              
  done clear
  B)
   \[N{{a}_{2}}S\]
  done clear
  C)
   \[{{(N{{H}_{4}})}_{3}}P{{O}_{4}}\]                          
  done clear
  D)
   \[{{K}_{2}}S{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer91) What is the order of a reaction which has a rate expression\[rate=k{{[A]}^{3/2}}{{[B]}^{-1}}\]?
  A)
  \[\frac{3}{2}\]                                   
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[0\]                                    
  done clear
  D)
   \[\frac{4}{2}\]
  done clear
  View Answer play_arrow

• question_answer92) Inductive effect involves
  A)
   displacement of \[\sigma -\]electrons
  done clear
  B)
   delocalisation of \[\pi -\]electrons
  done clear
  C)
    delocalisation of \[\sigma -\]electrons
  done clear
  D)
    displacement of \[\pi -\]electrons
  done clear
  View Answer play_arrow

• question_answer93) Which of the following compound is expected to be optically active?
  A)
  \[{{(C{{H}_{3}})}_{2}}CHCHO\]  
  done clear
  B)
  \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CHO\]
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}CHBrCHO\]          
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}CB{{r}_{2}}CHO\]
  done clear
  View Answer play_arrow

• question_answer94) The catalyst used in the preparation of an alkyl chloride by the action of dry HC1 on an alcohol is
  A)
   anhydrous\[AlC{{l}_{3}}\]          
  done clear
  B)
   \[FeC{{l}_{3}}\]
  done clear
  C)
    anhydrous\[ZnC{{l}_{2}}\]        
  done clear
  D)
   \[Cu\]
  done clear
  View Answer play_arrow

• question_answer95) By heating phenol with chloroform in alkali, it is converted into
  A)
   salicylic acid      
  done clear
  B)
    salicylaldehyde
  done clear
  C)
    anisole               
  done clear
  D)
    phenyl benzoate
  done clear
  View Answer play_arrow

• question_answer96) Which of the following does not give benzoic acid on hydrolysis?
  A)
   Phenyl cyanide
  done clear
  B)
   Benzoyl chloride
  done clear
  C)
   Benzyl chloride               
  done clear
  D)
    Methyl benzoate
  done clear
  View Answer play_arrow

• question_answer97) Glucose contains in addition to aldehyde group
  A)
   one secondary \[-OH\] and four primary\[-OH\] groups
  done clear
  B)
   one primary \[-OH\] and four secondary \[-OH\] groups
  done clear
  C)
    two primary \[-OH\] and three secondary\[-OH\] groups
  done clear
  D)
    three primary \[-OH\] and two secondary \[-OH\] groups
  done clear
  View Answer play_arrow

• question_answer98) The formula mass of Mohr's salt is\[392\]. The iron present in it is oxidised by \[KMn{{O}_{4}}\] in acid medium. The equivalent mass of Mohr's salt is
  A)
  \[392\]
  done clear
  B)
  \[31.6\]
  done clear
  C)
   \[278\]
  done clear
  D)
   \[156\]
  done clear
  View Answer play_arrow

• question_answer99) The brown ring test for nitrates depends on
  A)
   the reduction of nitrate to nitric oxide
  done clear
  B)
    oxidation of nitric oxide to nitrogen dioxide
  done clear
  C)
    reduction of ferrous sulphate to iron
  done clear
  D)
    oxidising action of sulphuric acid
  done clear
  View Answer play_arrow

• question_answer100) Which of the following solutions will exhibit highest boiling point?
  A)
  \[0.01\,\,M\,\,N{{a}_{2}}S{{O}_{4}}(aq)\]
  done clear
  B)
   \[0.01\,\,M\,\,KN{{O}_{3}}(aq)\]
  done clear
  C)
   \[0.015\,\,M\,\,urea(aq)\]
  done clear
  D)
  \[0.015\,\,M\,\,glucose(aq)\]
  done clear
  View Answer play_arrow

• question_answer101) \[\int_{0}^{\pi /2}{\frac{x\sin x\cdot \cos x}{{{\cos }^{4}}x+{{\sin }^{4}}x}}dx\]is equal to
  A)
  \[\frac{{{\pi }^{2}}}{8}\]                               
  done clear
  B)
  \[\frac{{{\pi }^{2}}}{16}\]
  done clear
  C)
  \[1\]                                     
  done clear
  D)
  \[0\]
  done clear
  View Answer play_arrow

• question_answer102) Equation of the tangent to the hyperbola\[2{{x}^{2}}-3{{y}^{2}}=6\]. Which is parallel to the line \[y-3x-4=0\]is
  A)
  \[y=3x+8\]                         
  done clear
  B)
  \[y=3x-8\]
  done clear
  C)
  \[y=3x+2\]                         
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer103) If the coefficient of correlation between two variables is\[0.32\], covariance is \[8\] and variance of \[x\] is\[25\], then variance of \[y\] is
  A)
  \[36\]                                   
  done clear
  B)
  \[25\]
  done clear
  C)
  \[64\]                                   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer104) Ten coins are thrown simultaneously, the probability of getting at least \[7\] heads is
  A)
  \[\frac{63}{256}\]                                            
  done clear
  B)
  \[\frac{121}{172}\]
  done clear
  C)
  \[\frac{113}{512}\]                                         
  done clear
  D)
  \[\frac{11}{64}\]
  done clear
  View Answer play_arrow

• question_answer105) When \[{{b}_{yx}}=0.03\] and\[{{b}_{xy}}=0.3\], then \[r\] is equal to approximately
  A)
  \[0.003\]                             
  done clear
  B)
  \[0.095\]
  done clear
  C)
  \[0.3\]                                  
  done clear
  D)
  \[-0.3\]
  done clear
  View Answer play_arrow

• question_answer106) Use Simpson's\[\frac{1}{3}\]rule to find the value of \[\int_{1}^{5}{f(x)}\,\,dx\]given

  \[x\]	\[1\]	\[2\]	\[3\]	\[4\]	\[4\]
  \[y\]	\[10\]	\[50\]	\[70\]	\[80\]	\[100\]

  A)
  \[140.88\]                           
  done clear
  B)
  \[256.66\]
  done clear
  C)
  \[160.26\]                           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer107) The feasible region represented by\[{{x}_{1}}+{{x}_{2}}\le 1\],\[-3{{x}_{1}}+{{x}_{2}}\ge 3,\,\,({{x}_{1}},\,\,{{x}_{2}}\ge 0)\]is
  A)
   a polygon          
  done clear
  B)
   a singleton set
  done clear
  C)
   empty set        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer108) The points on the curve \[{{x}^{2}}=2y\] which are closest to the point \[(0,\,\,5)\] are
  A)
  \[(2,\,\,2),\,\,(-2,\,\,2)\]
  done clear
  B)
  \[(2\sqrt{2},\,\,4),\,\,(-2\sqrt{2},\,\,4)\]
  done clear
  C)
  \[(\sqrt{6},\,\,3),\,\,(-\sqrt{6},\,\,3)\]
  done clear
  D)
  \[(2\sqrt{3},\,\,6),\,\,(-2\sqrt{3},\,\,6)\]
  done clear
  View Answer play_arrow

• question_answer109) Solve\[\left( \frac{dy}{dx} \right)\tan y=\sin (x+y)+\sin (x-y)\]
  A)
  \[\sec x-\frac{1}{2}\tan y=c\]
  done clear
  B)
  \[\log \sin (x+y)=c\]
  done clear
  C)
  \[\sec x+\tan y=c\]
  done clear
  D)
  \[\sec y+2\cos x=c\]
  done clear
  View Answer play_arrow

• question_answer110) \[\overset{\to }{\mathop{\mathbf{A}}}\,\cdot \{(\overset{\to }{\mathop{\mathbf{B}}}\,+\overset{\to }{\mathop{\mathbf{C}}}\,)\times (\overset{\to }{\mathop{\mathbf{A}}}\,+\overset{\to }{\mathop{\mathbf{B}}}\,+\overset{\to }{\mathop{\mathbf{C}}}\,)\}\]equals
  A)
  \[[\overset{\to }{\mathop{\mathbf{A}}}\,\overset{\to }{\mathop{\mathbf{B}}}\,\overset{\to }{\mathop{\mathbf{C}}}\,]\]                     
  done clear
  B)
  \[[\overset{\to }{\mathop{\mathbf{B}}}\,\overset{\to }{\mathop{\mathbf{A}}}\,\overset{\to }{\mathop{\mathbf{C}}}\,]\]
  done clear
  C)
  \[0\]                                     
  done clear
  D)
  \[1\]
  done clear
  View Answer play_arrow

• question_answer111) If\[y=\frac{{{y}^{3}}}{3}+\frac{{{y}^{5}}}{5}+...\infty =2\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+...\infty  \right]\] then value of \[y\] is
  A)
  \[\frac{x}{1-{{x}^{2}}}\]                
  done clear
  B)
  \[\frac{2x}{1+{{x}^{2}}}\]
  done clear
  C)
  \[\frac{1-{{x}^{2}}}{2x}\]                             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer112) If\[x=\frac{1}{2}(\sqrt{3}+i)\], then \[{{x}^{3}}\] is equal to
  A)
  \[1\]                                     
  done clear
  B)
  \[-1\]
  done clear
  C)
  \[i\]                                       
  done clear
  D)
  \[-i\]
  done clear
  View Answer play_arrow

• question_answer113) if the complex numbers \[\sin x+i\cos 2x\] and \[\cos x-i\sin 2x\] are complex conjugate to each other, then the value of \[x\] is
  A)
  \[\frac{\pi }{4}\]                                              
  done clear
  B)
  \[\frac{\pi }{8}\]
  done clear
  C)
  \[\frac{3\pi }{4}\]                                            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer114) \[\underset{x\to {{2}^{+}}}{\mathop{\lim }}\,\frac{|x-2|}{x-2}\]is equal to
  A)
  \[-1\]                                    
  done clear
  B)
  \[1\]
  done clear
  C)
  \[2\]                                     
  done clear
  D)
  \[-2\]
  done clear
  View Answer play_arrow

• question_answer115) If\[\left| \begin{matrix}    x & {{x}^{2}} & 1+{{x}^{3}}  \\    y & {{y}^{2}} & 1+{{y}^{3}}  \\    z & {{z}^{2}} & 1+{{z}^{3}}  \\ \end{matrix} \right|=0\], then
  A)
  \[z=xy\]                              
  done clear
  B)
  \[z=\frac{1}{xy}\]
  done clear
  C)
  \[z=-\frac{1}{xy}\]                          
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer116) \[{{\cos }^{4}}\frac{\pi }{8}+{{\cos }^{4}}\frac{3\pi }{8}+{{\cos }^{4}}\frac{5\pi }{8}+{{\cos }^{4}}\frac{7\pi }{8}\]is equal to
  A)
  \[\frac{3}{2}\]                                   
  done clear
  B)
  \[-\frac{2}{3}\]
  done clear
  C)
  \[-1\]                                    
  done clear
  D)
  \[1\]
  done clear
  View Answer play_arrow

• question_answer117) In a triangle\[ABC\], if\[\tan \frac{A}{2}=\frac{5}{6}\]and\[\tan \frac{B}{2}=\frac{20}{37}\], then \[a+c\]is equal to
  A)
  \[b\]                                     
  done clear
  B)
  \[2b\]
  done clear
  C)
  \[3b\]                                   
  done clear
  D)
  \[4b\]
  done clear
  View Answer play_arrow

• question_answer118) Number of solutions of the equation \[\tan x+\sec x=2\cos x\] lying in the interval\[[0,\,\,2\pi ]\]is
  A)
  \[0\]                                     
  done clear
  B)
  \[1\]
  done clear
  C)
  \[2\]                                     
  done clear
  D)
  \[3\]
  done clear
  View Answer play_arrow

• question_answer119) Equation of the pair of straight lines bisecting the angles between the lines represented by \[a{{x}^{2}}+hxy+b{{y}^{2}}=0\]is
  A)
  \[\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{2xy}{h}\]
  done clear
  B)
  \[\frac{{{x}^{2}}+{{y}^{2}}}{a+b}=\frac{xy}{2h}\]
  done clear
  C)
  \[\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{xy}{h}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer120) The equation of circle which touches the axes and the line \[\frac{x}{3}+\frac{y}{4}=1\] and whose centre lies in the first quadrant is\[{{x}^{2}}+{{y}^{2}}-2cx-2cy+{{c}^{2}}=0\]. Then, \[c\] is equal to
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[3\]                                     
  done clear
  D)
  .\[6\]
  done clear
  View Answer play_arrow

• question_answer121) Angle between any two diagonals of a cube is
  A)
  \[\frac{\pi }{3}\]                                              
  done clear
  B)
  \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]
  done clear
  C)
  \[{{\cos }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]                 
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer122) If`\[{{a}_{1}},\,\,{{a}_{2}},\,\,{{a}_{3}},...,{{a}_{n}}\]are in\[AP\]. Where\[{{a}_{i}}>0\]for all\[i\]. Find the sum of series \[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\frac{1}{\sqrt{{{a}_{3}}+{{a}_{4}}}}+...\]\[+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}\]
  A)
  \[\frac{n+1}{\sqrt{{{a}_{1}}+{{a}_{n}}}}\]                             
  done clear
  B)
  \[\frac{n-1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\]
  done clear
  C)
  \[\frac{n+1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]               
  done clear
  D)
  \[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]
  done clear
  View Answer play_arrow

• question_answer123) The ratio in which the \[xy-\]plane meets the line joining the points \[(-3,\,\,4,\,\,-8)\] and \[(5,\,\,-6,\,\,4)\]is
  A)
  \[2:3\]
  done clear
  B)
  \[2:1\]
  done clear
  C)
  \[4:5\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer124) The unit vector perpendicular to each of the vectors\[3\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+2\widehat{\mathbf{k}}\], and\[2\widehat{\mathbf{i}}-2\widehat{\mathbf{j}}+4\widehat{\mathbf{k}}\]
  A)
  \[\frac{\widehat{\mathbf{i}}-\widehat{\mathbf{j}}-\widehat{\mathbf{k}}}{\sqrt{3}}\]                 
  done clear
  B)
  \[\frac{\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}}}{\sqrt{3}}\]
  done clear
  C)
  \[\frac{\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}}}{\sqrt{3}}\]                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer125) \[y={{\tan }^{-1}}\frac{\sqrt{(1+{{x}^{2}})}+\sqrt{(1-{{x}^{2}})}}{\sqrt{(1+{{x}^{2}})}-\sqrt{(1-{{x}^{2}})}}\], then\[\frac{dy}{dx}\]is equal to
  A)
  \[\frac{1}{\sqrt{1+{{x}^{2}}}}\]                 
  done clear
  B)
  \[-\frac{1}{2}\]
  done clear
  C)
  \[-\frac{x}{\sqrt{(1-{{x}^{4}})}}\]                             
  done clear
  D)
  \[\frac{x\sqrt{1+{{x}^{2}}}}{1-{{x}^{4}}}\]
  done clear
  View Answer play_arrow

• question_answer126) \[\overrightarrow{\mathbf{a}},\,\,\overrightarrow{\mathbf{b}},\,\,\overrightarrow{\mathbf{c}}\] are coplanar vectors, then which of the following is not correct?
  A)
  \[\overrightarrow{\mathbf{a}}\cdot (\overrightarrow{\mathbf{b}}\times \overrightarrow{\mathbf{c}})=0\]
  done clear
  B)
  \[\overrightarrow{\mathbf{a}}\times (\overrightarrow{\mathbf{b}}\times \overrightarrow{\mathbf{c}})=0\]
  done clear
  C)
  \[[\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}},\,\,\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}},\,\,\overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{a}}]=0\]
  done clear
  D)
  \[\overrightarrow{\mathbf{a}}=p\overrightarrow{\mathbf{b}}+q\overrightarrow{\mathbf{c}}\]
  done clear
  View Answer play_arrow

• question_answer127) If\[|A|\ne 0\]and \[A\] is of order n, then\[adj\,\,(adj\,\,A)\]is equal to
  A)
  \[|A{{|}^{n}}\]                                 
  done clear
  B)
  \[|A{{|}^{2}}\]
  done clear
  C)
  \[|A{{|}^{n-1}}I\]                           
  done clear
  D)
  \[|A{{|}^{n-2}}\cdot A\]
  done clear
  View Answer play_arrow

• question_answer128) \[\int{\frac{x+\sin x}{1+\cos x}}dx\]is equal to
  A)
  \[x\log (1+\cos x)+c\]
  done clear
  B)
  \[\frac{1}{x}\log (1+\cos x)+c\]
  done clear
  C)
  \[x\tan \frac{x}{2}+c\]
  done clear
  D)
  \[{{x}^{2}}{{\tan }^{-1}}\frac{x}{2}+c\]
  done clear
  View Answer play_arrow

• question_answer129) Find the differential equation of curves \[y=A{{e}^{x}}+B{{e}^{-x}}\] for different values of \[A\] and \[B\]
  A)
  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-2y=0\]                    
  done clear
  B)
  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=y\]
  done clear
  C)
  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=4y+3\]                   
  done clear
  D)
  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]
  done clear
  View Answer play_arrow

• question_answer130) Solve\[\frac{dy}{dx}=\frac{{{y}^{2}}}{xy-{{x}^{2}}}\]
  A)
  \[y=c{{e}^{x/y}}\]                           
  done clear
  B)
  \[y=c{{e}^{-y/x}}+x\]
  done clear
  C)
  \[y=c{{e}^{y/x}}\]                           
  done clear
  D)
  \[xy=c{{e}^{y/x}}\]
  done clear
  View Answer play_arrow

• question_answer131) If\[\underset{x\to a}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{x}^{a}}}{{{x}^{x}}-{{a}^{a}}}=-1\], then
  A)
  \[a=1\]                                
  done clear
  B)
  \[a=0\]
  done clear
  C)
  \[a=e\]                
  done clear
  D)
  \[a=\frac{1}{e}\]
  done clear
  View Answer play_arrow

• question_answer132) If four digits are taken from the digits \[1,\,\,2,\,\,3,\,\,4,\] \[5,\,\,6,\,\,7\]. The probability that the sum of digits is less than\[12\], is
  A)
  \[\frac{3}{25}\]                                
  done clear
  B)
  \[\frac{4}{35}\]
  done clear
  C)
  \[\frac{2}{35}\]                                
  done clear
  D)
  \[\frac{1}{35}\]
  done clear
  View Answer play_arrow

• question_answer133) The probability of happening exactly one of a two events \[A\] and \[B\] is
  A)
  \[P(A)+P(B)-2P(A\cap B)\]
  done clear
  B)
  \[P(A)+P(B)-P(A\cap B)\]
  done clear
  C)
  \[P(A)-P(B)\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer134) Solve\[x\cos x\left( \frac{dy}{dx} \right)+y(x\sin x+\cos x)=1\]
  A)
  \[y=x\tan x+\sin x+c\]
  done clear
  B)
  \[x=y\tan x+c\]
  done clear
  C)
  \[yx\sec x=\tan x+c\]
  done clear
  D)
  \[xy\cos x=x+c\]
  done clear
  View Answer play_arrow

• question_answer135) If the equation\[({{a}^{2}}+4a+3){{x}^{2}}+({{a}^{2}}-a-2)x\]\[+a(a+1)=0\]has more than two roots, then value of \[a\] is
  A)
  \[0\]                                     
  done clear
  B)
  \[1\]
  done clear
  C)
  \[-1\]                                    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer136) \[{{S}_{1}},\,\,{{S}_{2}}\]and \[{{S}_{3}}\] are the sums of\[n,\,\,2n\] and \[3n\]terms of an arithmetic progression respectively, then
  A)
  \[{{S}_{2}}=3{{S}_{3}}-2{{S}_{1}}\]
  done clear
  B)
  \[{{S}_{3}}=4({{S}_{1}}+{{S}_{2}})\]
  done clear
  C)
  \[{{S}_{3}}=3({{S}_{2}}-{{S}_{1}})\]
  done clear
  D)
  \[{{S}_{3}}=2({{S}_{2}}+{{S}_{1}})\]
  done clear
  View Answer play_arrow

• question_answer137) If\[^{n}{{C}_{r-1}}=36,\,{{\,}^{n}}{{C}_{r}}=84\]and\[^{n}{{C}_{r+1}}=126\], then \[n\] is equal to
  A)
  \[8\]                                     
  done clear
  B)
  \[9\]
  done clear
  C)
  \[10\]                                   
  done clear
  D)
  \[11\]
  done clear
  View Answer play_arrow

• question_answer138) The sides \[AB,\,\,BC,\,\,CA\] of triangle \[ABC\] have \[3,\,\,\,4\] and \[5\] interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices
  A)
  \[201\]                                 
  done clear
  B)
  \[120\]
  done clear
  C)
  \[205\]                                 
  done clear
  D)
  \[435\]
  done clear
  View Answer play_arrow

• question_answer139) Coefficient of \[{{x}^{n}}\] in the expansion of\[1+\frac{a+bx}{1!}+\frac{{{(a+bx)}^{2}}}{2!}+\frac{{{(a+bx)}^{3}}}{3!}+...\]is
  A)
  \[\frac{{{e}^{a}}{{b}^{n}}}{n!}\]                               
  done clear
  B)
  \[\frac{{{(b\cdot a)}^{n}}}{n}\]
  done clear
  C)
  \[\frac{{{e}^{b}}\cdot {{b}^{n}}}{(n-1)!}\]                            
  done clear
  D)
  \[\frac{{{a}^{n}}\cdot {{b}^{n-1}}}{n!}\]
  done clear
  View Answer play_arrow

• question_answer140) \[\frac{{{C}_{0}}}{1}+\frac{{{C}_{2}}}{3}+\frac{{{C}_{4}}}{5}+\frac{{{C}_{6}}}{7}+...\]is equal to
  A)
  \[\frac{{{2}^{n-1}}}{n-1}\]                                           
  done clear
  B)
  \[\frac{{{2}^{n+1}}}{n+3}\]
  done clear
  C)
  \[\frac{{{2}^{n}}}{n+1}\]                              
  done clear
  D)
  \[\frac{{{2}^{n-2}}}{n}\]
  done clear
  View Answer play_arrow

• question_answer141) The equation of the parabola having the focus at the point \[(3,\,\,-1)\] and the vertex at \[(2,\,\,-1)\] is
  A)
  \[{{y}^{2}}-4x-2y+9=0\]
  done clear
  B)
  \[{{y}^{2}}+4x+2y-9=0\]
  done clear
  C)
  \[{{y}^{2}}-4x+2y+9=0\]
  done clear
  D)
  \[{{y}^{2}}+4x-2y+9=0\]
  done clear
  View Answer play_arrow

• question_answer142) The equation of lines joining the origin to the points of intersection of \[y=x+3\] and \[4{{x}^{2}}+4{{y}^{2}}=1\] is
  A)
  \[36({{x}^{2}}+{{y}^{2}})={{(x-y)}^{2}}\]
  done clear
  B)
  \[12({{x}^{2}}+{{y}^{2}})={{(x+y)}^{2}}\]
  done clear
  C)
  \[9({{x}^{2}}+{{y}^{2}})=4{{(x+y)}^{2}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer143) The angle of elevation of a jet fighter from a point \[A\] on the ground is\[{{60}^{o}}\]. After a flight of\[10\,\,s\], the angle of elevation changes to\[{{30}^{o}}\]. If the jet is flying at a speed of\[432\,\,km/h\]. Find the constant height at which the jet is flying.
  A)
  \[200\sqrt{3}m\]                             
  done clear
  B)
  \[400\sqrt{3}m\]
  done clear
  C)
  \[600\sqrt{3}m\]                             
  done clear
  D)
  \[800\sqrt{3}m\]
  done clear
  View Answer play_arrow

• question_answer144) Which is incorrect?
  A)
  \[(AB)'=B'A'\]   
  done clear
  B)
  \[{{(AB)}^{\theta }}={{B}^{\theta }}{{A}^{\theta }}\]
  done clear
  C)
  \[\overline{AB}=\bar{B}\bar{A}\]                            
  done clear
  D)
  \[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer145) Find the equation of plane through the line\[\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-4}{5}\]and parallel to \[x-\]axis.
  A)
  \[2x+3y+5z=1\]
  done clear
  B)
  \[2x-5y=4\]
  done clear
  C)
  \[5y-3z-3=0\]    
  done clear
  D)
  \[3y+4z=0\]
  done clear
  View Answer play_arrow

• question_answer146) Find the moment of the force\[5\widehat{\mathbf{i}}+10\widehat{\mathbf{j}}+16\widehat{\mathbf{k}}\] acting at the point\[2\widehat{\mathbf{i}}-7\widehat{\mathbf{j}}+10\widehat{\mathbf{k}}\], about the point \[-5\widehat{\mathbf{i}}+6\widehat{\mathbf{j}}-10\widehat{\mathbf{k}}\]
  A)
  \[41\widehat{\mathbf{i}}-8\widehat{\mathbf{j}}+55\widehat{\mathbf{k}}\]
  done clear
  B)
  \[-408\widehat{\mathbf{i}}-12\widehat{\mathbf{j}}+135\widehat{\mathbf{k}}\]
  done clear
  C)
  \[-36\widehat{\mathbf{i}}+14\widehat{\mathbf{j}}-35\widehat{\mathbf{k}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer147) Find the equation of tangents to the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], which cut off equal intercepts or the axes.
  A)
  \[y=\sqrt{3}x\pm \sqrt{3{{a}^{2}}+{{b}^{2}}}\]
  done clear
  B)
  \[y=\pm x\mp \sqrt{{{a}^{2}}+{{b}^{2}}}\]
  done clear
  C)
  \[y=\sqrt{3}\pm \sqrt{{{a}^{2}}+3{{b}^{2}}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer148) A square matrix \[A\] is called an orthogonal matrix if
  A)
  \[A\bar{A}=I\]                  
  done clear
  B)
  \[AA'=I\]
  done clear
  C)
  \[A{{A}^{\theta }}=I\]                   
  done clear
  D)
  \[{{A}^{2}}=I\]
  done clear
  View Answer play_arrow

• question_answer149) The value of \['c'\] Rolle's theorem for \[f(x)={{e}^{x}}\sin x\]in\[[0,\,\,\pi ]\]is given by
  A)
  \[\frac{\pi }{4}\]                                              
  done clear
  B)
  \[\frac{3\pi }{4}\]
  done clear
  C)
  \[\frac{5\pi }{6}\]                                            
  done clear
  D)
  \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer150) \[\int_{-a}^{a}{x\sqrt{({{a}^{2}}-{{x}^{2}})}}dx\]is equal to
  A)
  \[\frac{\pi }{4}\]                              
  done clear
  B)
  \[\frac{\pi }{3}\]
  done clear
  C)
  \[\frac{\pi }{8}\]                                              
  done clear
  D)
  \[0\]
  done clear
  View Answer play_arrow