Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2007

done BCECE Engineering Solved Paper-2007 Total Questions - 150

• question_answer1) A body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is
  A)
   \[{{42}^{o}}8\]                
  done clear
  B)
   \[{{53}^{o}}7\]
  done clear
  C)
   \[{{33}^{o}}7\]
  done clear
  D)
          \[{{25}^{o}}8\]
  done clear
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• question_answer2) A gas bubble formed from an explosion under water oscillates with a period T proportional to \[{{P}^{a}}{{d}^{b}}{{E}^{c}},\]where P is pressure, d is the density of water and E is the total energy of explosion.  The value of a, b, c are
  A)
   \[a=1,\,\,\,\,\,b=1,\,\,\,\,c=2\]
  done clear
  B)
   \[a=1,\,\,\,\,\,b=2,\,\,\,\,c=1\]
  done clear
  C)
   \[a=\frac{5}{6},\]\[b=\frac{1}{2},c=\frac{1}{3}\]
  done clear
  D)
   \[a=-\frac{5}{6},b=\frac{1}{2},c=\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer3) A particle moving with a uniform acceleration travels 24 A and 64m in the first two consecutive interval of 4s each. Its initial velocity will be
  A)
   5 m/s   
  done clear
  B)
          3 m/s   
  done clear
  C)
          1 m/s   
  done clear
  D)
          4 m/s
  done clear
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• question_answer4) Two equal vectors have a resultant equal to either of them, then the angle between them will be
  A)
   \[~{{120}^{o}}\]                              
  done clear
  B)
   \[~{{110}^{o}}\]              
  done clear
  C)
          \[{{60}^{o}}\]                   
  done clear
  D)
          \[~150{}^\circ \]
  done clear
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• question_answer5) If the radius of earth of R then the height h at which the value of g becomes one fourth, will be
  A)
   \[~~\frac{R}{8}~~~\]                    
  done clear
  B)
   \[~~\frac{3R}{8}~~~\]  
  done clear
  C)
          \[~~\frac{3R}{4}~~~\]  
  done clear
  D)
          \[\frac{R}{2}\]
  done clear
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• question_answer6) A body moves a distance of 10 m along a straight line under a action of 5 N force. If work done is 25 J, then angle between the force and direction of motion of the body will be
  A)
   \[{{75}^{o}}\]                                   
  done clear
  B)
   \[{{60}^{o}}\]                   
  done clear
  C)
   \[{{45}^{o}}\]                   
  done clear
  D)
          \[{{30}^{o}}\]
  done clear
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• question_answer7) If 150 J of heat is added to a system work done by the system is 110 J, the in internal energy will be
  A)
   40 J                                       
  done clear
  B)
   110 J    
  done clear
  C)
          150 J                    
  done clear
  D)
          260 J
  done clear
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• question_answer8) Sum of the two binary numbers \[{{(100010)}_{2}}\]and \[{{(11011)}_{2}}\]is  \[{{(11011)}_{2}}\]is
  A)
   \[{{(111111)}_{2}}\]
  done clear
  B)
   \[{{(101111)}_{2}}\]
  done clear
  C)
   \[{{(111001)}_{2}}\]
  done clear
  D)
   \[{{(111101)}_{2}}\]
  done clear
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• question_answer9) What is the velocity of the bob of pendulum at its mean position, if it is a1 to vertical height of 10 cm? \[(g=9.8\,m/{{s}^{2}})\]
  A)
   \[2.2\text{ }m/s\]          
  done clear
  B)
   \[1.8\text{ }m/s\]          
  done clear
  C)
          \[1.4\text{ }m/s\]       
  done clear
  D)
          \[0.6\text{ }m/s\]
  done clear
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• question_answer10) A body cools from \[60{{\,}^{o}}C\] to \[50{{\,}^{o}}C\] in 1 the room temperature is\[25{{\,}^{o}}C\] and assuming Newton law of cooling to hold g temperature of the body at the end of the next 10 min will be
  A)
   \[~45{{\,}^{o}}C\]                          
  done clear
  B)
   \[~42.85{{\,}^{o}}C\]    
  done clear
  C)
          \[40{{\,}^{o}}C\]             
  done clear
  D)
          \[~38.5{{\,}^{o}}C\]
  done clear
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• question_answer11) At \[27{}^\circ C\] a gas suddenly compressed such that its pressure becomes \[\frac{1}{8}\text{th}\] of original pressure. The temperature of the gas will be \[(\gamma =5/3)\]
  A)
   \[-142{{\,}^{o}}C\]                         
  done clear
  B)
   \[300\,K\]          
  done clear
  C)
          \[327{{\,}^{o}}C\]          
  done clear
  D)
          \[420\,K\]
  done clear
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• question_answer12) An ideal refrigerator has a freezer at a temperature of \[-\text{ }13{{\,}^{o}}C.\] The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) will be
  A)
   \[325{{\,}^{o}}C\]         
  done clear
  B)
   325 K   
  done clear
  C)
          \[~39{{\,}^{o}}C\]          
  done clear
  D)
          \[320{{\,}^{o}}C\]
  done clear
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• question_answer13) In a capacitor of capacitance \[20\,\mu F\] the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, then the new capacitance will be
  A)
   \[22\,\mu F\]                   
  done clear
  B)
   \[26.6\,\mu F\]               
  done clear
  C)
          \[52.2\text{ }\mu \text{F}\]        
  done clear
  D)
          \[~13\text{ }\mu \text{F}\]
  done clear
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• question_answer14) An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in this spring when it has been compressed by 0.2 m to the potential energy stored in a \[10\,\mu F\] capacitor at a potential difference of 10000 V will be
  A)
   1/4                       
  done clear
  B)
          1                            
  done clear
  C)
   1/2                       
  done clear
  D)
          2
  done clear
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• question_answer15) A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell having charge - Q. The radius of the sphere is a and that of the spherical shell is \[b(b>a).\]What is the electric field at a distance \[R(a<R<b)\]from the centre?
  A)
   \[\frac{4Q}{2\pi \,{{\varepsilon }_{0}}{{R}^{2}}}\]                            
  done clear
  B)
   \[\frac{3Q}{4\pi \,{{\varepsilon }_{0}}{{R}^{2}}}\]            
  done clear
  C)
          \[\frac{3Q}{2\pi \,{{\varepsilon }_{0}}{{R}^{2}}}\]            
  done clear
  D)
          \[\frac{Q}{2\pi \,{{\varepsilon }_{0}}R}\]
  done clear
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• question_answer16) Output \[Y\]is given by:
  A)
   \[(\bar{X}.\bar{Y}).Z\]                 
  done clear
  B)
   \[(X+Y)Z\]         
  done clear
  C)
          \[(X+Y)\bar{Z}\]             
  done clear
  D)
          \[\bar{X}.\bar{Y}+Z\]
  done clear
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• question_answer17) In a network as shown in the figure, the potential difference across the resistance 2R is (the cell has an emf of E volts and has no internal resistance)
  A)
   2E                                         
  done clear
  B)
   \[\frac{4E}{7}\]               
  done clear
  C)
   \[\frac{E}{7}\]                  
  done clear
  D)
          \[E\]
  done clear
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• question_answer18) The resistance of a galvanometer coil is R, then the shunt resistance required to convert it into a ammeter of range 4 times, will be
  A)
   4R                                         
  done clear
  B)
   \[\frac{R}{3}\]                 
  done clear
  C)
   \[\frac{R}{4}\]                 
  done clear
  D)
          \[\frac{R}{5}\]
  done clear
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• question_answer19) The instrument used by doctors for endoscopy works on the principle of
  A)
   total internal reflection
  done clear
  B)
   reflection
  done clear
  C)
   refraction
  done clear
  D)
   none of the above
  done clear
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• question_answer20) A meter stick is held vertically with one end on the floor and is then allowed to fall. Assuming that the end on the floor the stick does not slip, the velocity of the other end when it hits the floor, will be
  A)
   \[10.8\text{ }m/s\]        
  done clear
  B)
   \[~5.4\text{ }m/s\]       
  done clear
  C)
   \[~2.5\text{ }m/s\]     
  done clear
  D)
   none of these
  done clear
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• question_answer21) If the coefficient of static friction between the tyres and road is 0.5, what is the shortest distance in which an automobile can be stopped when travelling at 72 km/h?
  A)
   50 m                                    
  done clear
  B)
   60 m    
  done clear
  C)
          40.8 m                 
  done clear
  D)
          80.16 m
  done clear
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• question_answer22) A bullet fired at an angle of \[{{30}^{o}}\] with the horizontal hits the ground 3 km away. By adjusting its angle of projection, can one hope to hit a target 5 km away. Assume the muzzle speed to be same and the air resistance is negligible
  A)
   possible to hit a target 5 km away
  done clear
  B)
   not possible to hit a target 5 km away
  done clear
  C)
   prediction is not possible
  done clear
  D)
   none of the above
  done clear
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• question_answer23) Two springs of spring constant 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in ratio
  A)
   1 : 2                      
  done clear
  B)
          2 : 1                      
  done clear
  C)
   1 : 4                      
  done clear
  D)
          4 : 1
  done clear
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• question_answer24) The elastic energy stored in a wire of Youngs modulus Y is
  A)
   \[\frac{\text{1}}{\text{2}}\text{Y}\,\text{ }\!\!\times\!\!\text{ }\,\text{stress}\,\text{ }\!\!\times\!\!\text{  strain}\,\text{ }\!\!\times\!\!\text{ }\,\text{volume}\]
  done clear
  B)
   \[\frac{{{\text{(stress)}}^{\text{2}}}\text{ }\!\!\times\!\!\text{ }\,\text{volume}}{\text{2Y}}\]
  done clear
  C)
   \[stress\times strain\times volume\]
  done clear
  D)
   \[Y\times \frac{{{(stress)}^{2}}}{volume}\]
  done clear
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• question_answer25) A soap bubble A of radius 0.03 and another bubble B of radius 0.04 m are brought together so that the combined bubble has a common interface of radius r, then the value of r is
  A)
   0.24 m                                 
  done clear
  B)
   0.48 m 
  done clear
  C)
          0.12m                  
  done clear
  D)
          none of these
  done clear
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• question_answer26) An air bubble of radius \[{{10}^{-2}}\,m\] is rising up at a steady rate of \[2\times {{10}^{-3}}m/s\] through a liquid of density \[1.5\times {{10}^{3}}kg/{{m}^{3}},\] the coefficient of viscosity neglecting the density of. air, will be \[(g=10\,m/{{s}^{2}})\]
  A)
   23.2 units           
  done clear
  B)
   83.5 units           
  done clear
  C)
          334 units       
  done clear
  D)
          167 units
  done clear
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• question_answer27) A Carnot reversible engine converts 1/6 of heat input into work. When the temperature of the sink is reduced by 62 K, the efficiency of Carnots cycle becomes 1/3. The temperature of the source and sink will be
  A)
   \[372\text{ }K,\text{ }310\text{ }K\]      
  done clear
  B)
   \[~181\text{ }K,\text{ }150\text{ }K\]
  done clear
  C)
          \[~472\text{ }K,\text{ }410\text{ }K\]
  done clear
  D)
          none of the above
  done clear
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• question_answer28) The ratio of the coefficient of thermal conductivity of two different materials is \[5:3.\] If the thermal resistance of the rods of same thickness of these materials is same, then the ratio of the length of these rods will be
  A)
   3 : 5                                      
  done clear
  B)
   5 : 3
  done clear
  C)
   3 : 4                      
  done clear
  D)
          3 : 2
  done clear
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• question_answer29) Compressional wave pulses are sent to the bottom of sea from a ship and the echo is heard after 2 s. If bulk modulus of elasticity of water is \[2\times {{10}^{9}}\text{ }N/{{m}^{2}}\]and mean temperature is \[4{{\,}^{o}}C,\] the depth of the sea will be
  A)
   1014 m                                
  done clear
  B)
   1414 m
  done clear
  C)
          2828 m                
  done clear
  D)
          none of these
  done clear
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• question_answer30) Sound waves of \[f=600\,Hz\]fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration will be (speed of sound = 300 m/s)
  A)
   \[\frac{7}{8}m\]                              
  done clear
  B)
   \[\frac{3}{8}m\]                              
  done clear
  C)
   \[\frac{1}{8}m\]                              
  done clear
  D)
          \[\frac{1}{4}m\]
  done clear
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• question_answer31) A pipe closed at one end produces a fundamental note of 412 Hz. It is cut into two pieces of equal length the fundamental notes produced by the two pieces are
  A)
   \[~824\text{ }Hz,\text{ }1648\text{ }Hz\]
  done clear
  B)
   \[~412\text{ }Hz,\text{ }824\text{ }Hz\]
  done clear
  C)
   \[~206\text{ }Hz,\text{ }412\text{ }Hz\]
  done clear
  D)
   \[216\text{ }Hz,\text{ }824\text{ }Hz\]
  done clear
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• question_answer32) The refractive index of water and glycerine are 1.33 and 1.47 respectively. What is the critical angle for a light ray going from the later to the former?
  A)
  \[60{}^\circ 48\]               
  done clear
  B)
          \[64{}^\circ 48\]                              
  done clear
  C)
         \[74{}^\circ 48\]                               
  done clear
  D)
   None of these
  done clear
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• question_answer33) Lenses of power 3 D and -5D are combined to form a compound lens. An object is placed at a distance of 50 cm from this lens. Its image will be formed at a distance from the lens, will be
  A)
   25 cm                                  
  done clear
  B)
   20 cm                  
  done clear
  C)
          30 cm                  
  done clear
  D)
          40 cm
  done clear
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• question_answer34) If fringes width \[\lambda =5.89\times {{10}^{-5}}\] mm is 0.431 mm and shift of white central fringe on introducing a mica sheet in one path is 1.89 mm. Thickness of the mica sheet will be \[(\mu =1.59)\]
  A)
   \[4.38\,\times {{10}^{-6}}m\]                   
  done clear
  B)
   \[5.38\,\times {{10}^{-6}}m\]   
  done clear
  C)
          \[6.38\,\times {{10}^{-6}}m\]   
  done clear
  D)
          none of these
  done clear
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• question_answer35) A body is orbiting around earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is
  A)
   4 days                                 
  done clear
  B)
   16 days                               
  done clear
  C)
   \[2\sqrt{2}\] days          
  done clear
  D)
          64 days
  done clear
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• question_answer36) A radioactive substance has half-life of 60 min. During 3 h, the fraction of the substance that has to be decayed, will be
  A)
   87.5%                  
  done clear
  B)
   52.5%                  
  done clear
  C)
          25.5%                  
  done clear
  D)
          8.5%
  done clear
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• question_answer37) Voltage in the secondary coil of a transformer does not depend upon
  A)
   frequency of the source
  done clear
  B)
   voltage in the primary coil
  done clear
  C)
   ratio of number of turns in the two coils
  done clear
  D)
   both (b) and (c)
  done clear
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• question_answer38) When n-p-n transistor is used as an amplifier
  A)
   electrons move from emitter to base
  done clear
  B)
   electrons move from base to emitter
  done clear
  C)
   electrons move from collector to base
  done clear
  D)
   holes move from base to emitter
  done clear
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• question_answer39) \[_{\text{7}}{{\text{N}}^{\text{14}}}\]is bombarded with \[_{2}H{{e}^{\text{4}}}.\] The resulting nucleus is \[_{8}{{O}^{17}}\] with the emission of
  A)
   neutrino            
  done clear
  B)
          antineutrino     
  done clear
  C)
          proton                
  done clear
  D)
          neutron
  done clear
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• question_answer40) In the given figure the steady state current in the circuit is
  A)
  Zero                                     
  done clear
  B)
  0.6 A                    
  done clear
  C)
  0.9 A                    
  done clear
  D)
  1.5 A
  done clear
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• question_answer41) The time of vibration of a dip needle vibration in the vertical plane in the magnetic meridian is 3 s. When the same magnetic needle is made to vibrate in the horizontal plane, the time of vibration is 3\[\sqrt{2}\]s. Then angle of dip will be
  A)
  \[90{}^\circ \]                                   
  done clear
  B)
  \[60{}^\circ \]                   
  done clear
  C)
  \[45{}^\circ \]                                                   
  done clear
  D)
  \[30{}^\circ \]
  done clear
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• question_answer42) The inductance of the oscillatory circuit of a radio station is 10 mH and its capacitance is 0.25 \[\mu F\].Taking the effect of resistance negligible, wavelength of the broadcasted waves will be (velocity of light \[=3.0\,\times {{10}^{8}}\,m/s,\,\pi =3.14\])
  A)
   \[9.42\,\times {{10}^{4}}\,m\]                                  
  done clear
  B)
   \[18\,\times 8.\,{{10}^{4}}m\]  
  done clear
  C)
          \[4.5\,\times {{10}^{4}}\,m\]    
  done clear
  D)
          none of these
  done clear
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• question_answer43) The \[{{K}_{\alpha }}\] line of singly ionized calcium has a wavelength of 393.3 nm as measured on earth. In the spectrum of one of the observed galaxies, the spectral line is located at 401.8 nm. The speed with which this galaxy is moving away from us, will be
  A)
   7400 m/s                            
  done clear
  B)
   \[32.\,4\times {{10}^{2}}m/s\]
  done clear
  C)
   6480 km/s         
  done clear
  D)
          none of these
  done clear
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• question_answer44) In a common-base circuit of a transistor current amplification factor is 0.95. The base current when emitter current is 2 mA, will be
  A)
   0.2mA                                 
  done clear
  B)
   0.1mA                 
  done clear
  C)
   0.002 mA           
  done clear
  D)
          none of these
  done clear
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• question_answer45) Cathode rays of velocity \[{{10}^{6}}\,m/s\] describe an approximate circular path of radius 1 m in an electric field 300 V/cm. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be
  A)
   2400 V/cm                         
  done clear
  B)
   600 V/cm           
  done clear
  C)
          1200 V/cm         
  done clear
  D)
          12000 V/cm
  done clear
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• question_answer46) Light of wavelength \[5000\overset{\text{o}}{\mathop{\text{A}}}\,\] falling on a sensitive surface. If the surface has received \[{{10}^{-7}}J\] of energy, then the number of photons falling on the surface will be:
  A)
   \[5\times {{10}^{11}}\]                                
  done clear
  B)
   \[2.5\,\times {{10}^{11}}\]              
  done clear
  C)
              \[3\times {{10}^{11}}\]                
  done clear
  D)
          none of these
  done clear
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• question_answer47) An X-ray machine is opearated at 40 kV. The short wavelength limit of continuous X-rays will be \[(h=6.63\,\times {{10}^{-34}}\,Js,\,\,c=3\times {{10}^{8}}m/s,\,e=1.6\times {{10}^{-19}}C)\]
  A)
   \[0.31\,\overset{\text{o}}{\mathop{\text{A}}}\,\]                                         
  done clear
  B)
   \[0.62\,\overset{\text{o}}{\mathop{\text{A}}}\,\]                         
  done clear
  C)
   \[0.155\,\overset{\text{o}}{\mathop{\text{A}}}\,\]                       
  done clear
  D)
          \[0.62\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
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• question_answer48) The wavelength of the first spectral line of sodium is \[5896\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The first excitation potential of sodium atom will be \[(h=6.63\times {{10}^{-34}}\,Js)\]
  A)
   4.2 V                                    
  done clear
  B)
   3.5 V                    
  done clear
  C)
   2.1 V                    
  done clear
  D)
          None of these
  done clear
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• question_answer49) If 200 MeV energy is released in the fission of a single nucleus of \[_{92}{{U}^{235}}\]. How much fission must occur per second to produce a power of 1kW?
  A)
   \[3.125\,\times {{10}^{13}}\]                    
  done clear
  B)
   \[6.250\,\times {{10}^{13}}\]       
  done clear
  C)
              \[1.525\,\times {{10}^{13}}\]    
  done clear
  D)
          None of these
  done clear
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• question_answer50) The energy supplied to calculate by state electricity board during an average November day was 40 mkh. If this energy could be obtained by the conversion of matter, how much mass will be annihilated?
  A)
   3.2 g                                     
  done clear
  B)
          6.4 g                                     
  done clear
  C)
          1.6 g                                     
  done clear
  D)
          2.5 g
  done clear
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• question_answer51) Which one of the following represents noble gas configuration?
  A)
   \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{d}^{10}},\]\[5{{s}^{2}},5{{p}^{6}}5{{d}^{6}},6{{s}^{2}}\]
  done clear
  B)
   \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{d}^{10}},\]\[5{{s}^{2}}5{{p}^{6}}5{{d}^{1}},6{{s}^{2}}\]
  done clear
  C)
   \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{d}^{10}}\]\[5{{s}^{2}}5{{p}^{6}}\]
  done clear
  D)
   \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{f}^{14}},\]\[5{{s}^{2}}5{{p}^{6}}5{{d}^{1}}\]
  done clear
  View Answer play_arrow

• question_answer52) The number of unpaired electrons in \[\text{Ni(CO}{{\text{)}}_{\text{4}}}\]
  A)
   0            
  done clear
  B)
                          1
  done clear
  C)
   3                            
  done clear
  D)
          4
  done clear
  View Answer play_arrow

• question_answer53) Nitrobenzene on treatment with zinc dust and aqueous ammonium chloride gives
  A)
   \[{{C}_{6}}{{H}_{5}}-N=N-{{C}_{6}}{{H}_{5}}\]
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}NO\]
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}NHOH\]
  done clear
  View Answer play_arrow

• question_answer54) Which one of the following is a correct statement?
  A)
   All metal nitrates are insoluble in water
  done clear
  B)
   Solubility depends on temperature
  done clear
  C)
   All metal nitrates are soluble in water
  done clear
  D)
   All metal nitrates are soluble in alcohol
  done clear
  View Answer play_arrow

• question_answer55) Methyl \[-\alpha -D-\]glucoside and methyl\[-\beta -D-\]glucoside are
  A)
   epimers
  done clear
  B)
   anomers
  done clear
  C)
   enantiomers
  done clear
  D)
   conformational diastereomers
  done clear
  View Answer play_arrow

• question_answer56) Which one of the following shows maximum value of paramagnetic behaviour?
  A)
   \[{{[Sc{{(CN)}_{6}}]}^{3-}}\]      
  done clear
  B)
   \[{{[Co{{(CN)}_{6}}]}^{3-}}\]
  done clear
  C)
   \[{{[Fe{{(CN)}_{6}}]}^{4-}}\]
  done clear
  D)
          \[{{[Cr{{(CN)}_{6}}]}^{3-}}\]
  done clear
  View Answer play_arrow

• question_answer57) Carbolic acid is
  A)
  \[~HCOOH\]      
  done clear
  B)
          \[~C{{H}_{3}}COOH\]
  done clear
  C)
   \[~{{C}_{6}}{{H}_{5}}COOH\]
  done clear
  D)
          \[~{{C}_{6}}{{H}_{5}}OH\]
  done clear
  View Answer play_arrow

• question_answer58) The solubility product of \[BaC{{l}_{2}}\] is \[4\times {{10}^{-9}}.\] Its solubility in mol/L is
  A)
   \[4\times {{10}^{-3}}\]                 
  done clear
  B)
   \[4\times {{10}^{-9}}\]
  done clear
  C)
   \[1\times {{10}^{-3}}\] 
  done clear
  D)
          \[1\times {{10}^{-9}}\]
  done clear
  View Answer play_arrow

• question_answer59) Which one can differentiate between \[{{C}_{2}}{{H}_{5}}OH\] and\[C{{H}_{3}}OH\]?
  A)
   \[{{H}_{2}}O\] 
  done clear
  B)
          \[N{{a}_{2}}C{{O}_{3}}+{{I}_{2}}\]
  done clear
  C)
   \[N{{H}_{3}}\] 
  done clear
  D)
          \[HCl\]
  done clear
  View Answer play_arrow

• question_answer60) Zinc and cold dil. \[HN{{O}_{3}}\] reacts to produce
  A)
   NO                                       
  done clear
  B)
   \[N{{O}_{2}}\]
  done clear
  C)
   \[N{{H}_{4}}N{{O}_{3}}\]      
  done clear
  D)
          \[ZnN{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer61) For the reaction, \[{{H}_{2}}+{{I}_{2}}2HI,\]the equilibrium concentration of \[{{H}_{2}},{{I}_{2}}\]and HI are 8.0, 3.0 and 28.0 mol/L respectively. The equilibrium constant is
  A)
   28.34                                   
  done clear
  B)
   32.66
  done clear
  C)
   34.78                   
  done clear
  D)
          38.88
  done clear
  View Answer play_arrow

• question_answer62) Tincture of iodine is
  A)
   aqueous solution bf \[{{I}_{2}}\]
  done clear
  B)
   solution of \[{{I}_{2}}\] in aqueous \[KI\]
  done clear
  C)
   alcoholic solution of \[{{I}_{2}}\]
  done clear
  D)
   aqueous solution of \[KI\]
  done clear
  View Answer play_arrow

• question_answer63) The chemical formula of plaster of Paris is
  A)
  \[CaS{{O}_{4}}.\frac{1}{2}{{H}_{2}}O\]
  done clear
  B)
          \[CaS{{O}_{4}}.{{H}_{2}}O\]
  done clear
  C)
   \[CaS{{O}_{4}}.2{{H}_{2}}O\]
  done clear
  D)
          \[CaS{{O}_{4}}.3{{H}_{2}}O\]
  done clear
  View Answer play_arrow

• question_answer64) Which one of the following has square planar structure?
  A)
  \[{{[Ni{{(CN)}_{4}}]}^{2-}}\]                       
  done clear
  B)
   \[[Ni{{(CO)}_{4}}]\]
  done clear
  C)
   \[{{[NiC{{l}_{4}}]}^{2-}}\]            
  done clear
  D)
          All of the above
  done clear
  View Answer play_arrow

• question_answer65) The oxidation number of chromium in potassium dichromate is
  A)
   + 2                                        
  done clear
  B)
   + 4
  done clear
  C)
   + 6                        
  done clear
  D)
          + 8
  done clear
  View Answer play_arrow

• question_answer66) The electronic configuration of most electronegative element? is
  A)
  \[1{{s}^{2}},2{{s}^{2}}2{{p}^{5}}\]            
  done clear
  B)
          \[1{{s}^{2}},2{{s}^{2}}2{{p}^{4}},3{{s}^{1}}\]
  done clear
  C)
   \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{1}}3{{p}^{1}}\]
  done clear
  D)
   \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{5}}\]
  done clear
  View Answer play_arrow

• question_answer67) The molecular formula \[{{C}_{3}}{{H}_{9}}N\]cannot represent
  A)
   \[{{1}^{o}}\]amine                        
  done clear
  B)
  \[{{2}^{o}}\]amine
  done clear
  C)
   \[{{3}^{o}}\]amine      
  done clear
  D)
   quaternary salt
  done clear
  View Answer play_arrow

• question_answer68) The bond length between \[C-C\]bond in \[s{{p}^{2}}\]hybridized molecule is
  A)
   \[1.2\overset{\text{o}}{\mathop{\text{A}}}\,\]                               
  done clear
  B)
   \[1.39\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  C)
   \[1.33\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]              
  done clear
  D)
         \[~1.54\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  View Answer play_arrow

• question_answer69) The energy ratio of a photon of wavelength \[\text{3000 }\overset{\text{o}}{\mathop{\text{A}}}\,\]and \[\text{6000 }\overset{\text{o}}{\mathop{\text{A}}}\,\]is
  A)
   1 : 1                                      
  done clear
  B)
   2 : 1
  done clear
  C)
   1 : 2                      
  done clear
  D)
          1 : 4
  done clear
  View Answer play_arrow

• question_answer70) Gas equation \[PV=nRT\]is obeyed by ideal gas in             
  A)
   adiabatic process
  done clear
  B)
   isothermal process
  done clear
  C)
   both (a) and (b)
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer71) Clemmensens reduction of ketones is carried  out in
  A)
  \[LiAl{{H}_{4}}\]in \[{{H}_{2}}O\]             
  done clear
  B)
   glycol and KOH
  done clear
  C)
   \[Zn-Hg\]and \[HCl\]
  done clear
  D)
         \[{{H}_{2}}\]and \[Pd\]catalyst
  done clear
  View Answer play_arrow

• question_answer72) The planar structure of \[B{{F}_{3}}\]can be explained by the fact that \[B{{F}_{3}}\] is
  A)
   \[sp-\]hybridized           
  done clear
  B)
   \[s{{p}^{2}}-\]hybridized
  done clear
  C)
   \[s{{p}^{3}}-\]hybridized
  done clear
  D)
          \[s{{p}^{3}}d\]hybridized
  done clear
  View Answer play_arrow

• question_answer73) Reduction of aniline with acetyl chloride in presence of \[\text{NaOH}\]produce
  A)
   aniline hydrochloride
  done clear
  B)
   acetanilide
  done clear
  C)
   p-chloroaniline
  done clear
  D)
   a red dye
  done clear
  View Answer play_arrow

• question_answer74) Which of the following compounds has the highest boiling point?
  A)
  \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}Cl\]
  done clear
  B)
   \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}Cl\]
  done clear
  C)
   \[C{{H}_{3}}CH(C{{H}_{3}})C{{H}_{2}}Cl\]
  done clear
  D)
   \[{{(C{{H}_{3}})}_{3}}CCl\]
  done clear
  View Answer play_arrow

• question_answer75) An unknown compound D first oxidized to aldehyde and then acetic acid by a dilute solution of \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]and \[{{H}_{2}}S{{O}_{4}}.\]The compound D is
  A)
  \[C{{H}_{3}}OH\]      
  done clear
  B)
  \[{{C}_{2}}{{H}_{5}}OH\]                              
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}COOH\] 
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}CHO\]
  done clear
  View Answer play_arrow

• question_answer76) Which of the following is not possible?
  A)
  \[n=2,\,l=1,m=0\]           
  done clear
  B)
   \[n=2,\,l=0,m=-1\]
  done clear
  C)
   \[n=3,\,l=0,m=0\]
  done clear
  D)
   \[n=3,\,l=1,m=-1\]
  done clear
  View Answer play_arrow

• question_answer77) A gas expands isothermally against a constant external pressure of 1 atm from a volume of \[10\,d{{m}^{3}}\]to a volume of \[20\,d{{m}^{3}}.\] It absorbs 300 J of thermal energy from its surroundings. The \[\Delta U\]is
  A)
  \[-312\,J\]          
  done clear
  B)
         \[+\,123J\]
  done clear
  C)
  \[-213\,J\]          
  done clear
  D)
                         \[+\,231\,J\]
  done clear
  View Answer play_arrow

• question_answer78) Phenol is more acidic than alcohol because
  A)
   phenol is more soluble in polar solvents
  done clear
  B)
   alcohol does not lose hydrogen atom
  done clear
  C)
   phenoxide ion is stabilized by resonance
  done clear
  D)
   phenoxide ion do not exhibit resonance
  done clear
  View Answer play_arrow

• question_answer79) The element having highest electron affinity
  A)
   bromine       
  done clear
  B)
          iodine 
  done clear
  C)
          fluorine              
  done clear
  D)
          chlorine
  done clear
  View Answer play_arrow

• question_answer80) Bakelite is prepared by the reaction between
  A)
   phenol and formaldehyde
  done clear
  B)
   urea and formaldehyde
  done clear
  C)
   ethylene and glycol
  done clear
  D)
   tetramethylene and glycol
  done clear
  View Answer play_arrow

• question_answer81) Which one of the following is a conjugated protein?
  A)
   Phosphoprotein
  done clear
  B)
   Glycoprotein
  done clear
  C)
   Chromoprotein
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer82) Iodine test is shown by
  A)
   glucose                               
  done clear
  B)
   starch
  done clear
  C)
   glycogen       
  done clear
  D)
                          polypeptide
  done clear
  View Answer play_arrow

• question_answer83) A fruity smell is obtained by the reaction of ethanol with
  A)
  \[~C{{H}_{3}}COC{{H}_{3}}~~~~~~~\]   
  done clear
  B)
   \[PC{{l}_{5}}\]
  done clear
  C)
   \[C{{H}_{3}}COOH\]
  done clear
  D)
                          \[C{{H}_{3}}CHO\]         
  done clear
  View Answer play_arrow

• question_answer84) Cyanide process is used for extraction of
  A)
   Ag                                         
  done clear
  B)
   Ni                          
  done clear
  C)
   Pt                          
  done clear
  D)
          Zn
  done clear
  View Answer play_arrow

• question_answer85) An acid solution of 0.005 M has a pH of 5. The degree of ionization of acid is
  A)
  \[0.1\times {{10}^{-2}}\]                              
  done clear
  B)
   \[0.2\times {{10}^{-2}}\]                             
  done clear
  C)
   \[0.5\times {{10}^{-4}}\]             
  done clear
  D)
          \[0.6\times {{10}^{-6}}\]
  done clear
  View Answer play_arrow

• question_answer86) Which metal gives hydrogen gas on heating with hot concentrated alkali?
  A)
   Ag                                         
  done clear
  B)
   Ni                          
  done clear
  C)
   Zn                         
  done clear
  D)
          Cu
  done clear
  View Answer play_arrow

• question_answer87) The conversion of ethyl chloride into diethyl ether takes place by
  A)
   Williamsons synthesis
  done clear
  B)
   Perkins reaction
  done clear
  C)
   Wurtz reaction
  done clear
  D)
   Grignard reaction
  done clear
  View Answer play_arrow

• question_answer88) \[CHC{{l}_{3}}+{{C}_{6}}{{H}_{5}}N{{H}_{2}}+3NaOH\xrightarrow{{}}A\] \[+\,3B\,+3C\] In the above reaction, the product A is
  A)
   chlorobenzene               
  done clear
  B)
   phenyl isocyanide
  done clear
  C)
          phenyl cyanide
  done clear
  D)
          phenyl chloride
  done clear
  View Answer play_arrow

• question_answer89) A gas is found to have a formula \[{{[CO]}_{x}}.\]Its vapour density is 70, the \[x\] is
  A)
   3.0                        
  done clear
  B)
          3.5                        
  done clear
  C)
   5.0                          
  done clear
  D)
   6.5
  done clear
  View Answer play_arrow

• question_answer90) Which of the following is used as purgative?
  A)
  \[HgS\]                
  done clear
  B)
   \[H{{g}_{2}}C{{l}_{2}}\]
  done clear
  C)
          \[HgC{{l}_{2}}\]               
  done clear
  D)
          \[ZnS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer91) Least stable oxide of chlorine is
  A)
  \[C{{l}_{2}}O\]                  
  done clear
  B)
   \[Cl{{O}_{2}}\] 
  done clear
  C)
          \[C{{l}_{2}}{{O}_{7}}\]  
  done clear
  D)
          \[Cl{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer92) The sides of safety matches contains
  A)
   red phosphorus + sand powder
  done clear
  B)
  \[{{P}_{4}}{{S}_{3}}\]
  done clear
  C)
  \[C{{a}_{3}}{{(PO)}_{4}}+\text{glass}\,\text{pieces}\]
  done clear
  D)
  \[KCl{{O}_{3}},KN{{O}_{3}},\] sulphur + antimony
  done clear
  View Answer play_arrow

• question_answer93) Chemically aspirin is known as
  A)
   salicylic acid
  done clear
  B)
   salicylaldehyde
  done clear
  C)
   2-acetoxybenzoic acid
  done clear
  D)
   phenyl salicylate
  done clear
  View Answer play_arrow

• question_answer94) Gun metal is
  A)
  \[Cu+Zn\]           
  done clear
  B)
          \[Cu+Sn+Zn\]
  done clear
  C)
          \[Cu+Sn\]          
  done clear
  D)
          \[Zn+Sn\]
  done clear
  View Answer play_arrow

• question_answer95) Which cannot be oxidized by\[{{H}_{2}}{{O}_{2}}\]?
  A)
  \[N{{a}_{2}}S{{O}_{3}}\]              
  done clear
  B)
         \[PbS\]
  done clear
  C)
          \[KI\]                   
  done clear
  D)
          \[{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer96) The gas not absorbed by coconut charcoal is
  A)
   He                        
  done clear
  B)
          Ne                        
  done clear
  C)
   Ar                         
  done clear
  D)
          Kr
  done clear
  View Answer play_arrow

• question_answer97) KI and \[CuS{{O}_{4}}\]solutions on mixing produce
  A)
  \[C{{u}_{2}}{{I}_{2}}+{{K}_{2}}S{{O}_{4}}\]
  done clear
  B)
   \[C{{u}_{2}}{{I}_{2}}+{{I}_{2}}+{{K}_{2}}S{{O}_{4}}\]
  done clear
  C)
   \[Cu{{I}_{2}}+{{K}_{2}}S{{O}_{4}}\]
  done clear
  D)
   \[Cu{{I}_{2}}+{{I}_{2}}+{{K}_{2}}S{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer98) Vitamin \[{{B}_{12}}\]contains
  A)
   Co                         
  done clear
  B)
          Mn                       
  done clear
  C)
          Mg                       
  done clear
  D)
          Fe
  done clear
  View Answer play_arrow

• question_answer99) Water glass is
  A)
   glass made of water
  done clear
  B)
   sodium silicate
  done clear
  C)
   calcium formate
  done clear
  D)
   pyrex glass                      
  done clear
  View Answer play_arrow

• question_answer100) Purification of alumina takes place by
  A)
   Bosch process
  done clear
  B)
   Halls process
  done clear
  C)
   Hoopes process
  done clear
  D)
   Quartation process
  done clear
  View Answer play_arrow

• question_answer101) If \[f(x)=f(a-x)\] and \[g(x)+g(a-x)=2,\]then the value of \[\int\limits_{0}^{a}{f(x)g(x)dx}\] is
  A)
  \[\int_{0}^{a}{f(x)dx}\]                
  done clear
  B)
   \[\int_{0}^{a}{g(x)dx}\]              
  done clear
  C)
          \[\int_{0}^{a}{[g(x)-f(x)]dx}\]
  done clear
  D)
          \[\int_{0}^{a}{[g(x)+f(x)]dx}\]
  done clear
  View Answer play_arrow

• question_answer102) The differential equation of the family of the curves \[{{x}^{2}}+{{y}^{2}}-2ax=0\]is
  A)
  \[{{x}^{2}}-{{y}^{2}}-2ax=0\]
  done clear
  B)
   \[{{y}^{2}}-{{x}^{2}}=2xyy\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+2y=0\]
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer103) A body falls freely from the top of a tower and during the last second of its flight it falls \[\frac{\text{5}}{\text{9}}\text{th}\]of the whole distance. The height of the tower and time of motion are respectively
  A)
   44.1 m and 3s
  done clear
  B)
   44.1m and 5s
  done clear
  C)
   4.41 m and 3s
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer104) The sum of the series \[\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+...\]upto \[n\] term is
  A)
  \[n-1+\frac{1}{{{2}^{n}}}\]          
  done clear
  B)
          \[n+\frac{1}{{{2}^{n}}}\]             
  done clear
  C)
          \[2n+\frac{1}{{{2}^{n}}}\]           
  done clear
  D)
          \[n+1+\frac{1}{{{2}^{n}}}\]
  done clear
  View Answer play_arrow

• question_answer105) The equation of the plane passing through the mid point of the line of join of the points (1, 2, 3) and (3, 4, 5) and perpendicular to it is
  A)
  \[x+y+z=9\]
  done clear
  B)
         \[x+y+z=-9\]
  done clear
  C)
   \[2x+3y+4z=9\]
  done clear
  D)
          \[2x+3y+4z=-9\]
  done clear
  View Answer play_arrow

• question_answer106) The equation of the circle concentric to the circle \[2{{x}^{2}}+2{{y}^{2}}-3x+6y+2=0\] and having area double the area of this circle, is
  A)
  \[8{{x}^{2}}+8{{y}^{2}}-24x+48y-13=0\]
  done clear
  B)
   \[16{{x}^{2}}+16{{y}^{2}}+24x-48y-13=0\]
  done clear
  C)
   \[16{{x}^{2}}+16{{y}^{2}}-24x+48y-13=0\]
  done clear
  D)
   \[8{{x}^{2}}+8{{y}^{2}}+24x-48y-13=0\]
  done clear
  View Answer play_arrow

• question_answer107) The domain of the function \[f(x)=\frac{{{\cos }^{-1}}x}{[x]}\]is
  A)
  \[[-1,0)\cup \{1\}\]         
  done clear
  B)
          \[[-1,1]\]            
  done clear
  C)
          \[[-1,1)\]            
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer108) Let \[f(x)=\left\{ \begin{matrix}    \frac{\tan x-\cot x}{x-\frac{\pi }{4}}, & x\ne \frac{\pi }{4}  \\    a, & x=\frac{\pi }{4}  \\ \end{matrix} \right.\] the value of a so that \[f(x)\] is continuous at\[x=\frac{\pi }{4}\]
  A)
   2                            
  done clear
  B)
          4                            
  done clear
  C)
   3                            
  done clear
  D)
          1
  done clear
  View Answer play_arrow

• question_answer109) If e and e are the eccentricities of hyperbolas\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{^{2}}}}{{{b}^{2}}}=1\] and its conjugate hyperbola, then the value of \[\frac{1}{{{e}^{2}}}+\frac{1}{e{{}^{2}}}\]is
  A)
   0                            
  done clear
  B)
          1                            
  done clear
  C)
   2                            
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer110) The value of the\[\int_{{}}^{{}}{\frac{\sin x+\cos x}{3+\sin 2x}}dx\]is
  A)
  \[\frac{1}{4}\ln \left( \frac{2-\sin x+\cos x}{2+\sin x+\cos x} \right)+c\]
  done clear
  B)
   \[\frac{1}{2}\ln \]\[\left( \frac{2+\sin x}{2-\sin x} \right)+c\]
  done clear
  C)
   \[\frac{1}{4}\ln \]\[\left( \frac{1+\sin x}{1-\sin x} \right)+c\]
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer111) If forces of magnitude 12 kg-wt, 5 kg-wt and 13 kg-wt act at a point are in equilibrium, then the angle between the first two forces is
  A)
  \[~{{30}^{o}}\]                 
  done clear
  B)
         \[~{{90}^{o}}\]                 
  done clear
  C)
  \[~{{60}^{o}}\]                 
  done clear
  D)
          \[{{45}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer112) For a party 8 guests are invited by a husband and his wife. They sit in a row for dinner. The probability that the husband and his wife sit  together is
  A)
  \[\frac{2}{7}\]                   
  done clear
  B)
          \[\frac{2}{9}\]                  
  done clear
  C)
   \[\frac{1}{9}\]                  
  done clear
  D)
          \[\frac{4}{9}\]
  done clear
  View Answer play_arrow

• question_answer113) If\[{{I}_{m}}\left( \frac{z-1}{2z+1} \right)=-4,\]then locus of z is
  A)
   ellipse                 
  done clear
  B)
          parabola            
  done clear
  C)
          straight line    
  done clear
  D)
          circle
  done clear
  View Answer play_arrow

• question_answer114) The equation \[(x-b)(x-c)+(x-a)(x-b)\]\[+\,(x-a)(x-c)=0\] has all its roots
  A)
   positive              
  done clear
  B)
          real                      
  done clear
  C)
          imaginary     
  done clear
  D)
          negative
  done clear
  View Answer play_arrow

• question_answer115) The sum of coefficients of the expansion\[{{\left( \frac{1}{x}+2x \right)}^{n}}\]is 6561. The coefficient of term independent of \[x\] is
  A)
  \[16\,{{\,}^{8}}{{C}_{4}}\]            
  done clear
  B)
          \[^{8}{{C}_{4}}\]                             
  done clear
  C)
   \[^{8}{{C}_{5}}\]             
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer116) The area enclosed between the curves \[y=x\] and \[y=2x-{{x}^{2}}\]is (in sq. unit)
  A)
  \[\frac{1}{2}\]                   
  done clear
  B)
          \[\frac{1}{6}\]                  
  done clear
  C)
   \[\frac{1}{3}\]                  
  done clear
  D)
          \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer117) There are 12 white and 12 red balls in a bag. Balls are drawn one by one with replacement from the bag. The probability that 7th drawn ball is 4th white is
  A)
  \[\frac{1}{4}\]                   
  done clear
  B)
          \[\frac{1}{8}\]                  
  done clear
  C)
   \[\frac{1}{2}\]                  
  done clear
  D)
          \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer118) In an ellipse the angle between the lines joining the foci with the positive end of minor axis is a right angle, the eccentricity of the ellipse is
  A)
  \[\frac{1}{\sqrt{2}}\]                     
  done clear
  B)
          \[\frac{1}{\sqrt{3}}\]                    
  done clear
  C)
  \[\sqrt{2}\]                        
  done clear
  D)
          \[\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer119) If \[|\vec{a}|=3,\,\,\,|\vec{b}|=5\]and \[|\vec{c}|=4\]then and \[\vec{a}+\vec{b}+\vec{c}=0,\] then the value of \[\vec{a}+\vec{b}+\vec{c}=0,\]then the value of \[\vec{a}.\vec{b}\,+\,\vec{b}.\vec{c}\]is equal to
  A)
   0                            
  done clear
  B)
          -25                        
  done clear
  C)
          25                         
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer120) The    equation    of    a    line    is\[6x-2=3y-1=2z-2.\]The direction ratios of the line are
  A)
   1, 2, 3  
  done clear
  B)
          1, 1, 1  
  done clear
  C)
          \[\frac{1}{3},\frac{1}{3},\frac{1}{3}\]     
  done clear
  D)
          \[\frac{1}{3},\frac{-1}{3},\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer121) For the circuit shown below, the Boolean polynomial is
  A)
  \[(\tilde{\ }p\vee q)\vee (p\vee \tilde{\ }q)\]
  done clear
  B)
   \[(\tilde{\ }p\wedge p)\wedge (\tilde{\ }q\wedge q)\]
  done clear
  C)
   \[(\tilde{\ }p\wedge \tilde{\ }p)\wedge (q\wedge p)\]
  done clear
  D)
   \[(\tilde{\ }p\wedge q)\vee (q\wedge \tilde{\ }q)\]
  done clear
  View Answer play_arrow

• question_answer122) The value of \[\int_{{}}^{{}}{\frac{dx}{x+\sqrt{x-1}}}\]is
  A)
  \[\log (x+\sqrt{x-1})+{{\sin }^{-1}}\left( \sqrt{\frac{x-1}{x}} \right)+c\]
  done clear
  B)
   \[\log (x+\sqrt{x-1})+c\]
  done clear
  C)
   \[\log (x+\sqrt{x-1})-\frac{2}{\sqrt{3}}{{\tan }^{-1}}\]
  done clear
  D)
  \[\left( \frac{2\sqrt{x-1}+1}{\sqrt{3}} \right)\]  none of the above
  done clear
  View Answer play_arrow

• question_answer123) If \[y={{\sin }^{-1}}\frac{x}{2}+{{\cos }^{-1}}\frac{x}{2},\]then the value of \[\frac{dy}{dx}\]is
  A)
   1                                            
  done clear
  B)
   -1                          
  done clear
  C)
   0                                            
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer124) In Boolean algebra, the unit element 1
  A)
   has two values
  done clear
  B)
   is unique
  done clear
  C)
   has at least two values
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer125) On one bank of river there is a tree. On another bank, an observer makes an angle of elevation of \[{{60}^{o}}\] at the top of the tree. The angle of elevation of the top of the tree at a distance 20 m away from the bank is 30°. The width of the river is
  A)
   20 m                    
  done clear
  B)
          10 m    
  done clear
  C)
          5 m                                       
  done clear
  D)
   1 m
  done clear
  View Answer play_arrow

• question_answer126) The magnitude of cross product of two vectors is \[\sqrt{3}\]times the dot product. The angle between the vectors is
  A)
  \[\frac{\pi }{6}\]
  done clear
  B)
                                          \[\frac{\pi }{3}\]                             
  done clear
  C)
          \[\frac{\pi }{2}\]                             
  done clear
  D)
          \[\frac{\pi }{4}\]
  done clear
  View Answer play_arrow

• question_answer127) If \[{{D}_{r}}=\left| \begin{matrix}    r & 1 & \frac{n(n+1)}{2}  \\    2r-1 & 4 & {{n}^{2}}  \\    {{2}^{r-1}} & 5 & {{2}^{n-}}-1  \\ \end{matrix} \right|,\]then the value of \[\sum\limits_{r=0}^{n}{{{D}_{r}}}\]is
  A)
   0                            
  done clear
  B)
          1
  done clear
  C)
   \[\frac{n(n+1)(2n+1)}{6}\]
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer128) If\[\left| \begin{matrix}    -12 & 0 & \lambda   \\    0 & 2 & -1  \\    2 & 1 & 15  \\ \end{matrix} \right|=-360,\]then the value of \[\lambda \]is
  A)
   \[-1\]                   
  done clear
  B)
          \[-2\]                   
  done clear
  C)
          \[-3\]                                   
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer129) If \[A=\left[ \begin{matrix}    1 & x  \\    {{x}^{2}} & 4y  \\ \end{matrix} \right]\]and \[B\,=\left[ \begin{matrix}    -3 & 1  \\    1 & 0  \\ \end{matrix} \right]\]adj.\[A+B=\left[ \begin{matrix}    1 & 0  \\    0 & 1  \\ \end{matrix} \right],\]  then the value of \[x\]and \[y\]are
  A)
   1, 1                       
  done clear
  B)
          \[\pm \,1,1\]    
  done clear
  C)
          \[1,0\]                 
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer130) If \[{{\tan }^{-1}}\frac{1-x}{1+x}=\frac{1}{2}{{\tan }^{-1}}x,\]then values of \[x\]is
  A)
  \[\frac{1}{2}\]                   
  done clear
  B)
          \[\frac{1}{\sqrt{3}}\]                    
  done clear
  C)
   \[\sqrt{3}\]                       
  done clear
  D)
          2
  done clear
  View Answer play_arrow

• question_answer131) If \[{{x}^{2/3}}-7{{x}^{1/3}}+10=0\]then, the value of \[x\] is
  A)
  \[\{125\}\]         
  done clear
  B)
          \[\{8\}\]                             
  done clear
  C)
   \[\phi \]                             
  done clear
  D)
         \[\text{ }\!\!\{\!\!\text{ 125,8 }\!\!\}\!\!\text{ }\]
  done clear
  View Answer play_arrow

• question_answer132) The value of \[\underset{\alpha \to 0}{\mathop{\lim }}\,\frac{\begin{align}   & \cos e{{c}^{-1}}(sec\alpha )+co{{t}^{-1}}(tan\alpha ) \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+co{{t}^{-1}}\cos (si{{n}^{-1}}\alpha ) \\ \end{align}}{\alpha }\]is
  A)
   0                            
  done clear
  B)
          \[-1\]                   
  done clear
  C)
   \[-2\]                   
  done clear
  D)
          1
  done clear
  View Answer play_arrow

• question_answer133) If the second term in the expansion\[{{\left[ \sqrt[13]{a}\frac{a}{\sqrt{{{a}^{-1}}}} \right]}^{n}}\]is \[14{{a}^{5/2}},\] then the value of \[\frac{{{\,}^{n}}C{{\,}_{3}}}{{{\,}^{n}}{{C}_{2}}}\]is
  A)
   4                                            
  done clear
  B)
   3                            
  done clear
  C)
          12                         
  done clear
  D)
          6
  done clear
  View Answer play_arrow

• question_answer134) One of the  diameter of the circle \[{{x}^{2}}+{{y}^{2}}-12x+4y+6=0\] is given by
  A)
  \[~x+y=0\]         
  done clear
  B)
         \[~x+3y=0\]      
  done clear
  C)
          \[x=y\]
  done clear
  D)
          \[3x+2y=0\]
  done clear
  View Answer play_arrow

• question_answer135) Point D, E are taken on the side BC of the triangle ABC, such that \[BD=DE=EC.\]If \[\angle BAD=x,\angle DAE=y,\angle EAC=z,\] then the  value of \[\frac{\sin (x+y)\sin (y+z)}{\sin x\sin \,z}\] is equal to
  A)
   1                            
  done clear
  B)
          2                            
  done clear
  C)
          4                            
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer136) The number of real solution of\[{{\tan }^{-1}}\sqrt{x(x+1)}+{{\sin }^{-1}}\sqrt{{{x}^{2}}+x+1}=\frac{\pi }{2}\]is
  A)
   zero                     
  done clear
  B)
          one                      
  done clear
  C)
   two                      
  done clear
  D)
          infinite
  done clear
  View Answer play_arrow

• question_answer137) The equation \[{{\sin }^{-1}}x-{{\cos }^{-1}}x={{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] has
  A)
   no solution
  done clear
  B)
   unique solution
  done clear
  C)
   infinite number of solution
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer138) In a \[\Delta ABC,\,a,c,A\]are given and \[{{b}_{1}},{{b}_{2}}\]are two values, if the third side b such that \[{{b}_{2}}=2{{b}_{1}}\]then sin A is equal to
  A)
  \[\sqrt{\frac{9{{a}^{2}}-{{c}^{2}}}{8{{a}^{2}}}}\]
  done clear
  B)
          \[\sqrt{\frac{9{{a}^{2}}-{{c}^{2}}}{8{{c}^{2}}}}\]
  done clear
  C)
          \[\sqrt{\frac{9{{a}^{2}}+{{c}^{2}}}{8{{a}^{2}}}}\]              
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer139) A variable chord is drawn through the origin to  the circle \[{{x}^{2}}+{{y}^{2}}-2ax=0.\]The locus of the centre of the circle drawn on this chord as diameter is
  A)
   \[{{x}^{2}}+{{y}^{2}}+ax=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}-ax=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+ay=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}-ay=0\]
  done clear
  View Answer play_arrow

• question_answer140) If \[1,{{a}_{1}},{{a}_{2}},...,{{a}_{n-1}}\]are the n roots of unity, then the value of \[(1-{{a}_{1}})(1-{{a}_{2}})(1-{{a}_{3}})......(1-{{a}_{n-1}})\] is equal to
  A)
  \[\sqrt{3}\]                        
  done clear
  B)
          \[\frac{1}{2}\]                  
  done clear
  C)
   \[n\]                    
  done clear
  D)
          0
  done clear
  View Answer play_arrow

• question_answer141) Let a, b, c be real. If \[a{{x}^{2}}+bx+c=0\]has two real roots \[\alpha \]and\[\beta ,\]where \[a<-1\]and \[\beta >1,\]then \[1+\frac{c}{a}+\left| \frac{b}{a} \right|\]is
  A)
   \[<0\]                  
  done clear
  B)
          \[>0\]                  
  done clear
  C)
  \[\le 0\]               
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer142) Number of divisiors of the form \[(4n+2),n\ge 0\] of the integer 240 is
  A)
   4                            
  done clear
  B)
          8                            
  done clear
  C)
   10                         
  done clear
  D)
          3
  done clear
  View Answer play_arrow

• question_answer143) The expression \[{{\{x+{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}\]\[+\,{{\{x-{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}\] is a polynomial of degree
  A)
   5                            
  done clear
  B)
          6                            
  done clear
  C)
   7                            
  done clear
  D)
          8
  done clear
  View Answer play_arrow

• question_answer144) Let a, b, c be positive and not all equal, the  value of the determinant \[\left| \begin{matrix}    a & b & c  \\    b & c & a  \\    c & a & b  \\ \end{matrix} \right|\]is
  A)
  \[\text{+}\,\text{ve}\]                 
  done clear
  B)
          \[-\text{ve}\]  
  done clear
  C)
          zero                     
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer145) \[\underset{h\to 0}{\mathop{\lim }}\,\frac{{{(a+h)}^{2}}\sin (a+h)-{{a}^{2}}\sin a}{h}\]is equal to
  A)
  \[2a\,\sin \,a\] 
  done clear
  B)
          \[{{a}^{2}}\cos \,a\]      
  done clear
  C)
          \[{{a}^{2}}\cos a+2a\,\,\sin \,a\]
  done clear
  D)
          none of these
  done clear
  View Answer play_arrow

• question_answer146) If \[f(x)=x(\sqrt{x}+\sqrt{x+1}),\]then
  A)
   \[f(x)\]is continuous but not differentiable at \[x=0\]
  done clear
  B)
  \[f(x)\] is differentiable at \[x=0\]
  done clear
  C)
   \[f(x)\]is not differentiable at \[x=0\]
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer147) If \[y\]is a function of \[x\]and \[\log (x+y)=2xy,\] then the value of \[y(0)\]is equal to
  A)
   1                            
  done clear
  B)
          -1                          
  done clear
  C)
   2                            
  done clear
  D)
          0
  done clear
  View Answer play_arrow

• question_answer148) The angle between the tangent drawn from  the point (1, 4) to the parabola \[{{y}^{2}}=4x\]is
  A)
  \[\frac{\pi }{6}\]                              
  done clear
  B)
          \[\frac{\pi }{4}\]                             
  done clear
  C)
   \[\frac{\pi }{3}\]                             
  done clear
  D)
          \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer149) If \[y=a\log x+b{{x}^{2}}+x\]has its extremum value at \[x=-1\]and \[x=2,\]then
  A)
  \[x=-1\]and \[x=2,\]
  done clear
  B)
   \[a=2,\,b=-\frac{1}{2}\]
  done clear
  C)
   \[a=2,=-\frac{1}{2}\]
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer150) The value of \[\int_{{}}^{{}}{\frac{dx}{{{x}^{2}}{{({{x}^{4}}+1)}^{3/4}}}}\]is
  A)
  \[-\frac{{{({{x}^{4}}+1)}^{1/4}}}{x}+c\]
  done clear
  B)
   \[\frac{{{({{x}^{4}}+1)}^{1/4}}}{x}+c\]
  done clear
  C)
   zero
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow