Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2005

done JCECE Engineering Solved Paper-2005 Total Questions - 150

• question_answer1) If the velocity of light \[c\], gravitational constant \[G\] and Planck's constant \[h\], are chosen as fundamental units, the dimensional formula of length L in the new system is:
  A)
   \[[{{h}^{1}}{{c}^{1}}{{G}^{-1}}]\]
  done clear
  B)
   \[[{{h}^{1/2}}{{c}^{1/2}}{{G}^{-1/2}}]\]
  done clear
  C)
   \[[{{h}^{1}}{{c}^{-3}}{{G}^{1}}]\]
  done clear
  D)
   \[[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}]\]
  done clear
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• question_answer2) The radius of sphere is measured to be\[(2.1\pm 0.5)\,\,cm\]. Calculate its surface area with error limits:
  A)
   \[(55.4\pm 26.4)c{{m}^{2}}\]
  done clear
  B)
   \[(55.4\pm 0.02)c{{m}^{2}}\]
  done clear
  C)
   \[(55.4\pm 2.64)c{{m}^{2}}\]
  done clear
  D)
    \[(55.4\pm 0.26)c{{m}^{2}}\] Surface area, \[S=4\pi {{r}^{2}}=4\times \frac{22}{7}\times {{(2.1)}^{2}}=55.44=55.4\,\,c{{m}^{2}}\] Further,               \[\frac{\Delta S}{S}=2\cdot \frac{\Delta r}{r}\] or                            \[\Delta S=2\left( \frac{\Delta r}{r} \right)(S)\]         \[=\frac{2\times 0.5\times 55.4}{2.1}=26.38=26.4\,\,c{{m}^{2}}\] \[\therefore \]                    \[S=(55.4\pm 26.4)c{{m}^{2}}\]
  done clear
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• question_answer3) A block of mass \[2\,\,kg\] rests on a plane inclined at an angle of \[{{30}^{o}}\] with the horizontal. The coefficient of friction between the block and surface is \[0.7\]. The frictional force acting on the block is:
  A)
  \[11.9\,\,N\]                     
  done clear
  B)
  \[25\,\,N\]
  done clear
  C)
  \[50\,\,N\]                         
  done clear
  D)
   \[22.9\,\,N\]
  done clear
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• question_answer4) A particle moves along \[Y-\]axis in such a way that its \[y-\]coordinate varies with time \[t\] according to the relation \[y=3+5t+7{{t}^{2}}\]. The initial velocity and acceleration of the particle are respectively:
  A)
  \[14m{{s}^{-1}},\,\,5\,\,m{{s}^{-2}}\]
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  B)
   \[19m{{s}^{-1}},\,\,-9m{{s}^{-2}}\]
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  C)
   \[-14m{{s}^{-1}},\,\,-5m{{s}^{-2}}\]
  done clear
  D)
    \[5m{{s}^{-1}},\,\,14\,\,m{{s}^{-2}}\]
  done clear
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• question_answer5) An object travels north with a velocity of \[10\,\,m{{s}^{-1}}\] and then speeds up to a velocity of \[25\,\,m{{s}^{-1}}\]in\[5\,s\]. The acceleration of the object in these \[5\,s\] is:
  A)
   \[12\,\,m{{s}^{-2}}\] in north direction
  done clear
  B)
   \[3\,\,m{{s}^{-2}}\] in north direction
  done clear
  C)
   \[15\,\,m{{s}^{-2}}\]in north direction
  done clear
  D)
    \[3\,\,m{{s}^{-2}}\]in south direction
  done clear
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• question_answer6) An automobile travelling at \[50\,\,km/h\], can be stopped at a distance of \[40\,\,m\] by applying brakes. If the same automobile is travelling at \[90\,\,km/h\], all other conditions remaining same and assuming no skidding, the minimum stopping distance in metres is:
  A)
  \[72\]                                   
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  B)
  \[92.5\]
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  C)
  \[102.6\]                             
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  D)
  \[129.6\]
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• question_answer7) A rifle shoots a bullet with a muzzle velocity of \[500\,\,m{{s}^{-1}}\] at a small target \[50\,\,m\] away. To hit the target the rifle must be aimed: (Take\[g=10\,\,m{{s}^{-2}})\]
  A)
   exactly at the target
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  B)
   \[10\,\,cm\] below the target
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  C)
   \[10\,\,cm\] above the target
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  D)
   \[5\,\,cm\] above the target
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• question_answer8) The centripetal acceleration of particle of mass \[m\] moving with a velocity \[v\] in a circular orbit of radius \[r\] is:
  A)
   \[{{v}^{2}}/r\] along the radius, towards the centre
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  B)
   \[{{v}^{2}}/r\] along the radius, away from the centre
  done clear
  C)
   \[m{{v}^{2}}/r\] along the radius, away the centre
  done clear
  D)
   \[m{{v}^{2}}/r\]along the radius, towards the centre
  done clear
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• question_answer9) An \[\alpha -\]particle of mass m suffers one dimensional elastic collision with a nucleus of unknown mass. After the collision the \[\alpha -\]particle is scattered directly backwards losing \[75%\] of its kinetic energy. The mass of the unknown nucleus is:
  A)
  \[m\]                                    
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  B)
  \[2\,\,m\]
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  C)
  \[3\,\,m\]           
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  D)
  \[\frac{3}{2}m\]
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• question_answer10) If a transformer of an audio amplifier has output impedance \[8000\,\,\Omega \] and the speaker has input impedance of \[8\,\,\Omega \], the primary and secondary turns of this transformer connected between the output of amplifier and to loud speaker should have the ratio:
  A)
  \[1000:1\]                           
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  B)
  \[100:1\]
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  C)
  \[1:32\]                               
  done clear
  D)
  \[32:1\]
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• question_answer11) A stationary body of mass m explodes into the three parts having masses in the ratio\[1:3:3\]. The two fractions with equal masses move at right angles to each other with a velocity of\[1.5\,\,m{{s}^{-1}}\]. The velocity of the third part is:
  A)
  \[4.5\sqrt{2}m{{s}^{-1}}\]                           
  done clear
  B)
  \[5\,\,m{{s}^{-1}}\]
  done clear
  C)
  \[5\sqrt{32}m{{s}^{-1}}\]                             
  done clear
  D)
  \[1.5\,\,m{{s}^{-1}}\]
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• question_answer12) In the electromagnetic spectrum, the visible spectrum lies between:
  A)
   radio waves and microwaves-
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  B)
   infrared and ultraviolet rays
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  C)
   microwaves and infrared spectrum
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  D)
   \[X-\]ray and gamma ray spectrum
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• question_answer13) An object of mass \[m\] falls on to a spring of constant \[k\] from height \[h\]. The spring undergoes compression by a length \[x\]. The maximum compression \[x\] is given by the equation:
  A)
  \[m\,\,g\,\,h=\frac{1}{2}k{{x}^{2}}\]
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  B)
  \[m\,\,g(h+x)=\frac{1}{2}k{{x}^{2}}\]
  done clear
  C)
  \[m\,\,g(h+x)=-kx\]
  done clear
  D)
  \[m\,\,g\,\,h=-kx\]
  done clear
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• question_answer14) A \[5000\,\,kg\] rocket is set for vertical, firing. The exhaust speed, is \[800\,\,m/s\]. To, give an initial upward acceleration of \[20\,\,m/{{s}^{2}}\], the amount of gas ejected per second to supply the needed thrust will be:
  A)
  \[137.5\,\,kg/s\]                              
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  B)
  \[185.5\,\,kg/s\]
  done clear
  C)
  \[127.5\,\,kg/s\]                              
  done clear
  D)
  \[187.5\,\,kg/s\]
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• question_answer15) An elastic ball is dropped from a height \[h\] and it rebounds many times from the floor. If the coefficient of restitution is \[e\], the time interval between the second and the third impact, is:
  A)
  \[\frac{ev}{g}\]                                
  done clear
  B)
  \[\frac{{{e}^{2}}v}{g}\]
  done clear
  C)
  \[{{e}^{2}}\sqrt{\left( \frac{8h}{g} \right)}\]                       
  done clear
  D)
  \[{{e}^{2}}\sqrt{\left( \frac{h}{g} \right)}\]
  done clear
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• question_answer16) An object of mass \[m\] is attached to light string which passes through a hollow tube. The object is set into rotation in a horizontal circle of radius \[{{r}_{1}}\]. If the string is pulled shortening the radius to \[{{r}_{2}}\], the ratio of new kinetic energy to the original kinetic energy is:
  A)
  \[{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\]                             
  done clear
  B)
  \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\]
  done clear
  C)
  \[\frac{{{r}_{1}}}{{{r}_{2}}}\]                                      
  done clear
  D)
  \[\frac{{{r}_{2}}}{{{r}_{1}}}\]
  done clear
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• question_answer17) Total angular momentum of a rotating body remains constant, if the net torque acting on the body is:
  A)
   zero                                     
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  B)
   maximum
  done clear
  C)
   minimum                           
  done clear
  D)
   unity
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• question_answer18) A car is racing on a circular track of \[180\,\,m\] radius with a speed of \[32\,\,m{{s}^{-1}}\]. What should be the banking angle of the road to avoid chances of skidding of the vehicle at this speed without taking into consideration the friction between the tyre and the road?
  A)
  \[{{45}^{o}}\]                                    
  done clear
  B)
  \[{{60}^{o}}\]
  done clear
  C)
  \[{{30}^{o}}\]                                    
  done clear
  D)
  \[{{15}^{o}}\]
  done clear
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• question_answer19) When a ceiling fan is switched on it makes \[10\] rotations in the first \[3\,\,s\]. The number of rotations it makes in the next \[3\,\,s\], assuming uniform angular acceleration is:
  A)
  \[40\]                                   
  done clear
  B)
  \[30\]
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  C)
  \[20\]                                   
  done clear
  D)
  \[10\]
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• question_answer20) A body is projected vertically upwards from the surface of a planet of radius r with a velocity equal to l/3rd the escape velocity for the planet. The maximum height attained by the body is:
  A)
   \[R/2\]                                
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  B)
   \[R/3\]
  done clear
  C)
   \[R/5\]                                
  done clear
  D)
   \[R/9\]
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• question_answer21) A man weighs \[80\,\,kg\] on earth's surface. The height above ground where he will weigh \[40\,\,kg\], is: (Radius of earth is\[6400\,\,km)\]
  A)
   \[0.31\] times \[r\]        
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  B)
   \[0.41\] times \[r\]
  done clear
  C)
   \[0.51\] times \[r\]        
  done clear
  D)
   \[0.61\] times \[r\]
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• question_answer22) An adulterated sample of milk has a density of\[1032\,\,kg\text{-}{{m}^{-3}}\], while pure milk has a density of\[1080\,\,kg\text{-}{{m}^{-3}}\]. The volume of pure milk in a sample of \[10\,\,L\] adulterated milk is:
  A)
  \[0.5\,\,L\]                         
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  B)
  \[1.0\,\,L\]
  done clear
  C)
  \[2.0\,\,L\]                         
  done clear
  D)
  \[4.0\,\,L\]
  done clear
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• question_answer23) Typical silt (hard mud) particle of radius \[20\,\,\mu m\] is on the top of lake water, its density is \[2000\,\,kg/{{m}^{3}}\] and the viscosity of lake water is\[1.0\,\,m\,\,Pa\], density is \[1000\,\,kg/{{m}^{3}}\]. If the lake is still (has no internal fluid motion), the terminal speed with which the particle hits the bottom of the lake in \[mm/s\] is:
  A)
  \[0.67\]                               
  done clear
  B)
  \[0.77\]
  done clear
  C)
  \[0.87\]                               
  done clear
  D)
   \[0.97\]
  done clear
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• question_answer24) A solid sphere and a hollow sphere, both of the same size and same mass roll down an inclined plane. Then:
  A)
   solid sphere reaches the ground first
  done clear
  B)
   hollow sphere reaches the ground first
  done clear
  C)
   both spheres reaches the ground at the same time
  done clear
  D)
   the time at which the spheres reach the ground cannot be specified by the given data
  done clear
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• question_answer25) If \[P\] is the pressure, \[V\] the volume, \[R\] the gas constant, \[k\] the Boltzmann constant and \[T\] the absolute temperature, then the number of molecules in the given mass of the gas is given by:
  A)
  \[\frac{PV}{RT}\]                                             
  done clear
  B)
  \[\frac{PV}{kT}\]
  done clear
  C)
  \[\frac{PR}{T}\]                                
  done clear
  D)
   \[PV\]
  done clear
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• question_answer26) An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is \[100\,\,kPa\], the absolute pressure at the bottom of lake in \[kPa\] is ... (assume no temperature variation) :
  A)
  \[33.3\]                               
  done clear
  B)
  \[50.0\]
  done clear
  C)
  \[100.0\]                             
  done clear
  D)
  \[300.0\]
  done clear
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• question_answer27) Maxwell in his famous equation of electromagnetism introduced the concept:
  A)
   \[AC\] current
  done clear
  B)
   \[DC\] current
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  C)
   displacement current
  done clear
  D)
    impedance
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• question_answer28) \[1\,\,g\] of steam at \[{{100}^{o}}C\] and equal mass of ice at \[{{0}^{o}}C\] are mixed. The temperature of .the mixture in steady state will be (latent heat of steam\[=540\,\,cal/g\], latent heat of ice \[=80\,\,cal/g)\]:
  A)
  \[{{50}^{o}}C\]                 
  done clear
  B)
  \[{{100}^{o}}C\]
  done clear
  C)
  \[{{67}^{o}}C\]                 
  done clear
  D)
   \[{{33}^{o}}C\]
  done clear
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• question_answer29) The work done by a gas is maximum when it expands:
  A)
   isothermally     
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  B)
   adiabatically
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  C)
   isochorically      
  done clear
  D)
   isobarically
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• question_answer30) A tuning fork of frequency \[580\,\,Hz\] is employed to produce transverse waves on a long rope. The distance between the nearest crests is found to be \[20\,\,cm\]. The velocity of the wave is:
  A)
  \[58\,\,m{{s}^{-1}}\]                      
  done clear
  B)
  \[580\,\,m{{s}^{-1}}\]
  done clear
  C)
  \[20\,\,m{{s}^{-1}}\]                      
  done clear
  D)
  \[116\,\,m{{s}^{-1}}\]
  done clear
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• question_answer31) A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is \[T\]. When the sphere is immersed in a non-viscous liquid of density \[1/10\] that of brass, it will act as a simple pendulum of period:
  A)
  \[T\]                                     
  done clear
  B)
  \[\frac{10}{9}T\]
  done clear
  C)
  \[\sqrt{\left( \frac{9}{10} \right)T}\]                       
  done clear
  D)
   \[\sqrt{\left( \frac{10}{9} \right)T}\]
  done clear
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• question_answer32) The distance travelled by a sound wave when a tuning fork completes \[25\] vibrations is\[16.5\,\,m\]. If the frequency of the tuning fork is \[500\,\,Hz\], find the velocity of sound.
  A)
  \[350\,\,m{{s}^{-1}}\]                   
  done clear
  B)
  \[330\,\,m{{s}^{-1}}\]
  done clear
  C)
  \[300\,\,m{{s}^{-1}}\]                   
  done clear
  D)
   \[450\,\,m{{s}^{-1}}\]
  done clear
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• question_answer33) Two instruments having stretched strings are being played in unison. When the tension of one of, the instruments is increased by \[1%\], \[3\] beats are produced in \[2\,\,s\]. The initial frequency of vibration of each wire is:
  A)
  \[300\,\,Hz\]                     
  done clear
  B)
  \[500\,\,Hz\]
  done clear
  C)
  \[1000\,\,Hz\]                   
  done clear
  D)
  \[400\,\,Hz\]
  done clear
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• question_answer34) Three point charges \[1C,\,\,\,2C\] and \[3C\] are placed at the comers of an equilateral triangle of side \[1\,\,m\]. The work done in bringing these charges to the vertices of a smaller similar triangle of side\[0.5\,\,m\]is:
  A)
  \[2.7\times {{10}^{10}}J\]                            
  done clear
  B)
  \[9.9\times {{10}^{10}}J\]
  done clear
  C)
  \[10.8\times {{10}^{10}}J\]                         
  done clear
  D)
  \[5.4\times {{10}^{10}}J\]
  done clear
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• question_answer35) The capacitors \[A\] and \[B\] have identical geometry. A material with a dielectric constant \[3\] is present between the plates of \[B\]. The potential difference across \[A\] and \[B\] are respectively:
  A)
  \[2.5\,\,V,\,\,7.5\,\,V\]                
  done clear
  B)
  \[2\,\,V,\,\,8\,\,V\]
  done clear
  C)
  \[8\,\,V,\,\,2\,\,V\]                        
  done clear
  D)
  \[7.5\,\,V,\,\,2.5\,\,V\]
  done clear
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• question_answer36) An electric bulb is marked \[100\,\,W,\,\,230\,\,V\]. If the supply voltage drops to \[115\,\,V\], what is the total energy produced by the bulb in\[10\,\,\min ?\]
  A)
  \[30\,\,kJ\]                        
  done clear
  B)
  \[20\,\,kJ\]
  done clear
  C)
  \[15\,\,kJ\]                        
  done clear
  D)
  \[10\,\,kJ\]
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• question_answer37) A circular coil carrying a current has a radius\[R\]. The ratio of magnetic induction at the centre of the coil and at a distance equal to \[\sqrt{3}R\] from the centre of the coil on the axis is:
  A)
  \[1:1\]  
  done clear
  B)
  \[1:2\]
  done clear
  C)
  \[2:1\]                                  
  done clear
  D)
  \[8:1\]
  done clear
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• question_answer38) The examples of diamagnetic, paramagnetic and ferromagnetic materials are respectively:
  A)
   copper, aluminium, iron
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  B)
   aluminium, copper, iron
  done clear
  C)
   copper, iron, aluminium
  done clear
  D)
   aluminium, iron, copper
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• question_answer39) In the Wheatstone's bridge shown below, in order to balance the bridge we must have:
  A)
  \[{{R}_{1}}=3\Omega ,\,\,{{R}_{2}}=3\Omega \]
  done clear
  B)
  \[{{R}_{1}}=6\Omega ,\,\,{{R}_{2}}=1.5\Omega \]
  done clear
  C)
   \[{{R}_{1}}=1.5\Omega ,\,{{R}_{2}}=\]any finite value
  done clear
  D)
  \[{{R}_{1}}=3\Omega ,\,\,{{R}_{2}}=\]any finite value
  done clear
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• question_answer40) Four \[10\,\,\mu F\] capacitors are connected to a \[500\,\,V\] supply as shown in the figure. The equivalent capacitance of the network is :
  A)
  \[40\,\,\mu F\]                
  done clear
  B)
  \[20\,\,\mu F\]
  done clear
  C)
  \[13.3\,\,\mu F\]                             
  done clear
  D)
  \[10\,\,\mu F\]
  done clear
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• question_answer41) A resistor is constructed as hollow cylinder of dimensions \[{{r}_{a}}=0.5\,\,cm\] and \[{{r}_{b}}=1.0\,\,cm\] and\[\rho =3.5\times {{10}^{-5}}\Omega m\]. The resistance of the configuration for the length of \[5\,\,cm\] cylinder is \[...\times {{10}^{-3}}\Omega \]:
  A)
  \[7.43\]                               
  done clear
  B)
  \[10.56\]
  done clear
  C)
  \[14.38\]                             
  done clear
  D)
  \[16.48\]
  done clear
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• question_answer42) The resistors are connected as shown in the figure below. Find the equivalent resistance between the points \[A\] and \[B\].
  A)
  \[205\Omega \]                               
  done clear
  B)
  \[10\Omega \]
  done clear
  C)
  \[3.5\Omega \]                
  done clear
  D)
  \[5\Omega \]
  done clear
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• question_answer43) The figure below shows a \[2.0\,\,V\] potentiometer used for the determination of internal resistance of a \[2.5\,\,V\] cell. The balance point of the cell in the open circuit is \[75\,\,cm\]. When a resistor of \[10\Omega \] is used in the external circuit of the cell, the balance point shifts to \[65\,\,cm\] length of potentiometer wire. The internal resistance of the cell is:
  A)
  \[2.5\Omega \]                
  done clear
  B)
  \[2.0\Omega \]
  done clear
  C)
  \[1.54\Omega \]                              
  done clear
  D)
  \[1.0\Omega \]
  done clear
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• question_answer44) An electric heater boils \[1\,\,kg\] of water in a time\[{{t}_{1}}\]. Another heater boils the same amount of water in a time \[{{t}_{2}}\] When the two heaters are connected in parallel, the time required by them together to boil the same amount of water is:
  A)
  \[{{t}_{1}}+{{t}_{2}}\]                    
  done clear
  B)
  \[{{t}_{1}}{{t}_{2}}\]
  done clear
  C)
  \[\frac{{{t}_{1}}+{{t}_{2}}}{2}\]                 
  done clear
  D)
  \[\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]
  done clear
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• question_answer45) Two thin metallic strips, carrying current in the direction shown, cross each other perpendicularly without touching but being close to each other, as shown in the figure. The regions which contain some points of zero magnetic induction are:
  A)
   \[I\] and \[II\]                                  
  done clear
  B)
   \[I\] and \[III\]
  done clear
  C)
   \[I\] and \[IV\]                
  done clear
  D)
   \[II\] and\[III\]
  done clear
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• question_answer46) The force on a conductor of length (placed in a magnetic field of magnitude B and carrying a current \[i\] is given by \[(\theta \] is the angle, the conductor makes with the direction of \[B)\]:
  A)
  \[F=i\,\,l\,\,B\,\,\sin \,\,\theta \]             
  done clear
  B)
  \[F={{i}^{2}}l\,\,{{B}^{2}}\sin \theta \]
  done clear
  C)
  \[F=i\,\,l\,\,B\,\,\cos \theta \]  
  done clear
  D)
  \[F=\frac{{{i}^{2}}l}{B}\sin \theta \]
  done clear
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• question_answer47) A needle made of bismuth is suspended freely in a magnetic field. The angle which the needle makes with the magnetic field is:
  A)
  \[{{0}^{o}}\]                                      
  done clear
  B)
  \[{{45}^{o}}\]
  done clear
  C)
  \[{{90}^{o}}\]                                    
  done clear
  D)
  \[{{180}^{o}}\]
  done clear
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• question_answer48) The resonant frequency of an \[LCR\] circuit occurs at a frequency equal to:
  A)
  \[\frac{1}{LC}\]                                
  done clear
  B)
  \[\frac{1}{\sqrt{LC}}\]
  done clear
  C)
  \[\frac{1}{LCR}\]                              
  done clear
  D)
  \[\frac{1}{CR}\]
  done clear
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• question_answer49) An alternating current is given by\[i={{i}_{1}}\cos \theta t+{{i}_{2}}\sin \omega t\]. The rms current is given by:
  A)
  \[\frac{{{i}_{1}}+{{i}_{2}}}{\sqrt{2}}\]                     
  done clear
  B)
  \[\frac{{{i}_{1}}-{{i}_{2}}}{\sqrt{2}}\]
  done clear
  C)
  \[\sqrt{\left( \frac{i_{1}^{2}+i_{2}^{2}}{2} \right)}\]                        
  done clear
  D)
  \[\sqrt{\left( \frac{i_{1}^{2}-i_{2}^{2}}{2} \right)}\]
  done clear
  View Answer play_arrow

• question_answer50) The coefficient of mutual inductance between the primary and secondary of the coil is \[5\,\,H\]. A current of \[10\,\,A\] is cut-off in \[0.5\,\,s\]. The induced emf is:
  A)
  \[1\,\,V\]                                            
  done clear
  B)
  \[10\,\,V\]
  done clear
  C)
  \[5\,\,V\]                                            
  done clear
  D)
  \[100\,\,V\]
  done clear
  View Answer play_arrow

• question_answer51) The standard adopted for the determination of atomic weight of elements is based on:
  A)
  \[{{H}^{1}}\]                                      
  done clear
  B)
  \[{{C}^{12}}\]
  done clear
  C)
  \[{{O}^{16}}\]                                   
  done clear
  D)
   \[{{S}^{32}}\]
  done clear
  View Answer play_arrow

• question_answer52) Law of multiple proportions is illustrated by one of the following pairs:
  A)
   \[{{H}_{2}}S\]and\[S{{O}_{2}}\]               
  done clear
  B)
   \[N{{H}_{3}}\]and\[N{{O}_{2}}\]
  done clear
  C)
    \[N{{a}_{2}}S\]and\[N{{a}_{2}}O\]        
  done clear
  D)
    \[{{N}_{2}}O\]and\[NO\]
  done clear
  View Answer play_arrow

• question_answer53) Par magnetism of oxygen is explained on the basis of its electronic configuration of:
  A)
  \[(2\pi _{x}^{*}){{(2{{\pi }_{y}})}^{1}}\]                
  done clear
  B)
  \[{{({{\pi }^{*}}2{{p}_{y}})}^{1}}({{\pi }^{*}}2p_{z}^{1})\]
  done clear
  C)
  \[{{(2\sigma _{s}^{*})}^{1}}{{(2{{\pi }_{y}})}^{1}}\]                         
  done clear
  D)
  \[{{(2{{\sigma }_{s}}^{*})}^{1}}{{(2{{\pi }_{y}})}^{1}}\]
  done clear
  View Answer play_arrow

• question_answer54) The van der Waals' equation for a real gas is given by the formula \[\left( P+\frac{{{n}^{2}}a}{{{V}^{2}}} \right)(V-nb)=nRT\] where \[P,\,\,V,\,\,T\] and \[n\] are the pressure, volume, temperature and the number of moles of the gas. Which one is the correct interpretation for the parameter\[a?\]
  A)
   The parameter a accounts for the finite size of the molecule, not included temperature in the ideal gas law
  done clear
  B)
   The parameter a accounts for the shape of gas phase molecules
  done clear
  C)
   The parameter \[a\] accounts for intermolecular interaction?s present in the molecule
  done clear
  D)
    The parameter \[a\] has no physical significance and van der Waals? introduced it as a numerical correction factor only
  done clear
  View Answer play_arrow

• question_answer55) Avogadro's hypothesis states that:
  A)
   the ideal gas consists of a large number of small particles called molecules
  done clear
  B)
   under the same conditions of temperature and pressure equal volumes of gases contain the same number of molecules
  done clear
  C)
   volume of a definite quantity of gas at constant pressure is directly proportional to absolute temperature
  done clear
  D)
   a given mass of gas at constant pressure is , directly proportional to absolute temperature
  done clear
  View Answer play_arrow

• question_answer56) The observation that the ground state of nitrogen atom has \[3\] unpaired electrons in its electronic configuration and not otherwise is associated with:
  A)
   Pauli's exclusion principle
  done clear
  B)
   Hund's rule of maximum multiplicity
  done clear
  C)
   Heisenberg's uncertainty principle
  done clear
  D)
    Ritz combination principle.
  done clear
  View Answer play_arrow

• question_answer57) Which of the following overlaps leads to bonding?
  A)
   
  done clear
  B)
    
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer58) In the periodic table metallic character of elements shows one of the following trend:
  A)
   decreases down the group and increases across the period
  done clear
  B)
   increases down the group and decreases across the period
  done clear
  C)
   increases across the period and also down the group
  done clear
  D)
    decreases across the period and also down the group
  done clear
  View Answer play_arrow

• question_answer59) Which of the following statements is correct?
  A)
   All carbon to carbon bonds contain a sigma bond and one or more pi bonds
  done clear
  B)
   All carbon to hydrogen bonds are pi bonds
  done clear
  C)
   All oxygen to hydrogen bonds are hydrogen bonds
  done clear
  D)
    All carbon to hydrogen bonds are sigma bonds
  done clear
  View Answer play_arrow

• question_answer60) An example of a polar covalent compound is:
  A)
  \[KCl\]                                 
  done clear
  B)
  \[NaCl\]
  done clear
  C)
  \[CC{{l}_{4}}\]                  
  done clear
  D)
   \[HCl\]
  done clear
  View Answer play_arrow

• question_answer61) If \[117\,\,g\,\,NaCl\] is dissolved in \[1000\,\,g\] of water the concentration of the solution is said to be:
  A)
   \[2\,\,molar\]                  
  done clear
  B)
   \[2\,\,molal\]
  done clear
  C)
   \[1\,\,normal\]               
  done clear
  D)
    \[1\,\,molal\]
  done clear
  View Answer play_arrow

• question_answer62) A solution \[\text{of}\]\[4.5\,\,g\] of a pure non-electrolyte in \[100\,\,g\] of water was found to freeze at\[{{0.465}^{o}}C\]. The molecular weight of the solute is closest to\[({{k}_{f}}=1.86)\]:
  A)
  \[135.0\]                             
  done clear
  B)
  \[172.0\]
  done clear
  C)
   \[90.0\]                                              
  done clear
  D)
   \[180.0\]
  done clear
  View Answer play_arrow

• question_answer63) The enthalpy of vaporization of substance is \[840\,\,J\text{-}mo{{l}^{-1}}\] and its boiling point is\[-{{173}^{o}}C\]. Its entropy of vaporization is:
  A)
  \[42\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\]        
  done clear
  B)
  \[21\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\]
  done clear
  C)
   \[84\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\]       
  done clear
  D)
   \[8.4\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer64) Given the following thermochemical equations:                 \[Zn+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}ZnO+84,000\,\,cal\]                 \[Hg+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}HgO+21,700\,\,cal\] Accordingly the heat of reaction for the following reaction \[Zn+HgO\xrightarrow{{}}Hg+\]heat is:
  A)
  \[105,700\,\,cal\]                            
  done clear
  B)
  \[61,000\,\,cal\]
  done clear
  C)
  \[105,000\,\,cal\]                            
  done clear
  D)
   \[62,300\,\,cal\]
  done clear
  View Answer play_arrow

• question_answer65) A saturated solution of\[Ca{{F}_{2}}\]is\[2\times {{10}^{-4}}mol/L\]. Its solubility product constant is:
  A)
  \[2.6\times {{10}^{-9}}\]                              
  done clear
  B)
  \[4\times {{10}^{-8}}\]
  done clear
  C)
   \[8\times {{10}^{-12}}\]                              
  done clear
  D)
   \[3.2\times {{10}^{-11}}\]
  done clear
  View Answer play_arrow

• question_answer66) For the reaction\[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\] the equilibrium constants expressed in terms of concentrations \[{{K}_{c}}\] and in terms of partial pressures\[{{K}_{p}},\]are related as:
  A)
  \[{{K}_{p}}={{K}_{c}}{{(RT)}^{2}}\]          
  done clear
  B)
  \[{{K}_{p}}={{K}_{c}}{{(RT)}^{-2}}\]
  done clear
  C)
  \[{{K}_{p}}={{K}_{c}}\]                  
  done clear
  D)
   \[{{K}_{c}}={{K}_{p}}(RT)\]
  done clear
  View Answer play_arrow

• question_answer67) Which of the following \[1:1\] mixture will act as buffer solution?
  A)
   \[HCl\]and\[NaOH\]
  done clear
  B)
   \[KOH\]and\[C{{H}_{3}}COOH\]
  done clear
  C)
   \[C{{H}_{3}}COOH\]\[NaCl\]
  done clear
  D)
    \[C{{H}_{3}}COOH\]and\[C{{H}_{3}}COONa\]
  done clear
  View Answer play_arrow

• question_answer68) What is potential of platinum wire dipped into a solution of \[0.1\,\,M\]in\[S{{n}^{2+}}\] and \[0.01\,\,M\] in\[S{{n}^{4+}}\]?
  A)
  \[{{E}_{0}}\]                                      
  done clear
  B)
  \[{{E}_{0}}+0.059\]
  done clear
  C)
  \[{{E}_{0}}+\frac{0.059}{2}\]                      
  done clear
  D)
   \[{{E}_{0}}=\frac{0.059}{2}\]
  done clear
  View Answer play_arrow

• question_answer69) In one of the following reactions \[HN{{O}_{3}}\]does not behave as an oxidizing agent. Identify it:
  A)
  \[{{I}_{2}}+10HN{{O}_{3}}\xrightarrow[{}]{{}}2HI{{O}_{3}}+10N{{O}_{2}}+4{{H}_{2}}O\]
  done clear
  B)
  \[3Cu+8HN{{O}_{3}}\xrightarrow{{}}3Cu{{(N{{O}_{3}})}_{2}}\]\[+2NO+4{{H}_{2}}O\]
  done clear
  C)
  \[4Zn+10HN{{O}_{3}}\xrightarrow{{}}4Zn{{(N{{O}_{3}})}_{2}}\]\[+N{{H}_{4}}N{{O}_{3}}+3{{H}_{2}}O\]
  done clear
  D)
   \[2HN{{O}_{3}}+{{P}_{2}}{{O}_{3}}\xrightarrow{{}}2HP{{O}_{3}}+{{N}_{2}}{{O}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer70) Which of the following statement is not correct?
  A)
   In zero order reaction the rate of the reaction remains constant throughout
  done clear
  B)
   A second order reaction would become a pseudo first order reaction when one of the reactants is taken in large excess
  done clear
  C)
   The value of first order rate constant depends on the units of the concentration terms used
  done clear
  D)
   In a first order reaction the plot of \[\log (a-x)vs\] time gives a straight line
  done clear
  View Answer play_arrow

• question_answer71) Radioactive decay series of uranium is denoted as:
  A)
  \[4n+1\]                              
  done clear
  B)
  \[4n+2\]
  done clear
  C)
   \[4n\]                                  
  done clear
  D)
   \[4n+3\]
  done clear
  View Answer play_arrow

• question_answer72) The number of isomeric hexanes is:
  A)
  \[5\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[3\]                                     
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer73) The coagulating power of an electrolyte for arsenious sulphide decreases in the order:
  A)
  \[N{{a}^{+}}<A{{l}^{3+}}<B{{a}^{2+}}\]
  done clear
  B)
  \[PO_{4}^{3-}<SO_{4}^{2-}<C{{l}^{-}}\]
  done clear
  C)
   \[Cl<SO_{4}^{2-}<PO_{4}^{3-}\]
  done clear
  D)
    \[A{{l}^{3+}}<B{{a}^{2+}}<N{{a}^{+}}\]
  done clear
  View Answer play_arrow

• question_answer74) The two optical isomers given below, namely, \[(a)\]:
  A)
   enantiomers
  done clear
  B)
   geometrical isomers
  done clear
  C)
    diastereomers
  done clear
  D)
    structural isomers
  done clear
  View Answer play_arrow

• question_answer75) Which of the following statement is wrong?
  A)
   Using Lassaigne's test nitrogen and sulphur present in organic compound can be tested
  done clear
  B)
   Using Beilstein's test the presence of halogen in a compound can be tested
  done clear
  C)
   In Lassaigne's filtrate the nitrogen present in organic compound is converted into \[NaCN\]
  done clear
  D)
   In the estimation of carbon, an organic compound is heated with \[CaO\] in a combustion tube
  done clear
  View Answer play_arrow

• question_answer76) \[Cis-trans\] isomers generally:
  A)
   contain an asymmetric carbon atom
  done clear
  B)
   rotate the .plane of polarized light
  done clear
  C)
   are enantiomorphism
  done clear
  D)
   contain double bonded carbon atoms
  done clear
  View Answer play_arrow

• question_answer77) Wurtz's reaction involves the reduction of alkyl halide with:
  A)
   \[Zn/HCl\]                         
  done clear
  B)
   \[HI\]
  done clear
  C)
   \[Zn/Cu\]couple             
  done clear
  D)
    \[Na\]is ether
  done clear
  View Answer play_arrow

• question_answer78) The reaction \[{{C}_{12}}{{H}_{26}}\xrightarrow[{}]{{}}{{C}_{6}}{{H}_{12}}+{{C}_{6}}{{H}_{14}}\]represent:
  A)
   substitution      
  done clear
  B)
   synthesis
  done clear
  C)
   cracking                              
  done clear
  D)
   polymerization
  done clear
  View Answer play_arrow

• question_answer79) The compound that does not answer iodoform test is:
  A)
   ethanol                              
  done clear
  B)
   ethanol
  done clear
  C)
   methanol          
  done clear
  D)
    propanone
  done clear
  View Answer play_arrow

• question_answer80) Which one of the following compound reacts with chlorobenzene to produce\[DDT?\]
  A)
   Acetaldehyde
  done clear
  B)
   Nitrobenzene
  done clear
  C)
   \[m-\]chloroacetaldehyde
  done clear
  D)
    Trichloroacetaldehyde
  done clear
  View Answer play_arrow

• question_answer81) Conversion of benzaldehyde to 3-phenyl-prop-2-en-1-oic acid is:
  A)
   Perkin condensation
  done clear
  B)
   Claisen condensation
  done clear
  C)
   Oxidative addition
  done clear
  D)
    Aldol condensation
  done clear
  View Answer play_arrow

• question_answer82) Which of the following compounds forms an addition compound with \[C{{H}_{3}}MgBr\], which on hydrolysis produce a secondary alcohol?
  A)
  \[HCHO\]                            
  done clear
  B)
  \[C{{H}_{3}}CHO\]
  done clear
  C)
  \[C{{H}_{3}}OC{{H}_{3}}\]                           
  done clear
  D)
  \[C{{H}_{3}}COC{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer83) Which of the following pairs are correctly matched?

  1. Haber process	Manufacture of ammonia
  2. Leblanc process	Manufacture of sulphuric acid
  3. Birkeland-Eyde process	Manufacture of nitric acid
  4. Solvay process	Manufacture of sodium carbonate

  A)
   2, 3 and 4                           
  done clear
  B)
   1, 2, 3 and 4
  done clear
  C)
   1, 2 and                              
  done clear
  D)
    1, 3 and 4
  done clear
  View Answer play_arrow

• question_answer84) Which of the following compounds on treatment first with \[NaN{{O}_{2}}/HCl\] and then coupled     with     phenol     produces p-hydroxyazobenzene?
  A)
   Nitrobenzene                  
  done clear
  B)
   Azobenzene
  done clear
  C)
   Phenol                                
  done clear
  D)
    Aniline
  done clear
  View Answer play_arrow

• question_answer85) Initial setting of cement is mainly due to:
  A)
   hydration and gel formation
  done clear
  B)
   dehydration and gel formation
  done clear
  C)
   hydration and hydrolysis
  done clear
  D)
    dehydration and dehydrolysis
  done clear
  View Answer play_arrow

• question_answer86) A certain metal will liberate hydrogen from dilute acids. If will react with water to form hydrogen only when the metal is heated and the water is in the form of steam. The metal is probably:
  A)
   iron                                      
  done clear
  B)
   potassium
  done clear
  C)
   copper                                
  done clear
  D)
   mercury
  done clear
  View Answer play_arrow

• question_answer87) The number of alpha and beta particles emitted in the chain of reactions leading to the decay of\[_{92}^{238}U\]to\[_{82}^{206}Pb\]
  A)
   \[8\] beta particles and \[6\] alpha particles
  done clear
  B)
   \[5\] alpha particles and \[0\] beta particles
  done clear
  C)
    \[8\] alpha and \[6\] beta particles
  done clear
  D)
    \[10\] alpha particles and \[10\] beta particles
  done clear
  View Answer play_arrow

• question_answer88) Hydrogen peroxide when added to a solution of potassium permanganate acidified with sulphuric acid:
  A)
   forms water only
  done clear
  B)
   acts as an oxidizing agent
  done clear
  C)
   acts as a reducing agent
  done clear
  D)
    reduces sulphuric acid
  done clear
  View Answer play_arrow

• question_answer89) The equilibrium molecular structure of hydrogen peroxide is:
  A)
   planar as given below
  done clear
  B)
   linear
  done clear
  C)
   tetrahedral
  done clear
  D)
    non planar
  done clear
  View Answer play_arrow

• question_answer90) Consider the following compounds. 1. Sulphur dioxide 2. Hydrogen peroxide 3. Ozone Among these compounds identify those that can act as bleaching agent:
  A)
   \[1\] and \[3\]                 
  done clear
  B)
   \[2\] and \[3\]
  done clear
  C)
    \[1\] and \[2\]                                
  done clear
  D)
    \[1,\,\,2\] and \[3\]
  done clear
  View Answer play_arrow

• question_answer91) Alkali metals have high oxidation potential and hence, they behave as:
  A)
   oxidizing agents              
  done clear
  B)
   Lewis bases
  done clear
  C)
   reducing agents              
  done clear
  D)
    electrolytes
  done clear
  View Answer play_arrow

• question_answer92) Water is oxidized to oxygen by:
  A)
  \[Cl{{O}_{2}}\]                                  
  done clear
  B)
   \[KMn{{O}_{4}}\]
  done clear
  C)
   \[{{H}_{2}}{{O}_{2}}\]                                  
  done clear
  D)
    fluorine
  done clear
  View Answer play_arrow

• question_answer93) Identify the incorrect statement:
  A)
   The molarity of a solution is independent of temperature
  done clear
  B)
   The tendency for catenation is much higher for carbon than for silicon
  done clear
  C)
   Nitriles and iso nitriles constitute metamers
  done clear
  D)
    \[t-\]butyl carbocation has planar carbons and is very reactive
  done clear
  View Answer play_arrow

• question_answer94) The magnetic moment p, of transition metals is related to the number of unpaired electrons, \[n\] as:
  A)
  \[\mu =n{{(n+2)}^{2}}\]                               
  done clear
  B)
  \[\mu ={{n}^{2}}(n+2)\]
  done clear
  C)
  \[\mu =\frac{n}{(n+2)}\]                             
  done clear
  D)
  \[\mu =\frac{n}{\sqrt{n+2}}\]
  done clear
  View Answer play_arrow

• question_answer95) Which one of the following statement is wrong?
  A)
   The \[IUPAC\] name of \[[Co{{(N{{H}_{3}})}_{6}}C{{l}_{3}}]\] is hexamine cobalt \[(III)\] chloride
  done clear
  B)
   Dibenzol peroxide is a catalyst in the polymerization of\[PVC\]
  done clear
  C)
   Borosilicate glass is heat resistant
  done clear
  D)
    Concentrated \[HN{{O}_{3}}\] can be safely transported in aluminium containers
  done clear
  View Answer play_arrow

• question_answer96) Which of the following is not a thermoplastic?
  A)
   Polystyrene
  done clear
  B)
   Teflon
  done clear
  C)
    Polyvinyl chloride
  done clear
  D)
    Nylon\[-6,\,\,6\]
  done clear
  View Answer play_arrow

• question_answer97) Which set is the correct pairing set (or contains complementary pairs) responsible for the structure of\[DNA?\] (A-adenine,     G-guanine,     C-cystosine, T-thymine, U-uracil)
  A)
  \[A-T,\,\,G-C\]                 
  done clear
  B)
  \[A-C,\,\,G-T\]
  done clear
  C)
   \[A-G,\,\,C-T\]                
  done clear
  D)
   \[A-U,\,\,G-C\]
  done clear
  View Answer play_arrow

• question_answer98) Barbituric acid and its derivatives are well known as:
  A)
   tranquilizers     
  done clear
  B)
   antiseptics
  done clear
  C)
    analgesics         
  done clear
  D)
    antipyretics
  done clear
  View Answer play_arrow

• question_answer99) The rate of a reaction is doubled for every \[{{10}^{o}}\] rise in temperature. The increase in reaction rate as a result of temperature rise from \[{{10}^{o}}\] to \[{{100}^{o}}\] is:
  A)
  \[112\]                                 
  done clear
  B)
  \[512\]
  done clear
  C)
  \[400\]                                 
  done clear
  D)
  \[614\]
  done clear
  View Answer play_arrow

• question_answer100) The first artificial disintegration of an atomic nucleus was achieved by:
  A)
   Geiger                                
  done clear
  B)
   Wilson
  done clear
  C)
   Madam Curie  
  done clear
  D)
    Rutherford
  done clear
  View Answer play_arrow

• question_answer101) If \[f(x)={{\log }_{x}}({{\log }_{e}}x)\], then \[f'(x)\] at \[x=e\] is equal to:
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[0\]                                     
  done clear
  D)
  \[1/e\]
  done clear
  View Answer play_arrow

• question_answer102) The number of terms in the expansion of \[{{(a+b+c)}^{10}}\]is:
  A)
  \[11\]                                   
  done clear
  B)
  \[21\]
  done clear
  C)
  \[55\]                                   
  done clear
  D)
  \[66\]
  done clear
  View Answer play_arrow

• question_answer103) For what value of K, the system of equations\[x+y+z=6,\,\,x+2y+3z=10\],\[x+2y+\lambda z=10\]is consistent?
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[-1\]                                    
  done clear
  D)
  \[3\]
  done clear
  View Answer play_arrow

• question_answer104) Let\[f(x)\]be twice differentiable such that\[f'\,\,'(x)=-f(x),\,\,f'(x)=g(x)\], where \[f'(x)\] and\[f'\,\,'(x)\] represent the first and second derivatives of \[f(x)\] respectively. Also if \[h(x)={{[f(x)]}^{2}}+{{[g(x)]}^{2}}\]and \[h(5)=5\], then \[h(10)\] is equal to :
  A)
  \[3\]                                     
  done clear
  B)
  \[10\]
  done clear
  C)
  \[13\]                                   
  done clear
  D)
  \[5\]
  done clear
  View Answer play_arrow

• question_answer105) A straight line through \[P(1,\,\,2)\] is such that its intercept between the axes is bisected at P. Its equation is:
  A)
  \[x+y=-1\]                          
  done clear
  B)
  \[x+y=3\]
  done clear
  C)
  \[x+2y=5\]                         
  done clear
  D)
  \[2x+y=4\]
  done clear
  View Answer play_arrow

• question_answer106) The radius of any circle touching the lines \[3x-4y+5=0\] and \[6x-8y-9=0\] is:
  A)
  \[1.9\]                                  
  done clear
  B)
  \[0.95\]
  done clear
  C)
  \[2.9\]                                  
  done clear
  D)
  \[1.45\]
  done clear
  View Answer play_arrow

• question_answer107) The point on the curve  \[\sqrt{x}+\sqrt{y}=\sqrt{a}\], the normal at which is parallel to the \[x-\]axis, is:
  A)
  \[(0,\,\,0)\]                        
  done clear
  B)
  \[(0,\,\,a)\]
  done clear
  C)
  \[(a,\,\,0)\]                        
  done clear
  D)
  \[(a,\,\,a)\]
  done clear
  View Answer play_arrow

• question_answer108) If two circles of the same radius rand centres at \[(2,\,\,3)\] and \[(5,\,\,6)\] respectively cut orthogonally, then the value of \[r\] is:
  A)
  \[3\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[1\]                                     
  done clear
  D)
  \[5\]
  done clear
  View Answer play_arrow

• question_answer109) The equation to the sides of a triangle are \[x-3y=0,\]\[4x+3y=5\]and \[3x+y=0\]. The line \[3x-4y=0\] passes through the:
  A)
   in centre
  done clear
  B)
   centroid
  done clear
  C)
   orthocentre
  done clear
  D)
   circumcentre
  done clear
  View Answer play_arrow

• question_answer110) For\[|x|\,\,<1\], let\[y=1+x+{{x}^{2}}+...\]to\[\infty \], then\[\frac{dy}{dx}=-y\]is equal to:
  A)
  \[\frac{x}{y}\]                                   
  done clear
  B)
  \[\frac{{{x}^{2}}}{{{y}^{2}}}\]
  done clear
  C)
  \[\frac{x}{{{y}^{2}}}\]                                    
  done clear
  D)
  \[x{{y}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer111) If\[(-4,\,\,5)\] is one vertex and \[7x-y+8=0\] is one diagonal of a square, then the equation of the second diagonal is:
  A)
  \[x+3y=21\]                       
  done clear
  B)
  \[2x-3y=7\]
  done clear
  C)
  \[x+7y=31\]                       
  done clear
  D)
  \[2x+3y=21\]
  done clear
  View Answer play_arrow

• question_answer112) The number of common tangents to two circles \[{{x}^{2}}+{{y}^{2}}=4\] and \[{{x}^{2}}+{{y}^{2}}-8x+12=0\]is:
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[5\]                                     
  done clear
  D)
  \[3\]
  done clear
  View Answer play_arrow

• question_answer113) If \[y={{\log }^{n}}x\], where\[{{\log }^{n}}\]means\[\log \log \log ...\](repeated \[n\] times), then\[x\log x{{\log }^{2}}x{{\log }^{3}}x...{{\log }^{n-1}}x{{\log }^{n}}x\frac{dy}{dx}\]is equal to:
  A)
  \[\log x\]                            
  done clear
  B)
  \[x\]
  done clear
  C)
  \[\frac{1}{\log x}\]                          
  done clear
  D)
  \[{{\log }^{n}}x\]
  done clear
  View Answer play_arrow

• question_answer114) The focus of the parabola \[{{y}^{2}}-x-2y+2=0\] is:
  A)
  \[(1/4,\,\,0)\]                   
  done clear
  B)
  \[(1,\,\,2)\]
  done clear
  C)
  \[(5/4,\,\,1)\]                   
  done clear
  D)
  \[(3/4,\,\,5/2)\]
  done clear
  View Answer play_arrow

• question_answer115) The equation of the parabola with vertex at the origin and directrix \[y=2\] is:
  A)
  \[{{y}^{2}}=8x\]                               
  done clear
  B)
  \[{{y}^{2}}=-8x\]
  done clear
  C)
  \[{{y}^{2}}=\sqrt{8}x\]                  
  done clear
  D)
  \[{{x}^{2}}=-8y\]
  done clear
  View Answer play_arrow

• question_answer116) The point on the curve \[x{{y}^{2}}=1\] that is nearest to the origin, is:
  A)
  \[(1,\,\,1)\]                                        
  done clear
  B)
  \[(4,\,\,1/2)\]
  done clear
  C)
  \[(5/4,\,\,1)\]                   
  done clear
  D)
  \[(3/4,\,\,5/2)\]
  done clear
  View Answer play_arrow

• question_answer117) The distance of. the point \[A(2,\,\,3,\,\,4)\] from \[x-\]axis is:
  A)
  \[5\]                                     
  done clear
  B)
  \[\sqrt{13}\]
  done clear
  C)
  \[2\sqrt{5}\]                                      
  done clear
  D)
  \[5\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer118) The radius of the circle\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2y-4z-11=0\],\[x+2y+2z-15=0\]is:
  A)
  \[\sqrt{3}\]                                        
  done clear
  B)
  \[\sqrt{5}\]
  done clear
  C)
  \[\sqrt{7}\]                                        
  done clear
  D)
  \[3\]
  done clear
  View Answer play_arrow

• question_answer119) \[\int{{{x}^{2}}{{(ax+b)}^{-2}}dx}\]is equal to:
  A)
  \[\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}x\log (ax+b) \right)+c\]
  done clear
  B)
  \[\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}\log (ax+b) \right)-\frac{{{x}^{2}}}{a(ax+b)}+c\]
  done clear
  C)
  \[\frac{2}{{{a}^{2}}}\left( x+\frac{b}{a}\log (ax+b) \right)+\frac{{{x}^{2}}}{a(ax+b)}+c\]
  done clear
  D)
  \[\frac{2}{{{a}^{2}}}\left( x+\frac{b}{a}\log (ax+b) \right)-\frac{{{x}^{2}}}{a(ax+b)}+c\]
  done clear
  View Answer play_arrow

• question_answer120) If the coordinate of the vertices of a triangle\[ABC\]be\[A(-1,\,\,3,\,\,2),\]\[B(2,\,\,3,\,\,5)\]and\[C(3,\,\,5,\,\,-2)\] then \[\angle A\]is equal to:
  A)
  \[{{45}^{o}}\]                                    
  done clear
  B)
  \[{{60}^{o}}\]
  done clear
  C)
  \[{{90}^{o}}\]                                    
  done clear
  D)
  \[{{30}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer121) If\[\overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,=0\],\[|\overset{\to }{\mathop{\mathbf{a}}}\,|=3,\,\,|\overset{\to }{\mathop{\mathbf{b}}}\,|=5\]and\[|\overset{\to }{\mathop{\mathbf{c}}}\,|\,\,=7\], then the angle between \[\overset{\to }{\mathop{\mathbf{a}}}\,\] and \[\overset{\to }{\mathop{\mathbf{b}}}\,\] is:
  A)
  \[{{0}^{o}}\]                                      
  done clear
  B)
  \[{{30}^{o}}\]
  done clear
  C)
  \[{{90}^{o}}\]                                    
  done clear
  D)
  \[{{30}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer122) If\[f(t)\]is an odd function, then\[\int_{0}^{x}{f(t)}\,dt\]is:
  A)
   an odd function
  done clear
  B)
   an even function
  done clear
  C)
   neither even nor odd
  done clear
  D)
  \[0\]
  done clear
  View Answer play_arrow

• question_answer123) The projection of\[\widehat{\mathbf{i}}+3\widehat{\mathbf{j}}+\widehat{\mathbf{k}}\]on\[2\widehat{\mathbf{i}}-3\widehat{\mathbf{j}}+6\widehat{\mathbf{k}}\]is:
  A)
  \[1/7\]                                 
  done clear
  B)
  \[-1/7\]
  done clear
  C)
  \[7\]                                     
  done clear
  D)
  \[-7\]
  done clear
  View Answer play_arrow

• question_answer124) If\[\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,=0\]and\[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=0\], then:
  A)
  \[\overset{\to }{\mathop{\mathbf{a}}}\,\bot \overset{\to }{\mathop{\mathbf{b}}}\,\]
  done clear
  B)
  \[\overset{\to }{\mathop{\mathbf{a}}}\,||\overset{\to }{\mathop{\mathbf{b}}}\,\]
  done clear
  C)
   \[\overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]
  done clear
  D)
   \[\overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]
  done clear
  View Answer play_arrow

• question_answer125) If the area bounded by the parabola \[y=2-{{x}^{2}}\] and the line \[x+y=0\] is \[A\] sq unit, then \[A\] equals:
  A)
  \[\frac{1}{2}\]                                   
  done clear
  B)
  \[\frac{1}{3}\]
  done clear
  C)
  \[\frac{2}{9}\]                                   
  done clear
  D)
  \[\frac{9}{2}\]
  done clear
  View Answer play_arrow

• question_answer126) The points\[A(4,\,\,5,\,\,1),\] \[B(0,\,\,-1,\,\,1),\] \[C(3,\,\,9,\,\,4)\]and\[D(-4,\,\,4,\,\,4)\] are:
  A)
   collinear             
  done clear
  B)
   coplanar
  done clear
  C)
   non-coplanar                   
  done clear
  D)
   non-collinear
  done clear
  View Answer play_arrow

• question_answer127) \[{{(\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,)}^{2}}\] is equal to:
  A)
  \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-(\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,)\]
  done clear
  B)
  \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-{{(\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,)}^{2}}\]
  done clear
  C)
  \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-2\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,\]
  done clear
  D)
  \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-2\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,\]
  done clear
  View Answer play_arrow

• question_answer128) Let \[F\] denotes the family of ellipses whose centre is at the origin and major axis is the \[y-\]axis. Then equation of the family \[F\] is:
  A)
  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]
  done clear
  B)
  \[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]
  done clear
  C)
  \[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]
  done clear
  D)
  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]
  done clear
  View Answer play_arrow

• question_answer129) The value of\[\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right)\left( \cos \left( \frac{\pi }{{{2}^{2}}} \right)+i\sin \left( \frac{\pi }{{{2}^{2}}} \right) \right)\]\[\times \left( \cos \left( \frac{\pi }{{{2}^{3}}} \right)+i\sin \left( \frac{\pi }{{{2}^{3}}} \right) \right)...\infty \]is:
  A)
  \[-1\]                                    
  done clear
  B)
  \[1\]
  done clear
  C)
  \[0\]                                     
  done clear
  D)
  \[\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer130) If\[x+\frac{1}{x}=2\sin \alpha ,\] \[y+\frac{1}{y}=2\cos \beta \], then\[{{x}^{3}}{{y}^{3}}+\frac{1}{{{x}^{3}}{{y}^{3}}}\]is:
  A)
  \[2\cos 3(\beta -\alpha )\]          
  done clear
  B)
  \[2\cos 3(\beta +\alpha )\]
  done clear
  C)
  \[2\sin 3(\beta -\alpha )\]           
  done clear
  D)
  \[2\sin 3(\beta +\alpha )\]
  done clear
  View Answer play_arrow

• question_answer131) Solution of the equation\[x{{\left( \frac{dy}{dx} \right)}^{2}}+2\sqrt{xy}\frac{dy}{dx}+y=0\]is:
  A)
  \[x+y=a\]                           
  done clear
  B)
  \[\sqrt{x}-\sqrt{y}=\sqrt{a}\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]                              
  done clear
  D)
  \[\sqrt{x}+\sqrt{y}=\sqrt{a}\]
  done clear
  View Answer play_arrow

• question_answer132) A bag contains \[5\] white and \[3\] black balls and \[4\] balls are successively drawn out and not replaced. The probability that they are alternately of different colours, is:
  A)
  \[1/196\]                            
  done clear
  B)
  \[2/7\]
  done clear
  C)
  \[1/7\]                                 
  done clear
  D)
  \[13/56\]
  done clear
  View Answer play_arrow

• question_answer133) If\[\underset{x\to a}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{x}^{a}}}{{{x}^{x}}-{{a}^{a}}}=-1\]¸then\[a\]equals:
  A)
  \[1\]                                     
  done clear
  B)
  \[0\]
  done clear
  C)
  \[e\]                                     
  done clear
  D)
  \[(1/e)\]
  done clear
  View Answer play_arrow

• question_answer134) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}\]is equal to:
  A)
  \[0\]                                     
  done clear
  B)
  \[1\]
  done clear
  C)
  \[1/2\]                                 
  done clear
  D)
  \[-1/2\]
  done clear
  View Answer play_arrow

• question_answer135) \[\underset{x\to a}{\mathop{\lim }}\,\frac{\log (x-a)}{\log ({{e}^{x}}-{{e}^{a}})}\]is equal to:
  A)
  \[0\]                                     
  done clear
  B)
  \[1\]
  done clear
  C)
  \[a\]                                     
  done clear
  D)
   does not exist
  done clear
  View Answer play_arrow

• question_answer136) If\[f(x)=|x{{|}^{3}}\], then\[f'(0)\]equals:
  A)
  \[0\]                                     
  done clear
  B)
  \[1/2\]
  done clear
  C)
  \[-1\]                                    
  done clear
  D)
  \[-1/2\]
  done clear
  View Answer play_arrow

• question_answer137) \[\int{{{e}^{-\log x}}}dx\]is equal to:
  A)
  \[{{e}^{-\log x}}+c\]
  done clear
  B)
  \[-x{{e}^{-\log x}}+c\]
  done clear
  C)
  \[{{e}^{\log x}}+c\]
  done clear
  D)
  \[\log |x|+c\]
  done clear
  View Answer play_arrow

• question_answer138) The area cut off by the latus rectum from the parabola \[{{y}^{2}}=4ax\] is:
  A)
  \[(8/3)a\,\,sq\,\,unit\] 
  done clear
  B)
  \[(8/3)\sqrt{a}\,\,sq\,\,unit\]
  done clear
  C)
  \[(3/8)\sqrt{a}\,\,sq\,\,unit\]
  done clear
  D)
  \[(8/3){{a}^{2}}\,\,sq\,\,unit\]
  done clear
  View Answer play_arrow

• question_answer139) The solution of differential equation\[(x+y)(dx-dy)=dx+dy\]is:
  A)
  \[x-y=k{{e}^{x-y}}\]
  done clear
  B)
  \[x+y=k{{e}^{x+y}}\]
  done clear
  C)
  \[x+y=k(x-y)\]
  done clear
  D)
  \[x+y=k{{e}^{x-y}}\]
  done clear
  View Answer play_arrow

• question_answer140) In how many ways can 8 students be arranged in a row?
  A)
  \[8!\]                                    
  done clear
  B)
  \[7!\]
  done clear
  C)
  \[8\]                                     
  done clear
  D)
  \[7\]
  done clear
  View Answer play_arrow

• question_answer141) If the third term of a \[GP\] is \[p\]. Then the product of the first \[5\] terms of the \[GP\] is:
  A)
  \[{{p}^{3}}\]                                      
  done clear
  B)
  \[{{p}^{2}}\]
  done clear
  C)
  \[{{p}^{10}}\]                                    
  done clear
  D)
  \[{{p}^{5}}\]
  done clear
  View Answer play_arrow

• question_answer142) The sum of n terms of the series\[\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+...\]is:
  A)
  \[\frac{{{3}^{n}}(2n+1)+1}{2({{3}^{n}})}\]
  done clear
  B)
  \[\frac{{{3}^{n}}(2n+1)-1}{2({{3}^{n}})}\]
  done clear
  C)
  \[\frac{{{3}^{n}}n-1}{2({{3}^{n}})}\]
  done clear
  D)
  \[\frac{{{3}^{n}}-1}{2}\]
  done clear
  View Answer play_arrow

• question_answer143) If \[\alpha \] and \[\beta \] are the solutions of the quadratic equation \[a{{x}^{2}}+bx+c=0\] such that \[\beta ={{\alpha }^{1/3}}\], then:
  A)
  \[{{(ac)}^{1/3}}+{{(ab)}^{1/3}}+c=0\]
  done clear
  B)
  \[{{({{a}^{3}}b)}^{1/4}}+{{(a{{b}^{3}})}^{1/4}}+c=0\]
  done clear
  C)
  \[{{({{a}^{3}}c)}^{1/4}}+{{(a{{c}^{3}})}^{1/4}}+b=0\]
  done clear
  D)
  \[{{({{a}^{4}}c)}^{1/3}}+{{(a{{c}^{4}})}^{1/3}}+b=0\]
  done clear
  View Answer play_arrow

• question_answer144) \[^{20}{{C}_{4}}+2{{\cdot }^{20}}{{C}_{3}}{{+}^{20}}{{C}_{2}}{{-}^{22}}{{C}_{18}}\]is equal to :
  A)
  \[0\]                                     
  done clear
  B)
  \[1242\]
  done clear
  C)
  \[7315\]                              
  done clear
  D)
  \[6345\]
  done clear
  View Answer play_arrow

• question_answer145) If\[x=\frac{\left[ \begin{align}   & 729+6(2)(243)+15(4)(81)+20 \\  & \times (8)(27)+15(16)(9)+6(32)3+64 \\ \end{align} \right]}{1+4(4)+6(16)+4(64)+256}\]then \[\sqrt{x}-\frac{1}{\sqrt{x}}\] is equal to:
  A)
  \[0.2\]                                  
  done clear
  B)
  \[4.8\]
  done clear
  C)
  \[1.02\]                               
  done clear
  D)
  \[5.2\]
  done clear
  View Answer play_arrow

• question_answer146) Along a road lie an odd number of stones placed at intervals of \[10\,\,m\]. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man started the job with one of the end stones by carrying them in succession. In carrying all the stones, the man covered a total distance of\[3\,\,km\]. Then the total number of stones is:
  A)
  \[20\]                                   
  done clear
  B)
  \[25\]
  done clear
  C)
  \[12\]                                   
  done clear
  D)
  \[24\]
  done clear
  View Answer play_arrow

• question_answer147) If\[a=1+2+4+...\]to \[n\] terms,\[b=1+3+9+...\]to \[n\] terms and \[c=1+5+25+...\]to \[n\] terms, then\[\left| \begin{matrix}   a & 2b & 4c  \\    2 & 2 & 2  \\    {{2}^{n}} & {{3}^{n}} & {{5}^{n}}  \\ \end{matrix} \right|\]equals:
  A)
  \[{{(30)}^{n}}\]                
  done clear
  B)
  \[{{(10)}^{n}}\]
  done clear
  C)
  \[0\]                                     
  done clear
  D)
  \[{{2}^{n}}+{{3}^{n}}+{{5}^{n}}\]
  done clear
  View Answer play_arrow

• question_answer148) The matrix \[\left[ \begin{matrix}    5 & 10 & 3  \\    -2 & -4 & 6  \\    -1 & -2 & b  \\ \end{matrix} \right]\] is a singular matrix, if is equal to:
  A)
  \[-3\]                                    
  done clear
  B)
  \[3\]
  done clear
  C)
  \[0\]                                     
  done clear
  D)
   for any value of\[b\]
  done clear
  View Answer play_arrow

• question_answer149) Let \[N\] be the number of quadratic equations with coefficients from \[\{0,\,\,1,\,\,2,\,\,....,\,\,9\}\] such that zero is a solution of each equation. Then the value of \[N\] is:
  A)
   infinite                
  done clear
  B)
  \[{{2}^{9}}\]
  done clear
  C)
  \[90\]                                   
  done clear
  D)
  \[900\]
  done clear
  View Answer play_arrow

• question_answer150) For non-singular square matrices \[A,\,\,\,B\] and \[C\] of the same order, \[{{(A{{B}^{-1}}C)}^{-1}}\]is equal to:
  A)
  \[{{A}^{-1}}B{{C}^{-1}}\]                              
  done clear
  B)
  \[{{C}^{-1}}{{B}^{-1}}{{A}^{-1}}\]
  done clear
  C)
  \[CB{{A}^{-1}}\]                               
  done clear
  D)
  \[{{C}^{-1}}B{{A}^{-1}}\]
  done clear
  View Answer play_arrow