Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

done Jamia Millia Islamia Solved Paper-2011 Total Questions - 170

• question_answer1) With what minimum acceleration can a fireman slides down a rope while breaking strength of the rope is\[\frac{2}{3}\]of his weight?
  A)
   \[\frac{2}{3}g\]                               
  done clear
  B)
   \[g\]
  done clear
  C)
   \[\frac{1}{3}g\]                               
  done clear
  D)
   Zero
  done clear
  View Answer play_arrow

• question_answer2)     An ice cream has a marked value of 700 kcal. How many kilowatt-hour of energy will it deliver to the body as it if digested?
  A)
   0.81 kWh           
  done clear
  B)
   0.90 kWh
  done clear
  C)
   1.11 kWh           
  done clear
  D)
   0.71 kWh
  done clear
  View Answer play_arrow

• question_answer3)     A Uniform cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and perpendicular to it length then
  A)
   \[L=R\]               
  done clear
  B)
   \[L=\sqrt{3}R\]
  done clear
  C)
   \[L=\frac{R}{\sqrt{3}}\]               
  done clear
  D)
   \[L=\sqrt{\frac{3}{2}}R\]
  done clear
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• question_answer4)     The Youngs modulus of the material of a wire is\[6\times {{10}^{12}}N/{{m}^{2}}\]and there is no transverse Strain in it, then its modulus of rigidity will be
  A)
   \[3\times {{10}^{12}}N{{m}^{-2}}\]        
  done clear
  B)
   \[2\times {{10}^{12}}N{{m}^{-2}}\]
  done clear
  C)
   \[{{10}^{12}}N{{m}^{-2}}\]         
  done clear
  D)
   None of these
  done clear
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• question_answer5)     Oil spreads over the surface of water whereas water does not spread over the surface of the oil, due to
  A)
   surface tension of water is very high
  done clear
  B)
   surface tension of water is very low
  done clear
  C)
   viscosity of oil is high
  done clear
  D)
   viscosity of water is high
  done clear
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• question_answer6)     A student attempts to pull himself up by tugging on his hair, the will not succeed
  A)
   as the force exerted is small
  done clear
  B)
   the frictional force while gripping, is small
  done clear
  C)
   Newtons law of inertia is not applicable to living beings
  done clear
  D)
   as the force applied is internal to the system
  done clear
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• question_answer7)     A circular disc of mass 0.41 kg and radius 10 m rolls without slippling with a velocity of 2 m/s. The total kinetic energy of disc is
  A)
   0.41 J                   
  done clear
  B)
   1.23 J
  done clear
  C)
   0.82 J                                   
  done clear
  D)
   2.4 J
  done clear
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• question_answer8)     The cylindrical tube of a spray pump has a cross-section of\[8\text{ }c{{m}^{2}},\] are end of which has 45 fine holes each of area\[{{10}^{-8}}{{m}^{2}}\]. If the liquid flows inside the tube with a speed of 0.15 m \[mi{{n}^{-1}},\]the speed with which the liquid is ejected through the holes is
  A)
   \[50\,m{{s}^{-1}}\]
  done clear
  B)
   \[5\,m{{s}^{-1}}\]
  done clear
  C)
   \[0.05\,m{{s}^{-1}}\]
  done clear
  D)
   \[0.5\,m{{s}^{-1}}\]
  done clear
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• question_answer9)     At nodes in stationary waves
  A)
   change in pressure and density are maximum
  done clear
  B)
   change in pressure and density are minimum
  done clear
  C)
   strain is zero
  done clear
  D)
   energy is maximum
  done clear
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• question_answer10)     Eight dipoles of changes of magnitude are placed inside a cube. The total electric flux coming out of the cube will be
  A)
   \[\frac{8e}{{{\varepsilon }_{0}}}\]                                          
  done clear
  B)
   \[\frac{16e}{{{\varepsilon }_{0}}}\]
  done clear
  C)
   \[\frac{e}{{{\varepsilon }_{0}}}\]                                             
  done clear
  D)
   zero
  done clear
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• question_answer11)     The X-ray beam coming from on X-ray tube will be
  A)
   monochromatic
  done clear
  B)
   having all wavelength smaller than a certain maximum wavelength
  done clear
  C)
   having all wavelength larger than a certain minimum wavelength
  done clear
  D)
   having all wavelength lying between a minimum and a maximum wavelength
  done clear
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• question_answer12)     The half of\[^{215}At\]is 100 as. The time taken for the radioactivity of a sample of 215 At to decay to 1/ 16th of its initial value is
  A)
   400 as                                  
  done clear
  B)
   6.3 as
  done clear
  C)
   40 as                                    
  done clear
  D)
   30 as
  done clear
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• question_answer13)     In a hydrogen atom, the distance between the electron and proton is\[2.5\times {{10}^{-11}}m\]. The electrical force of attraction between them will be
  A)
   \[2.8\times {{10}^{-7}}N\]          
  done clear
  B)
   \[3.7\times {{10}^{-7}}N\]
  done clear
  C)
   \[6.2\times {{10}^{-7}}N\]          
  done clear
  D)
   \[9.1\times {{10}^{-7}}N\]
  done clear
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• question_answer14)     A cable of resistance\[10\,\Omega \] arrives electric power from a generator producing 250 kW at 10000 V. The current in the cable is
  A)
   25 A                                     
  done clear
  B)
   250 A
  done clear
  C)
   100 A                                   
  done clear
  D)
   1000 A
  done clear
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• question_answer15)     A particle moving along x-axis has acceleration \[f,\]at time t, given by\[f={{f}_{0}}\left( 1-\frac{t}{T} \right),\] where\[{{f}_{0}}\] and T are constants. The particle at\[t=0,\]has zero velocity. In the time interval between\[t=0,\]and the instant when\[f=0,\]the particles velocity\[({{v}_{s}})\]is
  A)
   \[{{f}_{o}}t\]                                    
  done clear
  B)
   \[\frac{1}{2}{{f}_{o}}{{T}^{2}}\]
  done clear
  C)
   \[{{f}_{o}}{{T}^{2}}\]                    
  done clear
  D)
   \[\frac{1}{2}{{f}_{o}}T\]
  done clear
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• question_answer16)     A particle moves towards east with velocity 5 \[m{{s}^{-1}}\]. After 10 s its direction changes towards north with same velocity. The average acceleration of the particle is
  A)
   zero                                     
  done clear
  B)
   \[\frac{1}{2}m{{s}^{-2}},N-W\]
  done clear
  C)
   \[\frac{1}{\sqrt{2}}m{{s}^{-2}},N-E\]     
  done clear
  D)
   \[\frac{1}{\sqrt{2}}m{{s}^{-2}},S-W\]
  done clear
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• question_answer17)     A soap bubble oscillates with time period T, which in turn depends on the pressure p, density\[\rho \]and surface tension o. Which of the following correctly represents the expression for\[{{T}^{2}}\]?
  A)
   \[\frac{\rho {{\sigma }^{2}}}{{{p}^{3}}}\]                             
  done clear
  B)
   \[\frac{\rho {{\sigma }^{3}}}{\sigma }\]
  done clear
  C)
   \[\frac{{{\rho }^{3}}\sigma }{\rho }\]                     
  done clear
  D)
   \[\frac{\rho }{{{p}^{3}}\sigma }\]
  done clear
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• question_answer18)     If an object weigh 270 N at the earths surface, what will be the weight of the object at an altitude equal to twice the radius of earth?
  A)
   270 N                                   
  done clear
  B)
   90 N
  done clear
  C)
   30 N                                     
  done clear
  D)
   60 N
  done clear
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• question_answer19)     A fixed mortar fires a bomb at an angle of\[53{}^\circ \]above the horizontal with a muzzle velocity of\[80\text{ }m{{s}^{-1}}\]. A tank is advancing directly towards the mortar on level ground at a constant speed of\[\text{5 }m{{s}^{-1}}\]. The initial separation (at the instant mortar is fired) between the mortar and tank so that the tank would be hit is [Take\[g=10\text{ }m{{s}^{-2}}\]]
  A)
   678.4m               
  done clear
  B)
   \[614.4\,\mu \]
  done clear
  C)
   64 m                                    
  done clear
  D)
   None of these
  done clear
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• question_answer20)     A rock is dropped from a 100 m high cliff. How long does it take to fall first 50 m and the second 50m?
  A)
   \[2s,3s\]                             
  done clear
  B)
   \[1.5s,\text{ }2.5s\]
  done clear
  C)
   \[1.2s,\text{ }3.2s\]                       
  done clear
  D)
   \[3.2s,1.3s\]
  done clear
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• question_answer21)     Two bodies of masses\[{{M}_{1}}\]and\[{{M}_{2}}\]are dropped from heights\[{{H}_{1}}\]and\[{{H}_{2}}\]respectively. They reach the ground after time\[{{T}_{1}}\]and\[{{T}_{2}}\] respectively. Which of the following relation is correct?
  A)
   \[\frac{{{T}_{1}}}{{{T}_{2}}}={{\left[ \frac{{{H}_{1}}}{{{H}_{2}}} \right]}^{1/2}}\]
  done clear
  B)
   \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{{{H}_{1}}}{{{H}_{2}}}\]
  done clear
  C)
   \[\frac{{{T}_{1}}}{{{T}_{2}}}={{\left[ \frac{{{M}_{1}}}{{{M}_{2}}} \right]}^{1/2}}\]             
  done clear
  D)
   \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{{{M}_{1}}}{{{M}_{2}}}\]
  done clear
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• question_answer22)     A circular ring having uniformly distributed mass m and radius r is as shown in the figure. If a point mass m is taken slowly from A to B, then work done by the external agent will be
  A)
   \[-\frac{GMm}{R}\left[ \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{5}} \right]\]      
  done clear
  B)
   \[\frac{GMm}{R}\times \frac{1}{\sqrt{5}}\]
  done clear
  C)
   \[\frac{GMm}{R}\left[ \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{5}} \right]\]        
  done clear
  D)
   \[\frac{GMm}{R}\left[ \frac{1}{\sqrt{10}} \right]\]
  done clear
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• question_answer23)     A plank of mass 12 kg is supported by two identical springs as shown in figure. The plank     always remains horizontal. When the plank is pressed down and released, it performs SHM with time period 3 s. When a block of mass m is attached to plank the time period changes to 6 s. The mass of the block is
  A)
   48 kg                                    
  done clear
  B)
   36 kg
  done clear
  C)
   24kg                                     
  done clear
  D)
   12kg
  done clear
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• question_answer24)     Two springs are made to oscillate simple harmonically due to the same mass individually. The time periods obtained are\[{{T}_{1}}\]and\[{{T}_{2}}\]. If both the springs are connected in series and then made to oscillate by the same mass, the resulting time will be
  A)
   \[{{T}_{1}}+{{T}_{2}}\]                 
  done clear
  B)
   \[\frac{{{T}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}\]
  done clear
  C)
   \[\sqrt{T_{1}^{2}+T_{2}^{2}}\]                 
  done clear
  D)
   \[\frac{{{T}_{1}}+{{T}_{2}}}{2}\]
  done clear
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• question_answer25)     A string fixed at both ends whose fundamental frequency is 240 Hz is vibrated with the help of tuning fork having frequency 480 Hz, then
  A)
   string will vibrate with a frequency of 240 Hz      
  done clear
  B)
   string will vibrate in resonance with the tuning fork
  done clear
  C)
   string will vibrate with a frequency of 480 Hz, but is not in resonance with the tuning fork
  done clear
  D)
   string is in resonance with tuning fork, and hence vibrates with a frequency of 240 Hz
  done clear
  View Answer play_arrow

• question_answer26)     A material has Poissons ratio 0.50. If a uniform rod of it suffers a longitudinal strain of \[2\times {{10}^{-3}},\]then the percentage change in volume is
  A)
   0.6                                        
  done clear
  B)
   0.4
  done clear
  C)
   0.2                                        
  done clear
  D)
   zero
  done clear
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• question_answer27)     The property of metals which allows them to be drawn readily into thin wires beyond the elastic limit without rupturing is known as
  A)
   malleability      
  done clear
  B)
   ductility
  done clear
  C)
   elasticity            
  done clear
  D)
   hardness
  done clear
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• question_answer28)     A solid sphere of radius fi made up of a material of bulk modulus K is surrounded by a liquid in cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere
  A)
   \[\frac{Mg}{AK}\]                          
  done clear
  B)
   \[\frac{Mg}{3AK}\]
  done clear
  C)
   \[\frac{3Mg}{AK}\]                        
  done clear
  D)
   \[\frac{Mg}{2AK}\]
  done clear
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• question_answer29)     An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel, as shown in the figure. The water which comes out from the hole at the instant when hole is at height H above the ground, strikes the ground at distance of\[x\]from P. Which of the following is correct for the situation described?
  A)
   The value of\[x\]is\[2\sqrt{\frac{2hH}{3}}\]
  done clear
  B)
   The value of\[x\]is\[\sqrt{\frac{4hH}{3}}\]
  done clear
  C)
   The value of\[x\]cant be computed, from information provided
  done clear
  D)
   The question is irreverent as no water comes out from the hole
  done clear
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• question_answer30)     Pressure p, volume V, and temperature T certain material are related by \[p=\frac{AT-B{{T}^{2}}}{V}\]where A and B are constants. Find an expression for the work done by the material if the temperature changes from\[{{T}_{1}}\]to\[{{T}_{2}}\]while the pressure remains constant.
  A)
   \[W=A(T_{1}^{2}-T_{2}^{2})-B(T_{2}^{2}-T_{1}^{2})\]
  done clear
  B)
   \[W=A(T_{2}^{2}-T_{1}^{2})-B({{T}_{2}}-{{T}_{1}})\]
  done clear
  C)
   \[W=A({{T}_{2}}-{{T}_{1}})-B\left( {{T}_{2}}-\frac{1}{2}{{T}_{1}} \right)\]
  done clear
  D)
   \[W=A({{T}_{2}}-{{T}_{1}})-B\left( T_{2}^{2}-T_{1}^{2} \right)\]
  done clear
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• question_answer31)     Four moles of an ideal gas undergo a reversible isothermal expansion from volume \[{{V}_{1}}\] to volume\[{{V}_{2}}=2{{V}_{1}}\]at temperature T = 400 K. Find the entropy change of the gas.
  A)
   \[9.22\times {{10}^{3}}J{{K}^{-1}}\]       
  done clear
  B)
   \[8.22\times {{10}^{2}}J{{K}^{-1}}\]
  done clear
  C)
   \[2.31J{{K}^{-1}}\]                         
  done clear
  D)
   \[10.00\times {{10}^{3}}J{{K}^{-1}}\]
  done clear
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• question_answer32)     A drop, having a mass of\[4.8\times {{10}^{-10}}g\]and a charge of\[2.4\times {{10}^{-8}}C\] is suspended between two charged horizontal plates at a distance 1.0 cm apart. Find the potential difference between the plates.
  A)
   \[1.96\times {{10}^{6}}V\]         
  done clear
  B)
   \[1.86\times {{10}^{4}}V\]
  done clear
  C)
   \[1.96\times {{10}^{4}}V\]         
  done clear
  D)
   \[2.96\times {{10}^{4}}V\]
  done clear
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• question_answer33)     In a potentiometer experiment the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of\[2\,\Omega \] the balancing length becomes 120 cm. The internal resistance of the cell is
  A)
   \[4\,\Omega \]               
  done clear
  B)
   \[2\,\Omega \]
  done clear
  C)
   \[1\,\Omega \]                               
  done clear
  D)
   \[0.5\,\Omega \]
  done clear
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• question_answer34)     In the combination of resistance shown in the figure, the potential difference between B and D, is zero, when unknown resistance is
  A)
   \[0.125\,\Omega \]                       
  done clear
  B)
   \[2\,\Omega \]
  done clear
  C)
   \[3\,\Omega \]
  done clear
  D)
   for finding the value of\[X,\]the emf of cell is required
  done clear
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• question_answer35)     At what distance along the central axis of a uniformly charged plastic disk of radius R is the magnitude of the electric field equal to one-half the. magnitude of the field at the centre of the surface of the disk?
  A)
   \[\frac{R}{\sqrt{2}}\]                                    
  done clear
  B)
   \[\frac{R}{\sqrt{3}}\]
  done clear
  C)
   \[\sqrt{2}R\]                    
  done clear
  D)
   \[\sqrt{3}R\]
  done clear
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• question_answer36)     potential of 500 V is observed near the surface with\[V=0\]at infinity). If two such drops of the same charge and radius combine to form a single spherical drop, the potential at the surface at the new drop?
  A)
   590V                                    
  done clear
  B)
   690V
  done clear
  C)
   790V                                    
  done clear
  D)
   890V
  done clear
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• question_answer37)     Two infinite long current carrying wires A and B are placed as shown in figure. Each wire carries same current\[I\]. The resultant magnetic field intensity at point P is
  A)
   \[\frac{{{\mu }_{0}}I}{2\pi a}\]                 
  done clear
  B)
   \[\frac{\sqrt{2}{{\mu }_{0}}I}{2\pi a}\]
  done clear
  C)
   \[\frac{{{\mu }_{0}}I}{2\sqrt{2}\pi a}\]                 
  done clear
  D)
   \[\frac{{{\mu }_{0}}I}{4\sqrt{2}\pi a}\]
  done clear
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• question_answer38)     The mutual inductance between two planar concentric rings of radii\[{{r}_{1}}\]and\[{{r}_{2}}\](with\[{{r}_{1}}>{{r}_{2}}\]) placed in air is given by
  A)
   \[\frac{{{\mu }_{0}}\pi r_{2}^{2}}{2{{r}_{1}}}\]                  
  done clear
  B)
   \[\frac{{{\mu }_{0}}\pi r_{1}^{2}}{2{{r}_{2}}}\]
  done clear
  C)
   \[\frac{{{\mu }_{0}}\pi ({{r}_{1}}+{{r}_{2}})}{2{{r}_{1}}}\]                             
  done clear
  D)
   \[\frac{{{\mu }_{0}}\pi {{({{r}_{1}}+{{r}_{2}})}^{2}}}{2{{r}_{2}}}\]
  done clear
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• question_answer39)     A charge\[4\mu C\]is placed on a small conducting sphere that is located at the end of thin insulating rod of length 0.5 m. The rod rotates in horizontal plane with a constant angular velocity of\[100\text{ }rad{{s}^{-1}}\]about a vertical axis that passes through its other end. The magnetic moment of the rotating charge is
  A)
   zero
  done clear
  B)
   \[0.5\times {{10}^{-4}}A{{m}^{2}}\]
  done clear
  C)
   \[1.25\times {{10}^{-4}}A{{m}^{2}}\]
  done clear
  D)
   magnetic moment is not defined for this case
  done clear
  View Answer play_arrow

• question_answer40)     A parallel plate capacitor is moving with a velocity of\[25\text{ }m{{s}^{-1}}\]through a uniform magnetic field of 1.5 T as shown in figure. If the electric field within the capacitor plates is\[175\text{ }N{{C}^{-1}}\] and plate area is\[25\times {{10}^{-7}}{{m}^{2}},\]then the magnetic force experienced by positive charge plate is
  A)
   \[1.45\times {{10}^{-13}}N\]
  done clear
  B)
   zero
  done clear
  C)
   \[8.67\times {{10}^{-15}}N\]
  done clear
  D)
   \[3.87\times {{10}^{-15}}N\]
  done clear
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• question_answer41)     In an AC circuit the potential difference V and current I are given respectively by \[V=100\sin (100t)volt\] and      \[I=100\sin \left( 100t+\frac{\pi }{3} \right)mA\] The power dissipated in the circuit will be
  A)
   \[{{10}^{4}}W\]               
  done clear
  B)
   \[10W\]
  done clear
  C)
   \[2.5\text{ }W\]              
  done clear
  D)
   \[5W\]
  done clear
  View Answer play_arrow

• question_answer42)     The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is\[{{B}_{0}}=510\,nT\]. What is the amplitude of the electric field part of the wave?
  A)
   \[140\text{ }N{{C}^{-1}}\]          
  done clear
  B)
   \[153\text{ }N{{C}^{-1}}\]
  done clear
  C)
   \[163\text{ }N{{C}^{-1}}\]          
  done clear
  D)
   \[133\text{ }N{{C}^{-1}}\]
  done clear
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• question_answer43)     Monochromatic light of wavelength 800 nm is used in double slit experiment. One of the slit is covered with a transparent slab of thickness\[2.4\times {{10}^{-5}}m\]. The refractive index of the material of slab is 1.4. What is the number of fringes that will shift due to introduction of the sheet?
  A)
   14                                         
  done clear
  B)
   12
  done clear
  C)
   16                                         
  done clear
  D)
   10
  done clear
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• question_answer44)     A simple pendulum has a time period\[{{T}_{1}}\]when on the earths surface and\[{{T}_{2}}\]when taken to a height R above the earths surface where R is the radius of the earth. The value of\[\frac{{{T}_{2}}}{{{T}_{1}}}\]is
  A)
   1                                            
  done clear
  B)
   \[\sqrt{2}\]
  done clear
  C)
   4                                            
  done clear
  D)
   2
  done clear
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• question_answer45)     A cube of side 3 m is placed in front of a concave mirror of focal length 2 m with its face P at a distance 4 m and face Q at a distance 7 m from the mirror. What is distance between the images of face P and Q?   
  A)
   1.2m                                    
  done clear
  B)
   2.4m
  done clear
  C)
   2.1m                                    
  done clear
  D)
   2.2m
  done clear
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• question_answer46)     Two stars are situated at distance of 8 light years from the earth. These are to be just resolved by a telescope of diameter 0.25 m. If the wavelength of light used is\[5000\,\overset{o}{\mathop{\text{A}}}\,\]then the distance between the stars must be
  A)
   \[3\times {{10}^{10}}m\]                            
  done clear
  B)
   \[3.35\times {{10}^{11}}m\]
  done clear
  C)
   \[1.95\times {{10}^{11}}m\]                      
  done clear
  D)
   \[4.32\times {{10}^{10}}m\]
  done clear
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• question_answer47)     Ultraviolet light of wavelength 350 nm and intensity\[1.00\text{ }W{{m}^{-2}}\]is incident on a potassium surface. If 0.5% of the photons participate in ejecting the photoelectrons, how many photo electrons, are emitted per second, if the potassium surface has an area of\[1\text{ }c{{m}^{2}}\]?
  A)
  \[1.76\times {{10}^{18}}\]photoelectrons/s
  done clear
  B)
   \[1.76\times {{10}^{14}}\]photoelectrons/s
  done clear
  C)
  \[8.8\times {{10}^{11}}\]photoelectrons/s
  done clear
  D)
   The value of work function is required to complete   the   value   of   emitted photoelectrons/s
  done clear
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• question_answer48)     An electron collides with a hydrogen atom in its ground state and excites it to\[n=3\]. The energy given to hydrogen atom in this inelastic collision is [Neglect the recoiling of hydrogen atom]
  A)
   10.2 eV               
  done clear
  B)
   12.1 eV
  done clear
  C)
   12.5 eV               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer49)     A black body radiates at two temperatures\[{{T}_{1}}\]and\[{{T}_{2}}\]. Such that\[{{T}_{1}}<{{T}_{2}}\]. The frequency corresponding to maximum intensity is
  A)
   less at \[{{T}_{1}}\]
  done clear
  B)
   more at \[{{T}_{1}}\]
  done clear
  C)
   equal in the two cases
  done clear
  D)
   cannot say
  done clear
  View Answer play_arrow

• question_answer50)     Three dielectric slabs of thickness\[\frac{d}{4},\frac{d}{7}\]and \[\frac{d}{2}\] having dielectric constants 2, 8/7 and 4 respectively are inserted between the plates of a parallel plate capacitor having plate separation d and plate area A. The remaining space is filled with a conducting medium. Find the capacitance of the System.
  A)
   \[\frac{8{{\varepsilon }_{0}}A}{d}\]                       
  done clear
  B)
   \[\frac{8{{\varepsilon }_{0}}A}{3d}\]
  done clear
  C)
   \[\frac{26{{\varepsilon }_{0}}A}{35d}\]                
  done clear
  D)
   \[\frac{12{{\varepsilon }_{0}}A}{35d}\]
  done clear
  View Answer play_arrow

• question_answer51)     Two bodies of different masses has been released from the top of tower. One is thrown in horizontal direction while other is dropped, then which will reach the ground first?
  A)
   The body which has been thrown horizontally
  done clear
  B)
   The body which has been dropped
  done clear
  C)
   Both will reach the ground simultaneously
  done clear
  D)
   Depends on the velocity with which the first bod has been projected horizontally
  done clear
  View Answer play_arrow

• question_answer52)     A body dropped from a height H reaches the ground with a speed of\[1.2\sqrt{gH}\]. Calculate the work done by air-friction.
  A)
   2.8 mgH              
  done clear
  B)
   \[-1.3\,mgH\]
  done clear
  C)
   1.3 mgH              
  done clear
  D)
   \[-0.28\,mgH\]
  done clear
  View Answer play_arrow

• question_answer53)     The resistance of a wire at\[20{}^\circ C\]is\[20\,\Omega \] and at \[500{}^\circ C\] is \[60\,\Omega \]. At which temperature its resistance will be\[25\,\Omega \]?
  A)
   \[50{}^\circ C\]                
  done clear
  B)
   \[60{}^\circ C\]
  done clear
  C)
   \[70{}^\circ C\]                
  done clear
  D)
   \[80{}^\circ C\]
  done clear
  View Answer play_arrow

• question_answer54)     Two cells connected in series have electromotive force of 1.5 V each. Their internal resistance are\[0.5\,\Omega \]. and\[0.25\,\Omega \] respectively. This combination is connected to a resistance of\[2.25\,\Omega \]. Potential difference across the terminals of each cell
  A)
   IV, 0.25V            
  done clear
  B)
   IV, 1.25V
  done clear
  C)
   1.5V, 2.25V       
  done clear
  D)
   1.5V, 2.56V
  done clear
  View Answer play_arrow

• question_answer55)     A swimmer of mass m rests on top of a Styrofoam slab, which has thickness h and density\[{{\rho }_{s}}\]. The area of the slab if it floats in water with its upper surface just awash is [Take density of water to be\[{{\rho }_{w}}\]].
  A)
   \[\frac{m}{h({{\rho }_{s}}+{{\rho }_{w}})}\]                       
  done clear
  B)
   \[\frac{m}{h{{\rho }_{w}}}\]
  done clear
  C)
   \[\frac{m}{h({{\rho }_{s}}-{{\rho }_{w}})}\]                        
  done clear
  D)
   \[\frac{m}{h({{\rho }_{w}}-{{\rho }_{s}})}\]
  done clear
  View Answer play_arrow

• question_answer56) Density of a crystal remains unchanged as a result of
  A)
   ionic defect      
  done clear
  B)
   Schottky defect
  done clear
  C)
   Frenkel defect                
  done clear
  D)
   crystal defect
  done clear
  View Answer play_arrow

• question_answer57)     The hydrocarbon which does not decolourise alkaline\[KMn{{O}_{4}}\]solution and also does not give any precipitate with ammonia Cal silver nitrate is
  A)
   acetylene          
  done clear
  B)
   benzene
  done clear
  C)
   propyne             
  done clear
  D)
   butyne-1
  done clear
  View Answer play_arrow

• question_answer58)     Which of the following organic compounds exhibits positive Fehling test as well as iodoform test?
  A)
   Methanal          
  done clear
  B)
   Ethanol
  done clear
  C)
   Ethanal                               
  done clear
  D)
   Propanone
  done clear
  View Answer play_arrow

• question_answer59)     Oxidation of toluene to benzaldehyde by the use of chromyi chloride is called
  A)
   Wurtz reaction
  done clear
  B)
   Etards reaction
  done clear
  C)
   Fittig reaction
  done clear
  D)
   Rosenmunds reaction
  done clear
  View Answer play_arrow

• question_answer60)     The only alcohol that can be prepared by the direct hydration of alkene is
  A)
   ethyl alcohol                    
  done clear
  B)
   methyl alcohol
  done clear
  C)
   propyl alcohol                  
  done clear
  D)
  \[iso-\]butyl alcohol
  done clear
  View Answer play_arrow

• question_answer61)     The fresh precipitate can be transformed in colloidal state by
  A)
   peptisation                       
  done clear
  B)
   coagulation
  done clear
  C)
   diffusion            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer62)     Which of the following has zero dipole moment?
  A)
  \[CIF\]                                 
  done clear
  B)
   \[PC{{l}_{3}}\]
  done clear
  C)
   \[Si{{F}_{4}}\]                                  
  done clear
  D)
   \[CFC{{l}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer63)     The hybrid orbital used by chlorine atom in \[CIO_{2}^{-}\]ion is
  A)
   \[s{{p}^{3}}\]
  done clear
  B)
   \[s{{p}^{2}}\]
  done clear
  C)
   \[sp\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer64)     The relationship between standard reduction potential of a cell and equilibrium constant is shown by
  A)
   \[E_{cell}^{o}=\frac{n}{0.059}\log {{K}_{c}}\]
  done clear
  B)
   \[E_{cell}^{o}=\frac{0.059}{n}\log {{K}_{c}}\]
  done clear
  C)
   \[E_{cell}^{o}=0.059\,n\,\log {{K}_{c}}\]
  done clear
  D)
   \[E_{cell}^{o}=\frac{\log {{K}_{c}}}{n}\]
  done clear
  View Answer play_arrow

• question_answer65)     The half-cell reactions for the corrosion are \[2{{H}^{+}}+\frac{1}{2}{{O}_{2}}+2{{e}^{-}}\xrightarrow[{}]{{}}{{H}_{2}}O;\]      \[E{}^\circ =1.23\,V\] \[F{{e}^{2+}}+2{{e}^{-}}\xrightarrow[{}]{{}}Fe(s);\]                         \[E{}^\circ =-0.44\,V\] Find the\[\Delta G{}^\circ \](in kJ) for the overall reaction.
  A)
   \[-76\]                                
  done clear
  B)
   \[-322\]
  done clear
  C)
   \[-161\]                              
  done clear
  D)
   \[-152\]
  done clear
  View Answer play_arrow

• question_answer66)     The vapour pressure of water at\[23{}^\circ C\]is i9.8 mm of Hg.0.1 mol of glucose is dissolved in 178.2 g of water. What is the vapour pressure (in mm Hg) of the resultant solution?
  A)
   19.0                                      
  done clear
  B)
   19.602
  done clear
  C)
   19.402                                 
  done clear
  D)
   19.202
  done clear
  View Answer play_arrow

• question_answer67)     The number of nodal planes in a\[{{p}_{x}}\]orbital is
  A)
   one                                      
  done clear
  B)
   two
  done clear
  C)
   three                                   
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer68)     3-phenyl propene on reaction with HBr gives (as a major product)
  A)
   \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}CH(Br)C{{H}_{3}}\]
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}CH(Br)C{{H}_{2}}C{{H}_{3}}\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}Br\]
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}CH(Br)CH=C{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer69)     Carbolic acid is
  A)
   \[{{C}_{6}}{{H}_{5}}CHO\]          
  done clear
  B)
   \[{{C}_{6}}{{H}_{6}}\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}COOH\]       
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}OH\]
  done clear
  View Answer play_arrow

• question_answer70)     A compound A when treated with methyl alcohol and few drops of\[{{H}_{2}}S{{O}_{4}},\], gave smell of winter green. The compound A is
  A)
   succinic acid     
  done clear
  B)
   salicylic acid
  done clear
  C)
   tartaric acid       
  done clear
  D)
   oxalic acid
  done clear
  View Answer play_arrow

• question_answer71)     Which of the following does give violet colour with neutral ferric chloride?
  A)
   Acetic acid         
  done clear
  B)
   Salicylic acid
  done clear
  C)
   Formic acid      
  done clear
  D)
   Benzoic acid
  done clear
  View Answer play_arrow

• question_answer72)     Cyanohydrin of which of the following forms lactic acid?
  A)
   \[HCHO\]           
  done clear
  B)
   \[C{{H}_{3}}COC{{H}_{3}}\]
  done clear
  C)
   \[C{{H}_{3}}CHO\]         
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}CHO\]
  done clear
  View Answer play_arrow

• question_answer73)     The most basic compound amongst the following is
  A)
   benzyl amine                   
  done clear
  B)
   aniline
  done clear
  C)
   p-nitroaniline                   
  done clear
  D)
   ethanamide
  done clear
  View Answer play_arrow

• question_answer74)     An aromatic molecule will
  A)
   have\[(4n+2)\pi -\]electrons
  done clear
  B)
   be planar
  done clear
  C)
   be cyclic
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer75)     The IUPAC name of the compound,\[{{(C{{H}_{2}}=CHCHC{{H}_{3}})}_{2}}\]is
  A)
   1,1-dimethylprop-2-ene
  done clear
  B)
   3-methylbut-1-ene
  done clear
  C)
   2-vinylpropane
  done clear
  D)
   1-iso-propylethylene
  done clear
  View Answer play_arrow

• question_answer76)     Which of the following is not a nucleophile?
  A)
   \[{{H}_{2}}O\]                                 
  done clear
  B)
   \[C{{H}_{3}}OH\]
  done clear
  C)
   \[{{H}_{2}}\]                                     
  done clear
  D)
   \[N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer77)     Which of the following is the smallest in size?
  A)
   \[{{N}^{3-}}\]                                   
  done clear
  B)
   \[{{O}^{2-}}\]
  done clear
  C)
   \[{{F}^{-}}\]                                      
  done clear
  D)
   \[N{{a}^{+}}\]
  done clear
  View Answer play_arrow

• question_answer78)     Which of the following oxides is amphoteric in character?
  A)
   \[CaO\]                              
  done clear
  B)
   \[C{{O}_{2}}\]
  done clear
  C)
   \[Si{{O}_{2}}\]                                 
  done clear
  D)
   \[Sn{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer79)     \[Ge(II)\]compounds are more powerful reducing agents whereas\[Pb(IV)\]compounds are strong oxidants. It can be due to
  A)
  \[Pb\]is more electropositive than\[Ge\]
  done clear
  B)
   ionisation potential of lead is less than that of\[Ge\]
  done clear
  C)
   ionic radii of\[P{{b}^{2+}}\]and\[P{{b}^{4+}}\]are larger than those of\[G{{e}^{2+}}\]and\[G{{e}^{4+}}\]
  done clear
  D)
   more pronounced inert pair effect in lead than in Ge
  done clear
  View Answer play_arrow

• question_answer80)     \[P{{H}_{3}},\]the hydride of phosphorus is
  A)
   metallic              
  done clear
  B)
   ionic
  done clear
  C)
   non-metallic                     
  done clear
  D)
   covalent
  done clear
  View Answer play_arrow

• question_answer81)     The oxidation number of Cr in\[Cr{{O}_{5}}\]is
  A)
   +2                                         
  done clear
  B)
   +4
  done clear
  C)
   +6                                         
  done clear
  D)
   +8
  done clear
  View Answer play_arrow

• question_answer82)     \[C{{N}^{-}}\]is a strong field ligand. This is due to the fact that   
  A)
   it carries a negative charge
  done clear
  B)
   it is a pseudo halide
  done clear
  C)
   it can accept electrons from metal species
  done clear
  D)
   it forms high spin complexes with metal Species
  done clear
  View Answer play_arrow

• question_answer83)     Which of the following compounds is square planar and does not have any unpaired electron?
  A)
   \[Ni{{(CO)}_{4}}\]                          
  done clear
  B)
   \[{{[Ni{{({{H}_{2}}O)}_{6}}]}^{2+}}\]
  done clear
  C)
   \[{{[NiC{{l}_{4}}]}^{2-}}\]            
  done clear
  D)
   \[{{[Ni{{(CN)}_{4}}]}^{2-}}\]
  done clear
  View Answer play_arrow

• question_answer84)     White anhydrous copper sulphate decomposes to give
  A)
   \[CuS{{O}_{4}}.5{{H}_{2}}O\]    
  done clear
  B)
   \[CuS{{O}_{4}}.{{H}_{2}}O\]
  done clear
  C)
  \[CuO+S{{O}_{3}}\]                        
  done clear
  D)
   \[Cu\]
  done clear
  View Answer play_arrow

• question_answer85)     If\[NaOH\]is added to an aqueous solution of zinc ions, a white precipitate appears and on adding excess of\[NaOH\], the precipitate dissolves. In this solution zinc exist in the
  A)
   cationic part
  done clear
  B)
   anionic part
  done clear
  C)
   both in cationic and anionic part
  done clear
  D)
   there is no zinc in the solution
  done clear
  View Answer play_arrow

• question_answer86)     Chlorine gas is dried over
  A)
   \[CaO\]                              
  done clear
  B)
   \[NaOH\]
  done clear
  C)
   \[KOH\]                              
  done clear
  D)
   \[conc.{{H}_{2}}S{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer87)     Which of the following halogens does not form its oxyacids?
  A)
   Fluorine             
  done clear
  B)
   Chlorine
  done clear
  C)
   Bromine             
  done clear
  D)
   Iodine
  done clear
  View Answer play_arrow

• question_answer88)     Which of the following hydrides has the lowest boiling point?
  A)
   \[{{H}_{2}}O\]                                 
  done clear
  B)
   \[{{H}_{2}}S\]
  done clear
  C)
   \[{{H}_{2}}Se\]                                
  done clear
  D)
   \[{{H}_{2}}Te\]
  done clear
  View Answer play_arrow

• question_answer89)     Glass is a
  A)
   polymeric mixture
  done clear
  B)
   microcrystalline solid
  done clear
  C)
   super cooled liquid
  done clear
  D)
   gel
  done clear
  View Answer play_arrow

• question_answer90)     Thermite is a mixture of iron oxide and
  A)
   zinc powder     
  done clear
  B)
   sodium shavings
  done clear
  C)
   potassium metal            
  done clear
  D)
   aluminium powder
  done clear
  View Answer play_arrow

• question_answer91)     The volume of water to be added to\[100\text{ }c{{m}^{3}}\]of \[0.5\text{ }N\text{ }{{H}_{2}}S{{O}_{4}}\]to get decinormal concentration is
  A)
   \[400\,c{{m}^{3}}\]                       
  done clear
  B)
   \[500\,c{{m}^{3}}\]
  done clear
  C)
   \[450\,c{{m}^{3}}\]                       
  done clear
  D)
   \[100\,c{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer92)     The   rate of a first order reaction is\[1.5\times {{10}^{-2}}\] \[mol\text{ }{{L}^{-1}}mi{{n}^{-1}}\]at 0.5 M concentration of the reactant. The half-life of the reaction is
  A)
   7.53 min             
  done clear
  B)
   0.383 min
  done clear
  C)
   23.1 min             
  done clear
  D)
   8.73 min 
  done clear
  View Answer play_arrow

• question_answer93)     The hydrolysis of ester in alkaline medium is a
  A)
   first order reaction with molecularity 1
  done clear
  B)
   second order reaction with molecularity 2
  done clear
  C)
   first order reaction with molecularity 2
  done clear
  D)
   second order reaction with molecularity 1
  done clear
  View Answer play_arrow

• question_answer94)     Which is correct statement?
  A)
   Starch is a polymer of a-glucose
  done clear
  B)
   Amylose is a component of cellulose
  done clear
  C)
   Proteins are compounds of only one type of amirio acid
  done clear
  D)
   Incyclic structure of fructose, there are four carbons and one oxygen atom
  done clear
  View Answer play_arrow

• question_answer95)     Oleic, stearic and palmitic acids are
  A)
   nucleic acids                     
  done clear
  B)
   amino acids
  done clear
  C)
   fatty acids        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer96)     Arrange the following halides in the decreasing order of\[{{S}_{N}}1\]reactivity. \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}Cl,\]     \[C{{H}_{2}}=CHCH(Cl)C{{H}_{3}},\]                 \[(I)\]                                    \[(II)\] \[C{{H}_{3}}c{{H}_{2}}CH(Cl)C{{H}_{3}}\]                 \[(III)\]
  A)
   \[I>II>III\]         
  done clear
  B)
   \[II>I>III\]
  done clear
  C)
   \[II>III>I\]         
  done clear
  D)
   \[III>II>I\]
  done clear
  View Answer play_arrow

• question_answer97)     Catalyst used in the dimerisation of acetylene to prepare chloroprene is
  A)
   \[HgS{{O}_{4}}+{{H}_{2}}S{{O}_{4}}\]   
  done clear
  B)
   \[C{{u}_{2}}C{{l}_{2}}\]
  done clear
  C)
   \[C{{u}_{2}}C{{l}_{2}}+N{{H}_{4}}Cl\]    
  done clear
  D)
   \[C{{u}_{2}}C{{l}_{2}}+N{{H}_{4}}OH\]
  done clear
  View Answer play_arrow

• question_answer98)     The phenomenon of radioactivity is associated with
  A)
   decay of nucleus
  done clear
  B)
   fusion of nucleus
  done clear
  C)
   emission of electrons or protons
  done clear
  D)
   rearrangement in the extra nuclear electron
  done clear
  View Answer play_arrow

• question_answer99)     If Z is the number of atoms in the unit cell that represents the closest packing sequence\[-ABC,\]\[ABC-,\] the number of tetrahedral voids in the unit cell is equal to
  A)
   Z                                            
  done clear
  B)
   \[2Z\]
  done clear
  C)
   \[\frac{Z}{2}\]                                  
  done clear
  D)
   \[\frac{Z}{4}\]
  done clear
  View Answer play_arrow

• question_answer100)     Conjugate acid of\[SO_{4}^{2-}\]is
  A)
   \[HSO_{4}^{-}\]                              
  done clear
  B)
   \[HS{{O}_{4}}\]
  done clear
  C)
   \[{{H}_{2}}S{{O}_{4}}\]                                
  done clear
  D)
   \[SO_{4}^{-}\]
  done clear
  View Answer play_arrow

• question_answer101)     \[AgCl+KIKCl+AgI\]In the above reaction as KI is added, the equilibrium is shifted towards right giving more.\[AgI\]precipitate, because
  A)
   both\[AgCl\]and\[AgI\]are sparingly soluble
  done clear
  B)
   the\[{{K}_{sp}}\]of\[AgI\]is lower than\[{{K}_{sp}}\]of\[AgCl\]
  done clear
  C)
   the\[{{K}_{sp}}\]of\[AgI\]is higher than\[{{K}_{sp}}\]of\[AgCl\]
  done clear
  D)
   both\[AgCl\]and\[AgI\]have same solubility product
  done clear
  View Answer play_arrow

• question_answer102)     The pH of a solution of hydrochloric acid is 4. The molarity of this solution is
  A)
   4.0                                        
  done clear
  B)
   0.4
  done clear
  C)
   0.0001                 
  done clear
  D)
   0.04
  done clear
  View Answer play_arrow

• question_answer103)     Sulphanilic acid is
  A)
   Arrhenius acid
  done clear
  B)
   Lewis base
  done clear
  C)
   Neither  nor
  done clear
  D)
   Both (a) and (b)
  done clear
  View Answer play_arrow

• question_answer104)     For how many orbitals, the quantum numbers, \[n=3,l=2,\text{ }m=+2\]are possible?
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   3                                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer105)     The number of gram-molecules of oxygen which are present in\[6.022\times {{10}^{24}}CO\]molecules is
  A)
   10 g-molecule                  
  done clear
  B)
   5 g-molecule
  done clear
  C)
   1 g-molecule                    
  done clear
  D)
   0.5 g-molecule
  done clear
  View Answer play_arrow

• question_answer106)     The number of elements present in the fifth period of the Periodic Table is
  A)
   8                                            
  done clear
  B)
   10
  done clear
  C)
   18                                         
  done clear
  D)
   32
  done clear
  View Answer play_arrow

• question_answer107)     Pyrolusite is
  A)
   an oxide ore                     
  done clear
  B)
   a sulphide ore
  done clear
  C)
   a carbide ore                    
  done clear
  D)
   not an ore
  done clear
  View Answer play_arrow

• question_answer108)     The reaction,\[{{H}_{2}}S+{{H}_{2}}{{O}_{2}}\xrightarrow{{}}S+2{{H}_{2}}O\]indicates
  A)
   acidic nature of\[{{H}_{2}}{{O}_{2}}\]
  done clear
  B)
   alkaline nature of\[{{H}_{2}}{{O}_{2}}\]
  done clear
  C)
   oxidising action of\[{{H}_{2}}{{O}_{2}}\]
  done clear
  D)
   reducing action of\[{{H}_{2}}{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer109)     One mole of a perfect gas expands isothermally to ten times of its original volume. The change in entropy is
  A)
   0.1 R                                    
  done clear
  B)
   2.303 R
  done clear
  C)
   10.0 R                                  
  done clear
  D)
   100.0 R
  done clear
  View Answer play_arrow

• question_answer110)     For the reaction,\[PC{{l}_{3}}(g)+C{{l}_{2}}(g)PC{{l}_{5}}(g)\]the value of\[{{K}_{c}}\]at\[250{}^\circ C\]is 26. The value of\[{{K}_{p}}\] at this temperature will be
  A)
   0.0006                 
  done clear
  B)
   0.46
  done clear
  C)
   0.57                                      
  done clear
  D)
   0.83
  done clear
  View Answer play_arrow

• question_answer111) The value of\[\int_{-2}^{3}{|1-{{x}^{2}}|}\,dx\]is
  A)
   \[\frac{7}{3}\]                                  
  done clear
  B)
   \[\frac{14}{3}\]
  done clear
  C)
   \[\frac{28}{3}\]                               
  done clear
  D)
   \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer112)     If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\]is four times their product, then c has the value
  A)
   2                                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   1                                            
  done clear
  D)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer113)     The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\]is
  A)
   [1,2]                                     
  done clear
  B)
   [2,3]
  done clear
  C)
   [2,3)                                     
  done clear
  D)
   [1,2)
  done clear
  View Answer play_arrow

• question_answer114)     Let\[f(x)=\frac{1-\tan x}{4x-\pi },x\ne \frac{\pi }{4},x\in \left[ 0,\frac{\pi }{2} \right].F(x)\]is  continuous in\[\left[ 0,\frac{\pi }{2} \right],\]then\[\frac{dy}{dx}\]is
  A)
   \[-\frac{1}{2}\]                                
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[1\]                                    
  done clear
  D)
   \[-1\]
  done clear
  View Answer play_arrow

• question_answer115)     If\[x={{e}^{y+{{e}^{y+......\infty }}}},x>0,\]then\[\frac{dy}{dx}\]is equal to
  A)
   \[\frac{1-x}{x}\]                              
  done clear
  B)
   \[\frac{1}{x}\]
  done clear
  C)
   \[\frac{x}{1+x}\]                             
  done clear
  D)
   \[\frac{1+x}{x}\]
  done clear
  View Answer play_arrow

• question_answer116)     A variable circle passes through fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is
  A)
   \[{{(y-p)}^{2}}=4qx\]    
  done clear
  B)
   \[{{(y-q)}^{2}}=4py\]
  done clear
  C)
   \[{{(x-p)}^{2}}=4qy\]    
  done clear
  D)
   \[{{(y-q)}^{2}}=4px\]
  done clear
  View Answer play_arrow

• question_answer117)     If\[f:R\to S\] defined by \[f(x)=\sin x-\sqrt{3}\cos x+1,\]is onto, then the interval of S is
  A)
   [0, 1]                                    
  done clear
  B)
  \[[-1,1]\]
  done clear
  C)
   [0, 3]                                    
  done clear
  D)
  \[[-1,3]\]
  done clear
  View Answer play_arrow

• question_answer118)     If\[2a+3b+6c=0,\] then at least one root of the equation\[a{{x}^{2}}+bx+c=0\]lies in the interval
  A)
   (2, 3)                                    
  done clear
  B)
   (1, 2)
  done clear
  C)
   (0, 1)                                    
  done clear
  D)
   (1, 3)
  done clear
  View Answer play_arrow

• question_answer119)     Let\[\alpha ,\beta \]be such that\[\pi <\alpha -\beta <3\pi \].If \[\sin \alpha +\sin \beta =\frac{21}{65}\]and\[\cos \alpha +\cos \beta =-\frac{27}{65},\] then the value of\[\cos \left( \frac{\alpha -\beta }{2} \right)\]is
  A)
   \[\frac{6}{65}\]                               
  done clear
  B)
   \[\frac{3}{\sqrt{130}}\]
  done clear
  C)
   \[-\frac{3}{\sqrt{130}}\]                              
  done clear
  D)
   \[-\frac{3}{65}\]
  done clear
  View Answer play_arrow

• question_answer120)     A function\[y=f(x)\]has a second order derivative\[f\,(x)=6(x-1).\]. If its graph passes through the point (2, 1) and at that point the tangent to the graph is\[y=3x-5,\]then the function is
  A)
   \[{{(x+1)}^{3}}\]             
  done clear
  B)
  \[{{(x-1)}^{3}}\]
  done clear
  C)
   \[{{(x-1)}^{2}}\]              
  done clear
  D)
  \[{{(x+1)}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer121)     If the two lines of regression are \[4x+3y+7=0\]and\[3x+4y+8=0,\]then the means of\[x\]and y are
  A)
   \[-\frac{4}{7},-\frac{11}{7}\]                      
  done clear
  B)
   \[-\frac{4}{7},\frac{11}{7}\]
  done clear
  C)
   \[\frac{4}{7},-\frac{11}{7}\]                       
  done clear
  D)
   \[4,\,7\]
  done clear
  View Answer play_arrow

• question_answer122)     A line with direction cosines proportional to 2, 1,2 meets each of the lines\[x=y+a=z\]and \[x+a=2y=2z\]. The coordinates of each of the points of intersection are given by
  A)
   \[(3d,\text{ }2a,\text{ }3a),\text{ }(a,\text{ }a,2a)\]
  done clear
  B)
   \[(3a,\text{ }2a,\text{ }3a),\text{ }(a,\text{ }a,\,a)\]
  done clear
  C)
   \[(3a,\text{ }3a,\text{ }3a),\text{ (}a,\text{ }a,\text{ }a\text{)}\]
  done clear
  D)
   \[(2a,\text{ }3a,\text{ }3a),\text{ (2}a,\text{ }a,\text{ }a\text{)}\]
  done clear
  View Answer play_arrow

• question_answer123)     The intersection of the spheres\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13\]and \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+3y+4z=8\]is the same as the intersection of one of the sphere and the plane
  A)
   \[x-y+2z=1\]   
  done clear
  B)
   \[x-2y-z=1\]
  done clear
  C)
   \[x-y-z=1\]        
  done clear
  D)
   \[2x-y-z=1\]
  done clear
  View Answer play_arrow

• question_answer124)     A particle moves towards East from a point A to a point B at the rate of 4 km/h and then towards North from B to C at the rate of 5 km/h. If\[AB=12\]km and\[BC=5\text{ }km,\]there its average speed for its journey from A to C are respectively
  A)
   \[\frac{17}{9}km/h\,and\,\frac{13}{9}km/h\]
  done clear
  B)
   \[\frac{13}{4}km/h\,and\,\frac{17}{4}km/h\]
  done clear
  C)
   \[\frac{17}{4}km/h\,and\,\frac{13}{4}km/h\]
  done clear
  D)
   \[\frac{13}{9}km/h\,and\,\frac{17}{9}km/h\]
  done clear
  View Answer play_arrow

• question_answer125)     A velocity\[\frac{1}{4}\]m/s is resolved into two components along OA and OB making angles \[30{}^\circ \]and\[45{}^\circ ,\]respectively with the given velocity. Then, the component along OB is
  A)
   \[\frac{1}{4}m/s\]                          
  done clear
  B)
   \[\frac{1}{4}(\sqrt{3}-1)m/s\]
  done clear
  C)
   \[\frac{1}{8}m/s\]                          
  done clear
  D)
   \[\frac{1}{8}(\sqrt{6}-\sqrt{2})m/s\]
  done clear
  View Answer play_arrow

• question_answer126)     Let two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation
  A)
   \[{{x}^{2}}+18x-16=0\]
  done clear
  B)
   \[{{x}^{2}}-18x+16=0\]
  done clear
  C)
   \[{{x}^{2}}+18x+16=0\]
  done clear
  D)
   \[{{x}^{2}}-18x-16=0\]
  done clear
  View Answer play_arrow

• question_answer127)     A point on the parabola\[{{y}^{2}}=18x\]at which the ordinate increases at twice the rate of the abscissa is
  A)
   \[\left( -\frac{9}{8},\frac{9}{2} \right)\]                
  done clear
  B)
   \[(2,-4)\]
  done clear
  C)
   \[(2,4)\]                             
  done clear
  D)
   \[\left( \frac{9}{8},\frac{9}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer128)     If a, b and c are non-coplanar vectors and\[\lambda \]is a real number, then the vectors\[2a+2b+3c,\]\[\lambda b+4c\]and\[(\lambda -1)c\]are non-coplanar for
  A)
   all except two values of\[\lambda \]
  done clear
  B)
   all except one value of\[\lambda \]
  done clear
  C)
   all values of\[\lambda \]
  done clear
  D)
   no value of\[\lambda \]
  done clear
  View Answer play_arrow

• question_answer129)     Let\[u,\text{ }v,\text{ }w\]be such that\[|u|=1,|v|=2,|w|=3\]If the projection v along u is equal to that of w along\[u\]and\[v,\text{ }w\]are perpendicular to each other, then\[|u-v+w|\]equals to
  A)
   \[\sqrt{14}\]                                     
  done clear
  B)
   \[\sqrt{7}\]
  done clear
  C)
   \[2\]                                    
  done clear
  D)
   14
  done clear
  View Answer play_arrow

• question_answer130)     The mean and the variance of a binomial distribution are 4 and 2 respectively. Then, the probability of 2 successes is
  A)
   \[\frac{128}{256}\]                        
  done clear
  B)
   \[\frac{219}{256}\]
  done clear
  C)
   \[\frac{37}{256}\]                                           
  done clear
  D)
   \[\frac{28}{256}\]
  done clear
  View Answer play_arrow

• question_answer131)     If\[\frac{\log x}{\log 5}=\frac{\log 36}{\log 6}=\frac{\log \,64}{\log y},\]what are the values of\[x\]and y respectively?
  A)
   8, 25                                     
  done clear
  B)
   25, 8
  done clear
  C)
   8,8                        
  done clear
  D)
   25,25   
  done clear
  View Answer play_arrow

• question_answer132)     If A = {1, 2, 3}, B = {3. 2} and C = {2, 3} which one of the following is correct?
  A)
   \[(A\times B)\cap (B\times A)=(A\times C)\cap (B\times C)\]
  done clear
  B)
   \[(A\times B)\cap (B\times A)=(C\times A)\cap (C\times B)\]
  done clear
  C)
   \[(A\times B)\cup (B\times A)=(A\times B)\cup (B\times C)\]
  done clear
  D)
   \[(A\times B)\cup (B\times A)=(A\times B)\cup (A\times C)\]
  done clear
  View Answer play_arrow

• question_answer133)     If\[y=\sin ({{x}^{2}}),z={{e}^{{{y}^{2}}}},t=\sqrt{z}\]what is\[\frac{dt}{dx}\]equal to?
  A)
   \[\frac{xyz}{t}\]                                              
  done clear
  B)
   \[2\frac{xyz}{t}\cos ({{x}^{2}})\]
  done clear
  C)
   \[\frac{-xyz\,cos({{x}^{2}})}{t}\]              
  done clear
  D)
   \[\frac{xyz\,t}{\cos ({{x}^{2}})}\]
  done clear
  View Answer play_arrow

• question_answer134)     Let\[f(x)=[x],\]where\[[x]\]denotes the greatest integer contained in\[x\]. Which one of the following is correct?
  A)
  \[f(x)\]is one-to-one
  done clear
  B)
  \[f(x)\]is onto
  done clear
  C)
   Domain of\[f(x)\]is set of renumbers and range of\[f(x)\]is set of integers\[x\]
  done clear
  D)
   Both domain and range of\[f(x)\]are set of real numbers
  done clear
  View Answer play_arrow

• question_answer135)     What is  the  period  of the function\[f(x)=|\sin x+\cos x|\]
  A)
   \[\frac{\pi }{6}\]                                             
  done clear
  B)
   \[\frac{\pi }{4}\]
  done clear
  C)
   \[\frac{\pi }{2}\]                                             
  done clear
  D)
   \[\pi \]
  done clear
  View Answer play_arrow

• question_answer136)     A man saves ` 135 in the first year, ` 150 in the second year and in this way he increases his savings by ` 15 every, year. In what time will his total saving be ` 5550?
  A)
   20 yr                                    
  done clear
  B)
   25 yr
  done clear
  C)
   30 yr                                    
  done clear
  D)
   35 yr
  done clear
  View Answer play_arrow

• question_answer137)     If\[tan\text{ }\theta +sec\text{ }\theta =p,\]then what is the value of \[\sec \theta \]?
  A)
   \[\frac{{{p}^{2}}+1}{{{p}^{2}}}\]                              
  done clear
  B)
   \[\frac{{{p}^{2}}+1}{\sqrt{p}}\]
  done clear
  C)
   \[\frac{{{p}^{2}}+1}{2p}\]                           
  done clear
  D)
   \[\frac{p+1}{2p}\]
  done clear
  View Answer play_arrow

• question_answer138)     If a particle is acted on by constant forces \[4i+j-3k\]and\[3i+j-k\]it displace from a point\[(i+2j+3k)\]to the point\[5i+4j+k,\] what is the total work done by the forces?
  A)
   50 units              
  done clear
  B)
   40 units
  done clear
  C)
   24 units              
  done clear
  D)
   0 unit
  done clear
  View Answer play_arrow

• question_answer139)     What is the number of common tangents to the circles\[{{x}^{2}}+{{y}^{2}}=1\]and\[{{x}^{2}}+{{y}^{2}}-4x+3=0\]?
  A)
   One                                     
  done clear
  B)
   Two
  done clear
  C)
   Three    
  done clear
  D)
   Four
  done clear
  View Answer play_arrow

• question_answer140)     If tangent to the curve\[{{y}^{2}}={{x}^{3}}\]at its point \[({{m}^{2}},{{m}^{3}})\]is also normal to the curve at \[({{M}^{2}},\text{ }{{M}^{3}}),\]then what is the value of\[mM\]?
  A)
   \[-\frac{4}{9}\]                                
  done clear
  B)
   \[-\frac{2}{9}\]
  done clear
  C)
   \[-\frac{1}{3}\]                                
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer141)     What is the value of b for which\[f(x)=\sin x-bx+c\] is decreasing in the interval\[(-\infty ,\infty )\]?
  A)
   \[b<1\]                               
  done clear
  B)
   \[b\ge 1\]
  done clear
  C)
   \[b>1\]                               
  done clear
  D)
   \[b\le 1\]
  done clear
  View Answer play_arrow

• question_answer142)     If\[\int{f(x)}dx=\frac{f(x)}{2}+C,\] then which one of the following is correct?
  A)
   \[f(x)={{e}^{2x}}+C\]
  done clear
  B)
   \[f(x)=x+C\]
  done clear
  C)
   \[f(x)=C\]
  done clear
  D)
   \[f(x)={{e}^{2x}}\]
  done clear
  View Answer play_arrow

• question_answer143)     If the sides of a triangle are as\[3:7:8,\]then\[R:r\]is equal to
  A)
   \[2:7\]
  done clear
  B)
                          \[7:2\]
  done clear
  C)
   \[3:7\]                                 
  done clear
  D)
   \[7:3\]
  done clear
  View Answer play_arrow

• question_answer144)     In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in AP, then the length of the third side can be
  A)
   \[5-2\sqrt{6}\]                 
  done clear
  B)
   \[3\sqrt{3}\]
  done clear
  C)
   5                                            
  done clear
  D)
   \[5+\sqrt{6}\]
  done clear
  View Answer play_arrow

• question_answer145)     The number of solutions of the equation\[\sqrt{1-\cos x}=\sin x,\pi <x<3\pi \] is
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   2                                            
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer146)     A tower subtends an angle of\[30{}^\circ \]at a point on the same level as the foot of the tower and at a second point, h metre above the first, the depression of the foot of the tower is\[60{}^\circ \]. The height of the tower is
  A)
   \[hm\]                                
  done clear
  B)
  \[3\,h\,m\]
  done clear
  C)
   \[\sqrt{3}\,h\,m\]                          
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer147)     If the ratio of the roots of\[a{{x}^{2}}+2bx+c=0\]is same as the ratio of the\[p{{x}^{2}}+2qx+r=0,\]then
  A)
   \[\frac{2b}{ac}=\frac{{{q}^{2}}}{pr}\]                    
  done clear
  B)
   \[\frac{b}{ac}=\frac{q}{pr}\]
  done clear
  C)
   \[\frac{{{b}^{2}}}{ac}=\frac{{{q}^{2}}}{pr}\]                       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer148)     If\[A(\theta )=\left[ \begin{matrix}    \sin \theta  & i\cos \theta   \\    i\cos \theta  & \sin \theta   \\ \end{matrix} \right],\]then which of the following is not true?
  A)
   \[A{{(\theta )}^{-1}}=A(\pi -\theta )\]
  done clear
  B)
  \[A(\theta )+A(\pi +\theta )\]is a null matrix
  done clear
  C)
  \[A(\theta )\]is invertible for all\[\theta \in R\]
  done clear
  D)
   \[A{{(\theta )}^{-1}}=A(-\theta )\]
  done clear
  View Answer play_arrow

• question_answer149)     If A is a skew-symmetric matrix and n is odd positive integer, then\[{{A}^{n}}\]is
  A)
   a skew-symmetric matrix
  done clear
  B)
   a symmetric matrix
  done clear
  C)
   a diagonal matrix
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer150)     If\[f(x)=\left| \begin{matrix}    a & -1 & 0  \\    ax & a & -1  \\  a{{x}^{2}} & ax & a  \\ \end{matrix} \right|,\]then\[f(2x)-f(x)\]is not divisible by
  A)
   \[x\]                                    
  done clear
  B)
   \[a\]
  done clear
  C)
   \[2a+3x\]          
  done clear
  D)
   \[d{{x}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer151)     If \[^{n}{{C}_{3}}{{+}^{n}}{{C}_{4}}{{>}^{n+1}}{{C}_{3}},\]then
  A)
   \[n>6\]                               
  done clear
  B)
   \[n>7\]
  done clear
  C)
   \[n<6\]                               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer152)     The first three terms in the expansion of \[{{(1+ax)}^{n}}(n\ne 0)\]are\[1,6x\]and\[16{{x}^{2}}\]. Then, the value of a and n are respectively
  A)
   2 and 9
  done clear
  B)
   3 and 2
  done clear
  C)
   2/3 and 9
  done clear
  D)
   3/2 and 6
  done clear
  View Answer play_arrow

• question_answer153)     \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin {{x}^{n}}}{{{(\sin x)}^{m}}},(m<n)\]is equal to
  A)
   1                                            
  done clear
  B)
   0
  done clear
  C)
   \[\frac{n}{m}\]                               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer154)     Let\[f(x)=|x|+|x-1|,\]then
  A)
  \[f(x)\]is continuous at\[x=0\]as well as at\[x=1\]
  done clear
  B)
  \[f(x)\]is continuous at\[x=0,\]but not at\[x=1\]
  done clear
  C)
  \[f(x)\]is continuous at\[x=1,\]but not at\[x=0\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer155)     On the curve\[{{x}^{3}}=12y,\]the abscissa changes at a faster rate than the ordinate. Then,\[x\]belongs to the interval
  A)
   \[(-2,2)\]            
  done clear
  B)
   \[(-1,1)\]
  done clear
  C)
   (0, 2)                                    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer156)     The value of C in Lagranges theorem for the function\[f(x)=log\text{ }sin\text{ }x\]in the interval\[\left[ \frac{\pi }{6},\frac{5\pi }{6} \right]\]is
  A)
   \[\frac{\pi }{4}\]                                             
  done clear
  B)
   \[\frac{\pi }{2}\]
  done clear
  C)
   \[\frac{2\pi }{3}\]                           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer157)     \[\int{\sin 2x\,d}(\tan x)\]is equal to
  A)
   \[2\log |\cos x|+C\]
  done clear
  B)
   \[\log |\cos x|+C\]
  done clear
  C)
   \[2\log |\sec x|+C\]
  done clear
  D)
   \[\log |\sec x|+C\]
  done clear
  View Answer play_arrow

• question_answer158)     The area bounded by the curve\[y=si{{n}^{-1}}x\]and the line \[x=0,|y|=\frac{\pi }{2}\] is
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   \[\pi \]                                
  done clear
  D)
   \[2\pi \]
  done clear
  View Answer play_arrow

• question_answer159)     The solution of\[y\text{ }dx-x\text{ }dy+3{{x}^{2}}{{y}^{2}}{{e}^{{{x}^{3}}}}\text{ }dx=0\]is.
  A)
   \[\frac{x}{y}+{{e}^{{{x}^{3}}}}=C\]                         
  done clear
  B)
   \[\frac{x}{y}-{{e}^{{{x}^{3}}}}=0\]
  done clear
  C)
   \[-\frac{x}{y}+{{e}^{{{x}^{3}}}}=C\]       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer160)     The   point   P   is   equidistant   from A (1, 3), B \[(-3,5)\]and\[C(5,-1)\]. Then, PA is equal to
  A)
   \[5\sqrt{5}\]                     
  done clear
  B)
   \[5\]
  done clear
  C)
   \[5\sqrt{10}\]                  
  done clear
  D)
   \[25\]
  done clear
  View Answer play_arrow

• question_answer161)     The coordinates of the foot of the perpendicular from  the  point   (2, 3)   on  the  line\[-y+3x+4=0\]are given by
  A)
   \[\left( \frac{37}{10},-\frac{1}{10} \right)\]                         
  done clear
  B)
   \[\left( -\frac{1}{10},\frac{37}{10} \right)\]
  done clear
  C)
   \[\left( \frac{10}{37},-10 \right)\]                            
  done clear
  D)
   \[\left( \frac{2}{3},-\frac{1}{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer162)     If the lines joining the origin to the intersection of the line\[y=mx+2\]and the curve\[{{x}^{2}}+{{y}^{2}}=1\] are at right angles, then
  A)
   \[{{m}^{2}}=1\]               
  done clear
  B)
   \[{{m}^{2}}=3\]
  done clear
  C)
   \[{{m}^{2}}=7\]               
  done clear
  D)
   \[2{{m}^{2}}=1\]
  done clear
  View Answer play_arrow

• question_answer163)     The ratio in which the line segment joining the points\[(4,-6)\]and (3, 1) is divided by the parabola\[{{y}^{2}}=4x\]is
  A)
   \[\frac{-20\pm \sqrt{155}}{11}:1\]          
  done clear
  B)
   \[\frac{-2\pm 2\sqrt{155}}{11}:2\]
  done clear
  C)
   \[-20\pm 2\sqrt{155}:11\]          
  done clear
  D)
   \[-20\pm \sqrt{155}:11\]
  done clear
  View Answer play_arrow

• question_answer164)     If the centre, one of the foci and semi-major axis of an ellipse be (0, 0), (0, 3) and 5, then its equation is
  A)
   \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1\]                  
  done clear
  B)
   \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\]
  done clear
  C)
   \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{25}=1\]                     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer165)     If\[{{m}_{1}}\]and\[{{m}_{2}}\]are the slopes of the tangents to the hyperbola\[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{16}=1\]which pass through the point (6, 2), then
  A)
   \[{{m}_{1}}+{{m}_{2}}=-\frac{24}{11}\]
  done clear
  B)
   \[{{m}_{1}}{{m}_{2}}=\frac{20}{11}\]
  done clear
  C)
   \[{{m}_{1}}+{{m}_{2}}=\frac{48}{11}\]  
  done clear
  D)
   \[{{m}_{1}}{{m}_{2}}=\frac{11}{20}\]
  done clear
  View Answer play_arrow

• question_answer166)     If\[a=i+j+k,~~b=4i+3j+4k\]and \[c=i+\alpha j+\beta k\]are linearly dependent vectors and\[|c|=\sqrt{3},\] then
  A)
   \[\alpha =1,\text{ }\beta =-1\]
  done clear
  B)
   \[\alpha =1,\text{ }\beta =\pm 1\]
  done clear
  C)
   \[\alpha =-1,\text{ }\beta =\pm 1\]
  done clear
  D)
   \[\alpha =\pm 1,\text{ }\beta =1\]
  done clear
  View Answer play_arrow

• question_answer167)     In an experiment with 15 observations on\[x,\]the following results were available \[\Sigma {{x}^{2}}=2830,\]\[\Sigma x=170\]. One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then, the corrected variance is
  A)
   80.33                                   
  done clear
  B)
   78.00
  done clear
  C)
   188.66                                 
  done clear
  D)
   177.33
  done clear
  View Answer play_arrow

• question_answer168)     If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is
  A)
   30                                         
  done clear
  B)
   30.1
  done clear
  C)
   29                                         
  done clear
  D)
   31
  done clear
  View Answer play_arrow

• question_answer169)     A bag contains 12 pairs of socks, 4 socks are picked up at random. Then, the probability that there is at least one pair is
  A)
   \[\frac{41}{161}\]                                           
  done clear
  B)
   \[\frac{120}{161}\]
  done clear
  C)
   \[\frac{21}{161}\]                                           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer170)     The odds against a certain event is\[5:2\]and the odds in favour of another event is\[6:5\]. If both the events are independent, then the probability that at least one of the events will happens is
  A)
   \[\frac{50}{77}\]                                             
  done clear
  B)
   \[\frac{52}{77}\]
  done clear
  C)
   \[\frac{25}{88}\]                                             
  done clear
  D)
   \[\frac{63}{88}\]
  done clear
  View Answer play_arrow