Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2010

done BCECE Engineering Solved Paper-2010 Total Questions - 150

• question_answer1) Find the dimensions of electric permittivity,
  A)
  \[\text{ }\!\![\!\!\text{ }{{\text{A}}^{\text{2}}}{{\text{M}}^{\text{-1}}}{{\text{L}}^{\text{-3}}}{{\text{T}}^{\text{4}}}\text{ }\!\!]\!\!\text{ }\]   
  done clear
  B)
   \[\text{ }\!\![\!\!\text{ }{{\text{A}}^{\text{2}}}{{\text{M}}^{\text{-1}}}{{\text{L}}^{\text{-3}}}{{\text{T}}^{0}}\text{ }\!\!]\!\!\text{ }\]
  done clear
  C)
   \[\text{ }\!\![\!\!\text{ A}{{\text{M}}^{-3}}{{\text{L}}^{\text{-3}}}{{\text{T}}^{4}}\text{ }\!\!]\!\!\text{ }\]    
  done clear
  D)
          \[\text{ }\!\![\!\!\text{ }{{\text{A}}^{\text{2}}}{{\text{M}}^{0}}{{\text{L}}^{\text{-3}}}{{\text{T}}^{4}}\text{ }\!\!]\!\!\text{ }\]
  done clear
  View Answer play_arrow

• question_answer2) A ship of mass \[3\times {{10}^{7}}kg,\] initially at rest, is pulled by a force of \[5\times {{10}^{4}}N\] through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is
  A)
   1.5 m/s               
  done clear
  B)
          60 m/s
  done clear
  C)
   0.1 m/s               
  done clear
  D)
          5 m/s
  done clear
  View Answer play_arrow

• question_answer3) If the external forces acting on a system have zero resultant, the centre of mass
  A)
   may move but not accelerate
  done clear
  B)
   may accelerate
  done clear
  C)
   must not move
  done clear
  D)
   None of die above
  done clear
  View Answer play_arrow

• question_answer4) An object is placed on the surface of a smooth inclined plane of inclination 8. It takes time t to reach the bottom. If the same object is allowed to slide down a rough inclined plane of inclination\[\theta ,\] it takes time \[nt\] to reach the bottom, where n is a number greater than 1. The coefficient of friction µ is given by
  A)
  \[\mu =\tan \,\theta \left( 1-\frac{1}{{{n}^{2}}} \right)\]              
  done clear
  B)
  \[\mu =\cos \,\theta \left( 1-\frac{1}{{{n}^{2}}} \right)\]
  done clear
  C)
   \[\mu =\tan \,\theta \sqrt{1-\frac{1}{\sqrt{{{n}^{2}}}}}\]
  done clear
  D)
  \[\mu =\cot \,\theta \sqrt{1-\frac{1}{\sqrt{{{n}^{2}}}}}\]
  done clear
  View Answer play_arrow

• question_answer5) A 500 kg horse pulls a can of mass 1500 kg along a level road with an acceleration of \[1\,m/{{s}^{2}}\]. If the coefficient of sliding friction is 0.2, then the horizontal force exerted by the earth on the horse is
  A)
   300 kg-wt                          
  done clear
  B)
   400 kg-wt
  done clear
  C)
   500 kg-wt          
  done clear
  D)
          600 kg-wt
  done clear
  View Answer play_arrow

• question_answer6) A spring is held compressed so that its stored energy is 2.4 J. its ends are in contact with masses 1 g and 48 g placed on a functionless table. When the spring is released, the heavier mass wilt acquire a speed of
  A)
  \[\frac{2.4}{49}m{{s}^{-1}}\]      
  done clear
  B)
         \[\frac{2.4\times 48}{49}m{{s}^{-1}}\]
  done clear
  C)
  \[\frac{{{10}^{3}}}{7}cm{{s}^{-1}}\]         
  done clear
  D)
         \[\frac{{{10}^{6}}}{7}cm{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer7) Two simple pendulums first of bob mass \[{{M}_{1}}\] and length \[{{L}_{1}},\] second of bob mass \[{{M}_{2}}\] and length \[{{L}_{2}}.\,{{M}_{1}}={{M}_{2}}\] and \[{{L}_{1}}=2{{L}_{2}}\]. If the vibrational energy of both is same. Then which of the following is correct?
  A)
   Amplitude of B is greater than chat of A
  done clear
  B)
   Amplitude of B is smaller than that of A
  done clear
  C)
   Amplitude will be same
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer8) Which logic gate is represented by the following combination of logic gales?
  A)
  OR           
  done clear
  B)
  NAND
  done clear
  C)
  AND                     
  done clear
  D)
  NOR
  done clear
  View Answer play_arrow

• question_answer9) A body of mass m is situated on the earth in the gravitational field of sun. For the body to escape from die gravitation pull of the solar system the body must be imparted an escape velocity of (assume earth to be stationary)
  A)
   11.2km/s
  done clear
  B)
                          22.4 km/s
  done clear
  C)
   33.6 km/s          
  done clear
  D)
          42 km/s
  done clear
  View Answer play_arrow

• question_answer10) Find the lifting force of a 4 kg cork life belt in sea water, if the densitites of cork and sea water are \[0.2\,\times {{10}^{3}}kg/{{m}^{3}}\] and \[1.03\,\times {{10}^{3}}kg/{{m}^{3}}\] respectively.
  A)
   163 N        
  done clear
  B)
                         273 N
  done clear
  C)
   119 N                   
  done clear
  D)
          298 N
  done clear
  View Answer play_arrow

• question_answer11) Nitrogen \[({{N}_{2}})\] is in equilibrium state at T = 421 K. The value of most probable speed, \[{{v}_{mp}}\]is
  A)
   400 m/s       
  done clear
  B)
                         421 m/s
  done clear
  C)
   500 m/s              
  done clear
  D)
          600 m/s
  done clear
  View Answer play_arrow

• question_answer12) The temperature at which the velocity of oxygen will be half that of hydrogen at NTP is
  A)
  \[1092{}^\circ C\]   
  done clear
  B)
                         \[1492{}^\circ C\]
  done clear
  C)
  \[273\text{ }K\]               
  done clear
  D)
         \[819{}^\circ C\]
  done clear
  View Answer play_arrow

• question_answer13) Two sound waves, each of amplitude A and frequency \[\omega ,\] superpose at a point with phase difference of \[\frac{\pi }{2}.\] The amplitude and frequency of the resultant wave are respectively
  A)
  \[\frac{A}{\sqrt{2}},\frac{\omega }{2}\]                                
  done clear
  B)
  \[\frac{A}{\sqrt{2}},\omega \]
  done clear
  C)
  \[\sqrt{2A,}\frac{\omega }{2}\]
  done clear
  D)
         \[\sqrt{2}A,\omega \]
  done clear
  View Answer play_arrow

• question_answer14) A source emits electromagnetic waves of wavelength 3 m. One beam reaches the observer directly and other after reflection from a water surface, travelling 1.5 m extra distance and with intensity reduced to (1/4) as compared to intensity due to direct beam alone. The resultant intensity will be
  A)
   (1/4) fold                           
  done clear
  B)
   (3/4) fold
  done clear
  C)
   (5/4) fold           
  done clear
  D)
          (9/4) fold
  done clear
  View Answer play_arrow

• question_answer15) 15.      A square of side 3, cm is located at a distance 25 cm from a concave mirror of focal length                 10 cm. The centre of square is at the axis of the mirror and the plane is normal to axis of mirror. The area enclosed by the image of the square is            
  A)
   \[4\,c{{m}^{2}}\]                            
  done clear
  B)
   \[6\,c{{m}^{2}}\]
  done clear
  C)
   \[16\,c{{m}^{2}}\]         
  done clear
  D)
          \[36\,c{{m}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer16) A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal
  A)
  \[-\frac{Q}{2}\]                                
  done clear
  B)
  \[-\frac{Q}{4}\]
  done clear
  C)
  \[+\frac{Q}{4}\]                               
  done clear
  D)
         \[+\frac{Q}{2}\]
  done clear
  View Answer play_arrow

• question_answer17) The numerical value of charge on either plate of capacitor C shown in figure
  A)
  \[CE\]                                   
  done clear
  B)
  \[\frac{CE{{R}_{1}}}{{{R}_{1}}+r}\]
  done clear
  C)
  \[\frac{CE{{R}_{2}}}{{{R}_{2}}+r}\]                                           
  done clear
  D)
  \[\frac{CE{{R}_{1}}}{{{R}_{2}}+r}\]
  done clear
  View Answer play_arrow

• question_answer18) A proton enters a magnetic field of flux density \[1.5\,Wb/{{m}^{2}}\] with a speed of \[2\times {{10}^{7}}\,m/s\] at angle of 30° with the field. The force on a proton will be
  A)
   \[\text{0}\text{.24 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{N}\]                
  done clear
  B)
   \[\text{2}\text{.4 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{N}\]
  done clear
  C)
   \[\text{24 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{N}\]                 
  done clear
  D)
          \[\text{0}\text{.024 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{N}\]
  done clear
  View Answer play_arrow

• question_answer19) Two long straight wires are set parallel to each other at separation rand each carries a current in the same direction. The strength of the magnetic field at any point midway between the two wires is
  A)
   \[\frac{{{\mu }_{0}}i}{\pi r}\]                                    
  done clear
  B)
  \[\frac{2{{\mu }_{0}}i}{\pi r}\]
  done clear
  C)
  \[\frac{{{\mu }_{0}}i}{2\pi r}\]                   
  done clear
  D)
          zero
  done clear
  View Answer play_arrow

• question_answer20) The work done in turning a magnet of magnetic moment At by an angle of 90° from the meridian is n times the corresponding work done to turn it through an angle of 60°
  A)
   \[n=\frac{1}{2}\]  
  done clear
  B)
                                          \[n=2\]
  done clear
  C)
   \[n=\frac{1}{4}\]                            
  done clear
  D)
  \[n=1\]
  done clear
  View Answer play_arrow

• question_answer21) An inductive coil has a resistance of 100\[\Omega \] When an AC signal of frequency 1000 Hz is applied to the coil, the voltage leads the current by \[45{}^\circ \]. The inductance of the coil is
  A)
   \[\frac{1}{10\pi }\]                                         
  done clear
  B)
  \[\frac{1}{20\pi }\]
  done clear
  C)
  \[\frac{1}{40\pi }\]                          
  done clear
  D)
         \[\frac{1}{60\pi }\]
  done clear
  View Answer play_arrow

• question_answer22) An inductor of 1 H is connected across a 220 V, 50 Hz supply. The peak value of the current is approximately
  A)
   0.5 A                                    
  done clear
  B)
   0.7 A
  done clear
  C)
   1 A                        
  done clear
  D)
          1.4 A
  done clear
  View Answer play_arrow

• question_answer23) The figure shows an equiconvex lens of focal length \[f.\] If the lens is cut along PQ, the focal length of each half will be
  A)
  \[\frac{f}{2}\]                                  
  done clear
  B)
  \[f\]
  done clear
  C)
  \[2f\]                   
  done clear
  D)
  \[4f\]
  done clear
  View Answer play_arrow

• question_answer24) Light of two different frequencies whose photons have energies 1 eV and 2.5 eV successively illuminate a metal of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons will be
  A)
   1 : 5
  done clear
  B)
                          1 : 4
  done clear
  C)
   1 : 2                      
  done clear
  D)
          1 : 1
  done clear
  View Answer play_arrow

• question_answer25) An electron Jumps from the first excited state to the ground State of hydrogen atom. Whit will be the percentage change in the speed of electron?
  A)
   25%                                      
  done clear
  B)
   50%
  done clear
  C)
   100%                   
  done clear
  D)
          200%
  done clear
  View Answer play_arrow

• question_answer26) The mutual inductance of a pair of coils, each of N rums, is M henry If a current of i ampere in one of the coils is brought to zero in t second, the emf induced per turn in the other coil, in volt will be
  A)
  \[\frac{Mi}{t}\]                                
  done clear
  B)
  \[\frac{NMi}{t}\]
  done clear
  C)
  \[\frac{MN}{it}\]                             
  done clear
  D)
         \[\frac{Mi}{Nt}\]
  done clear
  View Answer play_arrow

• question_answer27) A body falls from rest. In the last second of its fall it covers half of the total distance. If g is \[9.8\,\,m/{{s}^{2}},\] then the total time of its fall is (in second)
  A)
   2                                            
  done clear
  B)
   \[2+\sqrt{2}\]
  done clear
  C)
   \[2-\sqrt{2}\]                   
  done clear
  D)
          \[2\pm \sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer28) A force\[\mathbf{\vec{F}}=a\mathbf{\vec{i}}+3\mathbf{\vec{j}}+\mathbf{6\vec{k}}\] is acting at a point \[\mathbf{\vec{r}}=\mathbf{2\vec{i}}+\mathbf{6\vec{j}}+\mathbf{12\vec{k}}.\] The value of a for which angular momentum is conserved is
  A)
   zero                                     
  done clear
  B)
   1
  done clear
  C)
   -1                          
  done clear
  D)
          2
  done clear
  View Answer play_arrow

• question_answer29) A wooden block is floating in a liquid 50% of its volume inside the liquid when the vessel is stationary. Percentage of volume immersed when the vessel moves upwards with an acceleration\[a=g/3\] is
  A)
   30%                                      
  done clear
  B)
   50%
  done clear
  C)
   60%                      
  done clear
  D)
          67%
  done clear
  View Answer play_arrow

• question_answer30) Two resistors 400\[\Omega \] and 800\[\Omega \]are connected in series with a 6 V battery- The potential difference measured by voltmeter of 10\[k\Omega \] across \[400\,\Omega \] resistor is
  A)
   2 V                                        
  done clear
  B)
   1.95 V
  done clear
  C)
   3.8 V                    
  done clear
  D)
          4 V
  done clear
  View Answer play_arrow

• question_answer31) An  astronomical  telescope in normal adjustment receives light from a distant source S the tube length is now decreased slightly, then
  A)
   no image will be formed
  done clear
  B)
   a virtual image of S will be formed at a finite distance
  done clear
  C)
   a large, real image of S will be formed behind the eye-piece, far away from it
  done clear
  D)
   a small, real image of S will be formed behind the eye-piece close to it
  done clear
  View Answer play_arrow

• question_answer32) The potential difference in volt across the resistance R., in the circuit shown in figure, is \[({{R}_{1}}=15\,\Omega ,\,{{R}_{2}}=15\,\Omega ,\,{{R}_{3}}=30\,\Omega ,\,{{R}_{4}}=35\,\Omega )\]
  A)
  5                                            
  done clear
  B)
  7.5
  done clear
  C)
  15                         
  done clear
  D)
  12.5
  done clear
  View Answer play_arrow

• question_answer33) The ratio of molecular masses of two radioactive substances is 3/2 and the ratio of their decay constants is 4/3, Then, the ratio of their initial activities per mole will be
  A)
   2                                            
  done clear
  B)
   4/3
  done clear
  C)
   8/9                       
  done clear
  D)
          9/8
  done clear
  View Answer play_arrow

• question_answer34) The resultant of two forces P and Q is of magnitude p. If P be doubled, the resultant will be inclined to Q at an angle
  A)
  \[0{}^\circ \]                                      
  done clear
  B)
  \[30{}^\circ \]
  done clear
  C)
  \[60{}^\circ \]                   
  done clear
  D)
         \[90{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer35) A person is at a distance x from a bus when the bus begins 10 move with a constant acceleration a. What is the minimum velocity with which [he person should run towards the bus so as to catch it?
  A)
   \[2ax\]                                
  done clear
  B)
   \[\sqrt{2ax}\]
  done clear
  C)
   \[ax\]                  
  done clear
  D)
          \[\sqrt{ax}\]
  done clear
  View Answer play_arrow

• question_answer36) A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at die rate of \[a\,m/{{s}^{2}},\] then the resultant acceleration will be
  A)
  \[\left( \frac{{{v}^{2}}}{r}+a \right)\]                      
  done clear
  B)
  \[{{\left( \frac{{{v}^{2}}}{{{r}^{2}}}+a \right)}^{1/2}}\]
  done clear
  C)
  \[{{\left( \frac{{{v}^{4}}}{{{r}^{2}}}+{{a}^{2}} \right)}^{1/2}}\]    
  done clear
  D)
         \[{{\left( \frac{{{v}^{2}}}{{{r}^{2}}}-{{a}^{2}} \right)}^{1/2}}\]
  done clear
  View Answer play_arrow

• question_answer37) A body of mass 10 kg at rest explodes into two pieces of masses 7 kg and 3 kg. If the total increase in kinetic energy due to explosion is 1680 J, the magnitude of their relative velocity in m/s, after explosion is
  A)
   40                                         
  done clear
  B)
   50
  done clear
  C)
   70                         
  done clear
  D)
          80
  done clear
  View Answer play_arrow

• question_answer38) The moment of inertia of a body about a given axis is \[1.2\,\,kg\,{{m}^{2}}\]. Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of \[25\,rad/{{s}^{2}}\] must be applied about that axis for a duration of
  A)
   4 s                                         
  done clear
  B)
   2 s
  done clear
  C)
   8 s                         
  done clear
  D)
          10 s
  done clear
  View Answer play_arrow

• question_answer39) Steel and aluminium wires have equal resistances and masses. Which of die wires is longer and how many times? (Given, densities of steel and aluminium are \[7.8\,\times {{10}^{3}}\,kg\,{{m}^{-3}}\] and \[2.7\times {{10}^{3}}\,kg\,{{m}^{-3}}\] and their resistivities are \[0.15\,\mu \Omega .m\] and\[0.028\,\mu \Omega -m\] respectively)
  A)
   The aluminium wire is 3.9 times longer
  done clear
  B)
   The aluminium wire is 1.3 times longer
  done clear
  C)
   The aluminium wire is 2.6 times longer
  done clear
  D)
   The steel wire is 3.9 times longer
  done clear
  View Answer play_arrow

• question_answer40) Two cells of emfs \[{{E}_{1}}\] and\[{{E}_{2}}({{E}_{1}}>{{E}_{2}})\] are connected as shown in figure. When a potentiometer is connected between A and B, the balancing length of the potentiometer wire is 300 cm. On connecting the same potentiometer between A and C, the balancing length is 100 on. The ratio\[\frac{{{E}_{1}}}{{{E}_{2}}}\]is
  A)
   3 : 1                                      
  done clear
  B)
   1 : 3
  done clear
  C)
   2 : 3                      
  done clear
  D)
          3 : 2
  done clear
  View Answer play_arrow

• question_answer41) In hydrogen atom the electron is making \[6.6\,\times {{10}^{15}}\,rev/s\] around the nucleus of radius \[0.53\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The magnetic field produced at the centre of the orbit is nearly
  A)
   \[0.12\,Wb/{{m}^{2}}\]
  done clear
  B)
   \[1.2\,Wb/{{m}^{2}}\]
  done clear
  C)
   \[12\,Wb/{{m}^{2}}\]   
  done clear
  D)
          \[120\,Wb/{{m}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer42) An AC source is 120 V-60 Hz. The value of voltage after\[\frac{1}{720}\] from start will be
  A)
   20.2 V                                  
  done clear
  B)
   42.4 V
  done clear
  C)
   84.8 V                  
  done clear
  D)
          106.8 V
  done clear
  View Answer play_arrow

• question_answer43) The energy difference between the first two levels of hydrogen atom is 10.2eV. For another element of atomic number 10 and mass number 20, this will be
  A)
   1020 eV                              
  done clear
  B)
   2040 eV
  done clear
  C)
   0.51 eV               
  done clear
  D)
          0.102 eV
  done clear
  View Answer play_arrow

• question_answer44) The following equation represents induced transmutation \[_{4}B{{e}^{9}}{{+}_{2}}H{{e}^{4}}{{\xrightarrow{{}}}_{6}}{{C}^{12}}+X\] In this equation, X represents
  A)
   one \[{{\beta }^{-}}\] particle                   
  done clear
  B)
   \[\alpha -\]particle
  done clear
  C)
   a positron
  done clear
  D)
                                          a neutron
  done clear
  View Answer play_arrow

• question_answer45) The masses of neutron and proton are 1.0087 and 1.0073 amu respectively- If the neutrons and protons combine to form helium nucleus of mass 4.0015 amu the binding energy of the helium nucleus will be
  A)
   28.4 MeV                           
  done clear
  B)
   20.8 MeV
  done clear
  C)
   27.3 MeV           
  done clear
  D)
          14.2 MeV
  done clear
  View Answer play_arrow

• question_answer46) The activity of a radioactive sample is measured as 9750 count/min at t=0 and 975 count/min at t =5min. The decay constant is nearly
  A)
   \[0.922\,{{\min }^{-1}}\]
  done clear
  B)
   \[0.691\,{{\min }^{-1}}\]
  done clear
  C)
   \[0.461\,mi{{n}^{-1}}\] 
  done clear
  D)
              \[0.230{{\min }^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer47)                                 Light of wavelength \[\lambda ,\] strikes a photoelectric surface and electrons are ejected with an energy E. Iff is to be increased to exactly twice its original value, the wavelength changes to\[\lambda ;\] where
  A)
  \[\lambda \]is less than \[\frac{\lambda }{2}\]   
  done clear
  B)
  \[\lambda \]is greater than\[\frac{\lambda }{2}\]
  done clear
  C)
   \[\lambda \] is greater than \[\frac{\lambda }{2}\] but less than \[\lambda ,\]
  done clear
  D)
   \[\lambda \] is exactly equal to\[\frac{\lambda }{2}\]
  done clear
  View Answer play_arrow

• question_answer48) Three point masses, each of mass m are placed at the corners of an equilateral triangle of side The moment of inertia of this system about, an axis along one side of the triangle is
  A)
   \[3\,m{{a}^{2}}\]                            
  done clear
  B)
   \[2\,m{{a}^{2}}\]
  done clear
  C)
   \[\frac{3}{4}m{{a}^{2}}\]            
  done clear
  D)
         \[\frac{3}{2}m{{a}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer49) A pipe opened at both ends produces a note of frequency \[{{f}_{1.}}\] When the pipe is kept with \[\frac{3}{4}\]th of its length in water, it produces a note of frequency \[{{f}_{2.}}\] The ratio \[\frac{{{f}_{1}}}{{{f}_{2}}}\] is of
  A)
   \[\frac{3}{4}\]                                  
  done clear
  B)
          \[\frac{4}{3}\]
  done clear
  C)
         \[\frac{1}{2}\]                                   
  done clear
  D)
         \[2\]
  done clear
  View Answer play_arrow

• question_answer50) A solenoid is 1.5 m long and its inner diameter is 4.0 cm. It has 3 layers of windings of 1000 turns each and carries a current of 2.0A. The magnetic flux for a cross-section of the solenoid is nearly
  A)
   \[4.1\,\times {{10}^{-5}}Wb\]                   
  done clear
  B)
          \[5.2\,\times {{10}^{-5}}Wb\]
  done clear
  C)
          \[6.31\,\times {{10}^{-31}}Wb\]              
  done clear
  D)
          \[2.5\,\times {{10}^{-7}}Wb\]
  done clear
  View Answer play_arrow

• question_answer51) How many moles of helium gas occupy 22.4 L at \[\text{0}{{\,}^{\text{o}}}\text{C}\]and 1 atm pressure?
  A)
   0.11                                      
  done clear
  B)
   1.11                      
  done clear
  C)
          0.90                      
  done clear
  D)
                          1.0
  done clear
  View Answer play_arrow

• question_answer52) The compound which contains both ionic and covalent bond
  A)
  \[KCl\]                 
  done clear
  B)
          KCN                     
  done clear
  C)
  \[C{{H}_{4}}\]                   
  done clear
  D)
          \[{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer53) The following is endothermic reaction
  A)
   Decomposition of water
  done clear
  B)
   Conversion of graphite to diamond
  done clear
  C)
   Dehydrogenation of ethane to ethylene
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer54) A saturated solution of \[\text{A}{{\text{g}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]is \[\text{2}\text{.5}\times {{10}^{-2}}\,M.\] The value of its solubility product is
  A)
   \[62.5\times {{10}^{-6}}\]           
  done clear
  B)
          \[62.5\times {{10}^{-4}}\]           
  done clear
  C)
          \[15.625\times {{10}^{-6}}\]      
  done clear
  D)
   \[3.125\times {{10}^{-6}}\]
  done clear
  View Answer play_arrow

• question_answer55) The enthalpies of combustion of carbon and carbon monoxide are \[~-393.5\] and \[-283\text{ kJ mo}{{\text{l}}^{-1}}\]respectively. The enthalpy of formation of carbon monoxide per mole is
  A)
  \[\text{110}\text{.5kJ}\]                              
  done clear
  B)
   \[\text{676}\text{.5 kJ}\]                            
  done clear
  C)
  \[-\text{676}\text{.5 kJ}\]       
  done clear
  D)
         \[-\text{110}\text{.5kJ}\]
  done clear
  View Answer play_arrow

• question_answer56) 1 g ice absorbs 335 J of heat to melt at \[\text{0}{{\,}^{\text{o}}}\text{C}\text{.}\] The entropy change will be
  A)
  \[1.2\text{ J}{{\text{K}}^{-1}}\text{mo}{{\text{l}}^{-1}}\]             
  done clear
  B)
   \[335\text{ J}{{\text{K}}^{-1}}\text{ mo}{{\text{l}}^{-1}}\]
  done clear
  C)
         \[22.1\text{ J}{{\text{K}}^{-1}}\text{mo}{{\text{l}}^{-1}}\]          
  done clear
  D)
   \[0.8\text{ J}{{\text{K}}^{-1}}\text{ mo}{{\text{l}}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer57) An ideal gas cant be liquefied because
  A)
   its critical temperature is always above \[\text{0}{{\,}^{\text{o}}}\text{C}\]
  done clear
  B)
   its molecules are relatively smaller in size
  done clear
  C)
   it solidifies before becoming a liquid
  done clear
  D)
   forces operative between its molecules are negligible                                          
  done clear
  View Answer play_arrow

• question_answer58) What type of crystal defect is indicated in the diagram below?                                       \[N{{a}^{+}}C{{l}^{-}}N{{a}^{+}}C{{l}^{-}}N{{a}^{+}}C{{l}^{-}}\] \[\begin{matrix}    N{{a}^{+}} & C{{l}^{-}} & N{{a}^{+}} & C{{l}^{-}} & N{{a}^{+}} & C{{l}^{-}}  \\    {} & C{{l}^{-}} & {} & C{{l}^{-}} & N{{a}^{+}} & N{{a}^{+}}  \\    N{{a}^{+}} & C{{l}^{-}} & {} & C{{l}^{-}} & N{{a}^{+}} & C{{l}^{-}}  \\    {} & C{{l}^{-}} & N{{a}^{+}} & C{{l}^{-}} & N{{a}^{+}} & N{{a}^{+}}  \\ \end{matrix}\]
  A)
   Frenkel defect                                      
  done clear
  B)
   Schottky defect 
  done clear
  C)
                                       Interstitial defect
  done clear
  D)
   Frenkel and Schottky defects
  done clear
  View Answer play_arrow

• question_answer59) A metal has bcc structure and the edge length of its unit cell is \[\text{3}\text{.04}\overset{\text{o}}{\mathop{\text{A}}}\,\text{.}\] The volume of the unit cell in \[\text{c}{{\text{m}}^{\text{3}}}\]will be                                   
  A)
   \[\text{1}\text{.6}\times {{10}^{-21}}c{{m}^{3}}\]          
  done clear
  B)
   \[2.81\times {{10}^{-23}}\,c{{m}^{3}}\]                
  done clear
  C)
   \[6.02\times {{10}^{-23}}\,c{{m}^{3}}\]
  done clear
  D)
          \[6.6\times {{10}^{-24}}\,c{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer60) Peptisation denotes
  A)
   digestion of food
  done clear
  B)
                                        hydrolysis of proteins                    
  done clear
  C)
   breaking and dispersion into the colloidal state                                                  
  done clear
  D)
   precipitation of solid from colloidal dispersion
  done clear
  View Answer play_arrow

• question_answer61) Plaster of Paris is
  A)
  \[CaS{{O}_{4}}.2{{H}_{2}}O\]     
  done clear
  B)
   \[CaS{{O}_{4}}.{{H}_{2}}O\]
  done clear
  C)
                          \[CaS{{O}_{4}}.\frac{1}{2}{{H}_{2}}O\]
  done clear
  D)
          \[CaS{{O}_{4}}.4{{H}_{2}}O\]
  done clear
  View Answer play_arrow

• question_answer62) Conc.\[\text{HN}{{\text{O}}_{\text{3}}}\] reacts with\[{{\text{I}}_{\text{2}}}\]to form 
  A)
  \[\text{HI}\]                                      
  done clear
  B)
  \[\text{HOI}\]                    
  done clear
  C)
                          \[\text{HI}{{\text{O}}_{\text{2}}}\]                       
  done clear
  D)
         \[\text{HI}{{\text{O}}_{3}}\]                    
  done clear
  View Answer play_arrow

• question_answer63) Coal gas is a mixture of
  A)
  \[{{H}_{2}}O\]and \[CO\]
  done clear
  B)
          \[{{H}_{2}},CO\]and \[C{{H}_{4}}\]
  done clear
  C)
          \[{{H}_{2}}\]and \[CO\]                               
  done clear
  D)
   \[C{{H}_{4}}\]and \[CO\]
  done clear
  View Answer play_arrow

• question_answer64) Stainless steel contains
  A)
  \[\text{ }\!\!~\!\!\text{ Fe + Cr + Cu}\] 
  done clear
  B)
         \[\text{Fe + Cu + Ni}\]
  done clear
  C)
         \[\text{Fe + Cr + Ni}\]   
  done clear
  D)
          \[\text{Fe + Ni + Cu}\]
  done clear
  View Answer play_arrow

• question_answer65) The isomers which can be converted into another form by rotation of the molecule around single bond are
  A)
   geometrical isomers     
  done clear
  B)
   conformers
  done clear
  C)
   enantiomers
  done clear
  D)
   diastereomers
  done clear
  View Answer play_arrow

• question_answer66) An organic compound contains 49.3% carbon, 6.84% hydrogen and its vapour density is 73. Molecular formula of the compound is
  A)
   \[{{C}_{3}}{{H}_{5}}{{O}_{2}}\]                 
  done clear
  B)
   \[{{C}_{4}}{{H}_{10}}{{O}_{2}}\]              
  done clear
  C)
          \[{{C}_{6}}{{H}_{10}}{{O}_{4}}\]              
  done clear
  D)
          \[{{C}_{3}}{{H}_{10}}{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer67) Ozone in stratosphere is depleted by
  A)
   \[C{{F}_{2}}C{{l}_{2}}\]
  done clear
  B)
          \[{{C}_{7}}{{F}_{16}}\] 
  done clear
  C)
          \[{{C}_{6}}{{H}_{6}}C{{l}_{6}}\]
  done clear
  D)
          \[{{C}_{6}}{{F}_{6}}\]
  done clear
  View Answer play_arrow

• question_answer68) Iodine is formed when \[\text{KI}\]reacts with a solution of
  A)
  \[CuS{{O}_{4}}\]              
  done clear
  B)
          \[{{(N{{H}_{4}})}_{2}}S{{O}_{4}}\]          
  done clear
  C)
   \[ZnS{{O}_{4}}\]             
  done clear
  D)
          \[FeS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer69) Select the correct order of the strength of acids given below
  A)
  \[HCl{{O}_{4}}<HCl{{O}_{3}}<HClO<HCl{{O}_{2}}\]
  done clear
  B)
   \[HCl{{O}_{4}}<HCl{{O}_{3}}<HCl{{O}_{2}}<HClO\]
  done clear
  C)
   \[HClO<HCl{{O}_{2}}<HCl{{O}_{3}}<HCl{{O}_{4}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer70) Which one of the following statements regarding helium .is incorrect?
  A)
   It is used to fill gas balloons instead of hydrogen because it is lighter and non-inflammable
  done clear
  B)
   It is used as a cryogenic agent for carrying out experiments at low temperatures
  done clear
  C)
   It is used to produce and sustain powerful superconducting magnets
  done clear
  D)
   It is used in gas-cooled nuclear reactors
  done clear
  View Answer play_arrow

• question_answer71) One would expect proton to have very large
  A)
   ionization potential
  done clear
  B)
   radius
  done clear
  C)
   charge
  done clear
  D)
   hydration energy
  done clear
  View Answer play_arrow

• question_answer72) What is the correct orbital designation of an electron with the quantum number, \[n=4,l=3,m=-2,s=\frac{1}{2}?\]
  A)
  \[3s\]                                   
  done clear
  B)
   \[4f\]                   
  done clear
  C)
  \[~5p\]                
  done clear
  D)
          \[6s\]
  done clear
  View Answer play_arrow

• question_answer73) The energy of an electron in second Bohr orbit of hydrogen atom is            
  A)
   \[-5.44\times {{10}^{-19}}eV\] 
  done clear
  B)
   \[-5.44\times {{10}^{-19}}cal\] 
  done clear
  C)
   \[-5.44\times {{10}^{-19}}kJ\]   
  done clear
  D)
   \[-5.44\times {{10}^{-19}}J\]
  done clear
  View Answer play_arrow

• question_answer74) One of the following has greatest electron affinity. Identify it.
  A)
   O                                           
  done clear
  B)
   S                            
  done clear
  C)
   Se                         
  done clear
  D)
          Te
  done clear
  View Answer play_arrow

• question_answer75) The ONO angle is maximum in
  A)
  \[\text{NO}_{3}^{-}\]   
  done clear
  B)
          \[\text{NO}_{2}^{-}\]  
  done clear
  C)
   \[\text{N}{{\text{O}}_{\text{2}}}\]        
  done clear
  D)
          \[\text{NO}_{2}^{+}\]
  done clear
  View Answer play_arrow

• question_answer76) The pH value for \[\frac{1}{1000}\text{N}-\text{KOH}\]solution is
  A)
   3                                            
  done clear
  B)
   \[{{10}^{-11}}\]               
  done clear
  C)
          2                            
  done clear
  D)
          11
  done clear
  View Answer play_arrow

• question_answer77) The equilibrium constant for a reaction, \[{{N}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2NO(g)\] is \[4\times {{10}^{-4}}\] at \[\text{2000}\,\text{K}\text{.}\] In the presence of catalyst, the equilibrium is attained 10 times faster. The equilibrium constant in presence of catalyst at 2000 K is
  A)
  \[10\times {{10}^{-4}}\]               
  done clear
  B)
   \[4\times {{10}^{-2}}\] 
  done clear
  C)
          \[4\times {{10}^{-4}}\] 
  done clear
  D)
          \[4\times {{10}^{-4}}\]
  done clear
  View Answer play_arrow

• question_answer78) Consider the following \[{{\text{E}}^{\text{o}}}\]values \[E_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=+\,0.77\,V\] \[E_{S{{n}^{2+}}/Sn}^{o}=-0.14\,V\] Under standard conditions the potential for the reaction, \[Sn(s)+2F{{e}^{3+}}(aq)\xrightarrow{{}}2F{{e}^{2+}}(aq)+S{{n}^{2+}}(aq)\]is
  A)
   1.68 V                                  
  done clear
  B)
   1.40 V  
  done clear
  C)
          0.91 V                                  
  done clear
  D)
   0.63 V
  done clear
  View Answer play_arrow

• question_answer79) The relationship between the values of osmotic pressure of 0.1 M solutions of \[\text{KN}{{\text{O}}_{\text{3}}}\text{(}{{\text{p}}_{\text{1}}}\text{)}\]and \[C{{H}_{3}}COOH({{p}_{2}})\]is
  A)
   \[\frac{{{p}_{1}}}{{{p}_{1}}+{{p}_{2}}}=\frac{{{p}_{2}}}{{{p}_{1}}+{{p}_{2}}}\]    
  done clear
  B)
   \[{{p}_{1}}>{{p}_{2}}\] 
  done clear
  C)
          \[{{p}_{2}}>{{p}_{1}}\] 
  done clear
  D)
          \[{{p}_{1}}={{p}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer80) Volume of \[\text{0}\text{.6 M NaOH}\]required to neutralize \[\text{30}\,\text{c}{{\text{m}}^{\text{3}}}\]of \[\text{0}\text{.4}\,\text{M}\,\text{HCl}\]is
  A)
  \[30c{{m}^{3}}\]                              
  done clear
  B)
  \[45\,c{{m}^{3}}\]           
  done clear
  C)
         \[~20\,c{{m}^{3}}\]       
  done clear
  D)
         \[~50\,c{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer81) For nth order reaction, the half-life period, \[{{t}_{1/2}}\] is proportional to initial concentration as
  A)
  \[\frac{1}{{{a}^{n-1}}}\]               
  done clear
  B)
          \[{{a}^{n+1}}\]                
  done clear
  C)
   \[{{a}^{n-1}}\]                 
  done clear
  D)
          \[\frac{1}{{{a}^{n}}}\]
  done clear
  View Answer play_arrow

• question_answer82) Thermite is a mixture of
  A)
  \[C{{r}_{2}}{{O}_{3}}+A{{l}_{2}}{{O}_{3}}\]          
  done clear
  B)
   \[F{{e}_{2}}{{O}_{3}}+Al\]          
  done clear
  C)
          \[F{{e}_{2}}{{O}_{3}}+A{{l}_{2}}{{O}_{3}}\]
  done clear
  D)
          \[A{{l}_{2}}{{O}_{3}}+2Cr\]
  done clear
  View Answer play_arrow

• question_answer83) Of the ions\[Z{{n}^{2+}},N{{i}^{2+}}ad\,C{{r}^{3+}}\] (atomic number of and Cr = 24)
  A)
   all these are colourless
  done clear
  B)
   all these are coloured
  done clear
  C)
   only\[\text{N}{{\text{i}}^{\text{2+}}}\] is coloured and\[\text{Z}{{\text{n}}^{\text{2+}}}\] and \[\text{C}{{\text{r}}^{\text{3+}}}\]are colourless
  done clear
  D)
   only \[\text{Z}{{\text{n}}^{\text{2+}}}\] is colourless and \[\text{N}{{\text{i}}^{\text{2+}}}\]and \[\text{C}{{\text{r}}^{3+}}\] are coloured
  done clear
  View Answer play_arrow

• question_answer84) The coordination number of a central metal atom in a complex is determined by
  A)
   the number of ligands around a metal ion bonded by \[\sigma -\]bonds
  done clear
  B)
   the number of ligands around a metal ion bonded by it \[\pi -\]bonds
  done clear
  C)
   the number of ligands around a metal ion bonded by \[\sigma \] and \[\pi -\]bonds both
  done clear
  D)
   the number of only anionic ligands bonded to the metal ion
  done clear
  View Answer play_arrow

• question_answer85) Potassium ferricyanide on ionization produces
  A)
   2 ions                                  
  done clear
  B)
   1 ion    
  done clear
  C)
          3 ions                  
  done clear
  D)
          4 ions
  done clear
  View Answer play_arrow

• question_answer86) The IUPAC name of \[C{{H}_{3}}-\underset{OH}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-C{{H}_{2}}-\underset{OH}{\overset{C{{H}_{3}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{3}}\]is
  A)
   \[1,1-\]dimethyl\[-1,3-\]butanediol
  done clear
  B)
   \[2-\]methyl\[-2,4-\]pentanediol
  done clear
  C)
   \[4-\]methyl\[-2,4-\]pentanediol
  done clear
  D)
   \[1,3,3-\]trimethyl\[-1,3-\]propane diol
  done clear
  View Answer play_arrow

• question_answer87) The order of decreasing stability of the carbanions is \[{{(C{{H}_{3}})}_{3}}\bar{C}(1),{{(C{{H}_{3}})}_{2}}\bar{C}H(2),C{{H}_{3}}\bar{C}{{H}_{2}}(3),\]\[{{C}_{6}}{{H}_{5}}\bar{C}{{H}_{2}}(4)\]
  A)
   1 > 2 > 3 > 4                       
  done clear
  B)
   4 > 3 > 2 > 1       
  done clear
  C)
          1 > 2 > 4 > 3       
  done clear
  D)
          4 > 1 > 2 > 3
  done clear
  View Answer play_arrow

• question_answer88) Which set of products is expected on reductive ozonolysis of the following diolefin? \[C{{H}_{3}}CH=\overset{C{{H}_{3}}}{\mathop{\overset{|}{\mathop{C}}\,}}\,-CH=C{{H}_{2}}\]
  A)
   \[C{{H}_{3}}CHO;C{{H}_{3}}COCH=C{{H}_{2}}\]
  done clear
  B)
   \[C{{H}_{3}}CH=\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-CHO;C{{H}_{2}}O\]
  done clear
  C)
   \[C{{H}_{3}}CHO;C{{H}_{3}}COCHO;C{{H}_{2}}O\]
  done clear
  D)
   \[C{{H}_{3}}CHO;C{{H}_{3}}COC{{H}_{3}};C{{H}_{2}}O\]
  done clear
  View Answer play_arrow

• question_answer89) Which of the following pairs is/are correctly matched?

  	Reaction	Product
  (i)	\[RX+AgCN\]	\[RNC\]
  (ii)	\[RX+KCN\]	\[RCN\]
  (iii)	\[RX+KN{{O}_{2}}\]
  (iv)	\[RX+AgN{{O}_{2}}\]	\[R-O-N=O\]

  Select the correct answer using the codes given below
  A)
   I alone                                
  done clear
  B)
   I and II
  done clear
  C)
          III and IV        
  done clear
  D)
          I, II, III and IV
  done clear
  View Answer play_arrow

• question_answer90) A mixture of benzaldehyde and formaldehyde on heating with aqueous NaOH solution gives
  A)
   benzyl alcohol and sodium formate
  done clear
  B)
   sodium benzoate and methyl alcohol
  done clear
  C)
   sodium benzoate and sodium formate
  done clear
  D)
   benzyl alcohol and methyl alcohol
  done clear
  View Answer play_arrow

• question_answer91) Which of the following react with NaOH to produce an acid and an alcohol?
  A)
  \[HCHO\]                            
  done clear
  B)
  \[C{{H}_{3}}COOH\]
  done clear
  C)
  \[C{{H}_{3}}C{{H}_{2}}COOH\]  
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}COOH\]
  done clear
  View Answer play_arrow

• question_answer92) Which of the following has the maximum acidic strength?
  A)
   \[o-\]nitrobenzoic acid
  done clear
  B)
   \[m-\]nitrobenzoic acid
  done clear
  C)
   \[p-\]nitrobenzoic acid
  done clear
  D)
   \[p-\]nitrophenol
  done clear
  View Answer play_arrow

• question_answer93) Fentons reagent is
  A)
  \[Zn+HCl\]                         
  done clear
  B)
   \[Sn+HCl\]        
  done clear
  C)
          \[FeS{{O}_{4}}+{{H}_{2}}{{O}_{2}}\]
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer94) The energy stored in the cells of a living body is in the form of
  A)
   fats                                      
  done clear
  B)
   glucose               
  done clear
  C)
          ATP                      
  done clear
  D)
          proteins
  done clear
  View Answer play_arrow

• question_answer95) Saccharin is a/an
  A)
   aliphadc hydrocarbon
  done clear
  B)
          polynuclear compound
  done clear
  C)
          sweetening agent
  done clear
  D)
          sugar
  done clear
  View Answer play_arrow

• question_answer96) The nucleic acid the purine base having two possible binding sites is
  A)
   thymine             
  done clear
  B)
   cytosine             
  done clear
  C)
          guanine              
  done clear
  D)
          adenine
  done clear
  View Answer play_arrow

• question_answer97) On reduction secondary amine is given by
  A)
   nitroethane     
  done clear
  B)
   methylcyanide
  done clear
  C)
          methylisocyanide
  done clear
  D)
         nitrobenzene
  done clear
  View Answer play_arrow

• question_answer98) In chlorobenzene solution, the basic strength  of amines increases in the order
  A)
  \[{{({{C}_{2}}{{H}_{5}})}_{3}}N<{{({{C}_{2}}{{H}_{5}})}_{2}}NH<{{C}_{2}}{{H}_{5}}N{{H}_{2}}\]
  done clear
  B)
   \[{{C}_{2}}{{H}_{5}}N{{H}_{2}}<{{({{C}_{2}}{{H}_{5}})}_{2}}NH<{{({{C}_{2}}{{H}_{5}})}_{3}}N\]
  done clear
  C)
   \[{{({{C}_{2}}{{H}_{5}})}_{2}}NH<{{C}_{2}}{{H}_{5}}N{{H}_{2}}<{{({{C}_{2}}{{H}_{5}})}_{3}}N\]
  done clear
  D)
   \[{{({{C}_{2}}{{H}_{5}})}_{3}}N<{{C}_{2}}{{H}_{5}}N{{H}_{2}}<{{({{C}_{2}}{{H}_{5}})}_{2}}NH\]
  done clear
  View Answer play_arrow

• question_answer99) Dimethyl terephthalate and ethylene glycol react to form           
  A)
   nylon-6         
  done clear
  B)
          nylon-66            
  done clear
  C)
          dacron                
  done clear
  D)
          neoprene
  done clear
  View Answer play_arrow

• question_answer100) Gasoline is a mixture of
  A)
   \[{{C}_{6}}-{{C}_{11}}\]alkanes                
  done clear
  B)
  \[{{C}_{3}}-{{C}_{5}}\] alkanes
  done clear
  C)
         \[{{C}_{7}}-{{C}_{9}}\] alkanes 
  done clear
  D)
         \[{{C}_{15}}-{{C}_{20}}\]alkanes
  done clear
  View Answer play_arrow

• question_answer101) If \[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\theta d\theta ,}\] where n is a positive integer, then \[n({{I}_{n-1}}+{{I}_{n+1}})\]is equal to
  A)
   1                                            
  done clear
  B)
   \[n-1\]
  done clear
  C)
          \[\frac{1}{n-1}\]             
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer102) The minimum value of\[{{2}^{{{({{x}^{2}}-3)}^{3}}}}+27\]is
  A)
   1                            
  done clear
  B)
          2                            
  done clear
  C)
  \[{{2}^{27}}\]                    
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer103) The set of points of discontinuity of the function \[f(x),\]where\[f(x)=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{(2\sin x)}^{2n}}}{{{3}^{n}}-{{(2\cos x)}^{2n}}}\]is
  A)
   R           
  done clear
  B)
                          \[\left\{ n\pi \mp \frac{\pi }{3},n\in I \right\}\]
  done clear
  C)
                          \[\left\{ n\pi \pm \frac{\pi }{6},n\in I \right\}\]
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer104) The derivative of \[\cos e{{c}^{-1}}\left( \frac{1}{2{{x}^{2}}-1} \right)\] with respect to \[\sqrt{1-{{x}^{2}}}\]at \[x=\frac{1}{2}\]is
  A)
   - 4                         
  done clear
  B)
          4                            
  done clear
  C)
   -1                          
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer105) The equation of hyperbola conjugate to the hyperbola\[~2{{x}^{2}}+3xy-2{{y}^{2}}-5x+5y+2=0\] is
  A)
  \[~2{{x}^{2}}+\text{ }3xy-2{{y}^{2}}-\text{ }5x\,\,+\,\,5y-8=0\]
  done clear
  B)
   \[{{x}^{2}}+3xy-2{{y}^{2}}-5x+5y+8=0\]
  done clear
  C)
   \[2{{x}^{2}}+3xy-2{{y}^{2}}+5x-5y+8=0\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer106) The sum of the focal distances of any point on the conic \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\]is
  A)
   10                         
  done clear
  B)
   9                            
  done clear
  C)
   41                         
  done clear
  D)
   18
  done clear
  View Answer play_arrow

• question_answer107) The focus of the parabola \[{{y}^{2}}-x-2y+2=0\]is
  A)
   \[\left( \frac{1}{4},0 \right)\]    
  done clear
  B)
          \[(1,2)\]             
  done clear
  C)
          \[\left( \frac{5}{4},1 \right)\]    
  done clear
  D)
          \[\left( \frac{3}{4},\frac{5}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer108) Observe the following statements: (i) The   circle  \[{{x}^{2}}+{{y}^{2}}-6x-4y-7=0\] touches y-axis (ii) The   circle   \[{{x}^{2}}+\text{ }{{y}^{2}}+6x+4y-7=0\] touches \[x-\]axis Then, which of the following statements is/are correct?
  A)
   Both I and II    
  done clear
  B)
          Neither I nor II
  done clear
  C)
                          Only I                  
  done clear
  D)
          Only II
  done clear
  View Answer play_arrow

• question_answer109) The line \[x+y=a\]meets the axes of X and Y at A and B respectively. \[A\Delta AMN\]is inscribed in the \[\text{ }\!\!\Delta\!\!\text{ }\,\text{O}\,\text{A}\,\text{B,}\] O being the origin, with right angle at N. M and N lie on OB and AB respectively. If the area of the \[\Delta AMN\]is \[\frac{3}{8}\] of the area of the \[\Delta OAB,\] then\[\frac{AN}{BN}\] is equal to
  A)
   \[\frac{1}{3}\]                  
  done clear
  B)
  \[\frac{1}{3},3\]                              
  done clear
  C)
  \[\frac{2}{3},3\]                              
  done clear
  D)
  \[3\]
  done clear
  View Answer play_arrow

• question_answer110) The intercept made by a line on y-axis is double to the intercept made by it on x-axis and if it passes through\[(1,2),\]then its equation is
  A)
  \[2x+y=4\]     
  done clear
  B)
         \[2x+y+4=0\]    
  done clear
  C)
  \[2x-y=4\]      
  done clear
  D)
          \[2x-\text{ }y+4=0\]
  done clear
  View Answer play_arrow

• question_answer111) The area of the triangle formed by the lines  \[4{{x}^{2}}-9xy-9{{y}^{2}}=0\] and \[x=2\]is equal to
  A)
  \[\frac{20}{3}\,\text{sq}\,\text{units}\]
  done clear
  B)
          \[3\,\text{sq}\,\text{units}\]    
  done clear
  C)
          \[\frac{10}{3}\,\text{sq}\,\text{units}\]               
  done clear
  D)
          \[\text{2}\,\text{sq}\,\text{units}\]
  done clear
  View Answer play_arrow

• question_answer112) The area bounded by the parabolas \[{{y}^{2}}=4a(x+a)\]and \[{{y}^{2}}=-4a(x-a)\]is
  A)
   \[\frac{16}{3}{{a}^{2}}\text{sq units}\]
  done clear
  B)
          \[\frac{8}{3}\text{sq}\,\text{units}\]    
  done clear
  C)
          \[\frac{\text{4}}{\text{3}}{{\text{a}}^{\text{2}}}\text{sq}\,\text{units}\]
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer113) If the vectors \[\vec{a}=\hat{i}+a\hat{j}+{{a}^{2}}\hat{k},\vec{b}=\hat{i}+b\hat{j}+{{b}^{2}}\hat{k},\]\[\vec{c}=\hat{i}+c\hat{j}+{{c}^{2}}\hat{k}\]are three non-coplanar vectors and \[\left| \begin{matrix}    a & {{a}^{2}} & 1+{{a}^{3}}  \\    b & {{b}^{2}} & 1+{{b}^{3}}  \\    c & {{c}^{2}} & 1+{{c}^{3}}  \\ \end{matrix} \right|=0,\] then the value of aback is
  A)
   0                            
  done clear
  B)
          1                            
  done clear
  C)
   2                            
  done clear
  D)
          - 1
  done clear
  View Answer play_arrow

• question_answer114) If \[4{{\sin }^{2}}x-8\sin x+3=0,\]\[0\le x\le 2\pi ,\] then the solution set for \[x\]is
  A)
  \[\left[ 0,\frac{\pi }{6} \right]\] 
  done clear
  B)
          \[\left[ 0,\frac{5\pi }{6} \right]\]              
  done clear
  C)
          \[\left[ \frac{5\pi }{6},2\pi  \right]\]                       
  done clear
  D)
   \[\left[ \frac{5\pi }{6},\frac{\pi }{6} \right]\]
  done clear
  View Answer play_arrow

• question_answer115) The value of \[\left( 1+\cos \frac{\pi }{8} \right)\left( 1+\cos \frac{3\pi }{8} \right)\]\[\left( 1+\cos \frac{5\pi }{8} \right)\left( 1+\cos \frac{7\pi }{8} \right)\] is equal to
  A)
   \[\frac{1}{4}\]                  
  done clear
  B)
          \[\frac{1}{6}\]                  
  done clear
  C)
   \[\frac{1}{8}\]                  
  done clear
  D)
          \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer116) If the probability of A to fail in an examination is \[\frac{1}{5}\]and that of B is \[\frac{3}{10},\] then the probability that either A or B fails, is
  A)
   \[\frac{19}{50}\]                             
  done clear
  B)
          \[\frac{11}{25}\]                             
  done clear
  C)
   \[\frac{1}{2}\]                  
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer117) Which of the following is the empty set?       
  A)
   {\[x:x\] is a real number and \[{{x}^{2}}-1=0\]}     
  done clear
  B)
   {\[x:x\] is a real number and\[~{{x}^{2}}+1=0\]}
  done clear
  C)
   {\[x:x\] is real number and\[{{x}^{2}}-9=0\]}       
  done clear
  D)
   {\[x:x\] is a real number and\[{{x}^{2}}=x+2\]}     
  done clear
  View Answer play_arrow

• question_answer118) If \[f:[1,\infty )\to [2,\infty ]\]is given by \[f(x)=x+\frac{1}{x},\]then \[{{f}^{-1}}(x)\] is equal to                   
  A)
   \[\frac{x+\sqrt{{{x}^{2}}-4}}{2}\]
  done clear
  B)
          \[\frac{x}{1+{{x}^{2}}}\]              
  done clear
  C)
          \[\frac{x-\sqrt{{{x}^{2}}-4}}{2}\]
  done clear
  D)
          \[1+\sqrt{x-4}\]
  done clear
  View Answer play_arrow

• question_answer119) If\[A=\left[ \begin{matrix}    1 & 3  \\    2 & -2  \\ \end{matrix} \right],\] then \[{{A}^{-1}}\]is equal to
  A)
  \[-\frac{1}{8}\left[ \begin{matrix}    3 & 1  \\    -2 & 2  \\ \end{matrix} \right]\]
  done clear
  B)
          \[-\frac{1}{8}\left[ \begin{matrix}    -2 & -3  \\    -2 & 1  \\ \end{matrix} \right]\]
  done clear
  C)
   \[\frac{1}{8}\left[ \begin{matrix}    -1 & -3  \\    -2 & 2  \\ \end{matrix} \right]\]
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer120) The determinant \[\left| \begin{matrix}    \cos (\alpha +\beta ) & -\sin (\alpha +\beta ) & \cos 2\beta   \\    \sin \alpha  & \cos \alpha  & \sin \beta   \\    -\cos \alpha  & \sin \alpha  & \cos \beta   \\ \end{matrix} \right|\] is independent of
  A)
  \[\alpha \]                          
  done clear
  B)
          \[\beta \]                          
  done clear
  C)
   \[\alpha \]and\[\beta \]       
  done clear
  D)
   Neither \[\alpha \]nor \[\beta \]
  done clear
  View Answer play_arrow

• question_answer121) The ninth term in the expansion of\[{{[{{3}^{{{\log }_{3}}\sqrt{{{25}^{x-1}}+7}}}+{{3}^{-\frac{1}{8}{{\log }_{3}}({{5}^{x-1}}+1)}}]}^{10}}\]is equal  to 180, then \[x\]is equal to
  A)
   1              
  done clear
  B)
          2                            
  done clear
  C)
          3                            
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer122) The number of diagonals that can be drawn by joining the vertices of an octagon, is
  A)
   28                         
  done clear
  B)
          48                         
  done clear
  C)
   20                         
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer123) The coefficient of x in the quadratic equation \[a{{x}^{2}}+bx+c=0\]was wrongly taken as 17 in place of 13 and its roots were found to be - 2 and - 15, the actual roots of the equation are
  A)
   - 2 and 15       
  done clear
  B)
          - 3 and - 10        
  done clear
  C)
          - 4 and- 9           
  done clear
  D)
          -5 and -6
  done clear
  View Answer play_arrow

• question_answer124) It is given that \[\sum\limits_{r=1}^{\infty }{\frac{1}{{{(2r-1)}^{2}}}}=\frac{{{\pi }^{2}}}{8},\]then\[\sum\limits_{r=1}^{\infty }{\frac{1}{{{r}^{2}}}}\]is equal to
  A)
   \[\frac{{{\pi }^{2}}}{24}\]                            
  done clear
  B)
          \[\frac{{{\pi }^{2}}}{3}\]                              
  done clear
  C)
   \[\frac{{{\pi }^{2}}}{6}\]                              
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer125) The 10th common term between the series \[3+7+11+...\].and \[1+6+11+...\]is
  A)
   191                       
  done clear
  B)
          193                       
  done clear
  C)
   211                       
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer126) If \[x=a+b,\,y=a\omega +b{{\omega }^{2}}\]and \[z=a{{\omega }^{2}}+b\omega ,\]  then \[xyz\]is equal to
  A)
   \[{{(a+b)}^{2}}\]             
  done clear
  B)
          \[{{a}^{3}}+{{b}^{3}}\]
  done clear
  C)
   \[{{a}^{3}}-{{b}^{3}}\]  
  done clear
  D)
          \[{{(a+b)}^{3}}-3ab(a+b)\]
  done clear
  View Answer play_arrow

• question_answer127) If C is an obtuse angle in a triangle, then
  A)
   tan A tan B < 1  
  done clear
  B)
          tan A tan B > 1
  done clear
  C)
          tan A tan B = 1  
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer128) In any \[\Delta \,A \,B \,C,\frac{1}{r_{1}^{2}}+\frac{1}{r_{2}^{2}}+\frac{1}{r_{3}^{2}}+\frac{1}{{{r}^{2}}}\] is equal to
  A)
   \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{2{{\Delta }^{2}}}\]
  done clear
  B)
  \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{{{\Delta }^{2}}}\]
  done clear
  C)
  \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{3{{\Delta }^{2}}}\]
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer129) \[\tan \left[ {{\cos }^{-1}}\frac{4}{5}+{{\tan }^{-1}}\frac{2}{3} \right]\]is equal to
  A)
  \[\frac{13}{6}\]                
  done clear
  B)
          \[\frac{17}{6}\]               
  done clear
  C)
   \[-\frac{13}{6}\]              
  done clear
  D)
          \[-\frac{17}{6}\]
  done clear
  View Answer play_arrow

• question_answer130) A man on the top of a cliff 100 m high, observe the angles of depression of two points on the opposite sides of the cliff as \[\text{3}{{\text{0}}^{\text{o}}}\] and \[\text{6}{{\text{0}}^{\text{o}}}\] respectively. Then, the distance between the two points is equal to
  A)
  \[400\sqrt{3}\,m\]          
  done clear
  B)
          \[\frac{400}{\sqrt{3}}\,m\]        
  done clear
  C)
          \[\frac{100}{\sqrt{3}}\,m\]        
  done clear
  D)
          \[200\sqrt{3}\,m\]
  done clear
  View Answer play_arrow

• question_answer131) The sum of square of deviations for 10 observations taken from mean 50 is 250. The coefficient of variation is
  A)
   10                         
  done clear
  B)
          20                         
  done clear
  C)
          30                         
  done clear
  D)
          40
  done clear
  View Answer play_arrow

• question_answer132) The vector equation of a plane through the point \[(2\hat{i}-\hat{j}-4\hat{k})\] and parallel to the plane \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})-7=0\]is
  A)
  \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})=0\]
  done clear
  B)
                   \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})=32\]
  done clear
  C)
                   \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})=12\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer133) The equation\[{{x}^{3}}-3x+4=0\] has only one real root. What is its first approximate value as obtained by the method of false position in\[(-3,-2)?\]
  A)
  \[-2.125\]           
  done clear
  B)
  \[2.125\]             
  done clear
  C)
         \[-2.812\]         
  done clear
  D)
         \[~2.812\]
  done clear
  View Answer play_arrow

• question_answer134) An oil company required 13000, 20000 and 15000 barrels of high grade, medium grade and low grade oil respectively. Refinery A produces 100, 300 and 200 barrels per day of high grade, medium grade and low grade oil respectively. While, refinery B produces 200, 400 and 100 barrels per day of high grade, medium grade and low grade oil respectively. If refinery A costs Rs 400 per day and refinery B costs Rs 300 per day to operate, then the days should each be run to minimize costs, while satisfying requirements are              
  A)
   30, 60                  
  done clear
  B)
          60, 30  
  done clear
  C)
          40, 60                  
  done clear
  D)
          60, 40
  done clear
  View Answer play_arrow

• question_answer135) If in a\[\text{ABC,}\] \[a\tan A+b\,\tan \,B=(a+b)\tan \left( \frac{A+B}{2} \right),\]then
  A)
  \[A=B\]           
  done clear
  B)
         \[~A=-B\]           
  done clear
  C)
         \[A=2B\]          
  done clear
  D)
          \[B=2A.\]
  done clear
  View Answer play_arrow

• question_answer136) If A and B are two events such that\[P(A\cup B)=\frac{5}{6},P(A\cap B)=\frac{1}{3},P(\bar{B})=\frac{1}{2},\] then the events A and B are
  A)
   dependent
  done clear
  B)
   independent
  done clear
  C)
   mutually exclusive
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer137) If \[P(x,y,z)\]is a point on the line segment joining Q (2, 2, 4) and R (3, 5, 6) such that the projections of \[\overrightarrow{\text{OP}}\]on the axes are\[\frac{13}{5},\frac{19}{5},\frac{26}{5}\] respectively, then P divides QR in the ratio
  A)
   1 : 2                      
  done clear
  B)
          3 : 2                      
  done clear
  C)
   2 : 3                      
  done clear
  D)
          1 : 3
  done clear
  View Answer play_arrow

• question_answer138) The vector \[\vec{c}\] is perpendicular to the vectors\[\vec{a}=(2,-3,1),\vec{b}=(1,-2,3)\] and satisfies the condition \[\vec{c}.(\hat{i}+2\hat{j}-7\hat{k})=10.\]Then, \[\vec{c}\] is equal to  
  A)
  \[7\hat{i}+5\hat{j}+\hat{k}\]     
  done clear
  B)
          \[-7\hat{i}-5\hat{j}-\hat{k}\]
  done clear
  C)
          \[\hat{i}+\hat{j}-\hat{k}\]          
  done clear
  D)
          \[\hat{i}+\hat{j}+\hat{k}\]
  done clear
  View Answer play_arrow

• question_answer139) Consider the differential equation \[y=px+\sqrt{{{a}^{2}}{{p}^{2}}+{{b}^{2}}},\]where\[p=\frac{dy}{dx}.\]The  order and degree of the differential equation are
  A)
   1, 1                       
  done clear
  B)
          1, 2                       
  done clear
  C)
   2, 1                       
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer140) Solution of the differential equation \[y\left[ x\cos \left( \frac{y}{x} \right)+y\sin \left( \frac{y}{x} \right) \right]dx\] \[-x\left[ y\sin \left( \frac{y}{x} \right)-x\cos \left( \frac{y}{x} \right) \right]dy=0\]is
  A)
          \[xy\cos \left( \frac{y}{x} \right)=K\]
  done clear
  B)
          \[\cos \left( \frac{x}{y} \right)=K\,xy\]
  done clear
  C)
                   \[\frac{x}{y}\cos \left( \frac{y}{x} \right)=K\]    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer141) The value of \[\alpha \in (-\pi ,0)\]satisfying \[\sin \alpha +\int_{\alpha }^{2a}{\cos 2x\,dx=0}\]is
  A)
   0                                            
  done clear
  B)
   \[-\frac{\pi }{3}\]            
  done clear
  C)
          \[-\pi \]                              
  done clear
  D)
          All of these
  done clear
  View Answer play_arrow

• question_answer142) If curves \[y=1-a{{x}^{2}}\] and \[y={{x}^{2}}\]intersect orthogonally, then the value of a is
  A)
  \[\frac{1}{2}\]                   
  done clear
  B)
          \[\frac{1}{3}\]  
  done clear
  C)
    2                           
  done clear
  D)
          3
  done clear
  View Answer play_arrow

• question_answer143) If \[f(9)=9,\]\[f(9)=4,\]then \[\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}\] equals
  A)
   9                            
  done clear
  B)
          4            
  done clear
  C)
   36                         
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer144) Find the equation of chord of \[{{x}^{2}}-{{y}^{2}}=9\]which is bisected at \[(5,-3).\]
  A)
   \[5x+3y+16=0\]
  done clear
  B)
         \[~5x+3y-16=0\]
  done clear
  C)
  \[~3x+5y+16=0\]
  done clear
  D)
   \[3x+5y-16=0\]
  done clear
  View Answer play_arrow

• question_answer145) The normal chord at a point t on the parabola \[{{y}^{2}}=4ax\]subtends a right angle at the vertex. Then,\[{{t}^{2}}\] is equal to
  A)
   2              
  done clear
  B)
          \[\sqrt{2}\]                       
  done clear
  C)
   4                              
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer146) The equation of a circle of radius 5 which lies within the circle \[{{x}^{2}}+{{y}^{2}}+14x+10y-26=0\]and touches it at the point \[(-1,3)\] is
  A)
   \[{{x}^{2}}+{{y}^{2}}+\text{ }8x+2y+8=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}+8x+2y-8=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+8x+2y-14=0\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer147) The sum of the series \[\left[ 1+\left( \frac{1}{2}+\frac{1}{3} \right).\frac{1}{4}+\left( \frac{1}{4}+\frac{1}{5} \right).\frac{1}{{{4}^{2}}}+\left( \frac{1}{6}+\frac{1}{7} \right)\frac{1}{{{4}^{3}}}+...\infty  \right]\]is equal to
  A)
  \[\log \sqrt{12}\]             
  done clear
  B)
          \[\log \sqrt{10}\]            
  done clear
  C)
          \[{{e}^{12}}\]                   
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer148) If the AM and GM between two numbers are in the ratio m: n, then the numbers are in the ratio
  A)
  \[m+\sqrt{{{m}^{2}}-{{n}^{2}}}:n+\sqrt{{{m}^{2}}-{{n}^{2}}}\]
  done clear
  B)
   \[m+\sqrt{{{m}^{2}}-{{n}^{2}}}:m-\sqrt{{{m}^{2}}-{{n}^{2}}}\]
  done clear
  C)
   \[m+\sqrt{{{m}^{2}}+{{n}^{2}}}:n+\sqrt{{{m}^{2}}+{{n}^{2}}}\]
  done clear
  D)
   \[m+\sqrt{{{m}^{2}}+{{n}^{2}}}:m-\sqrt{{{m}^{2}}-{{n}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer149) A line is drawn through a fixed point \[(h,k)\] cutting the coordinate axes at P and Q respectively. The rectangle OPRQ is completed. Find the equation of locus of R.
  A)
   \[\frac{x}{h}+\frac{y}{k}=1\]     
  done clear
  B)
          \[\frac{x}{y}+\frac{h}{k}=1\]     
  done clear
  C)
          \[\frac{h}{x}+\frac{k}{y}=1\]     
  done clear
  D)
          \[\frac{x}{k}+\frac{y}{h}=1\]
  done clear
  View Answer play_arrow

• question_answer150) If the sum of m terms of an APIs the same as the sum of its n terms. The sum of its (m + n)  terms is                                                                
  A)
   0                            
  done clear
  B)
          \[1\]                    
  done clear
  C)
          \[\frac{m+n}{2}\]           
  done clear
  D)
          \[\sqrt{mn}\]
  done clear
  View Answer play_arrow