Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2011

done BCECE Engineering Solved Paper-2011 Total Questions - 150

• question_answer1) Which of the following pairs have identical dimensions?
  A)
  Momentum and force
  done clear
  B)
  Pressure and surface tension
  done clear
  C)
  Moment of force and angular momentum
  done clear
  D)
  Surface tension and surface energy
  done clear
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• question_answer2) A train 100 m long travelling at 40 m/s starts overtaking another train 200 m long travelling at 30 m/s. The time taken by the first train to pass the second train completely is
  A)
   30 s      
  done clear
  B)
                          40 s 
  done clear
  C)
   50 s                      
  done clear
  D)
          60 s
  done clear
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• question_answer3) A constant power P is applied to a particle of mass m. The distance travelled by the particle when its velocity increases from \[{{v}_{1}}\] to \[{{v}_{2}}\] is (neglect friction)
  A)
  \[\frac{\text{m}}{\text{3P}}\text{(v}\,_{\text{2}}^{\text{3}}\text{-v}\,_{\text{1}}^{\text{3}}\text{)}\]                  
  done clear
  B)
         \[\frac{\text{m}}{\text{3P}}\text{(}{{\text{v}}_{2}}\text{-}{{\text{v}}_{1}}\text{)}\]
  done clear
  C)
    \[\frac{3P}{m}\text{(v}\,_{2}^{2}\text{-v}\,_{1}^{2}\text{)}\]  
  done clear
  D)
         \[\frac{m}{3P}\text{(v}\,_{2}^{2}\text{-v}\,_{1}^{2}\text{)}\]
  done clear
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• question_answer4) A spring of constant \[5\,\times {{10}^{3}}\,N/m\] is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is
  A)
   6.25 Nm
  done clear
  B)
   12.5 Nm
  done clear
  C)
   18.75 Nm
  done clear
  D)
          25.00 Nm
  done clear
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• question_answer5) Four spheres each having mass m and radius r are placed with their centres on the four comers of a square of side a. Then the moment of inertia of the system about an axis along one of the sides of the square is
  A)
  \[\frac{8}{5}m{{r}^{2}}\]                                              
  done clear
  B)
  \[\frac{8}{5}m{{r}^{2}}+m{{a}^{2}}\]
  done clear
  C)
  \[\frac{8}{5}m{{r}^{2}}+2m{{a}^{2}}\]    
  done clear
  D)
         \[\frac{4}{5}m{{r}^{2}}+4m{{a}^{2}}\]
  done clear
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• question_answer6)                                  If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is
  A)
   \[2R\]                                                  
  done clear
  B)
  \[\frac{R}{2}\]                                  
  done clear
  C)
   \[R\]   
  done clear
  D)
         \[\frac{R}{4}\]
  done clear
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• question_answer7) A 2 kg copper block is heated to \[500{}^\circ C\] and then it is placed on a large block of ice at \[0{}^\circ C\]. If the specific heat capacity of copper is 400 J/kg/C and latent heat of water is \[3.5\times {{10}^{5}}J/kg\]. The amount of ice that can melt is
  A)
   7/8 kg                                  
  done clear
  B)
   7/5 kg                  
  done clear
  C)
   8/7 kg      
  done clear
  D)
          5/7 kg
  done clear
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• question_answer8) Number of waves in 8 cm of vacuum is same as number of waves in x cm of a medium. Refractive index of medium is 4/3, then the value x is
  A)
   32/3 cm 
  done clear
  B)
                          12 cm                  
  done clear
  C)
   6 cm      
  done clear
  D)
   4 cm
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• question_answer9) Consider a gas with density \[\rho \] and \[\overline{\text{c}}\] as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is
  A)
  \[\frac{1}{3}\rho {{\overline{\text{c}}}^{2}}\]                                    
  done clear
  B)
  \[\frac{1}{3}\rho {{(c+v)}^{2}}\]
  done clear
  C)
         \[\frac{1}{3}\rho {{(\overline{c}-v)}^{2}}\]          
  done clear
  D)
         \[\frac{1}{3}\rho {{({{\overline{c}}^{2}}-v)}^{2}}\]
  done clear
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• question_answer10) At 127°C radiated energy is \[2.7\,\times {{10}^{-3}}\,J/s\]. At what temperature radiated energy is \[4.32\,\times {{10}^{6}}J/s\]?
  A)
   400 K                                   
  done clear
  B)
   4000 K 
  done clear
  C)
          80000 K       
  done clear
  D)
          40000 K
  done clear
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• question_answer11) The minimum phase difference between two simple harmonic oscillations,
  A)
  \[{{y}_{1}}=\frac{1}{2}\sin \,\omega t+\frac{\sqrt{3}}{2}\cos \,\omega t\]   \[{{y}_{2}}=\sin \,\omega t+\,\omega t,\,\text{is}\]             \[\frac{7\pi }{12}\]                                                          
  done clear
  B)
              \[\frac{\pi }{12}\]            
  done clear
  C)
              \[\frac{-\pi }{6}\] 
  done clear
  D)
                                     \[\frac{\pi }{6}\]
  done clear
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• question_answer12) A rubber cord catapult has cross-sectional area \[25\,m{{m}^{2}}\] and initial length of rubber cord is 10 cm. It is stretched to 5 cm and then released to project a missile of mass 5 g. Taking \[{{Y}_{rubber}}\,=5\times {{10}^{8}}N{{m}^{-2}},\] velocity of projected missile is
  A)
   \[20\,m{{s}^{-1}}\] 
  done clear
  B)
                                          \[100\,m{{s}^{-1}}\]
  done clear
  C)
   \[250\,m{{s}^{-1}}\]    
  done clear
  D)
          \[200\,m{{s}^{-1}}\]
  done clear
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• question_answer13) The material of a wire has a density of \[1.4\,g/c{{m}^{3}}\]. If it is not wetted by a liquid of surface tension 44 dyne/cm, then the maximum radius of the wire which can float on the surface of liquid is
  A)
  \[\frac{10}{28}cm\]                                        
  done clear
  B)
  \[\frac{10}{14}cm\]
  done clear
  C)
   \[\frac{10}{7}cm\]         
  done clear
  D)
          \[0.7cm\]
  done clear
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• question_answer14) Binding energy of satellite is \[4\times {{10}^{8}}J\]. Its PE is
  A)
  \[-4\times {{10}^{8}}J\]                
  done clear
  B)
  \[-8\times {{10}^{8}}J\]
  done clear
  C)
  \[8\times {{10}^{8}}J\]  
  done clear
  D)
         \[4\times {{10}^{8}}J\]
  done clear
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• question_answer15) A current of 0.01 mA passes through the potentiometer wire of a resistivity of \[{{10}^{9}}\Omega \] and area of cross-section \[{{10}^{-2}}c{{m}^{2}}\]. The potential gradient is
  A)
   \[\text{1}{{\text{0}}^{\text{9}}}\text{V/m}\]                                   
  done clear
  B)
   \[\text{1}{{\text{0}}^{11}}\text{V/m}\]
  done clear
  C)
  \[\text{1}{{\text{0}}^{10}}\text{V/m}\]                
  done clear
  D)
          \[\text{1}{{\text{0}}^{8}}\text{V/m}\]
  done clear
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• question_answer16) A particle of mass m attached with a string of length l is just revolving on the vertical circle without slacking of the string. If \[{{v}_{A,}}{{v}_{B}}\]  and\[{{v}_{D}}\] are speeds at positions A, B and D, then
  A)
   \[{{v}_{B}}>{{v}_{D}}>{{v}_{V}}\]
  done clear
  B)
   tension in string at D = 3 mg
  done clear
  C)
   \[{{v}_{D}}=\sqrt{3gl}\]
  done clear
  D)
   All of the above
  done clear
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• question_answer17) A bucket of water is being revolved in vertical circle of radius 1 m. Minimum frequency required to prevent the water from getting down the path is \[(g=10m/{{s}^{2}})\]
  A)
  \[\frac{2\pi }{\sqrt{10}}\]                                            
  done clear
  B)
  \[\frac{2\pi }{\sqrt{5}}\]
  done clear
  C)
  \[\frac{\sqrt{10}}{2\pi }\]                                            
  done clear
  D)
  \[\frac{\sqrt{5}}{2\pi }\]
  done clear
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• question_answer18) A round disc of moment of inertia \[{{I}_{2}}\] about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia \[{{l}_{1}}\] rotating with an angular velocity co about the same axis. The final angular velocity of the combination of discs is
  A)
  \[\frac{{{I}_{2}}\omega }{{{I}_{1}}+{{I}_{2}}}\]                   
  done clear
  B)
  \[\omega \]
  done clear
  C)
  \[\frac{{{I}_{1}}\omega }{{{I}_{1}}+{{I}_{2}}}\]   
  done clear
  D)
         \[\frac{({{I}_{1}}+{{I}_{2}})\omega }{{{I}_{1}}}\]
  done clear
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• question_answer19) Two discs have same mass and thickness. Their materials are of densities \[{{\rho }_{1}}\] and \[{{\rho }_{2.}}\] The ratio of their moment of inertia about central axis will be
  A)
  \[{{\rho }_{1}}:{{\rho }_{2}}\]                                    
  done clear
  B)
  \[{{\rho }_{1}}:{{\rho }_{2}}:1\]
  done clear
  C)
  \[1:{{\rho }_{1}}\,{{\rho }_{2}}\]               
  done clear
  D)
         \[{{\rho }_{2}}:\,{{\rho }_{1}}\]
  done clear
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• question_answer20) A 4 m long wire of resistance \[8\,\Omega \] is connected in series with a battery of emf 2 V and a resistor of \[7\Omega .\] The internal resistance of the battery is \[1\Omega .\] What is the potential gradient along the wire?
  A)
  \[1.00\,V{{m}^{-1}}\]                                    
  done clear
  B)
   \[0.75\,V{{m}^{-1}}\]
  done clear
  C)
   \[0.50\,V{{m}^{-1}}\]                   
  done clear
  D)
          \[0.25\,V{{m}^{-1}}\]
  done clear
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• question_answer21) A uniform wire of \[16\,\Omega \] resistance is made into the form of a square. Two opposite corners of the square are connected by a wire of resistance \[16\,\Omega .\] The effective resistance between the other two opposite comers is
  A)
   \[32\,\Omega \]                             
  done clear
  B)
   \[16\,\Omega \]
  done clear
  C)
   \[8\,\Omega \]               
  done clear
  D)
          \[4\,\Omega \]
  done clear
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• question_answer22) A \[6\times {{10}^{-4}}\,F\] parallel plate air capacitor is connected to a 500 V batten. When air is replaced by another   dielectric material, \[7.5\,\times {{10}^{-4}}C\] charge flows into the capacitor. The value of the dielectric constant of the material is
  A)
   1.5                                        
  done clear
  B)
   2.0  
  done clear
  C)
   1.0025
  done clear
  D)
          3.5
  done clear
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• question_answer23) The 90 pF capacitor is connected to a 12 V battery. How many electrons are transferred from one plate to another?
  A)
   \[1.1\,\times {{10}^{9}}\]                           
  done clear
  B)
   \[6.7\,\times {{10}^{9}}\]
  done clear
  C)
   \[4\times {{10}^{19}}\]                
  done clear
  D)
          \[5\times {{10}^{19}}\]
  done clear
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• question_answer24) Given mass number of gold = 197, Density of gold \[=19.7\,g/c{{m}^{3}}\] Avogadros number \[=6\times {{10}^{23}}\]. The radius of the gold atom is approximately
  A)
   \[1.5\times {{10}^{-8}}m\]         
  done clear
  B)
   \[1.7\times {{10}^{-9}}m\]
  done clear
  C)
   \[1.5\times {{10}^{-10}}m\]       
  done clear
  D)
         \[1.5\times {{10}^{-12}}m\]
  done clear
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• question_answer25) In Youngs double slit experiment, two slits are separated by 1 m. The slits are illuminated by a light of wavelength 650 nm. The source of light is placed symmetrically with respect to the two slits. Interference pattern is observed on a screen at a distance of 1 m from the slits. The distance between the third dark fringe and the fifth bright fringe from the centre of the pattern will be
  A)
   1.62 mm                             
  done clear
  B)
   2.62 mm
  done clear
  C)
   5.62 mm             
  done clear
  D)
          3.62 mm
  done clear
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• question_answer26) R is a radius of a planet and p is its density. The escape velocity on its surface will be
  A)
   \[{{R}^{2}}\sqrt{4\pi G\rho /3}\]    
  done clear
  B)
  \[R\sqrt{4\pi G\rho /3}\]
  done clear
  C)
  \[{{R}^{2}}\sqrt{8\pi G\rho /3}\]              
  done clear
  D)
         \[R\sqrt{8\pi G\rho /3}\]
  done clear
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• question_answer27) A satellite is moving in a circular orbit at a certain height above the earths surface. It takes \[5.26\,\times {{10}^{3}}\,s\] to complete one revolution with a centripetal acceleration equal to \[9.32\,\,m/{{s}^{2}}\]. The height of satellite orbiting above the earth is (Earths radius \[=6.37\,\times {{10}^{6}}\,m\])
  A)
  220 km                
  done clear
  B)
  160 km
  done clear
  C)
   70 km                  
  done clear
  D)
  120 km
  done clear
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• question_answer28) The surface tension of soap solution is 0.03 N/m. The amount of work done in forming a bubble of radius 5 cm is
  A)
   3.77 J                                   
  done clear
  B)
   1.885 J
  done clear
  C)
   \[0.95\times {{10}^{-3}}J\]    
  done clear
  D)
                          \[1.9\times {{10}^{-3}}J\]
  done clear
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• question_answer29) The minimum velocity of capillary waves on the surface of water is (surface tension of water is \[=7.2\,\times {{10}^{-2}}N/m\])
  A)
   0.23 m/s                             
  done clear
  B)
   0.46 m/s
  done clear
  C)
   0.69 m/s             
  done clear
  D)
          0.92 m/s
  done clear
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• question_answer30) 30.      A wire has a breaking stress of\[6\times {{10}^{5}}N/{{m}^{2}}\] and          a density of \[3\times {{10}^{4}}kg/{{m}^{3}}\]. The length of the wire of the same material which will break under its town weight, (if \[g=10\,m/{{s}^{2}}\]) is
  A)
   2000 m                                
  done clear
  B)
   2500 m
  done clear
  C)
   20 m                    
  done clear
  D)
          2 m
  done clear
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• question_answer31) A man measures the period of simple pendulum inside a stationary lift and finds it to be T second. If the lift accelerates  downwards with acceleration of \[\frac{g}{4},\] the period of oscillation will be
  A)
  \[T\times \frac{\sqrt{3}}{2}s\]                                   
  done clear
  B)
  \[T\times \frac{2}{\sqrt{3}}s\]
  done clear
  C)
   \[\frac{T}{2}s\]                
  done clear
  D)
         \[\sqrt{T}s\]
  done clear
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• question_answer32) A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and temperature be doubled, the power radiated in watt would be
  A)
   1800                                     
  done clear
  B)
   900
  done clear
  C)
   3600                     
  done clear
  D)
          850
  done clear
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• question_answer33) If the emissive power of black surface at same temperature is \[400\,W/{{m}^{2}},\] the emissive and absorptive powers of the surface assuming it was initially ordinary surface, are (Given, Mass of the body m = 4.2 kg, area of body \[=5\times {{10}^{-2}}{{m}^{2}},\] rate of cooling \[\frac{d\theta }{dt}=\frac{1}{12}\times {{10}^{-2}}{{\,}^{\text{o}}}\text{C/min,}\] specific heat\[s=420J/kg{{\,}^{\text{0}}}\text{C)}\]
  A)
  e=\[a\]= 0.0735              
  done clear
  B)
   e = \[a\] = 0.0435
  done clear
  C)
  e =\[a\]=0.0535   
  done clear
  D)
  e=\[a\]= 0.0235
  done clear
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• question_answer34) The expression for total kinetic energy per unit volume of gas is
  A)
  \[\frac{E}{V}=\frac{P}{2}\]                          
  done clear
  B)
  \[\frac{E}{V}=\frac{1}{3}P\]
  done clear
  C)
  \[\frac{E}{V}=\frac{2}{3}P\]        
  done clear
  D)
         \[\frac{E}{V}=\frac{3}{2}P\]
  done clear
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• question_answer35) A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational KE per. oxygen molecule that per nitrogen molecule is
  A)
   1 : 1
  done clear
  B)
   1 : 2
  done clear
  C)
   2 : 1
  done clear
  D)
   depends on the moments of inertia of the two molecules
  done clear
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• question_answer36) The wavelength and frequency of beam of light in water of refractive index 4/3 having wavelength 0.48 micron in air are
  A)
  \[0.16\,\times {{10}^{-6}}\,m,\,\,6.25\,\times {{10}^{14}}\,Hz\]
  done clear
  B)
   \[0.36\,\times {{10}^{-6}}\,m,\,\,6.25\,\times {{10}^{14}}\,Hz\]
  done clear
  C)
   \[0.36\,\times {{10}^{-6}}\,m,\,\,3.25\,\times {{10}^{14}}\,Hz\]
  done clear
  D)
   \[0.26\,\times {{10}^{-6}}\,m,\,\,3.25\,\times {{10}^{14}}\,Hz\]
  done clear
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• question_answer37) A ray of light is incident on glass slab making an angle of incidence sin\[^{-1}\left( \frac{\sqrt{3}}{2} \right).\] What will be the angle of refraction in glass of refractive index 1.5?
  A)
  \[40{}^\circ \text{ }18\]                                
  done clear
  B)
   \[24{}^\circ \text{ }49\]
  done clear
  C)
  \[25{}^\circ \text{ }17\]                
  done clear
  D)
         \[35{}^\circ \text{ }16\]
  done clear
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• question_answer38) An electron at rest is accelerated through a potential difference of 200 V. If the electron acquires a velocity \[8.4\,\times {{10}^{6}}\,m/s,\] the value of e/m of electron is
  A)
   \[1.76\,\times {{10}^{-4}}C/kg\]
  done clear
  B)
   \[1.76\,\times {{10}^{14}}C/kg\]
  done clear
  C)
   \[1.76\,\times {{10}^{11}}C/kg\]
  done clear
  D)
   \[1.76\,\times {{10}^{-16}}C/kg\]
  done clear
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• question_answer39) A radio transmitter operates at a frequency of 880 kHz and power of 10 kW. The number of photons emitted per second is
  A)
   \[13.27\,\times {{10}^{4}}\]
  done clear
  B)
   \[13.27\,\times {{10}^{34}}\]
  done clear
  C)
   \[1327\,\times {{10}^{34}}\]     
  done clear
  D)
                          \[1.71\times {{10}^{31}}\]
  done clear
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• question_answer40) What is the voltage gain in a common emitter amplifier, when input resistance is \[3\,\Omega \] and load resistance is \[24\,\Omega \] with \[\beta =60\,?\]
  A)
   480                                       
  done clear
  B)
   2.4  
  done clear
  C)
   4.8                        
  done clear
  D)
          8.4
  done clear
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• question_answer41) The input resistance or a common emitter transistor amplifier, if the output resistance is \[500\,k\Omega ,\], the current gain \[\alpha \] = 0.98 and the power gain is \[6.0625\,\times {{10}^{6}},\] is
  A)
   198 \[\Omega \]                             
  done clear
  B)
  \[300\,\Omega \]
  done clear
  C)
   \[100\,\Omega \]                           
  done clear
  D)
   \[400\,\Omega \]
  done clear
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• question_answer42) Which of the following transitions in hydrogen atom produces longest wavelength of radiation (or photon of minimum energy)?
  A)
  \[n=2,p=4\]       
  done clear
  B)
         \[n=3,p=4\]
  done clear
  C)
  \[n=6,p=8\]       
  done clear
  D)
         \[n=5,p=6\]
  done clear
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• question_answer43) If\[\left( \frac{0.51\times {{10}^{-10}}}{4} \right)\]m, is the radius of smallest electron orbit in hydrogen like atom, then this atom is
  A)
   H-atom                               
  done clear
  B)
   \[H{{e}^{+}}\]
  done clear
  C)
   \[L{{i}^{2+}}\]                  
  done clear
  D)
          \[B{{e}^{3+}}\]
  done clear
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• question_answer44) A series resonant circuit contains \[L=\frac{5}{\pi }mH,\]  \[C=\frac{200}{\pi }\mu F\] and R = 100 \[\Omega \] If a source of emf It e = 200 sin 1000 \[1000\,\pi t\] is applied, then the rms current is
  A)
   2 A                        
  done clear
  B)
          200\[\sqrt{2}\] A
  done clear
  C)
   100\[\sqrt{2}\] A            
  done clear
  D)
          1.41 A
  done clear
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• question_answer45) A rod of length 1.0 m is rotated in a plane perpendicular to a uniform magnetic field of induction 0.25 T with a frequency of 12 rev/s. The induced emf across the ends of the rod is
  A)
   18.89 V               
  done clear
  B)
          3 V
  done clear
  C)
   15 V                     
  done clear
  D)
          9.42 V
  done clear
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• question_answer46) A ferromagnetic material is heated above its curie temperature. Which one is a correct statement?
  A)
   Ferromagnetic domains are perfectly arranged
  done clear
  B)
   Ferromagnetic domains become random
  done clear
  C)
   Ferromagnetic domains are not influenced
  done clear
  D)
   Ferromagnetic material changes into diamagnetic material
  done clear
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• question_answer47) A material is placed in a magnetic field and. It is thrown out of it. Then the material is
  A)
   paramagnetic  
  done clear
  B)
          diamagnetic
  done clear
  C)
   ferromagnetic
  done clear
  D)
          non-magnetic
  done clear
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• question_answer48) A charged particle of mass m and charge q is accelerated through a potential difference of V volt. It enters a region of uniform magnetic field which is directed perpendicular to the direction of motion of the particle. The particle will move on a circular path of radius given by
  A)
  \[\sqrt{\frac{Vm}{q{{B}^{2}}}}\]               
  done clear
  B)
         \[\frac{2Vm}{q{{B}^{2}}}\]
  done clear
  C)
  \[\sqrt{\frac{2Vm}{q}}.\left( \frac{1}{B} \right)\]              
  done clear
  D)
         \[\sqrt{\frac{Vm}{q}}.\left( \frac{1}{B} \right)\]
  done clear
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• question_answer49) An electron moves at right angle to a magnetic field of \[1.5\times {{10}^{-2}}T\] with a speed of \[6\times {{10}^{7}}\,m/s\]. If the specific charge on the electron is \[1.7\,\times {{10}^{11}}\,C/kg,\] the radius of the circular path will be
  A)
   2.9 cm                 
  done clear
  B)
          3.9 cm
  done clear
  C)
   2.35 cm               
  done clear
  D)
          2 cm
  done clear
  View Answer play_arrow

• question_answer50) In a circuit, 5 percent of total current passes through a galvanometer. If resistance of the galvanometer is G. Then the value of the shunt is
  A)
   19 G                     
  done clear
  B)
          20 G 
  done clear
  C)
   \[\frac{G}{20}\]                              
  done clear
  D)
          \[\frac{G}{19}\]
  done clear
  View Answer play_arrow

• question_answer51) Given, C (diamond)\[+\,{{O}_{2}}\xrightarrow{{}}C{{O}_{2}};\Delta H =-395\,kJ\] C (graphite) \[+\,{{O}_{2}}\xrightarrow{{}}C{{O}_{2}};\Delta H =-393\,kJ\] The heat of formation of diamond from graphite is
  A)
  \[+\,2.0\,kJ\]                    
  done clear
  B)
  \[-1.5\,kJ\]        
  done clear
  C)
  \[-788\,kJ\]       
  done clear
  D)
  \[788\,kJ\]
  done clear
  View Answer play_arrow

• question_answer52) The type of isomerism observed in benzaldoxime is
  A)
   optical                 
  done clear
  B)
          functional          
  done clear
  C)
          geometrial   
  done clear
  D)
          tautomerism
  done clear
  View Answer play_arrow

• question_answer53) Sodium metal is prepared commercially by electrolysis of fused NaCl by
  A)
   Downs process
  done clear
  B)
   Nelson cell
  done clear
  C)
   Solvay process
  done clear
  D)
   Castner and Kellners cell
  done clear
  View Answer play_arrow

• question_answer54) The value of \[x\] is maximum for
  A)
   \[MgS{{O}_{4}}.\,x\,{{H}_{2}}O\]
  done clear
  B)
   \[CaS{{O}_{4}}.\,x\,{{H}_{2}}O\]
  done clear
  C)
   \[BaS{{O}_{4}}.\,x\,{{H}_{2}}O\]
  done clear
  D)
   All have the same value of \[x\]
  done clear
  View Answer play_arrow

• question_answer55) Heating of ore in absence of air below its melting point is called
  A)
   leaching                             
  done clear
  B)
   roasting              
  done clear
  C)
          smelting             
  done clear
  D)
          calcination
  done clear
  View Answer play_arrow

• question_answer56) In fluorine group of Periodic Table, on going down
  A)
   ionic radius increases
  done clear
  B)
   electronegativity increases
  done clear
  C)
   ionization potential increases
  done clear
  D)
   reactivity increases
  done clear
  View Answer play_arrow

• question_answer57) The ether that undergoes electrophilic substitution reactions is
  A)
  \[C{{H}_{3}}O{{C}_{2}}{{H}_{5}}\]                            
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}OC{{H}_{3}}\]
  done clear
  C)
          \[C{{H}_{3}}OC{{H}_{3}}\]          
  done clear
  D)
          \[{{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer58) The order of reactivity of alcohols towards sodium metal is
  A)
   Primary > Secondary > Tertiary
  done clear
  B)
   Primary < Secondary < Tertiary
  done clear
  C)
   Primary < Secondary > Tertiary
  done clear
  D)
   Primary > Secondary < Tertiary
  done clear
  View Answer play_arrow

• question_answer59) If one mole of a substance is present in 1 kg of solvent then its concentration is called
  A)
   molar cone.     
  done clear
  B)
   molal cone.       
  done clear
  C)
          normality       
  done clear
  D)
          strength wt/wt.
  done clear
  View Answer play_arrow

• question_answer60) If the pressure and absolute temperature of 2 L of carbondioxide gas are doubled, the value of the gas would become
  A)
   2 L  
  done clear
  B)
                                         4 L  
  done clear
  C)
   5 L                         
  done clear
  D)
          7 L
  done clear
  View Answer play_arrow

• question_answer61) \[C{{H}_{3}}CO{{O}^{-}}\] ion is a
  A)
   weak conjugate base
  done clear
  B)
   strong conjugate base
  done clear
  C)
   weak conjugate acid
  done clear
  D)
   strong conjugate add
  done clear
  View Answer play_arrow

• question_answer62) The hybrid state of C in charcoal is
  A)
   \[s{{p}^{3}}\]                                   
  done clear
  B)
  \[s{{p}^{2}}\]                    
  done clear
  C)
  \[sp\]                   
  done clear
  D)
          No specific state
  done clear
  View Answer play_arrow

• question_answer63) The shape of \[\text{Cl}{{\text{F}}_{\text{3}}}\]molecule is
  A)
   triangular planar
  done clear
  B)
   pyramidal
  done clear
  C)
   T-shape
  done clear
  D)
   trigonal bipyramidal
  done clear
  View Answer play_arrow

• question_answer64) Equivalent weight of crystalline oxalic acid is
  A)
   90                                         
  done clear
  B)
   63         
  done clear
  C)
          53                         
  done clear
  D)
          45
  done clear
  View Answer play_arrow

• question_answer65) If \[x\,\text{mol}\,{{\text{L}}^{-1}}\]is the solubility of \[\text{KAl(S}{{\text{O}}_{\text{4}}}{{\text{)}}_{\text{2}}}\] then \[{{\text{K}}_{\text{sp}}}\]is equal to
  A)
  \[{{x}^{3}}\]                      
  done clear
  B)
          \[4{{x}^{4}}\]                   
  done clear
  C)
   \[{{x}^{4}}\]                     
  done clear
  D)
          \[4{{x}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer66) In the reaction, \[{{N}_{2}}(g)+{{O}_{2}}(g)2NO(g)-180.7\,kJ,\] on increasing the  temperature,  the production of NO
  A)
   increases
  done clear
  B)
   decreases
  done clear
  C)
   remains same
  done clear
  D)
   Cannot be predicted
  done clear
  View Answer play_arrow

• question_answer67) In an experiment, 20 mL of decinormal \[HCl\] solution was added to 10 mL of a decinormal \[\text{AgN}{{\text{O}}_{\text{3}}}\]solution. \[\text{AgCl}\]was precipitated out and the excess acid was titrated against a decinormal \[\text{NaOH}\] solution. Volume of \[\text{NaOH}\].required for this back titration is
  A)
   10 mL 
  done clear
  B)
   5 mL     
  done clear
  C)
          20 mL                  
  done clear
  D)
          30 mL
  done clear
  View Answer play_arrow

• question_answer68) Consider the following statements.

  I. The colour of the hydrophobic sol depends on the wavelength of the light scattered by the dispersed particle.

  II. The smaller the gold number value of a hydrophilic colloid, the greater is its protective power.

  III. The movement of sol particle under an applied electric potential is called electro osmosis.

  Which of the above statements are correct?
  A)
   I and II                                
  done clear
  B)
   I and III               
  done clear
  C)
          II and III              
  done clear
  D)
          I, II and III
  done clear
  View Answer play_arrow

• question_answer69) Natural gas is
  A)
  \[CO+{{H}_{2}}\]                             
  done clear
  B)
   \[CO+{{N}_{2}}\]            
  done clear
  C)
          \[C{{H}_{4}}+{{O}_{2}}+{{N}_{2}}\]
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer70) Colemanite is
  A)
  \[N{{a}_{2}}{{B}_{4}}{{O}_{7}}.10{{H}_{2}}O\]    
  done clear
  B)
   \[C{{a}_{2}}{{B}_{6}}{{O}_{11}}.5{{H}_{2}}O\]
  done clear
  C)
          \[NaB{{O}_{2}}\]            
  done clear
  D)
          \[{{H}_{3}}B{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer71) Arsenic drugs are mainly used in the treatment of
  A)
   jaundice        
  done clear
  B)
          typhoid              
  done clear
  C)
          syphilis          
  done clear
  D)
          cholera
  done clear
  View Answer play_arrow

• question_answer72) Which of the following statements is not correct?
  A)
   Methylamine is more basic than \[\text{N}{{\text{H}}_{\text{3}}}\]
  done clear
  B)
   Amines form hydrogen bonds
  done clear
  C)
   Ethylamine has higher boiling point than propane
  done clear
  D)
   Dimethylamine is less basic than methylamine
  done clear
  View Answer play_arrow

• question_answer73) Which one of the following will be most basic?
  A)
   Aniline                
  done clear
  B)
          p-methoxyaniline
  done clear
  C)
          p-nitroaniline   
  done clear
  D)
          Benzylamine
  done clear
  View Answer play_arrow

• question_answer74) The final product of oxidation of 2-propanol with hot cone. \[\text{HN}{{\text{O}}_{\text{3}}}\]is
  A)
   propanal       
  done clear
  B)
          ethanoic acid
  done clear
  C)
          propanone      
  done clear
  D)
          ethanol
  done clear
  View Answer play_arrow

• question_answer75) Bimolecular reduction of acetone gives
  A)
   diacetoneamine
  done clear
  B)
         pinacol
  done clear
  C)
          chloretone        
  done clear
  D)
   propane
  done clear
  View Answer play_arrow

• question_answer76) Aldehydes and ketones give addition reaction with
  A)
   hydrazine
  done clear
  B)
   phenyl hydrazine
  done clear
  C)
   semicarbazide
  done clear
  D)
   hydrogen cyanide
  done clear
  View Answer play_arrow

• question_answer77) Amongst the following, the compound which  is most difficult to sulphonate is
  A)
   benzene        
  done clear
  B)
          nitrobenzene
  done clear
  C)
                          toluene              
  done clear
  D)
   chlorobenzene
  done clear
  View Answer play_arrow

• question_answer78) Acetonitrile is prepared by treating an alcoholic solution of methyl iodide with
  A)
   silver cyanide
  done clear
  B)
   potassium cyanide
  done clear
  C)
   hydrogen cyanide
  done clear
  D)
   ammonia
  done clear
  View Answer play_arrow

• question_answer79) During polymerization of acetylene to benzene, the state of hybridisation of carbon changes from
  A)
   \[s{{p}^{2}}\]to \[sp\]  
  done clear
  B)
          \[s{{p}^{3}}\]to \[sp\]  
  done clear
  C)
          \[sp\]to \[s{{p}^{3}}\]  
  done clear
  D)
          \[sp\]to \[s{{p}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer80) Which one of the following series contains electrophiles only?
  A)
   \[{{H}_{2}}O,S{{O}_{3}},{{H}_{3}}{{O}^{+}}\]
  done clear
  B)
          \[N{{H}_{3}},{{H}_{2}}O,AlC{{l}_{3}}\]
  done clear
  C)
          \[AlC{{l}_{3}},S{{O}_{3}},\overset{+}{\mathop{N}}\,{{O}_{2}}\]
  done clear
  D)
          \[{{H}_{2}}O,\overset{+}{\mathop{C}}\,l,N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer81) The equilibrium constants for the reactions \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}\]                 and        \[\frac{1}{2}{{N}_{2}}+\frac{3}{2}{{H}_{2}}N{{H}_{3}}\] are\[{{K}_{1}}\]and \[{{K}_{2}}\]respectively. Which one of the following is the correct relationship?
  A)
  \[{{K}_{1}}=2{{K}_{2}}\]
  done clear
  B)
          \[{{K}_{1}}=\frac{1}{2}{{K}_{2}}\]            
  done clear
  C)
          \[{{K}_{2}}=\sqrt{{{K}_{1}}}\]   
  done clear
  D)
          \[{{K}_{1}}={{K}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer82) When we increase the temperature, the rate of reaction increases because of
  A)
   more number of collisions
  done clear
  B)
   decrease in mean free path
  done clear
  C)
   more number of energetic electrons
  done clear
  D)
   less number of energetic electrons
  done clear
  View Answer play_arrow

• question_answer83) The pH of buffer of \[\text{N}{{\text{H}}_{\text{4}}}\text{Cl}\]type is given by
  A)
  \[pH=p{{K}_{b}}\]                           
  done clear
  B)
   \[pH=1/2p{{K}_{b}}-1/2\,\log [salt]/[base]\]
  done clear
  C)
   \[pH=14-p{{K}_{b}}-\log [salt]/[base]\]
  done clear
  D)
   \[pH=pOH-p{{K}_{b}}+\log [salt]/[base]\]
  done clear
  View Answer play_arrow

• question_answer84) Azimuthal quantum number determines the
  A)
   size                      
  done clear
  B)
          spin                     
  done clear
  C)
              orientation
  done clear
  D)
   angular momentum of orbitals
  done clear
  View Answer play_arrow

• question_answer85) The formation of colloid from suspension is called
  A)
   peptisation      
  done clear
  B)
          condensation
  done clear
  C)
                          sedimentation   
  done clear
  D)
          fragmentation
  done clear
  View Answer play_arrow

• question_answer86) Other things being equal, the EMF of a Daniell cell may be increased by
  A)
   keeping low temperature
  done clear
  B)
   using large copper electrodes
  done clear
  C)
   using large zinc electrodes
  done clear
  D)
   decreasing concentration of \[\text{C}{{\text{u}}^{\text{2+}}}\]ions
  done clear
  View Answer play_arrow

• question_answer87) Which one of the following can be considered as a weak electrolyte?
  A)
  \[\text{NaCl}\]                 
  done clear
  B)
          \[\text{HCl}\]  
  done clear
  C)
          \[C{{H}_{3}}COOH\]
  done clear
  D)
          \[{{K}_{2}}S{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer88) lodoform can be prepared from all except
  A)
   acetaldehyde
  done clear
  B)
   3-methyl-2-butanone
  done clear
  C)
   iso-butyl alcohol
  done clear
  D)
   acetophenone
  done clear
  View Answer play_arrow

• question_answer89) The end product C in the following sequence  of chemical reactions is \[C{{H}_{3}}COOH\xrightarrow{CaC{{O}_{3}}}A\xrightarrow{Heat}B\xrightarrow{N{{H}_{2}}OH}C\]
  A)
   acetaldehyde oxime
  done clear
  B)
   formaldehyde oxime
  done clear
  C)
   methyl nitrate
  done clear
  D)
   acetoxime
  done clear
  View Answer play_arrow

• question_answer90) Synthetic human hair wigs are made from a copolymer of vinyl chloride and acrylonitrile and is called
  A)
   PVC                      
  done clear
  B)
          polyacrylonitrile
  done clear
  C)
          cellulose         
  done clear
  D)
          dynel
  done clear
  View Answer play_arrow

• question_answer91) Which one of the following is not an example of chain growth polymer?
  A)
   Neoprene      
  done clear
  B)
          Buna-S
  done clear
  C)
          PMMA                
  done clear
  D)
          Glyptal
  done clear
  View Answer play_arrow

• question_answer92) Most abundant water pollutant is
  A)
   detergents       
  done clear
  B)
          industrial wastes
  done clear
  C)
   pesticides        
  done clear
  D)
          oil spills
  done clear
  View Answer play_arrow

• question_answer93) Paulings electronegativity values for elements are useful in predicting
  A)
   polarity of the molecules
  done clear
  B)
   position in the EMF series
  done clear
  C)
   coordination numbers
  done clear
  D)
   dipole moments
  done clear
  View Answer play_arrow

• question_answer94) A neutral ferilizer among the following is
  A)
   CAN
  done clear
  B)
   ammonium sulphate
  done clear
  C)
   ammonium nitrate
  done clear
  D)
   Urea
  done clear
  View Answer play_arrow

• question_answer95) Transition metal with low oxidation number will act as
  A)
   an oxidizing agent
  done clear
  B)
         a base
  done clear
  C)
   an acid                
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer96) In \[\text{LiAl}{{\text{H}}_{\text{4}}}\text{,}\]the ligand is
  A)
   H                           
  done clear
  B)
          \[{{\text{H}}^{\text{+}}}\]
  done clear
  C)
   \[{{\text{H}}^{-}}\]                        
  done clear
  D)
          \[2{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer97) Iodide of Millons base is
  A)
  \[\text{Hg}{{\text{I}}_{\text{2}}}\]         
  done clear
  B)
          \[{{\text{K}}_{\text{2}}}\text{Hg}{{\text{I}}_{\text{4}}}\]
  done clear
  C)
   \[\text{N}{{\text{H}}_{\text{4}}}\text{HgO}\text{.HgI}\]
  done clear
  D)
          \[\text{N}{{\text{H}}_{\text{4}}}\text{I}\]
  done clear
  View Answer play_arrow

• question_answer98) Ce-58 is a member of                   
  A)
   \[s-\]block elements    
  done clear
  B)
   \[p-\]block elements
  done clear
  C)
   \[d-\]block elements   
  done clear
  D)
  \[f-\]block elements
  done clear
  View Answer play_arrow

• question_answer99) Complete hydrolysis of \[\text{Xe}{{\text{F}}_{\text{2}}}\]gives
  A)
   Xe                         
  done clear
  B)
          \[{{\text{O}}_{\text{2}}}\]
  done clear
  C)
   HF                         
  done clear
  D)
          All of these
  done clear
  View Answer play_arrow

• question_answer100) The alloy best suited for making metre scales is
  A)
   stainless steel
  done clear
  B)
   invar
  done clear
  C)
   alnicos
  done clear
  D)
   tungsten steel
  done clear
  View Answer play_arrow

• question_answer101) The value of \[\sum\limits_{n=1}^{13}{({{i}^{n}}+{{i}^{n+1}}),}\]where \[i=\sqrt{-1}\] equals
  A)
   \[i\]                                       
  done clear
  B)
          \[i-1\]                   
  done clear
  C)
          \[-i\]                                      
  done clear
  D)
          0
  done clear
  View Answer play_arrow

• question_answer102) If \[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\] then the value of \[x\]is
  A)
   0                                            
  done clear
  B)
          \[1/2\]                  
  done clear
  C)
          1                                            
  done clear
  D)
          \[-\text{ }1\]
  done clear
  View Answer play_arrow

• question_answer103) There are n different books and p copies of each. The number of ways in which a selection can be made from them, is
  A)
   \[{{n}^{p}}\]                                         
  done clear
  B)
          \[{{p}^{n}}\]                         
  done clear
  C)
          \[{{(p+1)}^{n}}-1\]                              
  done clear
  D)
          \[{{(n+1)}^{p}}-1\]
  done clear
  View Answer play_arrow

• question_answer104) The circle \[{{S}_{1}}\]with centre \[{{C}_{1}}({{a}_{1}},{{b}_{1}})\]and radius \[{{r}_{1}}\]touches externally the circle \[{{S}_{2}}\]with centre \[{{C}_{2}}({{a}_{2}},{{b}_{2}})\]and radius \[{{r}_{2}}.\] If the tangent at their common point passes through the origin, then
  A)
   \[(a_{1}^{2}+a_{2}^{2})+(b_{1}^{2}+b_{2}^{2})=r_{1}^{2}+r_{2}^{2}\]
  done clear
  B)
          \[(a_{1}^{2}-a_{2}^{2})+(b_{1}^{2}-b_{2}^{2})=r_{1}^{2}-r_{2}^{2}\]
  done clear
  C)
          \[{{(a_{1}^{2}-{{b}_{2}})}^{2}}+(a_{2}^{2}+b_{2}^{2})=r_{1}^{2}+r_{2}^{2}\]
  done clear
  D)
          \[(a_{1}^{2}-b_{1}^{2})+(a_{1}^{2}+b_{2}^{2})=r_{1}^{2}+r_{2}^{2}\]
  done clear
  View Answer play_arrow

• question_answer105) If three vectors a, b, c are such that \[a\ne 0\]and \[a\times b=2(a\times c),|a|=|c|=1,|b|=4\]and the angle between b and c is \[{{\cos }^{-1}}\left( \frac{1}{4} \right).\]Also \[b-2c=\lambda a,\]then find the value of \[\lambda \]
  A)
  \[~\pm \,4\]                                         
  done clear
  B)
          14                                         
  done clear
  C)
         \[\pm \text{ }2~\]                                
  done clear
  D)
          12
  done clear
  View Answer play_arrow

• question_answer106)  A vector which makes equal angle with the vectors \[1/3(i-2j+2k),1/5(-4i-3k)\]and j is
  A)
   \[5i+j+jk\]                            
  done clear
  B)
          \[-6i+j+5k\]         
  done clear
  C)
                          \[5i-j-5k\]                             
  done clear
  D)
          \[5i+j-5k\]
  done clear
  View Answer play_arrow

• question_answer107) If \[a.b=0\]and \[a+b\]makes an angle of \[{{30}^{o}}\] with a, then
  A)
   \[|b|=2|a|\]                       
  done clear
  B)
          \[|a|=2|b|\]                       
  done clear
  C)
         \[|a|=\sqrt{3}|b|\]             
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer108) In Simpsons one-third rule the curve \[y=f(x)\]is assumed to be a
  A)
   circle                                    
  done clear
  B)
          parabola                              
  done clear
  C)
          hyperbola                            
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer109) Objective of LPP is
  A)
   a constraint
  done clear
  B)
          a function to be optimized
  done clear
  C)
          a relation between the variables
  done clear
  D)
          None of the above
  done clear
  View Answer play_arrow

• question_answer110) The variance of first \[n\] natural number is
  A)
  \[\frac{{{n}^{2}}+1}{12}\]                   
  done clear
  B)
          \[\frac{{{n}^{2}}-1}{12}\]                   
  done clear
  C)
          \[\frac{(n+1)(2n+1)}{6}\]  
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer111) In Boolean algebra, which of the following statement is correct
  A)
   \[(a+b)=a+b\]
  done clear
  B)
          \[(a+b)=a.b\]
  done clear
  C)
          \[(a+b)=(a.b)\]
  done clear
  D)
          None of the above
  done clear
  View Answer play_arrow

• question_answer112) The function \[{{x}^{x}}\]decreases in the interval
  A)
   (0, e)                                     
  done clear
  B)
          (0, 1)                     
  done clear
  C)
           (0, 1/e)                                
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer113) The period of the function \[f(x)=(\sin 3x)+|\cos 6x|\]is
  A)
   \[\pi \]                                  
  done clear
  B)
          \[2\pi /3\]                            
  done clear
  C)
          \[2\pi \]                                
  done clear
  D)
          \[\pi /2\]
  done clear
  View Answer play_arrow

• question_answer114) The differential equation representing the family of curves \[{{y}^{2}}=2x(x+\sqrt{c}),\]where c is a positive perimeter, is of
  A)
   order 1, degree 3              
  done clear
  B)
          order 2, degree 2              
  done clear
  C)
          degree 3, order 3              
  done clear
  D)
          degree 4, order 4
  done clear
  View Answer play_arrow

• question_answer115) If \[\int_{{}}^{{}}{\sqrt{1+\sin x}}.f(x)dx=\frac{2}{3}{{(1+\sin x)}^{3/2}}+C,\] then \[f(x)\] is equal to
  A)
  \[\cos x\]                              
  done clear
  B)
         \[\sin x\]               
  done clear
  C)
          \[\tan x\]                              
  done clear
  D)
          1
  done clear
  View Answer play_arrow

• question_answer116) \[\int_{{}}^{{}}{x\sqrt{\frac{1-x}{1+x}}}dx\]is equal to
  A)
   \[\left( \frac{x}{2}-1 \right)\sqrt{1-{{x}^{2}}}+\frac{1}{2}{{\sin }^{-1}}x+C\]
  done clear
  B)
          \[\left( \frac{x}{2}-1 \right)\sqrt{1-{{x}^{2}}}-\frac{1}{2}{{\sin }^{-1}}x+C\]
  done clear
  C)
          \[\sqrt{1-{{x}^{2}}}+\frac{1}{2}{{\sin }^{-1}}x+C\]
  done clear
  D)
          None of the above
  done clear
  View Answer play_arrow

• question_answer117) If \[x=\sec \theta -\cos \theta \]and \[y={{\sec }^{n}}\theta -{{\cos }^{n}}\theta ,\]then \[{{\left( \frac{dy}{dx} \right)}^{2}}\]is
  A)
  \[\frac{{{n}^{2}}({{y}^{2}}+4)}{{{x}^{2}}+4}\]                   
  done clear
  B)
          \[\frac{{{n}^{2}}({{y}^{2}}-4)}{{{x}^{2}}}\]                       
  done clear
  C)
          \[n\frac{({{y}^{2}}-4)}{{{x}^{2}}-4}\]                
  done clear
  D)
          \[{{\left( \frac{ny}{x} \right)}^{2}}-4\]
  done clear
  View Answer play_arrow

• question_answer118) The area formed by triangular shaped region bounded by the curves \[y=\sin x,y=\cos x\]and \[x=0\]is
  A)
   \[(\sqrt{2}-1)sq\,unit\]      
  done clear
  B)
          \[\text{1}\,\text{sq}\,\text{unit}\]                   
  done clear
  C)
          \[\sqrt{\text{2}}\,\text{sq}\,\text{units}\]                      
  done clear
  D)
          \[(\sqrt{2}+1)\,sq\,unit\]
  done clear
  View Answer play_arrow

• question_answer119) Find the value of \[\int_{0}^{\pi /2}{\frac{dx}{1+{{\tan }^{3}}x}}\]
  A)
   0                                            
  done clear
  B)
          1                                            
  done clear
  C)
                          \[\pi /2\]                              
  done clear
  D)
          \[\pi /4\]
  done clear
  View Answer play_arrow

• question_answer120) The angle of intersection of the curve \[y={{x}^{2}}\] and \[6y=7-{{x}^{3}}\]at \[(1,1)\] is
  A)
   \[\pi /4\]                              
  done clear
  B)
          \[\pi /3\]                              
  done clear
  C)
          \[\pi /2\]                              
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer121) If \[{{I}_{m,n}}=\int_{0}^{1}{{{x}^{m}}{{(\log x)}^{n}}}dx,\]then it  is equal to
  A)
   \[\frac{n}{n+1}{{I}_{m,n}}_{-1}\]                      
  done clear
  B)
          \[\frac{-m}{n+1}{{I}_{m,n-1}}\]                         
  done clear
  C)
          \[\frac{-n}{m+1}{{I}_{m,n-1}}\]                         
  done clear
  D)
          None of the above
  done clear
  View Answer play_arrow

• question_answer122) \[\frac{d}{dx}\cos e{{c}^{-1}}\left( \frac{1+{{x}^{2}}}{2x} \right)\]is equal to
  A)
   \[\frac{-2}{(1+{{x}^{2}})},x\ne 0\]    
  done clear
  B)
          \[\frac{2}{(1+{{x}^{2}})},x\ne 0\]     
  done clear
  C)
          \[\frac{2(1-{{x}^{2}})}{(1+{{x}^{2}})|1-{{x}^{2}}|},x\ne \pm 1,0\]
  done clear
  D)
          None of the above
  done clear
  View Answer play_arrow

• question_answer123) If \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x)={{a}^{3}},a\ne 0,\] then \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x/a)\] is equal to
  A)
   \[{{a}^{2}}\]                                         
  done clear
  B)
          \[1/{{a}^{3}}\]
  done clear
  C)
          \[1/{{a}^{2}}\]                     
  done clear
  D)
          \[{{a}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer124) If \[(1+tan\theta )(1+tan\phi )=2,\]then \[(\theta +\phi )\]is equal to
  A)
  \[{{30}^{o}}\]                                        
  done clear
  B)
          \[{{45}^{o}}\]                       
  done clear
  C)
         \[{{60}^{o}}\]                                        
  done clear
  D)
         \[~{{75}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer125) If in a\[\Delta A B C,\cos A+\cos B+\cos C=3/2,\] then triangle is
  A)
  right angled         
  done clear
  B)
  isosceles                              
  done clear
  C)
  acute                                    
  done clear
  D)
  equilateral
  done clear
  View Answer play_arrow

• question_answer126) If the line \[x-1=0\]is the directrix of parabola \[{{y}^{2}}-kx+8=0,\] then one of the value of \[k\]is
  A)
   1/8                                        
  done clear
  B)
          8                            
  done clear
  C)
          4                                            
  done clear
  D)
          1/4
  done clear
  View Answer play_arrow

• question_answer127) The centre of the sphere through the points \[(0,3,4),(0,5,0),(4,0,3)\]and \[(-3,4,0)\]is
  A)
                   \[(1/4,3,7/4)\]    
  done clear
  B)
          (0, 0, 0)
  done clear
  C)
                                           \[(-4,3,0)\]                          
  done clear
  D)
          None of the above
  done clear
  View Answer play_arrow

• question_answer128) Solve \[(y\,\log \,x-1)ydx=x\,dy\]
  A)
  \[y(\log ex+cx)=1\]
  done clear
  B)
          \[y(\log ex+cx)\]
  done clear
  C)
          \[y(\log ex-(x))=-1\]
  done clear
  D)
          None of the above
  done clear
  View Answer play_arrow

• question_answer129) If \[f(x)=\int_{-1}^{x}{|t|dt,x\ge -1,}\]then
  A)
   \[f\]and\[f\] are continuous for \[x+1>0\]
  done clear
  B)
          \[f\]is continuous but \[f\] is not continuous for \[x+1>0\]
  done clear
  C)
         \[f\] and\[f\] are not continuous at \[x=0\]
  done clear
  D)
          \[f\]is continuous at \[x=0\]but\[f\] is not so
  done clear
  View Answer play_arrow

• question_answer130) AB, AC are tangents to a parabola \[{{y}^{2}}=4ax,\]If  \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] are the lengths of perpendiculars from A, B, C on any tangents to the parabola, then
  A)
   \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]are in GGP
  done clear
  B)
          \[{{l}_{2}},{{l}_{1}},{{l}_{3}}\]are in GP
  done clear
  C)
          \[{{l}_{3}},{{l}_{1}},{{l}_{2}}\]are in GP
  done clear
  D)
          \[{{l}_{3}},{{l}_{2}},{{l}_{1}}\]are in GP
  done clear
  View Answer play_arrow

• question_answer131) A   family   of   lines   is   given   by \[(1+2\lambda )x+(1-\lambda )y+\lambda =0,\,\lambda \] being the parameter. The line belonging to this family at the maximum distance from the point\[(1,4)\]is
  A)
   \[4x-y+1=0\]       
  done clear
  B)
          \[33x+12y+7=0\]               
  done clear
  C)
          \[12x+33y=7\]    
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer132) If the eccentricity of the hyperbola \[{{x}^{2}}-{{y}^{2}}{{\sec }^{2}}\alpha =5\]is \[\sqrt{3}\]times the eccentricity of the ellipse \[{{x}^{2}}{{\sec }^{2}}\alpha +{{y}^{2}}=25,\]then the value of \[\alpha \] is
  A)
   \[\pi /6\]                              
  done clear
  B)
          \[\pi /4\]                              
  done clear
  C)
          \[\pi /3\]                              
  done clear
  D)
          \[\pi /2\]
  done clear
  View Answer play_arrow

• question_answer133) Lines of regressions of \[y\] on \[x\] and \[x\] on \[y\] are respectively \[y=ax+b\]and\[x=\alpha y+\beta ,\] If mean of \[x\]and\[y\] series is same, then its value. is
  A)
   \[\frac{b}{1-a}\]                  
  done clear
  B)
          \[\frac{1-a}{b}\]                  
  done clear
  C)
          \[\frac{\beta }{1-\beta }\]                 
  done clear
  D)
          \[\frac{a}{1-\alpha }\]
  done clear
  View Answer play_arrow

• question_answer134) A solution of the differential equation \[{{\left( \frac{dy}{dx} \right)}^{2}}-x\frac{dy}{dx}+y=0\]is
  A)
   \[y=2\]                 
  done clear
  B)
          \[y=2x\]
  done clear
  C)
          \[y=2x-4\]                            
  done clear
  D)
          \[y=2{{x}^{2}}-4\]
  done clear
  View Answer play_arrow

• question_answer135) The relation between the time t and distance \[x\] is given by \[t=p{{x}^{2}}+qx,\]where p and q are constants. The relation between velocity v and acceleration \[f\] is
  A)
   \[f\propto v\]                      
  done clear
  B)
          \[f\propto {{v}^{4}}\]                         
  done clear
  C)
          \[f\propto {{v}^{2}}\]                         
  done clear
  D)
          \[f\propto {{v}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer136) The product of\[{{x}^{1/2}}.{{x}^{1/4}},{{x}^{1/8}}....\infty \]equals
  A)
   0                                            
  done clear
  B)
          1                            
  done clear
  C)
          \[x\]                                      
  done clear
  D)
          \[\infty \]
  done clear
  View Answer play_arrow

• question_answer137) If the equation \[{{x}^{2}}+ix+a=0,\]\[{{x}^{2}}-2x+ia=0,a\ne 0\]have a common root, then
  A)
   a is real                
  done clear
  B)
          \[a=1/2+i\]
  done clear
  C)
          \[a=1/2-i\]
  done clear
  D)
          the other root is also common
  done clear
  View Answer play_arrow

• question_answer138) The distance between the lines \[y=2x+4\]and \[3y=6x-5\] is equal to
  A)
   1                                            
  done clear
  B)
          \[3/\sqrt{5}\]
  done clear
  C)
          \[\frac{17\sqrt{5}}{15}\]                   
  done clear
  D)
          \[\frac{17}{\sqrt{3}}\]
  done clear
  View Answer play_arrow

• question_answer139) The equation\[\frac{{{x}^{2}}}{12-k}+\frac{{{y}^{2}}}{8-k}=1\]represents
  A)
   a hyperbola, if k < 8
  done clear
  B)
          an ellipse, if \[k>8\]
  done clear
  C)
          a hyperbola, if \[8<k<12\]
  done clear
  D)
          None of the above
  done clear
  View Answer play_arrow

• question_answer140) The series \[\frac{1}{(n+1)}+\frac{1}{2{{(n+1)}^{2}}}+\frac{1}{3{{(n+1)}^{3}}}+...\] has the same sum as the series
  A)
   \[\frac{1}{n}-\frac{1}{2{{n}^{2}}}+\frac{1}{3{{n}^{3}}}-\frac{1}{4{{n}^{4}}}+...\]
  done clear
  B)
          \[\frac{1}{n}+\frac{1}{2{{n}^{2}}}+\frac{1}{3{{n}^{3}}}+\frac{1}{4{{n}^{4}}}+...\]
  done clear
  C)
          \[\frac{1}{n}+\frac{1}{{{2}^{2}}}.\frac{1}{{{n}^{2}}}+\frac{1}{{{2}^{3}}}.\frac{1}{{{n}^{3}}}+...\]
  done clear
  D)
           None of the above
  done clear
  View Answer play_arrow

• question_answer141) The sum of the infinite series \[\frac{2}{3!}+\frac{4}{5!}+\frac{6}{7!}+\frac{8}{9!}+....\infty \]is
  A)
                   \[e\]                                      
  done clear
  B)
          \[{{e}^{-1}}\]                        
  done clear
  C)
                                          \[2e\]                                   
  done clear
  D)
          \[{{e}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer142) If the roots of the equation \[a(b-c){{x}^{2}}+b(c-a)x+c(a-b)=0\]are equal, then a, b, c are in
  A)
   AP           
  done clear
  B)
                                          GP                         
  done clear
  C)
          HP                                         
  done clear
  D)
          None of these                                                     
  done clear
  View Answer play_arrow

• question_answer143) The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, then the probability of his shooting the target is
  A)
   1                                            
  done clear
  B)
          \[1-{{(0.7)}^{10}}\]                             
  done clear
  C)
          \[{{(0.7)}^{10}}\]                 
  done clear
  D)
          \[{{(0.3)}^{10}}\]
  done clear
  View Answer play_arrow

• question_answer144) Let A and B be two events such that\[P(A)=0.3\] and \[P(A\cup B)=0.8\]If A and B. are independent events. Then, \[P(B)\] is equal to
  A)
   5/7          
  done clear
  B)
          2/3                                        
  done clear
  C)
          1                                            
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer145) The number of distinct real roots of \[\left| \begin{matrix}    \sin x & \cos x & \cos x  \\    \cos x & \sin x & \cos x  \\    \cos x & \cos x & \sin x  \\ \end{matrix} \right|=0\]in the interval\[x\in \left[ \frac{-\pi }{4},\frac{\pi }{4} \right]\]is
  A)
   0                                            
  done clear
  B)
          2                                            
  done clear
  C)
          1                                            
  done clear
  D)
          3
  done clear
  View Answer play_arrow

• question_answer146) If \[A=\left| \begin{matrix}    a & 0 & 0  \\    0 & a & 0  \\    0 & 0 & a  \\ \end{matrix} \right|,\] then the value of\[|A||adj(A)|\]is
  A)
  \[{{a}^{3}}\]                                          
  done clear
  B)
          \[{{a}^{6}}\]                         
  done clear
  C)
          \[{{a}^{9}}\]                                         
  done clear
  D)
          \[{{a}^{27}}\]
  done clear
  View Answer play_arrow

• question_answer147) The term independent of \[x\]in \[{{\left[ \sqrt{\frac{x}{3}}+\sqrt{\frac{3}{2{{x}^{2}}}} \right]}^{10}}\] is
  A)
   \[{{\,}^{10}}{{C}_{1}}\]                       
  done clear
  B)
          \[5/12\]               
  done clear
  C)
          1                                            
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer148) \[\frac{\frac{1}{2}.\frac{2}{2}}{{{1}^{3}}}+\frac{\frac{2}{2}.\frac{3}{2}}{{{1}^{3}}+{{2}^{3}}}+\frac{\frac{3}{2}.\frac{4}{2}}{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}+...\]upto \[n\] terms
  A)
   \[\frac{n-1}{2}\]                  
  done clear
  B)
                          \[\frac{n}{n+1}\]                 
  done clear
  C)
          \[\frac{n+1}{n+2}\]                            
  done clear
  D)
          \[\frac{(n+1)}{n}\]
  done clear
  View Answer play_arrow

• question_answer149) The    solution    of    the    equation \[{{\cos }^{2}}\theta +\sin \theta +1=0,\] lies in the interval
  A)
   \[\left( \frac{-\pi }{4},\frac{\pi }{4} \right)\]                   
  done clear
  B)
          \[\left( \frac{\pi }{4},\frac{3\pi }{4} \right)\]                  
  done clear
  C)
          \[\left( \frac{3\pi }{4},\frac{5\pi }{4} \right)\]               
  done clear
  D)
          \[\left( \frac{5\pi }{4},\frac{7\pi }{4} \right)\]
  done clear
  View Answer play_arrow

• question_answer150) \[{{\log }_{3}}2,lo{{g}_{6}}2,{{\log }_{12}}2\]are in
  A)
   AP                                         
  done clear
  B)
          GP                         
  done clear
  C)
          HP                         
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow