Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2006

done CET - Karnataka Engineering Solved Paper-2006 Total Questions - 180

• 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
  done clear
  B)
   directly as the width of the slit
  done clear
  C)
   directly as the distance between the slit and the screen
  done clear
  D)
   inversely as the size of the source from which the slit is illuminated
  done clear
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• question_answer3) An unpolarised beam of intensity \[{{I}_{0}}\] is incident on a pair of nicols 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)
   \[{{I}_{0}}/2\]
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  C)
   \[{{I}_{0}}/4\]                                  
  done clear
  D)
   \[{{I}_{0}}/8\]
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• question_answer4) Look at the graphs (a) to (d) carefully and indicate which of these possibly represents one dimensional motion of a particle?
  A)
                 
  done clear
  B)
   
  done clear
  C)
                
  done clear
  D)
    
  done clear
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• question_answer5) A cyclist starts from the centre 0 of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference and returns to the centre along O as shown in the figure. If the round trip takes 10 min, the net displacement and average speed of the cyclist (in meters and kilometre per hour) are:
  A)
   \[0,1\]                                 
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  B)
   \[\frac{\pi +4}{2},0\]
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  C)
   \[21.4,\frac{\pi +4}{2}\]                               
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  D)
   \[0,21.4\]
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• question_answer6) 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 mageneric flux occuring due to the passage of aircraft
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  D)
   vibration created by the passage of aircraft
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• question_answer7) 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_answer8) 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_answer9) 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                                    
  done clear
  D)
   8.5 V
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• question_answer10) 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 ammeter 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
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  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
  done clear
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• question_answer11) The electron dirft 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
  done clear
  D)
   the electron number density of the conductor is enormous
  done clear
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• question_answer12) 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 tesia) is: (assume \[g=9.8\text{ }m{{s}^{-2}}\])
  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_answer13) In the circuit shown the value of \[I\] in ampere is:
  A)
   1                                            
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  B)
   0.60
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  C)
   0.4                                        
  done clear
  D)
   1.5
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• question_answer14) 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_answer15) 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_answer16) A comb run through ones 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 in the paper get polarised by the charged comb
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  D)
   the comb possesses magnetic properties
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• question_answer17) The top of the atmosphere is about 400 kv with respect to the surface of the earth corresponding to an electric field that decreases with altitude. Near the surface the earth, the field is about \[100\,\,V{{m}^{-1}}\] do not get an electric shock as we step out of our house into the open house because (assume the house to be a steel cage so that there is no field inside)
  A)
   there is a potential difference between our body and the ground
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  B)
   \[100\,\,V{{m}^{-1}}\] is not a high electric field so that we do not feel the shock
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  C)
   our body and the ground forms a equipotential surface
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  D)
   the dry atmosphere is not a conductor
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• question_answer18) The specific charge of a proton is\[9.6\times {{10}^{7}}Ck{{g}^{-1}}\]. The specific charge of alpha particle will be:
  A)
   \[9.6\times {{10}^{7}}C\text{ }k{{g}^{-1}}\]        
  done clear
  B)
   \[19.2\times {{10}^{7}}C\text{ }k{{g}^{-1}}\]
  done clear
  C)
   \[4.8\times {{10}^{7}}C\text{ }k{{g}^{-1}}\]        
  done clear
  D)
   \[2.4\times {{10}^{7}}C\text{ }k{{g}^{-1}}\]
  done clear
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• question_answer19) 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_answer20) 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_answer21) 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_answer22) 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_answer23) Identify the operation performed by the circuit given below:
  A)
   NOT                                     
  done clear
  B)
   AND
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  C)
   OR                                        
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  D)
   NAND
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• question_answer24) 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_answer25) 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_answer26) 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                                 
  done clear
  D)
   0.04 m
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• question_answer27) White light is incident on one of the refracting surfaces of a prism of angle \[{{5}^{o}}\]. If the refractring indices for red and blue colours are 1.641 and 1.659 respectively, the angular separation between these two colours when they emerge out of the prism is:
  A)
   \[{{0.9}^{o}}\]                                 
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  B)
   \[{{0.9}^{o}}\]
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  C)
   \[{{1.8}^{o}}\]                                 
  done clear
  D)
   \[{{1.2}^{o}}\]
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• question_answer28) For a given lens, the magnification was found to be twice as large as when the object was 0.15 m distant from it as when the distance was 0.2 m. The focal length of the lens is:
  A)
   1.5 m                                   
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  B)
   0.20 m
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  C)
   0.10 m                                 
  done clear
  D)
   0.05 m
  done clear
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• question_answer29) 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_answer30) A thin prism \[{{P}_{1}}\] with angle \[{{4}^{o}}\] made from a glass of refractive index 1.54 is combined with another thin prism \[{{P}_{2}}\] made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism \[{{P}_{2}}\]is:
  A)
   \[{{5.33}^{o}}\]                               
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  B)
   \[{{4}^{o}}\]
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  C)
   \[{{3}^{o}}\]                                     
  done clear
  D)
   \[{{2.6}^{o}}\]
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• question_answer31) If white light is used in the Newtons 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
  done clear
  B)
   \[{{180}^{o}}\] change of phase in one of the reflected waves
  done clear
  C)
   \[{{145}^{o}}\] change of phase in one of the reflected waves
  done clear
  D)
   \[{{45}^{o}}\] change of phase in one the reflected waves
  done clear
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• question_answer32) Specific rotation of sugar solution is \[0.5\text{ }deg\text{ }{{m}^{2}}/kg.\text{ }200\text{ }kg{{m}^{-3}}\] of impure sugar solution is taken in a sample polarimeter tube of length 20 cm and optical rotation is found to be \[{{19}^{o}}\]. The percentage of purity of sugar is:
  A)
   20 %                                     
  done clear
  B)
   80 %
  done clear
  C)
   95 %                                     
  done clear
  D)
   89 %
  done clear
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• question_answer33) A simple pendulum has a length \[l\] and the mass of the bob is m. The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by:
  A)
   \[2\pi \sqrt{\frac{l}{g}}\]                             
  done clear
  B)
   \[2\pi \sqrt{\frac{l}{\sqrt{g+\frac{qE}{m}}}}\]
  done clear
  C)
   \[2\pi \sqrt{\frac{l}{\sqrt{g-\frac{qE}{m}}}}\]
  done clear
  D)
   \[2\pi \sqrt{\frac{l}{\sqrt{{{g}^{2}}+{{\left( \frac{qE}{m} \right)}^{2}}}}}\]
  done clear
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• question_answer34) A gang capacitor is formed by interlocking a number of plates as, shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is \[5\text{ }c{{m}^{2}}\]. The capacity of the unit is:
  A)
                   1.06 pF                                
  done clear
  B)
   4 pF
  done clear
  C)
   6.36 pF                                
  done clear
  D)
   12.72 pF
  done clear
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• question_answer35) A satellite in a circular orbit of radius R has a period of 4 h. Another satellite with orbital radius 3 R around the same planet will have a period (in hours):
  A)
   16                                         
  done clear
  B)
   4
  done clear
  C)
   \[4\sqrt{27}\]                  
  done clear
  D)
   \[4\sqrt{8}\]
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• question_answer36) 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
  done clear
  D)
   the heat gained from the environment is low
  done clear
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• question_answer37) The unit of Stefans constant is:
  A)
   \[W{{m}^{-2}}{{K}^{-1}}\]                          
  done clear
  B)
  \[Wm\,{{K}^{-4}}\]
  done clear
  C)
   \[W{{m}^{-2}}{{K}^{-4}}\]                          
  done clear
  D)
   \[N{{m}^{-2}}{{K}^{-4}}\]
  done clear
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• question_answer38) 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                                         
  done clear
  B)
   40/3
  done clear
  C)
   24/5                                     
  done clear
  D)
   8
  done clear
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• question_answer39) 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                                       
  done clear
  B)
   1/3
  done clear
  C)
   2/3                                       
  done clear
  D)
   200/209
  done clear
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• question_answer40) 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
  done clear
  C)
   20                                         
  done clear
  D)
   30
  done clear
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• question_answer41) A battery consists of a variable number (n) of identical cells, each having an internal resistance r connected in series. The terminals of the battery are short-circuited. A graph of current \[(I)\] in the circuit versus the number of cells will be as shown in figure:
  A)
        
  done clear
  B)
   
  done clear
  C)
        
  done clear
  D)
   
  done clear
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• question_answer42) 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                                 
  done clear
  B)
   316 Hz
  done clear
  C)
   324 Hz                                 
  done clear
  D)
   320 Hz
  done clear
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• question_answer43) When the length of the vibrating segment of a sonometer wire is increased by 1%, the percentage change in its frequency is:
  A)
   \[\frac{100}{101}\]                        
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  B)
   \[\frac{99}{100}\]
  done clear
  C)
   1                                            
  done clear
  D)
   2
  done clear
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• question_answer44) The sprinkling of water reduces slightly the temperature of a closed room because:
  A)
   temperature of water is less than that of the room
  done clear
  B)
   specific heat of water is high
  done clear
  C)
   water has large latent heat of vaporization
  done clear
  D)
   water is a bad conductor of heat
  done clear
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• question_answer45) The equation of a simple harmonic wave is given by \[y=5\sin \frac{\pi }{2}\left( 100t-x \right)\] where \[x\]- and y are in metre and time is in second. The period of the wave in second will be:
  A)
   0.04                      
  done clear
  B)
   0.01
  done clear
  C)
   1                                            
  done clear
  D)
   5
  done clear
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• question_answer46) The loudness and pitch of a sound note depends on:
  A)
   intensity and frequency
  done clear
  B)
   frequency and number of harmonics
  done clear
  C)
   intensity and velocity
  done clear
  D)
   frequency and velocity
  done clear
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• question_answer47) For ordinary terrestrial experiments, the observer in an inertial frame in the following cases is:
  A)
   a child revolving in a giant wheel
  done clear
  B)
   a driver in a sports car moving with a constant high speed of \[200\text{ }km{{h}^{-1}}\] on a straight rod
  done clear
  C)
   the pilot of an aeroplane which is taking off
  done clear
  D)
   a cyclist negotiating a sharp curve
  done clear
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• question_answer48) 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                                   
  done clear
  B)
   7 min
  done clear
  C)
   5 min                                   
  done clear
  D)
   3 min
  done clear
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• question_answer49) If there were no gravity, which of the following will not be there for a fluid?
  A)
   Viscosity                            
  done clear
  B)
   Surface tension
  done clear
  C)
   Pressure            
  done clear
  D)
   Archimedes upward thrust
  done clear
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• question_answer50) 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
  done clear
  C)
   130 V                                   
  done clear
  D)
   10 V
  done clear
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• question_answer51) When deuterium and helium are subjected to an accelerating field simultaneously then:
  A)
   both acquire same energy
  done clear
  B)
   deuterium accelerates faster
  done clear
  C)
   helium accelerates faster
  done clear
  D)
   neither of them is accelerated
  done clear
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• question_answer52) A solenoid 1.5m 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)
   \[4\pi \times {{10}^{-3}}T\]
  done clear
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• question_answer53) A wire PQR is bent as shown in figure and is placed in a region of uniform magnetic field B. The length of \[PQ=QR=l.\text{ }A\] current \[I\]ampere flows through the wire as shown. The magnitude of the force on PQ and Q.R will be:
  A)
   \[BIl,0\]                              
  done clear
  B)
   \[2BIl,0\]
  done clear
  C)
   \[0,BIl\]                              
  done clear
  D)
   0,0
  done clear
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• question_answer54) A choke is preferred to a resistance for limiting current in AC circuit because:
  A)
   choke is cheap
  done clear
  B)
   there is no wastage of power
  done clear
  C)
   choke is compact in size
  done clear
  D)
   choke is a good absorber of heat
  done clear
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• question_answer55) A current of 6 A enters one comer P of an equilateral triangle PQR having 3 wires of resistances \[2\Omega \] each and leaves by the comer R. Then the current \[{{I}_{1}}\] and \[{{I}_{2}}\] are:
  A)
   2 A, 4 A               
  done clear
  B)
   4 A, 2 A
  done clear
  C)
   1 A, 2 A                               
  done clear
  D)
   2 A, 3 A
  done clear
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• question_answer56) To a germanium crystal equal number of aluminium and indium atoms are added. Then:
  A)
   it remains an intrinsic semiconductor
  done clear
  B)
   it becomes a n-type semiconductor
  done clear
  C)
   it becomes a p-type semiconductor
  done clear
  D)
   it becomes an insulator
  done clear
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• question_answer57) Maxium velocity of the photoelectrons emitted by a metal surface is \[1.2\times {{10}^{6}}m{{s}^{-1}}\]. Assuming the specific charge of the electron to be \[1.8\times {{10}^{11}}C\text{ }k{{g}^{-1}}\], the value of the stopping potential in volt will be:
  A)
   2                            
  done clear
  B)
   3
  done clear
  C)
   4                                            
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer58) Which of the following figures represents the variation of particle momentum and associated de-Broglie wavelength?
  A)
        
  done clear
  B)
    
  done clear
  C)
        
  done clear
  D)
     
  done clear
  View Answer play_arrow

• question_answer59) The term liquid crystal refers to a state that is intermediate between:
  A)
   crystalline solid and amorphous liquid
  done clear
  B)
   crystalline solid and vapour
  done clear
  C)
   amorphous liquid and its vapour
  done clear
  D)
   a crystal immersed in a liquid
  done clear
  View Answer play_arrow

• question_answer60) 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)
   \[\frac{5}{4}\]                                  
  done clear
  D)
   \[\frac{4}{5}\]  
  done clear
  View Answer play_arrow

• question_answer61) Which of the following is not an ore of magnesium?
  A)
   Carnal lite                          
  done clear
  B)
   Dolomite
  done clear
  C)
   Calamine           
  done clear
  D)
   Sea water
  done clear
  View Answer play_arrow

• question_answer62) The atomic number of Ni and Cu are 28 and 29 respectively. The electronic configuration. \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}3{{d}^{10}}\] represents :
  A)
   \[C{{u}^{+}}\]                  
  done clear
  B)
   \[C{{u}^{2+}}\]
  done clear
  C)
   \[N{{i}^{2+}}\]                                 
  done clear
  D)
   Ni
  done clear
  View Answer play_arrow

• question_answer63) 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_answer64) In the conversion of \[B{{r}_{2}}\] to \[BrO_{3}^{-}\], the oxidation number of Br changes from :
  A)
   zero to 4 - 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_answer65) 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_answer66) Which of the following represents the Lewis structure of \[{{N}_{3}}\] molecule?
  A)
   \[_{\times }^{\times }N\equiv N_{\times }^{\times }\]                
  done clear
  B)
   \[_{\times }^{\times }\overset{\times \,\,\,\times }{\mathop{N}}\,\equiv \overset{\times \,\,\,\times }{\mathop{N_{\times }^{\times }}}\,\]
  done clear
  C)
   \[_{\times }^{\times }\overset{\times \,\,\,\times }{\mathop{N_{\times }^{\times }}}\,\equiv \overset{\times \,\,\,\times }{\mathop{\underset{\times }{\mathop{N}}\,_{\times }^{\times }}}\,\]       
  done clear
  D)
   \[_{\times }^{\times }\overset{\times \,\,\,\times }{\mathop{\underset{\times \,\,\,\times }{\mathop{N}}\,_{\times }^{\times }}}\,=\overset{\times \,\,\,\times }{\mathop{\underset{\times \,\,\,\times }{\mathop{N}}\,_{\times }^{\times }}}\,\]
  done clear
  View Answer play_arrow

• question_answer67) Hydrogen bond is strongest in :
  A)
   S-H...O                                
  done clear
  B)
   O-H...S
  done clear
  C)
   F-H...F                                 
  done clear
  D)
   O-H...N
  done clear
  View Answer play_arrow

• question_answer68) The decomposition of a certain mass of \[CaC{{O}_{3}}\] gave \[11.2\text{ }d{{m}^{3}}\] of \[C{{O}_{2}}\] gas at STR The mass of KOH required to completely neutralise the gas is :
  A)
   56 g                                      
  done clear
  B)
   28 g
  done clear
  C)
   42 g                                      
  done clear
  D)
   20 g
  done clear
  View Answer play_arrow

• question_answer69) The density of a gas is 1.964 g \[d{{m}^{-3}}\] 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_answer70) 0.06 mole of \[KN{{O}_{3}}\] solid is added to \[100\,c{{m}^{3}}\]of water at 298K. The enthalpy of \[KN{{O}_{3}}\]aqueous solution is \[35.8\text{ }kJ\text{ }rno{{l}^{-1}}\]. After the solute is dissolved the temperature of the solution will be:
  A)
   293 K                                   
  done clear
  B)
   298 K
  done clear
  C)
   301 K                                   
  done clear
  D)
   304 K
  done clear
  View Answer play_arrow

• question_answer71) 4 moles each of \[S{{O}_{2}}\] and \[{{O}_{2}}\] gases are allowed to react to form \[S{{O}_{3}}\] in a closed vessel. At equilibrium 25% of \[{{O}_{2}}\]  is used up. The total number of moles of all the gases at equilibrium is :
  A)
   6.5                                        
  done clear
  B)
   7.0   
  done clear
  C)
   8.0                                        
  done clear
  D)
   2.0
  done clear
  View Answer play_arrow

• question_answer72) An example for autocatalysis is :
  A)
   oxidation of NO to \[N{{O}_{3}}\]
  done clear
  B)
   oxidation of \[S{{O}_{2}}\] to \[S{{O}_{3}}\]
  done clear
  C)
   decomposition of \[KCl{{O}_{3}}\] to \[KCl\] and \[{{O}_{2}}\]
  done clear
  D)
   oxidation of oxalic acid by acidified \[KMn{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer73) During the fusion of an organic compound with sodium metal, nitrogen of the compound is converted into :
  A)
   \[NaN{{O}_{2}}\]                           
  done clear
  B)
   \[NaN{{H}_{2}}\]
  done clear
  C)
   NaCN                                  
  done clear
  D)
   NaNC
  done clear
  View Answer play_arrow

• question_answer74) Identify the product Y in the following reaction sequence :
  A)
   pentane                             
  done clear
  B)
   cyclobutane
  done clear
  C)
   cyclopentane   
  done clear
  D)
   cyclopentanone
  done clear
  View Answer play_arrow

• question_answer75) The reaction \[{{C}_{2}}{{H}_{5}}ONa+{{C}_{2}}{{H}_{5}}I\to \]\[{{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}\] \[+NaI\] is known as :
  A)
   Kolbes synthesis
  done clear
  B)
   Wurtzs synthesis
  done clear
  C)
   Williamsons synthesis
  done clear
  D)
   Grignards synthesis
  done clear
  View Answer play_arrow

• question_answer76) \[\Delta {{G}^{o}}vs\,T\] plot in the Ellinghams diagram slopes downwards for the reactions :
  A)
   \[Mg+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}MgO\]
  done clear
  B)
   \[2Ag+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}A{{g}_{2}}O\]
  done clear
  C)
   \[C+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}CO\]
  done clear
  D)
   \[CO+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer77) Which of the following taking place in the blast furnace is endothermic?
  A)
   \[CaC{{O}_{3}}\xrightarrow{{}}CaO+C{{O}_{2}}\]
  done clear
  B)
                   \[2C+{{O}_{2}}\xrightarrow{{}}2CO\]
  done clear
  C)
   \[C+{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}\]
  done clear
  D)
   \[F{{e}_{2}}{{O}_{3}}+3CO\xrightarrow{{}}2Fe+3C{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer78) Liquor ammonia bottles are opened only after cooling. This is because:
  A)
   it is a mild explosive
  done clear
  B)
   it is a corrosive liquid
  done clear
  C)
   it is a lachrymatory
  done clear
  D)
   it generates high vapour pressure
  done clear
  View Answer play_arrow

• question_answer79) The formation of \[O_{2}^{+}\,{{[Pt{{F}_{6}}]}^{-}}\] is the basis for the formation of xenon fluorides. This is because:
  A)
   \[{{O}_{2}}\] and \[Xe\]have comparable sizes
  done clear
  B)
   Both \[{{O}_{2}}\] and \[Xe\] are gases
  done clear
  C)
   \[{{O}_{2}}\] and \[Xe\] have comparable ionisation energies
  done clear
  D)
   \[{{O}_{2}}\] and \[Xe\] have comparable electro- negativities
  done clear
  View Answer play_arrow

• question_answer80) The highest magnetic moment is shown by the transition metal ion with the configuration:
  A)
   \[3{{d}^{2}}\]                                   
  done clear
  B)
   \[3{{d}^{5}}\]
  done clear
  C)
   \[3{{d}^{7}}\]                                   
  done clear
  D)
   \[3{{d}^{9}}\]
  done clear
  View Answer play_arrow

• question_answer81) A transition metal ion exists in its highest oxidation state. It is expected to behave as:
  A)
   a chelating agent
  done clear
  B)
   a central metal in a coordination compound
  done clear
  C)
   an oxidising agent
  done clear
  D)
   a reducing agent
  done clear
  View Answer play_arrow

• question_answer82) In which of the following complex ion, the central metal ion is in a state of \[s{{p}^{3}}{{d}^{2}}\]hybridisation?
  A)
                   \[{{[Co{{F}_{6}}]}^{3-}}\]            
  done clear
  B)
                   \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
  done clear
  C)
   \[{{[Fe{{(CN)}_{6}}]}^{3-}}\]     
  done clear
  D)
   \[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
  done clear
  View Answer play_arrow

• question_answer83) Which of the following can participate in linkage isomerism?
  A)
   \[N{{O}_{2}}\]                
  done clear
  B)
   \[{{H}_{2}}\overset{\,\,\bullet \,\,\bullet }{\mathop{N}}\,C{{H}_{2}}C{{H}_{2}}\overset{\,\,\bullet \,\,\bullet }{\mathop{N}}\,{{H}_{2}}\]
  done clear
  C)
   \[{{H}_{2}}O\]                 
  done clear
  D)
   \[_{\bullet }^{\bullet }N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer84) Which of the following has the highest bond order?
  A)
   \[{{N}_{2}}\]                                    
  done clear
  B)
   \[{{O}_{2}}\]
  done clear
  C)
   \[H{{e}_{2}}\]                                  
  done clear
  D)
   \[{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer85) Which of the following is diamagnetic?
  A)
   \[H_{2}^{+}\]                                   
  done clear
  B)
   \[{{O}_{2}}\]
  done clear
  C)
   \[L{{i}_{2}}\]                                     
  done clear
  D)
   \[He_{2}^{+}\]
  done clear
  View Answer play_arrow

• question_answer86) The concentration of a reactant X decreases from 0.1 M to 0.005 M in 40 minute. If the reaction follows 1 order kinetics, the rate of the reaction when the concentration of X is 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_answer87) Chemical reactions with very high \[{{E}_{a}}\] values are generally:
  A)
   very fast            
  done clear
  B)
   very slow
  done clear
  C)
   moderately fast              
  done clear
  D)
   spontaneous
  done clear
  View Answer play_arrow

• question_answer88) 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_answer89) When a quantity of electricity is passed through \[CuS{{O}_{4}}\]solution, 0.16 g of copper gets deposited. If the same quantity of electricity is passed through acidulated water, then the volume of \[{{H}_{2}}\] liberated at STP will be : [given: atomic weight of \[Cu=64\]]
  A)
   \[4.0\,\,c{{m}^{3}}~\]                  
  done clear
  B)
   \[56\,\,c{{m}^{3}}~\]
  done clear
  C)
   \[604\,\,c{{m}^{3}}~\]                 
  done clear
  D)
   \[8.0\,\,c{{m}^{3}}~\]
  done clear
  View Answer play_arrow

• question_answer90) Solubility product of a salt AB is \[1\times {{10}^{-8}}{{M}^{2}}\]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 \[{{10}^{-8}}\]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_answer91) Which one of the following condition will increase the voltage of the cell represented by the equation? \[Cu(s)+2A{{g}^{+}}(aq)C{{u}^{2+}}(aq)+2Ag(s)\]
  A)
   Increase in the dimension of Cu electrode
  done clear
  B)
   Increase in the dimension of Ag electrode
  done clear
  C)
   Increase in the concentration of \[C{{u}^{2+}}\]ions
  done clear
  D)
   Increase in the concentration of \[A{{g}^{+}}\] ions
  done clear
  View Answer play_arrow

• question_answer92) 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_answer93) The mass of glucose that should be dissolved in 50 g of water in order to produce the same lowering of vapour pressure as is produced by dissolving 1 g of urea in the same quantity of water is :
  A)
   1 g                                        
  done clear
  B)
   3 g
  done clear
  C)
   6 g                                        
  done clear
  D)
   18 g
  done clear
  View Answer play_arrow

• question_answer94) Osmotic pressure observed when benzoic acid is dissolved in benzene is less than that expected from theoretical considerations. This is because :
  A)
   benzoic acid is an organic solute
  done clear
  B)
   benzoic acid has higher molar mass than benzene
  done clear
  C)
   benzoic acid gets associated in benzene
  done clear
  D)
   benzoic acid gets dissociated in benzene
  done clear
  View Answer play_arrow

• question_answer95) 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_answer96) Which of the following electrolyte 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_answer97) For a reversible reaction: \[X(g)+3Y(g)2Z(g);\,\,\Delta H=-40\,kJ\], the standard entropies of X, Y and Z are 60, 40 and \[50\,\,J{{K}^{-1}}\,mo{{l}^{-1}}\] respectively. The temperature at which the above reaction attains equilibrium is about:
  A)
   400 K                                   
  done clear
  B)
   500 K
  done clear
  C)
   273 K                                   
  done clear
  D)
   373 K
  done clear
  View Answer play_arrow

• question_answer98) The radii of \[N{{a}^{+}}\] and \[C{{l}^{-}}\]ions are 95 pm and 181 pm respectively. The edge length of \[NaCl\] unit cell is :
  A)
   276 pm                               
  done clear
  B)
   138 pm
  done clear
  C)
   552 pm                               
  done clear
  D)
   415 pm
  done clear
  View Answer play_arrow

• question_answer99) 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_answer100) The basicity of aniline is less than that of cyclohexylamine. This is due to:
  A)
   +R-effect of\[-N{{H}_{2}}\] group
  done clear
  B)
   \[-I\]effect of\[-N{{H}_{2}}\] group
  done clear
  C)
   -R effect of \[-N{{H}_{2}}\] group
  done clear
  D)
   hyperconjugation effect
  done clear
  View Answer play_arrow

• question_answer101) Methyl bromide is converted into ethane by heating it in ether medium with :
  A)
   Al                                          
  done clear
  B)
   Zn
  done clear
  C)
   Na                                        
  done clear
  D)
   Cu
  done clear
  View Answer play_arrow

• question_answer102) 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)
  \[C{{H}_{3}}C{{H}_{2}}CHBr\,\,CHO\]     
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}CBrCHO\]
  done clear
  View Answer play_arrow

• question_answer103) Which cycloalkane has the lowest heat of combustion per \[C{{H}_{2}}\] group?
  A)
   Cyclopropane                  
  done clear
  B)
   Cyclobutane
  done clear
  C)
   Cyclopentane                  
  done clear
  D)
   Cyclohexane
  done clear
  View Answer play_arrow

• question_answer104) The catalyst used in the preparation of an alkyl chloride by the action of dry \[HCl\] 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_answer105) In the reaction,\[R-X\xrightarrow{alcoholic\text{ }KCN}A\xrightarrow{dilute\text{ }HCl}B\] The product B is :
  A)
   alkyl chloride    
  done clear
  B)
   aldehyde
  done clear
  C)
   carboxylic acid                 
  done clear
  D)
   ketone
  done clear
  View Answer play_arrow

• question_answer106) Which of the following compound would not evolve \[C{{O}_{2}}\] when treated with \[NaHC{{O}_{3}}\]solution?
  A)
   Salicylic acid
  done clear
  B)
   Phenol
  done clear
  C)
   Benzoic acid
  done clear
  D)
   4-nitrobenzoic acid
  done clear
  View Answer play_arrow

• question_answer107) 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_answer108) When a mixture of calcium benzoate and calcium acetate is dry distilled, the resulting compound is :
  A)
   cetophenone
  done clear
  B)
   benzaldehyde
  done clear
  C)
   benzophenone
  done clear
  D)
   acetaldehyde
  done clear
  View Answer play_arrow

• question_answer109) 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_answer110) Which of the following would undergo Hofmann reaction to give a primary amine?
  A)
   \[R-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-Cl~~~\]                         
  done clear
  B)
   \[RCONHC{{H}_{3}}\]
  done clear
  C)
   \[RCON{{H}_{2}}\]                         
  done clear
  D)
   \[RCOOR\]
  done clear
  View Answer play_arrow

• question_answer111) 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_answer112) A distinctive and characteristic functional group of fats is
  A)
   a peptide group              
  done clear
  B)
   an ester group
  done clear
  C)
   an alcoholic group          
  done clear
  D)
   a ketonic group
  done clear
  View Answer play_arrow

• question_answer113) At \[pH=4\], glycine exists as :
  A)
   \[{{H}_{3}}\overset{+}{\mathop{N}}\,-C{{H}_{2}}-CO{{O}^{-}}\]
  done clear
  B)
   \[{{H}_{3}}\overset{+}{\mathop{N}}\,-C{{H}_{2}}-CO{{O}^{-}}\]
  done clear
  C)
   \[{{H}_{2}}N-C{{H}_{2}}-COOH\]
  done clear
  D)
   \[{{H}_{2}}N-C{{H}_{2}}-CO{{O}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer114) Insulin regulates the metabolism of :
  A)
   minerals             
  done clear
  B)
   ammo acids
  done clear
  C)
   glucose                               
  done clear
  D)
   vitamins
  done clear
  View Answer play_arrow

• question_answer115) The formula mass of Mohrs salt is 392. The iron present in it is oxidised by \[KMn{{O}_{4}}\] in acid medium. The equivalent mass of Mohrs salt is:
  A)
   392                                       
  done clear
  B)
   31.6
  done clear
  C)
   278                                       
  done clear
  D)
   156
  done clear
  View Answer play_arrow

• question_answer116) 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_answer117) Acrolein test is positive for :
  A)
   polysaccharides              
  done clear
  B)
   proteins
  done clear
  C)
   oils and fats      
  done clear
  D)
   reducing sugars
  done clear
  View Answer play_arrow

• question_answer118) An organic compound which produces a bluish green coloured flame on heating in presence of copper is :
  A)
   chlorobenzene
  done clear
  B)
   benzaldehyde
  done clear
  C)
   aniline
  done clear
  D)
   benzoic acid
  done clear
  View Answer play_arrow

• question_answer119) For a reaction \[A+B\xrightarrow{{}}C+D\] if the concentration of A is doubled without alteming the concentration of B, the rate gets doubled. If the concentration of B is increased by nine times without alteming the concentration of A, the rate gets tripled. The order of the reaction is :
  A)
   2                                            
  done clear
  B)
   1
  done clear
  C)
   3/2                                       
  done clear
  D)
   4/3
  done clear
  View Answer play_arrow

• question_answer120) 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_answer121) If \[(P\wedge \sim r)\to \,(\sim p\vee q)\] is false, then the truth values of p, q and r are respectively :
  A)
   T, F and F                           
  done clear
  B)
   F, F and T
  done clear
  C)
   F, T and T                           
  done clear
  D)
   T, F and T
  done clear
  View Answer play_arrow

• question_answer122) If \[\alpha ,\,\beta \] and \[\gamma \] are the. roots, of the equation\[{{x}^{3}}-8x+8=0\], then \[\sum \,\,{{\alpha }^{2}}\] and \[\sum \frac{1}{\alpha \beta }\] are respectively :
  A)
   0 and-16                             
  done clear
  B)
   16 and 8
  done clear
  C)
   -16 and 0                            
  done clear
  D)
   16 and 0
  done clear
  View Answer play_arrow

• question_answer123) The gcd of 1080 and 675 is :
  A)
   145                                       
  done clear
  B)
   135
  done clear
  C)
   225                                       
  done clear
  D)
   125
  done clear
  View Answer play_arrow

• question_answer124) If \[a\,|(b+c)\] and \[\,|(b-c)\] where \[a,\,b,\,c\,\in N\] then:
  A)
   \[{{b}^{2}}\equiv {{c}^{2}}(\bmod \,{{a}^{2}})\]               
  done clear
  B)
   \[{{b}^{2}}\equiv {{c}^{2}}(\bmod \,{{a}^{2}})\]
  done clear
  C)
   \[{{a}^{2}}\equiv {{b}^{2}}(\bmod \,{{c}^{2}})\]               
  done clear
  D)
   \[{{c}^{2}}\equiv {{a}^{2}}(\bmod \,{{b}^{2}})\]
  done clear
  View Answer play_arrow

• question_answer125) If a, b and \[c\in N\], then which one of the following is not true?
  A)
   \[a\left| \text{ }b\text{ }and\text{ }a \right|c\Rightarrow a|3b+2c\]
  done clear
  B)
   \[a\left| \text{ }b\text{ }and\text{ }b \right|c\Rightarrow a|c\]
  done clear
  C)
   \[a\left| \text{(}b+b)\Rightarrow a \right|b\Rightarrow and\,a|c\]
  done clear
  D)
   \[a\left| \text{(}b\,\,and\,a \right|c\Rightarrow \,a\,|b+c\]
  done clear
  View Answer play_arrow

• question_answer126) \[x=4\,(1+\cos \theta )\] and \[y=3\,\,(1+\sin \theta )\] are the parametric equations of:
  A)
   \[\frac{{{(x-3)}^{2}}}{9}+\frac{{{(y-4)}^{2}}}{16}=1\]      
  done clear
  B)
   \[\frac{{{(x+4)}^{2}}}{16}+\frac{{{(y+3)}^{2}}}{9}=1\]
  done clear
  C)
   \[\frac{{{(x-4)}^{2}}}{16}-\frac{{{(y-3)}^{2}}}{9}=1\]
  done clear
  D)
   \[\frac{{{(x-4)}^{2}}}{16}+\frac{{{(y-3)}^{2}}}{9}=1\]
  done clear
  View Answer play_arrow

• question_answer127) If the distance between the foci and the distance between the directories of the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] are in the ratio \[3:2\], then \[a:b\] is :
  A)
   \[\sqrt{2}:1\]                   
  done clear
  B)
   \[\sqrt{3}:\sqrt{2}\]
  done clear
  C)
   \[1:2\]                                 
  done clear
  D)
   \[2:1\]
  done clear
  View Answer play_arrow

• question_answer128) The ellipse \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{\mathbf{2}}}}{16}=1\] and the hyperbola\[\frac{{{x}^{2}}}{25}-\frac{{{y}^{\mathbf{2}}}}{16}=1\] have in common :
  A)
   centre only
  done clear
  B)
   centre, foci and directrices
  done clear
  C)
   centre, foci and vertices
  done clear
  D)
                   centre and vertices only
  done clear
  View Answer play_arrow

• question_answer129) If \[\sec \theta =m\] and \[\tan \theta =n\], then\[\frac{1}{m}\left[ \,(m+n)+\frac{1}{(m+n)} \right]\] is :
  A)
   2                                            
  done clear
  B)
   2m
  done clear
  C)
   2n                                         
  done clear
  D)
   mn
  done clear
  View Answer play_arrow

• question_answer130) The value of \[\frac{\sin {{85}^{o}}-\sin {{35}^{o}}}{\cos {{65}^{o}}}\] is :
  A)
   2                                            
  done clear
  B)
   -1
  done clear
  C)
   1                                            
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer131) If the length of the tangent from any point on the circle \[{{(x-3)}^{2}}+{{(y+2)}^{2}}=5{{r}^{2}}\] to the circle \[{{(x-3)}^{2}}+{{(y+2)}^{2}}={{r}^{2}}\] is 16 unit, then the area between the two circles in sq unit is:
  A)
   \[32\pi \]                           
  done clear
  B)
   \[4\pi \]
  done clear
  C)
   \[8\pi \]                                              
  done clear
  D)
   \[256\pi \]
  done clear
  View Answer play_arrow

• question_answer132) The circles \[a{{x}^{2}}+a{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\] and \[b{{x}^{2}}+b{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0\](\[a\ne 0\] and \[b\ne 0\]) cut orthogonally if:
  A)
   \[{{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}}=a{{c}_{1}}+{{b}_{2}}\]
  done clear
  B)
   \[2({{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}})=b{{c}_{1}}+a{{c}_{2}}\]
  done clear
  C)
                   \[b{{g}_{1}}{{g}_{2}}+a{{f}_{1}}{{f}_{2}}=b{{c}_{1}}+a{{c}_{2}}\]
  done clear
  D)
   \[{{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer133) The equation of the common tangent of the two touching circles, \[{{y}^{2}}+{{x}^{2}}-6x-12y+37=0\] and\[{{x}^{2}}+{{y}^{2}}-6y+7=0\] is :
  A)
   \[x-y-5=0\]       
  done clear
  B)
   \[x-y+5=0\]
  done clear
  C)
   \[c-y-5=0\]        
  done clear
  D)
   \[r+y+5=0\]
  done clear
  View Answer play_arrow

• question_answer134) The equation of the parabola with vertex at (-1,1) and focus (2, 1) is :
  A)
   \[{{y}^{2}}-2y-12x-11=0\]
  done clear
  B)
   \[{{x}^{2}}+2x-12y+13=0\]
  done clear
  C)
   \[{{y}^{2}}-2y+12x+11=0\]
  done clear
  D)
   \[{{y}^{2}}-2y-12x+13=0\]
  done clear
  View Answer play_arrow

• question_answer135) The equation of the line which is tangent to both the circle \[{{x}^{2}}+{{y}^{2}}=5\] and the parabola\[{{y}^{2}}=40x\] is:
  A)
   \[2x-y\pm 5=0\]             
  done clear
  B)
   \[2x-y+5=0\]
  done clear
  C)
   \[2x-y-5=0\]     
  done clear
  D)
   \[2x+y+5=0\]
  done clear
  View Answer play_arrow

• question_answer136) If \[2A+3B=\left[ \begin{align}   & \begin{matrix}    2 & -1 & 4  \\ \end{matrix} \\  & \begin{matrix}    3 & 2 & 5  \\ \end{matrix} \\ \end{align} \right]\] and\[A+2B=\left[ \begin{align}   & \begin{matrix}    5 & 0 & 3  \\ \end{matrix} \\  & \begin{matrix}    1 & 6 & 2  \\ \end{matrix} \\ \end{align} \right]\] then B is:
  A)
   \[\left[ \begin{align}   & \begin{matrix}    8 & -1 & 2  \\ \end{matrix} \\  & \begin{matrix}    -1 & 10 & -1  \\ \end{matrix} \\ \end{align} \right]\]       
  done clear
  B)
   \[\left[ \begin{align}   & \begin{matrix}    8 & -1 & 2  \\ \end{matrix} \\  & \begin{matrix}    -1 & 10 & -1  \\ \end{matrix} \\ \end{align} \right]\]
  done clear
  C)
   \[\left[ \begin{align}   & \begin{matrix}    8 & 1 & -2  \\ \end{matrix} \\  & \begin{matrix}    -1 & 10 & -1  \\ \end{matrix} \\ \end{align} \right]\]       
  done clear
  D)
   \[\left[ \begin{align}   & \begin{matrix}    8 & 1 & 1  \\ \end{matrix} \\  & \begin{matrix}    1 & 10 & 1  \\ \end{matrix} \\ \end{align} \right]\]
  done clear
  View Answer play_arrow

• question_answer137) If \[O(A)=2\times 3,\,O(B)=3\times 2\], and \[O(C)=3\times 3\], which one of the following is not defined?
  A)
   \[CB+A\]                            
  done clear
  B)
   BAC
  done clear
  C)
   \[C(A+B)\]                        
  done clear
  D)
   \[C(A+B)\]
  done clear
  View Answer play_arrow

• question_answer138) If \[A=\left[ \begin{matrix}    1 & -3  \\    2 & k  \\ \end{matrix} \right]\] and \[{{A}^{2}}-4A+10I=A\], then \[k\] is equal to:
  A)
   0                                            
  done clear
  B)
   -4
  done clear
  C)
   4 and not 1        
  done clear
  D)
   1 or 4
  done clear
  View Answer play_arrow

• question_answer139) The value of \[\left| \begin{matrix}    x+y & y+z & z+x  \\    x & y & z  \\    x-y & y-z & z-x  \\ \end{matrix} \right|\] is equal to:
  A)
   \[2{{(x+y+z)}^{2}}\]      
  done clear
  B)
   \[2{{(x+y+z)}^{3}}\]
  done clear
  C)
   \[{{(x+y+z)}^{3}}\]                        
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer140) On the set Q of all rational numbers the operation * which is both associative and commutative is given by a * b, is :
  A)
   \[a+b+ab\]      
  done clear
  B)
   \[{{a}^{2}}+{{b}^{2}}\]
  done clear
  C)
   \[ab+1\]                             
  done clear
  D)
   \[2a+3b\]
  done clear
  View Answer play_arrow

• question_answer141) From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the aeroplane are observed to be \[{{30}^{o}}\] and \[{{60}^{o}}\] respectively. The height at which the aeroplane is flying in km is :
  A)
   \[\frac{4}{\sqrt{3}}\]                                    
  done clear
  B)
   \[\frac{\sqrt{3}}{2}\]
  done clear
  C)
   \[\frac{2}{\sqrt{3}}\]                                    
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer142) If the angles of a triangle are in the ratio\[3:4:5\], then the sides are in the ratio :
  A)
   \[2:\sqrt{6}:\sqrt{3}+1\]
  done clear
  B)
   \[\sqrt{2}:\sqrt{6}:\sqrt{3}+1\]
  done clear
  C)
   \[2:\sqrt{3}:\sqrt{3}+1\]
  done clear
  D)
   \[3:4:5\]
  done clear
  View Answer play_arrow

• question_answer143) If \[{{\cos }^{-1}}x=\alpha ,\,(0<x<1)\] and \[{{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}})+{{\sec }^{-1}}\left( \frac{1}{2{{x}^{2}}-1} \right)=\frac{2\pi }{3}\], then \[{{\tan }^{-1}}(2x)\] equals :
  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_answer144) If \[a>b>0\], then the value of\[{{\tan }^{-1}}\left( \frac{a}{b} \right)+{{\tan }^{-1}}\left( \frac{a+b}{a-b} \right)\] depends on :
  A)
   both a and b     
  done clear
  B)
   b and not a
  done clear
  C)
   a and not b       
  done clear
  D)
   neither a nor b
  done clear
  View Answer play_arrow

• question_answer145) Which one of the following equations has no solution?
  A)
   \[\cos ec\theta -\sec \theta =\cos ec\theta \,.\,\,\sec \theta \]
  done clear
  B)
   \[\cos ec\theta \,.\,\,\sec \theta =1\]
  done clear
  C)
                   \[\cos \theta +\sin \theta =\sqrt{2}\]
  done clear
  D)
   \[\sqrt{3}\,\sin \theta -\cos \theta =2\]
  done clear
  View Answer play_arrow

• question_answer146) If \[A=\{a,\,b,\,c\},\,B=\{b,\,c,\,d\}\] and \[C=\{a,\,d,\,c\}\]then \[(A-B)\times (B\cap C)\] is equal to :
  A)
   \[\{(a,c),(a,d)\}\]           
  done clear
  B)
   \[\{(a,\text{ }6),(c,\text{ }d)\}\]
  done clear
  C)
   \[\{(c,\text{ }a),(d,\text{ }a)\}\]              
  done clear
  D)
                  \[\{(a,\text{ }c),(a,\text{ }d),(b,\text{ }d)\text{ }\!\!\}\!\!\text{ }\]
  done clear
  View Answer play_arrow

• question_answer147) The function \[f:X\to Y\] defined by \[f(x)=\sin x\] is one-one but not onto, if X and Y are respectively equal to :
  A)
                   R and R
  done clear
  B)
   \[\left[ 0,\frac{\pi }{2} \right]\] and [0,1]
  done clear
  C)
   \[\left[ \frac{-\pi }{2},\frac{\pi }{2} \right]\] and [-1, 1]
  done clear
  D)
   \[\left[ \frac{-\pi }{2},\frac{\pi }{2} \right]\] and [-1, 1]
  done clear
  View Answer play_arrow

• question_answer148) If \[{{\log }_{4}}2+{{\log }_{4}}4+{{\log }_{4}},\,x+{{\log }_{4}}16=6\], then value of \[x\]is :
  A)
   64             
  done clear
  B)
   4
  done clear
  C)
   8                                            
  done clear
  D)
   32
  done clear
  View Answer play_arrow

• question_answer149) If  \[{{S}_{n}}=\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+.....\] to n terms, then \[6{{S}_{n}}\], equals :
  A)
   \[\frac{5n-4}{5n+6}\]                   
  done clear
  B)
   \[\frac{n}{(5n+6)}\]
  done clear
  C)
   \[\frac{2n-1}{5n+6}\]                   
  done clear
  D)
   \[\frac{1}{(5n+6)}\]
  done clear
  View Answer play_arrow

• question_answer150) The remainder obtained when \[{{(1!)}^{2}}+{{(2!)}^{2}}+{{(3!)}^{2}}+....+{{(100!)}^{2}}\] is divided by \[{{10}^{2}}\] is:
  A)
   27                                         
  done clear
  B)
   28
  done clear
  C)
   17                                         
  done clear
  D)
   14
  done clear
  View Answer play_arrow

• question_answer151) In the group G = {1,5,7,11} under multiplication modulo 12, the solution of\[{{7}^{-1}}{{\otimes }_{12}}\,(x\,{{\otimes }_{12}}11)=5\] is equals :
  A)
   5                                            
  done clear
  B)
   1
  done clear
  C)
   7                                            
  done clear
  D)
   11
  done clear
  View Answer play_arrow

• question_answer152) A subset of the additive group of real numbers which is not a subgroup is :
  A)
   ({0}, +)                                
  done clear
  B)
   (Z, +)
  done clear
  C)
   (N, +)                  
  done clear
  D)
   (Q, +)
  done clear
  View Answer play_arrow

• question_answer153) If \[\vec{p}=\hat{i}=+\hat{j},\vec{q}=4k-\text{ }\hat{j}\] and \[\vec{r}=\hat{i}+\hat{k}\] then the unit vector in the direction of \[3\vec{p}+\vec{q}-2\vec{r}\] is:
  A)
   \[\frac{1}{3}(\hat{i}+2\hat{j}+2\hat{k})\]            
  done clear
  B)
   \[\frac{1}{3}(\hat{i}-2\hat{j}-2\hat{k})\]
  done clear
  C)
   \[\frac{1}{3}(\hat{i}-2\hat{j}+2\hat{k})\]             
  done clear
  D)
   \[\hat{i}+2\hat{j}+2\hat{k}\]
  done clear
  View Answer play_arrow

• question_answer154) If a and b are the two vectors such that \[|\vec{a}|=3\sqrt{3},\,|\vec{b}|=4\] and \[|\vec{a}+\vec{b}|=\sqrt{7}\], then the angle between a and b is:
  A)
   \[{{120}^{o}}\]                
  done clear
  B)
   \[{{60}^{o}}\]
  done clear
  C)
   \[{{30}^{o}}\]                                   
  done clear
  D)
   \[{{150}^{o}}\]  
  done clear
  View Answer play_arrow

• question_answer155) If \[\vec{a}\] is vector perpendicular to both \[\vec{b}\] and \[\vec{c}\], then :
  A)
   \[\vec{a}+(\vec{b}+\vec{c})=\vec{0}\] 
  done clear
  B)
   \[\vec{a}\times (\vec{b}+\vec{c})=\vec{0}\]
  done clear
  C)
   \[\vec{a}\times (\vec{b}\times \vec{c})=\vec{0}\]         
  done clear
  D)
   \[\vec{a}\,\,.\,\,(\vec{b}\times \vec{c})=\vec{0}\]
  done clear
  View Answer play_arrow

• question_answer156) If the area of the parallelogram with \[\vec{a}\] and \[\vec{b}\]as two adjacent sides is 15 sq unit, then the area of the parallelogram having, \[3\vec{a}+2\vec{b}\] and \[\vec{a}+3\vec{b}\] as two adjacent sides in sq unit is :
  A)
   120                                       
  done clear
  B)
   105
  done clear
  C)
   75                                         
  done clear
  D)
   45
  done clear
  View Answer play_arrow

• question_answer157) The locus of the point which moves such that the ratio of its distance from two fixed point in the plane is always a constant \[k\,(<1)\] is :
  A)
   hyperbola         
  done clear
  B)
   ellipse
  done clear
  C)
   straight line      
  done clear
  D)
   circle
  done clear
  View Answer play_arrow

• question_answer158) If the lines \[x+3y-9=0,4x+by-2=0\] and \[2x-y-4=0\] are concurrent, then b equals :
  A)
   -5                                          
  done clear
  B)
   5
  done clear
  C)
   1                                            
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer159) The lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] are perpendicular to each other, if:
  A)
   \[{{h}^{2}}=a+b\]           
  done clear
  B)
   \[a+b=0\]
  done clear
  C)
   \[{{h}^{2}}=ab\]                             
  done clear
  D)
   \[h=0\]
  done clear
  View Answer play_arrow

• question_answer160) The equation of the circle having \[x-y-2=0\]and \[x-y+2=0\] as two tangents and \[x-y=0\] as a diameter is :
  A)
   \[{{x}^{2}}+{{y}^{2}}+2x-2y+1=0\]
  done clear
  B)
                   \[{{x}^{2}}+{{y}^{2}}-2x+2y-1=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}=2\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}=1\]
  done clear
  View Answer play_arrow

• question_answer161) If the curve \[y=2{{x}^{3}}+a{{x}^{2}}+bx+c\] passes through the origin and the tangents drawn to it at \[x=-1\] and \[x=2\] are parallel to the x-axis, then the values of a, b and c are respectively:
  A)
   12,-3 and 0        
  done clear
  B)
   - 3,-12 and 0
  done clear
  C)
   - 3,12 and 0       
  done clear
  D)
   3, -12 and 0
  done clear
  View Answer play_arrow

• question_answer162) A circular sector of perimeter 60 m with maximum area is to be constructed. The radius of the circular arc in metre must be :
  A)
   20                                         
  done clear
  B)
   5
  done clear
  C)
   15                                         
  done clear
  D)
   10
  done clear
  View Answer play_arrow

• question_answer163) The tangent and the normal drawn to the curve \[y={{x}^{2}}-x+4\] at P(1, 4) cut the x-axis at A and B respectively. If the length of the sub tangent drawn to the curve at P is equal to the length of the subnormal, then the area of the triangle PAB in sq unit is :
  A)
   4              
  done clear
  B)
   32
  done clear
  C)
   8              
  done clear
  D)
   16
  done clear
  View Answer play_arrow

• question_answer164) \[\int{\frac{({{x}^{3}}+3{{x}^{2}}+3x+1)}{{{(x+1)}^{5}}}}\] is equal to :
  A)
   \[-\frac{1}{(x+1)}+c\]                   
  done clear
  B)
   \[\frac{1}{5}\log \,\,(x+1)+c\]
  done clear
  C)
   \[\log \,(x+1)+c\]           
  done clear
  D)
   \[{{\tan }^{-1}}x+c\]
  done clear
  View Answer play_arrow

• question_answer165) \[\int{\frac{\cos ecx}{{{\cos }^{2}}\left( 1+\log \,\tan \frac{x}{2} \right)}dx}\] is equal to :
  A)
   \[{{\sin }^{2}}\left[ 1+\log \,\tan \frac{x}{2} \right]+c\]
  done clear
  B)
   \[\tan \left[ 1+\log \,\tan \frac{x}{2} \right]+c\]
  done clear
  C)
   \[{{\sec }^{2}}\left[ 1+\log \,\tan \frac{x}{2} \right]+c\]
  done clear
  D)
   \[-\tan \left[ 1+\log \,\tan \frac{x}{2} \right]+c\]
  done clear
  View Answer play_arrow

• question_answer166) The complex number \[\frac{(-\sqrt{3}+3i)\,(1-i)}{(3+\sqrt{3}\,i)\,(i)\,(\sqrt{3}+\sqrt{3}i)}\] when represented in the Argand diagram is :
  A)
                   in the second quadrant
  done clear
  B)
   in the first quadrant
  done clear
  C)
   on the y-axis (imaginary axis)
  done clear
  D)
   on the x-axis (real axis).
  done clear
  View Answer play_arrow

• question_answer167) If \[2x=-1\,+\sqrt{3}\,i\], then the value of \[{{(1-{{x}^{2}}+x)}^{6}}-{{(1-x+{{x}^{2}})}^{6}}\] is equal to :
  A)
   32                                         
  done clear
  B)
   -64
  done clear
  C)
   64                                         
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer168) The modulus and amplitude of \[{{(1+i\sqrt{3})}^{8}}\] are respectively:
  A)
   256 and \[\frac{\pi }{3}\]             
  done clear
  B)
   256 and \[\frac{2\pi }{3}\]
  done clear
  C)
   2and \[\frac{2\pi }{3}\]                
  done clear
  D)
   256 and \[\frac{8\pi }{3}\]
  done clear
  View Answer play_arrow

• question_answer169) The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{5}^{x}}-{{5}^{-x}}}{2x}\] is :
  A)
   \[\log 5\]                           
  done clear
  B)
   0
  done clear
  C)
   1                                            
  done clear
  D)
   \[2\,\log 5\]
  done clear
  View Answer play_arrow

• question_answer170) Which one of the following is not true always?
  A)
   If \[f(x)\] is not continuous at \[x=a\], then it is not differentiable at \[x=a\]
  done clear
  B)
   If \[f(x)\] is continuous at \[x=a\], then it is differentiable at \[x=a\]
  done clear
  C)
   If \[f(x)\] and \[g(x)\] are differentiable at \[x=a\], then \[f(x)+g(x)\] is also differentiable at \[x=a\]
  done clear
  D)
   If a function \[f(x)\] is continuous at \[x=a\], then \[\underset{x\to a}{\mathop{\lim }}\,f(x)\] exists
  done clear
  View Answer play_arrow

• question_answer171) \[\int{\frac{dx}{x\sqrt{{{x}^{6}}-16}}}\] is equal; to :  
  A)
   \[\frac{1}{3}{{\sec }^{-1}}\left( \frac{{{x}^{3}}}{4} \right)+c\]     
  done clear
  B)
   \[{{\cosh }^{-1}}\left( \frac{{{x}^{3}}}{4} \right)+c\]
  done clear
  C)
   \[\frac{1}{12}{{\sec }^{-1}}\left( \frac{{{x}^{3}}}{4} \right)+c\]   
  done clear
  D)
   \[{{\sec }^{-1}}\left( \frac{{{x}^{3}}}{4} \right)+c\]
  done clear
  View Answer play_arrow

• question_answer172) If \[{{I}_{1}}=\int_{0}^{\pi /2}{x\sin x\,dx}\] and \[{{I}_{2}}=\int_{0}^{\pi /2}{x\cos x\,dx}\], then which one of the following is true?
  A)
   \[{{I}_{1}}+{{I}_{2}}=\frac{\pi }{2}\]
  done clear
  B)
   \[{{I}_{2}}-{{I}_{1}}=\frac{\pi }{2}\]
  done clear
  C)
   \[{{I}_{1}}+{{I}_{2}}=0\]
  done clear
  D)
   \[{{I}_{1}}={{I}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer173) If \[f(x)\] is defined [-2,2] by \[f(x)=4{{x}^{3}}-3x+1\] and\[g(x)=\frac{f(-x)-f(x)}{{{x}^{2}}+3}\],then \[\int_{-2}^{2}{g\,(x)\,dx}\] is equal to :
  A)
   64                                         
  done clear
  B)
   -48
  done clear
  C)
   0                                            
  done clear
  D)
   24
  done clear
  View Answer play_arrow

• question_answer174) The area enclosed between the parabola\[y={{x}^{2}}-x+2\] and the line \[y=x+2\] in sq unit equals :
  A)
   \[\frac{8}{3}\]                                  
  done clear
  B)
   \[\frac{1}{3}\]
  done clear
  C)
   \[\frac{2}{3}\]                                  
  done clear
  D)
   \[\frac{4}{3}\]
  done clear
  View Answer play_arrow

• question_answer175) The solution of the differential equation \[{{e}^{-x}}(y+1)\,dy+({{\cos }^{2}}x+\sin 2x)y\,dx=0\]subjected to the condition that \[y=1\] when\[x=0\] is :
  A)
   \[y+\log \,\,y+{{e}^{x}}{{\cos }^{2}}x=2\]
  done clear
  B)
   \[\log \,\,(y+1)+{{e}^{x}}{{\cos }^{2}}x=1\]
  done clear
  C)
   \[y+\log \,y={{e}^{x}}{{\cos }^{2}}x\]
  done clear
  D)
   \[(y+1)+{{e}^{x}}{{\cos }^{2}}x=2\]
  done clear
  View Answer play_arrow

• question_answer176) If \[y=1+\frac{1}{x}+\frac{1}{{{x}^{2}}}+\frac{1}{{{x}^{3}}}+.....\] to \[\infty \] with \[|x|>1\], then \[\frac{dy}{dx}\] is :
  A)
   \[\frac{{{x}^{2}}}{{{y}^{2}}}\]                                    
  done clear
  B)
   \[{{x}^{2}}{{y}^{2}}\]
  done clear
  C)
   \[\frac{{{y}^{2}}}{{{x}^{2}}}\]                                    
  done clear
  D)
   \[\frac{-{{y}^{2}}}{{{x}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer177) If \[f(x)\] and \[g(x)\] are two functions with\[g(x)=x-\frac{1}{x}\] and \[fog(x)={{x}^{3}}-\frac{1}{{{x}^{3}}}\], then \[f(x)\] is:
  A)
   \[3{{x}^{2}}+3\]                              
  done clear
  B)
   \[{{x}^{2}}-\frac{1}{{{x}^{2}}}\]
  done clear
  C)
   \[1+\frac{1}{{{x}^{2}}}\]                              
  done clear
  D)
   \[3{{x}^{2}}+\frac{3}{{{x}^{4}}}\]
  done clear
  View Answer play_arrow

• question_answer178) The derivative of \[{{a}^{\sec x}}\] w.r.t. \[{{a}^{\tan x}}(a>0)\] is.
  A)
   \[\sec x\,{{a}^{\sec x-\tan x}}\]               
  done clear
  B)
   \[\sin x\,{{a}^{\tan x-\sec x}}\]
  done clear
  C)
   \[\sin x\,{{a}^{\sec x-\tan x}}\]
  done clear
  D)
   \[{{a}^{\sec x-\tan x}}\]
  done clear
  View Answer play_arrow

• question_answer179) If \[\sin \,(x+y)\,+\cos \,(x+y)=\log \,(x+y)\], then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] is :
  A)
   \[\frac{-y}{x}\]                                
  done clear
  B)
   0
  done clear
  C)
   - 1                                         
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer180) If \[f(x)\] is a function such that\[f(x)+f(x)=0\] and \[g(x)={{[f(x)]}^{2}}+{{[f(x)]}^{2}}\] and \[g(3)=3\] then\[g(8)\] is equal to :
  A)
   5                                            
  done clear
  B)
   0
  done clear
  C)
   3                                            
  done clear
  D)
   8  
  done clear
  View Answer play_arrow