Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

done Jamia Millia Islamia Solved Paper-2010 Total Questions - 170

• question_answer1) A car leaves station\[X\]for station Y every 10 min. The distance between\[X\]and Y is 60 km. The car travels at a speed of 60 km/h. A man drives a car from Y station towards\[X\]station at speed 60 km/h. If he starts at the moment when one of the car leaves station\[X\]how many cars would be meet on route?
  A)
   10                                         
  done clear
  B)
   11
  done clear
  C)
   20                                         
  done clear
  D)
   21
  done clear
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• question_answer2)     A ball rolls off the stairway with a horizontal velocity of magnitude 1.8 m/s. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first?
  A)
   First                                     
  done clear
  B)
   Second
  done clear
  C)
   Third                                    
  done clear
  D)
   Fourth
  done clear
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• question_answer3)     A sphere of mass 0.20 kg is attached to an inextensible string of length 0.5m whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 0.3 m. The speed of the sphere will be
  A)
   1.5 m/s                               
  done clear
  B)
   2.5 m/s
  done clear
  C)
   3.2 m/s               
  done clear
  D)
   4.7 m/s
  done clear
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• question_answer4)     Steady rain giving 5 mm an hour, turns suddenly into a downpour 20 mm an hour and the speed of rain drops falling vertically on to a flat roof simultaneously doubles. The pressure exerted by the falling rain on the roof rises by a factor of
  A)
   2                                            
  done clear
  B)
  \[2\sqrt{2}\]
  done clear
  C)
   \[4\sqrt{2}\]                                     
  done clear
  D)
   8
  done clear
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• question_answer5)     An open knife edge of mass M is dropped from a height h on a wooden floor. If the blade penetrates distance into the wood, the average resistance offered by the wood to the blade is
  A)
   \[Mg\]                                
  done clear
  B)
   \[Mg\left( 1+\frac{h}{s} \right)\]
  done clear
  C)
   \[Mg\left( \frac{1-h}{s} \right)\]                             
  done clear
  D)
   \[Mg{{\left( \frac{1+h}{s} \right)}^{2}}\]
  done clear
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• question_answer6)     A particle moves in\[X-Y\]plane under the influence of a force\[\overrightarrow{F}\]such that its instantaneous momentum is\[\overrightarrow{P}=\hat{i}2\cos t+\hat{j}2\sin t\]. What is the angle between the force and instantaneous momentum?
  A)
   \[0{}^\circ \]                                     
  done clear
  B)
   \[180{}^\circ \]
  done clear
  C)
   \[90{}^\circ \]                                  
  done clear
  D)
   \[45{}^\circ \]
  done clear
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• question_answer7)     The KE of a body varies directly as the time (t) elapsed. The force acting varies directly as
  A)
   \[{{t}^{-1}}\]                                    
  done clear
  B)
   \[{{t}^{-1/2}}\]
  done clear
  C)
   \[{{t}^{1/2}}\]                                  
  done clear
  D)
   \[t\]
  done clear
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• question_answer8)     A gas at the temperature 250 K is contained in a closed vessel. If the gas is heated through 1 K, then the percentage increase in its pressure will be
  A)
   0.4%                                    
  done clear
  B)
   0.2%
  done clear
  C)
   0.1%                                    
  done clear
  D)
   0.8%
  done clear
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• question_answer9)     A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from 20 n rad/s to 40 n rad/s in 10 s. How many rotations did it make in this period?
  A)
   80                                         
  done clear
  B)
   100
  done clear
  C)
   120                                       
  done clear
  D)
   150
  done clear
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• question_answer10)     A point P lies on the axis of a ring of mass M and radius R at a distance 2R from its centre\[O\] A small particle starts from P and reaches Q under gravitational attraction only. Its speed at \[O\]will be
  A)
   zero                                     
  done clear
  B)
   \[\sqrt{\frac{2GM}{R}}\]
  done clear
  C)
   \[\sqrt{\frac{2GM}{R}(\sqrt{5}-1)}\]     
  done clear
  D)
   \[\sqrt{\frac{2GM}{R}\left( 1-\frac{1}{\sqrt{5}} \right)}\]
  done clear
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• question_answer11)     Two vertical glass plates 1 mm apart are dipped into water. How high will be the water rise between the plates, if the surface tension of water is\[70\text{ }dyne/c{{m}^{2}}\]?
  A)
   2.86cm                                
  done clear
  B)
   1.43cm
  done clear
  C)
   5.72cm                                
  done clear
  D)
   1.63cm
  done clear
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• question_answer12)     A steel ball is dropped from a height h and it makes a perfectly elastic collision with a horizontal plane. Following its initial release, it will make periodic motion with frequency
  A)
   \[2\pi \sqrt{\frac{g}{h}}\]                           
  done clear
  B)
   \[2\pi \sqrt{\frac{h}{g}}\]
  done clear
  C)
   \[\frac{1}{2}\sqrt{\frac{g}{2h}}\]                             
  done clear
  D)
   \[\frac{1}{2}\sqrt{\frac{2h}{g}}\]
  done clear
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• question_answer13)     Two closed organ pipes A and B have the same length, A is wider than B. They resonate in the fundamental mode at frequencies\[{{n}_{A}}\]and\[{{n}_{B}}\] respectively
  A)
   \[{{n}_{A}}={{n}_{B}}\]
  done clear
  B)
   \[{{n}_{A}}>{{n}_{B}}\]
  done clear
  C)
   \[{{n}_{A}}<{{n}_{B}}\]
  done clear
  D)
   Either  or  depending on the ratio of their diameters
  done clear
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• question_answer14)     Shown below is a distribution of charges. The flux of electric field due to these charges through the surface is
  A)
   \[\frac{3q}{{{\varepsilon }_{0}}}\]                                          
  done clear
  B)
   zero
  done clear
  C)
   \[\frac{2q}{{{\varepsilon }_{0}}}\]                                          
  done clear
  D)
   \[\frac{q}{{{\varepsilon }_{0}}}\]
  done clear
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• question_answer15)     A parallel plate capacitor is connected across a 2 V battery and charged. The battery is then disconnected and a glass slab is introduced between plates. Which of the following pairs of quantities decrease?
  A)
   Charge and potential difference
  done clear
  B)
   Potential difference and energy stored
  done clear
  C)
   Energy stored and capacitance
  done clear
  D)
   Capacitance and charge
  done clear
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• question_answer16)     Four resistances of\[10\,\Omega ,60\,\Omega ,100\,\Omega \]and\[200\,\Omega \]. respectively taken in order are used to form a Wheatstones bridge. A 15 V battery is connected to the ends of a\[200\,\Omega \] resistance. The current through it will be
  A)
   \[7.5\times {{10}^{-5}}A\]          
  done clear
  B)
   \[7.5\times {{10}^{-4}}A\]
  done clear
  C)
   \[7.5\times {{10}^{-3}}A\]          
  done clear
  D)
   \[7.5\times {{10}^{-2}}A\]
  done clear
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• question_answer17)     Magnetic field at the centre of a circular loop of area A is B. The magnetic moment of the loop will be
  A)
   \[\frac{B{{A}^{2}}}{{{\mu }_{0}}\pi }\]                  
  done clear
  B)
   \[\frac{B{{A}^{3/2}}}{{{\mu }_{0}}\pi }\]
  done clear
  C)
   \[\frac{B{{A}^{3/2}}}{{{\mu }_{0}}{{\pi }^{1/2}}}\]                           
  done clear
  D)
   \[\frac{2B{{A}^{3/2}}}{{{\mu }_{0}}{{\pi }^{1/2}}}\]
  done clear
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• question_answer18)     A thin magnet is cut into two equal parts by cutting it parallel to its length. If the original time period of vibration is 4 s the time period of each part in the same field will be
  A)
   \[4s\]                                  
  done clear
  B)
   \[2s\]
  done clear
  C)
   \[4\sqrt{2}s\]                                   
  done clear
  D)
   None of these
  done clear
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• question_answer19)     The moment of magnet is\[0.1\text{ }A{{m}^{2}}\]and the force acting on each pole in a uniform magnetic field of 0.36 oersted is\[1.44\times {{10}^{-4}}N\]. The distance between the poles of magnet is
  A)
   2.5 cm                                 
  done clear
  B)
   5.0 cm
  done clear
  C)
   1.25cm                                
  done clear
  D)
   1.17cm
  done clear
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• question_answer20)     A solenoid 600 mm long has 50 turns on it and is wound on an iron rod of 7.5 mm radius. Find the flux through the solenoid when the current in it is 3 A. The relative permeabillity of iron is 600.
  A)
   1.66 Wb                              
  done clear
  B)
   1.66 N Wb
  done clear
  C)
   1.66 m Wb     
  done clear
  D)
  \[1.66\text{ }\mu \,Wb\]
  done clear
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• question_answer21)     A transformer has an efficiency of 80%. It works at 4 kW and 100 V. If secondary voltage is 240 V the current in primary coil is
  A)
   0.4 A                                    
  done clear
  B)
   4 A
  done clear
  C)
   10 A                                     
  done clear
  D)
   40 A
  done clear
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• question_answer22)     sIn a plane electromagnetic wave, the electric field oscillates sinusoid ally at a frequency \[2\times {{10}^{10}}Hz\]and amplitude 48V/m. The wavelength of the wave is      
  A)
   \[24\times {{10}^{-10}}m\]        
  done clear
  B)
   \[1.5\times {{10}^{-2}}m\]
  done clear
  C)
   \[4.16\times {{10}^{8}}m\]        
  done clear
  D)
   \[3\times {{10}^{8}}m\]
  done clear
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• question_answer23)     A parallel beam of monochromatic unpolarised light is incident on a transparent dielectric plate of refractive indie\[\frac{1}{\sqrt{3}}\]. The reflected beam is completely polarised. Then the angle of incidence is
  A)
   \[30{}^\circ \]                                  
  done clear
  B)
   \[60{}^\circ \]
  done clear
  C)
   \[45{}^\circ \]                                  
  done clear
  D)
   \[75{}^\circ \]
  done clear
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• question_answer24)     A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark again in focus?
  A)
   2 cm upward   
  done clear
  B)
   1 cm upward
  done clear
  C)
   4.5 cm downward,         
  done clear
  D)
   1 cm downward
  done clear
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• question_answer25)     The wavelength of 1 keV photon is\[1.24\times {{10}^{-9}}\] m What is the frequency of 1 MeV photon?
  A)
   \[2.4\times {{10}^{15}}Hz\]       
  done clear
  B)
   \[2.4\times {{10}^{20}}Hz\]
  done clear
  C)
   \[1.24\times {{10}^{15}}Hz\]     
  done clear
  D)
   \[1.24\times {{10}^{20}}Hz\]
  done clear
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• question_answer26)     An electron revolving in an orbit of radius 0.5 A in a hydrogen atom executes\[{{10}^{16}}rev/s\]. The magnetic moment of electron due to its orbital motion will be,
  A)
  \[1256\times {{10}^{-26}}A{{m}^{2}}\]
  done clear
  B)
   \[6.53\times {{10}^{-26}}A{{m}^{2}}\]
  done clear
  C)
   zero
  done clear
  D)
   \[256\times {{10}^{-26}}A{{m}^{2}}\]
  done clear
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• question_answer27)     The ratio of electron and hole currents in a semiconductor is 7/4 and the ratio of drift velocities of electrons and holes is 5/4 then ratio of concentrations of electrons and holes will be
  A)
   5/7                                       
  done clear
  B)
   7/5
  done clear
  C)
   25/49                                   
  done clear
  D)
   49/25
  done clear
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• question_answer28)     In a common base transistor circuit, the current gain is 0.98 on changing emitter current by 5 mA, the change in collector current is
  A)
   0.196mA            
  done clear
  B)
   2.45mA
  done clear
  C)
   4.9mA   
  done clear
  D)
   5.1mA
  done clear
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• question_answer29)     A bus starts moving with acceleration\[2\text{ }m/{{s}^{2}}\]. A cyclist 96 m behind the bus starts simultaneously towards the bus of 20 m/s. After what time will he be able to overtake the bus?
  A)
   \[4s\]                                  
  done clear
  B)
   \[8s\]
  done clear
  C)
   \[12s\]                                
  done clear
  D)
   \[16s\]
  done clear
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• question_answer30)     Geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then the time period of a spy satellite orbiting a 500 km above the earths surface (radius of earth = 6400 km) will approximately be
  A)
   \[\frac{1}{2}h\]                               
  done clear
  B)
   \[1\,h\]
  done clear
  C)
   \[2\,h\]                                              
  done clear
  D)
   \[4\,h\]
  done clear
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• question_answer31)     The upper end of a wire 1 m long and 2 mm radius is clamped. The lower end is twisted through an angle of\[45{}^\circ \]. The angle of shear is
  A)
   \[0.09{}^\circ \]                               
  done clear
  B)
   \[0.9{}^\circ \]
  done clear
  C)
   \[9{}^\circ \]                                     
  done clear
  D)
   \[90{}^\circ \]
  done clear
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• question_answer32)     An air filled parallel plate capacitor charged to potential\[{{V}_{1}}\]is connected to an uncharged identical parallel plate capacitor with dielectric constant K. The common potential is\[{{V}_{2}}\]. The value of K is
  A)
   \[\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}+{{V}_{2}}}\]                          
  done clear
  B)
   \[\frac{{{V}_{1}}}{{{V}_{1}}-{{V}_{2}}}\]
  done clear
  C)
   \[\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{2}}}\]                               
  done clear
  D)
   \[\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}}\]
  done clear
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• question_answer33)     Three charged particles are initially in position\[-1\]. They are free to move and they come to position-2, after some time. Let\[{{U}_{1}}\]and\[{{U}_{2}}\]be the electrostatic potential energies in position\[-1\]and 2 then
  A)
   \[{{U}_{1}}={{U}_{2}}\]               
  done clear
  B)
   \[{{U}_{2}}\ge {{U}_{1}}\]
  done clear
  C)
   \[{{U}_{2}}>{{U}_{1}}\]               
  done clear
  D)
   \[{{U}_{1}}>{{U}_{2}}\]
  done clear
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• question_answer34)     In Youngs double slit experiment one slit is covered with red filter and another slit is covered by green filter, then interference pattern will be
  A)
   red                                       
  done clear
  B)
   green
  done clear
  C)
   yellow                 
  done clear
  D)
   invisible
  done clear
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• question_answer35)     Two plano-convex lenses of radius of curvature R and refractive index\[\mu =1.5\]will have equivalent focal length equal to R when they are placed
  A)
   at distance R/4
  done clear
  B)
   at distance R/2
  done clear
  C)
   at distanced
  done clear
  D)
   in contact with each other
  done clear
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• question_answer36)     If energy E, velocity v and time T were taken as fundamental units, the dimensions for surface tension in these units are
  A)
   \[[{{E}^{-2}}{{V}^{1}}{{T}^{-2}}]\]           
  done clear
  B)
   \[[{{E}^{-2}}{{V}^{-2}}{{T}^{1}}]\]
  done clear
  C)
   \[[{{E}^{1}}{{V}^{-2}}{{T}^{-2}}]\]           
  done clear
  D)
   \[[{{E}^{-2}}{{V}^{-2}}{{T}^{-2}}]\]
  done clear
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• question_answer37)     The angle between\[(\overrightarrow{A}\times \overrightarrow{B})\]and\[(\overrightarrow{A}+\overrightarrow{B})\]is
  A)
   \[\frac{\pi }{4}\]                                             
  done clear
  B)
   \[\frac{\pi }{2}\]
  done clear
  C)
   \[\pi \]                                                
  done clear
  D)
   zero
  done clear
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• question_answer38)     Two stones are projected with the same velocity but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is\[\frac{\pi }{3}\]and maximum height is\[{{y}_{1}}\], then the maximum height of other will be
  A)
   \[3{{y}_{1}}\]                                   
  done clear
  B)
   \[2{{y}_{1}}\]
  done clear
  C)
   \[\frac{{{y}_{1}}}{2}\]                                   
  done clear
  D)
   \[\frac{{{y}_{1}}}{3}\]
  done clear
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• question_answer39)     A disc of mass 10 g is kept horizontally in air by firing bullets of mass 5 g each at the rate of 10 per second. If the bullets rebound with the same speed, what is the velocity with which the bullets are fired?
  A)
   49cm/s                               
  done clear
  B)
   98 cm/s
  done clear
  C)
   147 cm/s            
  done clear
  D)
   196 cm/s
  done clear
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• question_answer40)     A sphere of mass 100 g is attached to an inextensible string of length 1.3m whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 50 cm. The time period of the revolution is
  A)
   5.0s                                      
  done clear
  B)
   4.5s
  done clear
  C)
   3.2s                                      
  done clear
  D)
   2.3s
  done clear
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• question_answer41)     A uniform rod of length\[l\]is free to rotate in a vertical plane about a fixed horizontal axis through point B. The rod begins rotating from rest from its unstable equilibrium position. When it has turned through an angle\[\theta \]its angular velocity co is given as
  A)
   \[\sqrt{\frac{6g}{l}}\sin \theta \]                             
  done clear
  B)
   \[\sqrt{\frac{6g}{l}}\sin \frac{\theta }{2}\]
  done clear
  C)
   \[\sqrt{\frac{6g}{l}}\cos \frac{\theta }{2}\]                         
  done clear
  D)
   \[\sqrt{\frac{6g}{l}}\cos \theta \]
  done clear
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• question_answer42)     The displacement of a particle executing periodic motion is given by \[y=4{{\cos }^{2}}\frac{t}{2}\sin 1000t\] The expression may be considered to be a result of superposition of ......... independent harmonic motions.
  A)
   1                                            
  done clear
  B)
   3
  done clear
  C)
   4                                            
  done clear
  D)
   5
  done clear
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• question_answer43)     Oxygen gas is contained in a cylinder of volume \[1\times {{10}^{-3}}{{m}^{3}}\]at a temperature of 320 K and a pressure of\[3.53\times {{10}^{5}}N/{{m}^{2}}\]. After some of the oxygen is used at constant temperature, the pressure falls to\[2.7\times {{10}^{5}}N/{{m}^{2}}\]. The mass of oxygen used is
  A)
   0.01 kg                                
  done clear
  B)
   0.001 kg
  done clear
  C)
   0.002 kg                              
  done clear
  D)
   0.003 kg
  done clear
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• question_answer44)     A reversible engine working between the temperature limits of 600 K and 1200K receives 50 kJ of heat. The work done by the engine will be
  A)
   50 kJ                                    
  done clear
  B)
   100 kJ
  done clear
  C)
   25 kJ                                    
  done clear
  D)
   \[-25\text{ }kJ\]
  done clear
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• question_answer45)     For the stationary wave\[y=4\sin \frac{\pi x}{15}\cos 96\pi t\] The distance between a node and the next antinode is
  A)
   7.5cm                                  
  done clear
  B)
   15cm
  done clear
  C)
   22.5cm                                
  done clear
  D)
   30cm
  done clear
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• question_answer46)     Two waves each of frequency 540 Hz travel at a speed of 330 m/s. If the source are in phase, in the beginning, the phase difference of the waves at a point 4 m from one source and 4.4 m from the other is
  A)
   \[59{}^\circ \]                                  
  done clear
  B)
   \[118{}^\circ \]
  done clear
  C)
   \[177{}^\circ \]                                
  done clear
  D)
   \[236{}^\circ \]
  done clear
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• question_answer47)     Two point charges\[+36\mu C\]and\[-16\mu C\]are placed 10 cm apart. At a point\[X\], there is no resultant force on unit positive charge. The distance of\[X\]from\[+36\mu C\]charge is
  A)
   10cm                                   
  done clear
  B)
   20cm
  done clear
  C)
   30 cm                                  
  done clear
  D)
   35 cm
  done clear
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• question_answer48)     Five resistors are connected between points\[X\]and V as shown in the diagram. A current of 10 A flows in the network from\[X\]to\[Y\].
  A)
   The potential difference between X and Z is equal to that between Z and Y
  done clear
  B)
   The potential difference between X and Z is more than that between Z and Y
  done clear
  C)
   The potential difference between X and Z is less than that between Z and Y
  done clear
  D)
   The potential difference between Z and Y is 24V
  done clear
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• question_answer49)     The resistance of a galvanometer is\[25\,\Omega \], and it requires\[50\,\mu A\]for full deflection. The value of the shunt resistance required to convert it into an ammeter of 5 A is
  A)
   \[2.5\times {{10}^{-4}}\Omega \]           
  done clear
  B)
   \[1.25\times {{10}^{-3}}\Omega \]
  done clear
  C)
   \[0.05\,\Omega \]                         
  done clear
  D)
   \[2.5\,\Omega \]
  done clear
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• question_answer50)     In circuit shown in figure if both the bulbs\[{{B}_{1}}\]and\[{{B}_{2}}\]are identical
  A)
   their brightness will be same
  done clear
  B)
   \[{{B}_{1}}\]will be brighter than\[{{B}_{2}}\]
  done clear
  C)
   as frequency of supply voltage is increased, brightness of\[{{B}_{1}}\]will increase and that of\[{{B}_{2}}\]will decrease
  done clear
  D)
   only\[{{B}_{2}}\]will glow because the capacitor has infinite impedance
  done clear
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• question_answer51)     A certain radioactive substance has a half-life of 5 yr. Thus, for a nucleus in a sample of the element, the probability of decay in 10 yr is
  A)
   50%                                      
  done clear
  B)
   75%
  done clear
  C)
   100%                                   
  done clear
  D)
   60%
  done clear
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• question_answer52)     An\[L-C\]resonant circuit contains a 400 pF capacitor and a\[100\,\mu H\]inductor. It is set into oscillation coupled to an antenna. The wavelength of the radiated electromagnetic waves is
  A)
   377 mm                              
  done clear
  B)
   377 m
  done clear
  C)
   377cm                                 
  done clear
  D)
   3.77cm
  done clear
  View Answer play_arrow

• question_answer53)     The potential difference between the target and the cathode of an X-ray tube is 50 kV and the current in tube is 20 mA. Only 1% of the total energy supplied is emitted as X-radiation. What is the maximum frequency of the emitted radiation?
  A)
   \[1.2\times {{10}^{17}}Hz\]       
  done clear
  B)
   \[1.2\times {{10}^{19}}Hz\]
  done clear
  C)
   \[6\times {{10}^{15}}Hz\]           
  done clear
  D)
   \[2.4\times {{10}^{18}}Hz\]
  done clear
  View Answer play_arrow

• question_answer54)     In the depletion region of an unbiased\[p-n\] junction diode there are
  A)
   only electrons
  done clear
  B)
   only holes
  done clear
  C)
   both electrons and holes
  done clear
  D)
  only fixed ions
  done clear
  View Answer play_arrow

• question_answer55)     A particle of mass\[m=5\]is moving with a uniform speed\[v=3\sqrt{2}\]in the XOY plane along the line\[y=x+4\]. The magnitude of the angular momentum of the particle about the origin is
  A)
   7.5 unit               
  done clear
  B)
   60 unit
  done clear
  C)
   \[40\sqrt{2}\]unit          
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer56) An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of faces of the cube. The empirical formula of the compound would be
  A)
   AB                                        
  done clear
  B)
   \[{{A}_{2}}B\]
  done clear
  C)
   \[A{{B}_{3}}\]                                  
  done clear
  D)
   \[{{A}_{3}}B\]
  done clear
  View Answer play_arrow

• question_answer57)     Acetylene hydrocarbons are acidic because
  A)
   acetylene contains least number of hydrogen atoms
  done clear
  B)
   acetylene has only one hydrogen atom at each carbon atom
  done clear
  C)
   acetylene belongs to the class of alkynes with formula\[{{C}_{n}}{{H}_{2n-2}}\]
  done clear
  D)
   sigma electron density of\[C-H\]bond in acetylene is nearer a carbon which has 50% \[s-\]character
  done clear
  View Answer play_arrow

• question_answer58)     Which of the following does not contain \[-COOH\]group?
  A)
   Aspirin
  done clear
  B)
   Benzoic acid
  done clear
  C)
   Picric acid
  done clear
  D)
   All have \[-COOH\]group
  done clear
  View Answer play_arrow

• question_answer59)     Only an aldehyde having ... can undergoes the aldol condensation.
  A)
   at least one alpha H atom
  done clear
  B)
   at least one beta H atom
  done clear
  C)
   no alpha H atom
  done clear
  D)
   an aromatic ring
  done clear
  View Answer play_arrow

• question_answer60)     When sodium is added to ethanol,
  A)
   no action occurs
  done clear
  B)
  \[{{H}_{2}}\]is formed
  done clear
  C)
  \[NaO{{C}_{2}}{{H}_{5}}\]and\[{{O}_{2}}\]are formed
  done clear
  D)
   \[NaO{{C}_{2}}{{H}_{5}}\]and\[{{H}_{2}}\]are formed
  done clear
  View Answer play_arrow

• question_answer61)     The gold number of some colloidal solutions are given below

  Colloidal solution	Gold number
  A	0.01
  B	2.5
  C	20

  The protective nature of these colloidal solutions follows the order
  A)
   \[C>B>A\]         
  done clear
  B)
   \[~A>B>C\]
  done clear
  C)
   \[A=B=C\]         
  done clear
  D)
   \[B>A>C\]
  done clear
  View Answer play_arrow

• question_answer62)     The reaction of\[HBr\]with\[C{{H}_{3}}\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}\]in the presence of peroxide will give
  A)
   \[C{{H}_{3}}\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,BrC{{H}_{3}}\]             
  done clear
  B)
  \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}Br\]
  done clear
  C)
   \[C{{H}_{3}}\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{2}}Br\]          
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer63)     The alcohol manufactured from water gas is
  A)
   ethanol              
  done clear
  B)
   methanol
  done clear
  C)
   isobutanol         
  done clear
  D)
   butanol
  done clear
  View Answer play_arrow

• question_answer64)     The iodoform test is not given by
  A)
   \[C{{H}_{3}}\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{3}}\]    
  done clear
  B)
   \[C{{H}_{3}}\overset{\begin{smallmatrix}  O \\  |\,| \end{smallmatrix}}{\mathop{C}}\,C{{H}_{2}}C{{H}_{3}}\]
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}OH\]
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix}  O \\  |\,| \end{smallmatrix}}{\mathop{C}}\,C{{H}_{2}}C{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer65)     When 3,3-dimethyl-2-butanol is heated with \[{{H}_{2}}S{{O}_{4}},\]the major product obtained is
  A)
   2,2-dimethyl-l-butene
  done clear
  B)
   2,3-dimethyl-l-butene
  done clear
  C)
   2,3-dimethyl-2-butene
  done clear
  D)
  \[cis\]and trans isomers of 2,3-dimethyl-2- butane
  done clear
  View Answer play_arrow

• question_answer66)     The correct order of basicity of amines in water is
  A)
   \[{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N\]
  done clear
  B)
   \[C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N\]
  done clear
  C)
   \[{{(C{{H}_{3}})}_{3}}N>{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer67)     The number of nodes present in radial wave function of 3d orbital is
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   0                                            
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer68)     Which of the following has largest negative electron gain enthalpy?
  A)
   \[F\]                                    
  done clear
  B)
   \[Cl\]
  done clear
  C)
   \[Br\]                                  
  done clear
  D)
  \[I\]
  done clear
  View Answer play_arrow

• question_answer69)     Bromine belongs to period
  A)
   third                                    
  done clear
  B)
   fourth
  done clear
  C)
   fifth                                     
  done clear
  D)
   second
  done clear
  View Answer play_arrow

• question_answer70)     \[PC{{l}_{5}}\]molecule has the following geometry
  A)
   trigonal bipyramidal
  done clear
  B)
   octahedral.
  done clear
  C)
   square planar
  done clear
  D)
   planar triangular
  done clear
  View Answer play_arrow

• question_answer71)     In an octahedral structure, the pair of d-orbitals involved in\[{{d}^{2}}s{{p}^{3}}\]hybridisation is
  A)
   \[{{d}_{{{x}^{2}}-{{y}^{2}}}},{{d}_{xz}}\]                              
  done clear
  B)
   \[{{d}_{{{z}^{2}}}},{{d}_{zx}}\]
  done clear
  C)
   \[{{d}_{xy}},{{d}_{yz}}\]                              
  done clear
  D)
   \[{{d}_{{{x}^{2}}-{{y}^{2}}}},{{d}_{{{z}^{2}}}}\]
  done clear
  View Answer play_arrow

• question_answer72)     For the electrode reaction,\[{{M}^{n+}}(aq)+n{{e}^{-}}\xrightarrow[{}]{{}}M(s)\]Nernst equation is
  A)
   \[E=E{}^\circ +\frac{RT}{nF}\log \frac{1}{[{{M}^{n+}}]}\]
  done clear
  B)
   \[E{}^\circ =E+RT\,in\,[{{M}^{n+}}]\]
  done clear
  C)
   \[E=E{}^\circ -\frac{RT}{nF}\,in\frac{1}{\,[{{M}^{n+}}]}\]
  done clear
  D)
   \[\frac{E}{E{}^\circ }=\frac{RT}{nF}\,in[{{M}^{n+}}]\]
  done clear
  View Answer play_arrow

• question_answer73)     Two liquids A and B boil at\[145{}^\circ C\]and \[190{}^\circ C\] respectively. At\[80{}^\circ C\]which of them has higher vapour pressure?
  A)
   Liquid A
  done clear
  B)
   Liquid B
  done clear
  C)
   Both have equal vapour pressure
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer74)     What is the effect of carbon dioxide in water on corrosion?
  A)
   Increase rusting of iron
  done clear
  B)
   Decrease rusting of iron
  done clear
  C)
   Does not affect
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer75)     Delocalised electrons are present in
  A)
   1,3-butadiene                 
  done clear
  B)
   \[{{C}_{6}}{{H}_{6}}\]
  done clear
  C)
   1,3,5-hexatriene            
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer76)     The chemical name of isoprene is
  A)
   2-methyl-1,3-butadiene
  done clear
  B)
   2-chloro-1,3-butadiene
  done clear
  C)
   2-methoxypropene
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer77)     Assertion/Reason Type Question  Answer Codes (i) Both Assertion  and Reason (R) are correct and (R) is the correct explanation of (ii) Both  and (R) are correct but (R) is not the correct explanation of (iii)  is correct but (R) is incorrect (iv)  is incorrect but (R) is correct Assertion  Methyl cyanide on reaction with\[LiAl{{H}_{4}}\]does not form ethyl amine. Reason (R) Acidic hydrolysis, of JRCN forms\[RCOOH\].
  A)
   (i)                                          
  done clear
  B)
   (ii)
  done clear
  C)
   (iii)                        
  done clear
  D)
   (iv)
  done clear
  View Answer play_arrow

• question_answer78)     The Birch reduction of toluene gives
  A)
     
  done clear
  B)
   
  done clear
  C)
    
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer79)     Given below is the sketch of a plant for carrying out a process. Name the process occurring in the above plant.
  A)
   Reverse osmosis            
  done clear
  B)
   Osmosis
  done clear
  C)
   Diffusion            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer80)     In a reaction between A and B, the initial rate of reaction\[({{r}_{o}})\]was measured for different initial concentrations of A and B as given below

  \[A/mol\,{{L}^{-1}}\]	0.20	0.20	0.40
  \[B/mol\,{{L}^{-1}}\]	0.30	0.10	0.05
  \[{{r}_{0}}/\]\[mol\,{{L}^{-1}}{{s}^{-1}}\]	\[5.07\times {{10}^{-5}}\]	\[5.07\times {{10}^{-5}}\]	\[1.43\times {{10}^{-4}}\]

  What is the order of the reaction with respect to A and B?
  A)
   2.5, 1.0                
  done clear
  B)
   1.5,0
  done clear
  C)
   2.5,0                                    
  done clear
  D)
   1.5, 1
  done clear
  View Answer play_arrow

• question_answer81)     The most stable conformation of 1,2-diphenyl ethane is
  A)
   
  done clear
  B)
   
  done clear
  C)
                       
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer82)     According to nuclear reaction,\[_{4}Be+_{2}^{4}He\xrightarrow[{}]{{}}_{6}^{12}C+_{0}^{1}n,\]the mass number of Be atom is
  A)
   4                                            
  done clear
  B)
   8
  done clear
  C)
   6                                            
  done clear
  D)
   9
  done clear
  View Answer play_arrow

• question_answer83)     Formula of asbestos is
  A)
   \[{{[M{{g}_{3}}S{{i}_{4}}{{O}_{10}}{{(OH)}_{2}}]}_{n}}\]
  done clear
  B)
   \[C{{a}_{2}}M{{g}_{5}}{{(S{{i}_{4}}{{O}_{11}})}_{2}}{{(OH)}_{2}}\]
  done clear
  C)
   \[CaMg{{(Si{{O}_{3}})}_{2}}\]
  done clear
  D)
   \[C{{a}_{3}}S{{i}_{3}}{{O}_{9}}\]
  done clear
  View Answer play_arrow

• question_answer84)     Which of the following resonating structures is not correct for\[C{{O}_{2}}\]?
  A)
   \[\overset{\bullet \,\,\bullet }{\mathop{{}_{\bullet }^{\bullet }O}}\,=C=\overset{\bullet \,\bullet }{\mathop{O_{\bullet }^{\bullet }}}\,\] 
  done clear
  B)
   \[\underset{\bullet \,\,\,\bullet }{\mathop{^{-}\overset{\bullet \,\,\bullet }{\mathop{{}_{\bullet }^{\bullet }O}}\,}}\,=C=\overset{+}{\mathop{O_{\bullet }^{\bullet }}}\,\]
  done clear
  C)
   \[\underset{\,\,\,\,\,\,\bullet \,\,\bullet }{\mathop{\overset{+}{\mathop{{}_{\bullet }^{\bullet }O}}\,}}\,-C\equiv \underset{\bullet \,\bullet }{\mathop{O{{_{\bullet }^{\bullet }}^{-}}}}\,\]            
  done clear
  D)
   \[\overset{+}{\mathop{{}_{\bullet }^{\bullet }O}}\,\equiv C-\overset{\bullet \,\bullet }{\mathop{\underset{\bullet \,\bullet }{\mathop{O{{_{\bullet }^{\bullet }}^{-}}}}\,}}\,\]
  done clear
  View Answer play_arrow

• question_answer85)     At\[25{}^\circ C,\]3 g of a solute A in 100 mi/of an aqueous solution gave an osmotic pressure of 2.5 atmosphere. What is the molar mas5 of solute?
  A)
   293
  done clear
  B)
   239
  done clear
  C)
   392                                       
  done clear
  D)
   932
  done clear
  View Answer play_arrow

• question_answer86)     The correct IUPAC name of\[C{{H}_{3}}C{{H}_{2}}CH(C{{H}_{3}})CH{{({{C}_{2}}{{H}_{5}})}_{2}}\]is
  A)
   4-ethyl-3-methylhexane
  done clear
  B)
   3-ethyl-4-metbylhexane
  done clear
  C)
   3-methy-4-ethyihexane
  done clear
  D)
   3-iso-pentylpropane
  done clear
  View Answer play_arrow

• question_answer87)                                     Reduction of carbonyl compounds to alkanes with\[N{{H}_{2}}N{{H}_{2}}\]and\[NaOH\]is called
  A)
   Ponndrof verley reduction
  done clear
  B)
   Clemmensens reduction
  done clear
  C)
   Wurtz reaction                       
  done clear
  D)
   Wolff-Kishner reduction
  done clear
  View Answer play_arrow

• question_answer88)     General formula of alkynes is
  A)
   \[{{C}_{n}}{{H}_{2n}}\]                
  done clear
  B)
   \[{{C}_{n}}{{H}_{2n+2}}\]
  done clear
  C)
   \[{{C}_{2n+2}}{{H}_{n}}\]                           
  done clear
  D)
   \[{{C}_{n}}{{H}_{2n-2}}\]
  done clear
  View Answer play_arrow

• question_answer89)     Alkaline\[KMn{{O}_{4}}\]oxidises acetylene to
  A)
   acetic acid         
  done clear
  B)
   ethyl alcohol
  done clear
  C)
   ethylene glycol               
  done clear
  D)
   oxalic acid
  done clear
  View Answer play_arrow

• question_answer90)     Dehydration of alcohol is an example of
  A)
   redox reaction
  done clear
  B)
   elimination reaction
  done clear
  C)
   substitution reaction
  done clear
  D)
   addition reaction
  done clear
  View Answer play_arrow

• question_answer91)     Gun metal is
  A)
   \[Cu,Zn,Sn\]                     
  done clear
  B)
   \[Cu,Zn,Ni\]
  done clear
  C)
   \[Cu,Zn,P\]                       
  done clear
  D)
   \[C,N,Fe\]
  done clear
  View Answer play_arrow

• question_answer92)     How many moles of nitrogen are needed to produce 8.2 moles of ammonia by reaction with hydrogen?
  A)
   2.1                                        
  done clear
  B)
   3.1
  done clear
  C)
   3.2                                        
  done clear
  D)
   4.1
  done clear
  View Answer play_arrow

• question_answer93)     The temperature of a gas in a closed container is\[27{}^\circ C\]. If the temperature is raised to\[327{}^\circ C,\]the pressure exerted is
  A)
   reduced to half
  done clear
  B)
   doubled
  done clear
  C)
   reduced to one third
  done clear
  D)
   cannot be predicted
  done clear
  View Answer play_arrow

• question_answer94)     Molar heat capacity of ethanol is\[110.4\text{ }J{{K}^{-1}}\]. Its specific heat capacity is
  A)
   2.4                                        
  done clear
  B)
   55.2
  done clear
  C)
   5.078                                   
  done clear
  D)
   110.4
  done clear
  View Answer play_arrow

• question_answer95)     For the water gas reaction,\[C(s)+{{H}_{2}}O(g)CO(g)+{{H}_{2}}O(g)\]the standard Gibbs energy at 1000 K is\[-8.1\text{ }kJ\,mo{{l}^{-1}}\]. What is its equilibrium constant?
  A)
   2.60                                      
  done clear
  B)
   4.62
  done clear
  C)
   2.64                                      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer96)     For the reaction,\[2NO(g)+C{{l}_{2}}(g)2NOCl(g)\]which is true?                 
  A)
   \[{{K}_{p}}={{K}_{C}}\times RT\]             
  done clear
  B)
   \[{{K}_{p}}={{K}_{C}}{{(RT)}^{2}}\]
  done clear
  C)
   \[{{K}_{p}}=\frac{{{K}_{C}}}{RT}\]                           
  done clear
  D)
   \[{{K}_{p}}=\frac{{{K}_{C}}}{{{(RT)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer97)     Oxidation number of\[Mn\]in\[MnO_{4}^{-}\]ion is
  A)
   \[+1\]                                  
  done clear
  B)
   \[-7\]
  done clear
  C)
   \[-1\]                                   
  done clear
  D)
   \[+7\]
  done clear
  View Answer play_arrow

• question_answer98)     Which of the following is not alkali metal?
  A)
  \[Na\]                                  
  done clear
  B)
  \[Fr\]
  done clear
  C)
  \[Ca\]                                   
  done clear
  D)
  \[K\]
  done clear
  View Answer play_arrow

• question_answer99)     Inert pair effect is predominant in
  A)
  \[~Si\]                                  
  done clear
  B)
  \[Pb\]
  done clear
  C)
  \[Ge\]                                  
  done clear
  D)
  \[Sn\]   
  done clear
  View Answer play_arrow

• question_answer100)     How many o and n bonds are there in the molecule of tetracyanoethene? \[{{(NC)}_{2}}C=C{{(CN)}_{2}}\]
  A)
   \[9\sigma ,7\pi \]                           
  done clear
  B)
   \[5\sigma ,9\pi \]
  done clear
  C)
   \[5\sigma ,8\pi \]                           
  done clear
  D)
   \[9\sigma ,9\pi \]
  done clear
  View Answer play_arrow

• question_answer101)     Baeyers reagent is
  A)
   aqueous \[KMn{{O}_{4}}\]
  done clear
  B)
   neutral\[KMn{{O}_{4}}\]
  done clear
  C)
   alkaline\[KMn{{O}_{4}}\]
  done clear
  D)
   aqueous bromine water
  done clear
  View Answer play_arrow

• question_answer102)     Percentage of lead in lead pencile is
  A)
   zero                                     
  done clear
  B)
   20
  done clear
  C)
   80                                         
  done clear
  D)
   60
  done clear
  View Answer play_arrow

• question_answer103)     Low spin complex is formed by
  A)
  \[s{{p}^{3}}{{d}^{2}}\]hybridization
  done clear
  B)
  \[s{{p}^{3}}d\]hybridization
  done clear
  C)
  \[{{d}^{2}}s{{p}^{3}}\]hybridization
  done clear
  D)
  \[s{{p}^{3}}\]hybridization
  done clear
  View Answer play_arrow

• question_answer104)     Hybrid state of central oxygen atom in ether is
  A)
   \[sp\]                                  
  done clear
  B)
   \[s{{p}^{2}}\]
  done clear
  C)
   \[s{{p}^{3}}d\]                                
  done clear
  D)
   \[s{{p}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer105)     Clemmensen reduction of a ketone is carried out in the presence of
  A)
   \[LiAl{{H}_{4}}\]in ether
  done clear
  B)
   \[Zn-Hg\]with\[HCl\]
  done clear
  C)
   glycol with \[KOH\]
  done clear
  D)
  \[{{H}_{2}}\]with\[Pd\]as catalyst
  done clear
  View Answer play_arrow

• question_answer106)     The electrophile involved in the nitration of benzene is
  A)
  \[NO\]                                 
  done clear
  B)
   \[NO_{2}^{-}\]
  done clear
  C)
  \[N{{O}_{2}}\]                                  
  done clear
  D)
   \[NO_{2}^{+}\]
  done clear
  View Answer play_arrow

• question_answer107)     In the reaction,\[{{C}_{6}}{{H}_{5}}-{{N}^{+}}\equiv NC{{l}^{-}}+{{H}_{3}}P{{O}_{2}}+{{H}_{2}}O\xrightarrow[{}]{{}}?\]the product formed will be
  A)
   \[{{C}_{6}}{{H}_{5}}OH\]                             
  done clear
  B)
   \[{{C}_{6}}{{H}_{6}}\]
  done clear
  C)
   \[{{C}_{6}}{{H}_{5}}Cl\]
  done clear
  D)
   \[{{C}_{6}}{{H}_{5}}-{{C}_{6}}{{H}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer108)     Amylopectin is a polymer of
  A)
   \[\beta -D-\]glucose
  done clear
  B)
   \[\alpha -D-\]glucose
  done clear
  C)
   \[\beta -D-\]fructose
  done clear
  D)
  \[\alpha -D-\]mannose
  done clear
  View Answer play_arrow

• question_answer109)     Across the lanthanide series, the basicity of the lanthanide hydroxides
  A)
   increases
  done clear
  B)
   decreases
  done clear
  C)
   first increases and then decreases
  done clear
  D)
   first decreases and then increases
  done clear
  View Answer play_arrow

• question_answer110)     When sodium and chlorine ion react, energy is
  A)
   released and ionic bonds are formed
  done clear
  B)
   released and covalent bonds are formed
  done clear
  C)
   absorbed and ionic bonds are formed
  done clear
  D)
   absorbed and covalent bonds are formed
  done clear
  View Answer play_arrow

• question_answer111) The value of\[\sum\limits_{k=1}^{6}{\left( \sin \frac{2\pi k}{7}-i\cos \frac{2\pi k}{7} \right)}\]is
  A)
                                         
  done clear
  B)
   \[-i\]
  done clear
  C)
   1                                            
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer112)     If\[{{a}_{n}}\]be the nth term of an AP and if\[{{a}_{7}}=15,\]then the value of the common difference that would make\[{{a}_{2}}{{a}_{7}}{{a}_{12}}\]greatest is
  A)
   9                                            
  done clear
  B)
   9/4
  done clear
  C)
   0                                            
  done clear
  D)
   18
  done clear
  View Answer play_arrow

• question_answer113)     If\[{{a}_{1}},{{a}_{2}},{{a}_{3}},...,{{a}_{n}}\]are in AP, where\[{{a}_{i}}>0\]for all\[i\], then value of the expression \[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+.....\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}\]
  A)
   \[\frac{n-1}{\sqrt{{{a}_{n}}}-\sqrt{{{a}_{1}}}}\]                
  done clear
  B)
   \[\frac{n-1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\]
  done clear
  C)
   \[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer114)     If one root of\[{{x}^{2}}-x-k=0\]is square of the other, then k is equal to
  A)
   \[2\pm \sqrt{3}\]          
  done clear
  B)
   \[3\pm \sqrt{2}\]
  done clear
  C)
   \[2\pm \sqrt{5}\]                           
  done clear
  D)
   \[5\pm \sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer115)     The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is
  A)
   27378                                  
  done clear
  B)
   27405
  done clear
  C)
   27399                                  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer116)     The coefficient of\[{{x}^{n}}\]in the expansion of \[{{(1-4x)}^{-1/2}}\]is
  A)
   \[\frac{(2n)!}{{{(n!)}^{2}}}\]                      
  done clear
  B)
   \[\frac{2n}{{{(n!)}^{2}}}\]
  done clear
  C)
   \[\frac{(2n)!}{{{n}^{2}}}\]                           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer117)     Let A and B be symmetric matrices of the same order, then
  A)
  \[A+B\]is symmetric matrix
  done clear
  B)
  \[AB-BA\]is skew symmetric matrix
  done clear
  C)
  \[AB+BA\]is symmetric matrix
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer118)     If\[\alpha ,\beta ,\gamma \]are the roots of\[{{x}^{3}}+a{{x}^{2}}+b=0,\]then  the value of\[\left| \begin{matrix}    \alpha  & \beta  & \gamma   \\    \beta  & \gamma  & \alpha   \\    \gamma  & \alpha  & \beta   \\ \end{matrix} \right|\]is
  A)
   \[-{{a}^{3}}\]                                    
  done clear
  B)
   \[{{a}^{3}}-3b\]
  done clear
  C)
   \[{{a}^{3}}\]                                     
  done clear
  D)
   \[{{a}^{2}}-3b\]
  done clear
  View Answer play_arrow

• question_answer119)     If the axes are shifted to the point\[(1,-2)\]without     rotation     the     equation \[2{{x}^{2}}+{{y}^{2}}-4x+4y=0\]becomes
  A)
   \[2{{X}^{2}}+{{Y}^{2}}=6\]
  done clear
  B)
   \[2{{X}^{2}}+{{Y}^{2}}+6=0\]
  done clear
  C)
   \[{{X}^{2}}+2{{Y}^{2}}=6\]
  done clear
  D)
   \[2{{X}^{2}}+{{Y}^{2}}=0\]
  done clear
  View Answer play_arrow

• question_answer120)     The lines represented by the equation \[A{{x}^{2}}+2Bxy+H{{y}^{2}}=0\]are perpendicular, if
  A)
   \[A+B=0\]         
  done clear
  B)
   \[B+H=0\]
  done clear
  C)
   \[A+H=0\]         
  done clear
  D)
   \[AH=-1\]
  done clear
  View Answer play_arrow

• question_answer121)     The number of common tangents to the circles \[{{x}^{2}}+{{(y-1)}^{2}}=9\]and\[{{(x-1)}^{2}}+{{y}^{2}}=25\]is
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   2                                            
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer122)     The length of focal chord which makes an angle \[\alpha \]with the axis. of the parabola\[{{y}^{2}}=4ax\]is
  A)
   \[2a\text{ }co{{t}^{2}}\alpha \]                
  done clear
  B)
   \[4a\text{ }cose{{c}^{2}}\alpha \]
  done clear
  C)
   \[4a\text{ }cot\,\alpha \]            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer123)     The point of intersection of the tangents at two points on the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]whose eccentric angles differ by a right angle lies on the ellipse
  A)
   \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=2\]                         
  done clear
  B)
   \[\frac{{{x}^{2}}}{{{b}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}}=1\]
  done clear
  C)
   \[\frac{{{x}^{2}}}{{{b}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}}=2\]                         
  done clear
  D)
   \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=4\]
  done clear
  View Answer play_arrow

• question_answer124)     If the normal at\[\left( ct,\frac{c}{t} \right)\]on the curve\[xy={{c}^{2}}\]meets the curve again in t, then
  A)
   \[t=-\frac{1}{{{t}^{3}}}\]                             
  done clear
  B)
   \[t=-\frac{1}{t}\]
  done clear
  C)
   \[t=\frac{1}{{{t}^{2}}}\]                               
  done clear
  D)
   \[t{{}^{2}}=-\frac{1}{{{t}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer125)     If\[f(x)=\left\{ \begin{matrix}    \frac{|x-4|}{x-4}, & x\ne 4  \\    0, & x=4  \\ \end{matrix} \right.\]then\[\underset{x\to 4}{\mathop{\lim }}\,f(x)\]is equal to
  A)
   1                                            
  done clear
  B)
  \[-1\]
  done clear
  C)
   0                                            
  done clear
  D)
   does not exist
  done clear
  View Answer play_arrow

• question_answer126)     The equation\[\left| \begin{matrix}    x-a & x-b & x-c  \\    x-b & x-c & x-a  \\    x-c & x-a & x-b  \\ \end{matrix} \right|=0\]where a, b, c are different is satisfied by
  A)
   \[x=0\]               
  done clear
  B)
   \[x=a\]
  done clear
  C)
   \[x=\frac{1}{3}(a+b+c)\]             
  done clear
  D)
   \[x=a+b+c\]
  done clear
  View Answer play_arrow

• question_answer127)     The function\[f(x)=\left\{ \begin{matrix}    x & for & x<1  \\    2-x & for & 1\le x\le 2  \\    -2+3x-{{x}^{2}} & for & x>2  \\ \end{matrix} \right.\]is differentiable
  A)
   at\[x=2\]and at\[x=1\]
  done clear
  B)
   at\[x=2\]but not at\[x=1\]
  done clear
  C)
   at\[x=1\]but not at\[x=2\]
  done clear
  D)
   neither at\[x=2\]nor at\[x=1\]
  done clear
  View Answer play_arrow

• question_answer128)     Find the points on the curve\[y={{x}^{3}}-2{{x}^{2}}-x\] at which the tangent lines are parallel to the line\[y~=3x-2\]
  A)
   \[(2,2),\left( -\frac{2}{3},-\frac{14}{27} \right)\]
  done clear
  B)
   \[(2,-2),\left( -\frac{2}{3},-\frac{14}{37} \right)\]
  done clear
  C)
   \[(2,-2),\left( -\frac{2}{3},-\frac{14}{27} \right)\]
  done clear
  D)
   None of the above:
  done clear
  View Answer play_arrow

• question_answer129)     If\[f\]and g are two increasing functions such that fog is denned, then
  A)
   fog is an increasing function
  done clear
  B)
   fog is a decreasing function
  done clear
  C)
   fog is neither increasing nor decreasing
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer130)     The value of the integral\[\int{\frac{2x\,dx}{({{x}^{2}}+1)({{x}^{2}}+2)}}\]is
  A)
   \[\log |{{x}^{2}}+1|+\log |{{x}^{2}}+2|+c\]
  done clear
  B)
   \[-[\log |{{x}^{2}}+1|+\log |{{x}^{2}}+2|+c\]
  done clear
  C)
   \[\log |{{x}^{2}}+1|-\log |{{x}^{2}}+2|+c\]
  done clear
  D)
   \[\log |{{x}^{2}}+2|-\log |{{x}^{2}}+1|+c\]
  done clear
  View Answer play_arrow

• question_answer131)     The area of the figure bounded by the curves \[y=|x-1|\]is\[y=3|x|\]
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   3                                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer132)     If the unit vectors\[\overrightarrow{a}\]and\[\overrightarrow{b}\]are inclined at an angle\[2\theta \]such that\[|\overrightarrow{a}-\overrightarrow{b}|<1\]and\[0\le \theta k,\pi \]then \[\theta \]lies in the interval
  A)
   \[\left[ 0,\frac{\pi }{6} \right)\]                
  done clear
  B)
   \[\left( \frac{5\pi }{6},\pi  \right]\]
  done clear
  C)
   Both  and           
  done clear
  D)
   Neither (a) nor (b)
  done clear
  View Answer play_arrow

• question_answer133)     The plane\[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\]meets the coordinate axes at A, B and C respectively, find the equation of the sphere OABC
  A)
  \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+ax+by+cz=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-ax-by-cz=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+ax-by+cz=0\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer134)     A bag contains 16 coins of which two are counterfeit with heads on both sides. The rest are fair coins. One coin is selected at random from the bag and tossed. The probability of getting a head is
  A)
   \[\frac{9}{16}\]                               
  done clear
  B)
   \[\frac{11}{16}\]
  done clear
  C)
   \[\frac{5}{9}\]                                  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer135)     The value of\[\sqrt{3}\cot 20{}^\circ -4\cos 20{}^\circ \]is equal to
  A)
   1                                            
  done clear
  B)
  \[-1\]
  done clear
  C)
   0                                            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer136)     If\[sin\text{ }x+cosec\text{ }x=2,\]then\[{{\sin }^{n}}x+\cos e{{c}^{n}}x\]is equal to
  A)
   2                                            
  done clear
  B)
   \[{{2}^{n}}\]
  done clear
  C)
   \[{{2}^{n-1}}\]                                 
  done clear
  D)
   \[{{2}^{n-2}}\]
  done clear
  View Answer play_arrow

• question_answer137)     The number of solutions of the equation tan \[x+sec\text{ }x=2\text{ }cos\text{ }x,\]lying in the interval \[[0,2\pi ]\]is
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   2                                            
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer138)     The arithmetic mean of a set of observations is \[\overline{X}\]. If each observation is divided by a and then is increased by 10, then the mean of the new series is
  A)
   \[\frac{\overline{X}}{\alpha }\]                                
  done clear
  B)
   \[\frac{\overline{X}+10}{\alpha }\]
  done clear
  C)
   \[\frac{\overline{X}+10\,\alpha }{\alpha }\]                       
  done clear
  D)
   \[\alpha \overline{X}+10\]
  done clear
  View Answer play_arrow

• question_answer139)     If\[x\]and y are two uncorrelated variables and if \[u=x+y,v=x-y,\]then\[r(u,v)\]is equal to
  A)
   \[\frac{\sigma _{x}^{2}+\sigma _{y}^{2}}{\sigma _{x}^{2}-\sigma _{y}^{2}}\]
  done clear
  B)
   \[\frac{\sigma _{x}^{2}-\sigma _{y}^{2}}{\sigma _{x}^{2}+\sigma _{y}^{2}}\]
  done clear
  C)
   \[\frac{\sigma _{x}^{2}+\sigma _{y}^{2}}{{{\sigma }_{x}}{{\sigma }_{y}}}\]                          
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer140)     If\[u\]and\[v\]be the components of the resultant velocity w of a particle such that\[u=v=w,\]then the angle between the velocities is
  A)
   \[60{}^\circ \]                                  
  done clear
  B)
  \[150{}^\circ \]
  done clear
  C)
   \[120{}^\circ \]                                
  done clear
  D)
   \[30{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer141)     \[\left\{ \frac{1+\cos \frac{\pi }{8}+i\sin \frac{\pi }{8}}{1+\cos \frac{\pi }{8}-i\sin \frac{\pi }{8}} \right\}\]is equal to
  A)
   \[1+i\]                                 
  done clear
  B)
  \[1-i\]
  done clear
  C)
   1                                            
  done clear
  D)
   \[-1\]
  done clear
  View Answer play_arrow

• question_answer142)     The arithmetic mean of two positive numbers and\[b(a>b)\]is twice their geometric mean, then\[a:b\]is
  A)
   \[2+\sqrt{3}:2-\sqrt{3}\]             
  done clear
  B)
   \[7+4\sqrt{3}:7-4\sqrt{3}\]
  done clear
  C)
   \[2:7+4\sqrt{3}\]                            
  done clear
  D)
   \[2\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer143)     Given that tan A and tan B are the roots of the equation\[{{x}^{2}}-px+q=0,\]the value of \[{{\sin }^{2}}(A+B)\]is
  A)
   \[\frac{{{p}^{2}}}{{{p}^{2}}+{{(1-q)}^{2}}}\]       
  done clear
  B)
   \[\frac{{{p}^{2}}}{{{p}^{2}}+{{q}^{2}}}\]
  done clear
  C)
   \[\frac{{{q}^{2}}}{{{p}^{2}}+{{(1-q)}^{2}}}\]       
  done clear
  D)
   \[\frac{{{p}^{2}}}{{{(p+q)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer144)     How many four letter words can be formed using the letters of the word FAILURE, so that F is included in each word?
  A)
   400                                       
  done clear
  B)
   420
  done clear
  C)
   460                                       
  done clear
  D)
   480
  done clear
  View Answer play_arrow

• question_answer145)     Find the coefficient of\[{{x}^{4}}\]in the expansion of
  A)
   4                                            
  done clear
  B)
   8
  done clear
  C)
   12                                         
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer146)     If A is a skew symmetric matrix, then the matrix \[{{B}^{T}}AB\]is
  A)
   symmetric         
  done clear
  B)
   skew symmetric
  done clear
  C)
   cant say              
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer147)     If the lines\[x+2ay+a=0,\text{ }x+3by+b=0\]and \[x+4cy+c=0\]are concurrent, then a, b, c are in
  A)
   AP                                        
  done clear
  B)
   GP
  done clear
  C)
   HP                                        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer148)     The distance between the parallel lines represented      by      the      equation \[{{x}^{2}}+6xy+9{{y}^{2}}+4x+12y-5=0\]is
  A)
   \[\frac{6}{5}\]                                  
  done clear
  B)
   \[\frac{6}{\sqrt{10}}\]
  done clear
  C)
   \[\frac{6}{\sqrt{5}}\]                                    
  done clear
  D)
   \[\frac{3}{2}\]
  done clear
  View Answer play_arrow

• question_answer149)     If the lengths of the tangents from the point (1,2) to the circles\[{{x}^{2}}+{{y}^{2}}+x+y-4=0\]and                  \[3{{x}^{2}}+3{{y}^{2}}-x-y-\lambda =0\]are in the ratio\[4:3,\]then the value of\[\lambda \]is
  A)
   \[\frac{21}{2}\]                               
  done clear
  B)
   \[\frac{21}{4}\]
  done clear
  C)
   \[\frac{21}{5}\]                               
  done clear
  D)
   \[\frac{21}{11}\]
  done clear
  View Answer play_arrow

• question_answer150)     If M is the foot of the perpendicular from a point P oh a parabola to its directrix and SPM is an equilateral triangle, where\[S\]is the focus, then PM is equal to
  A)
   \[a\]                                    
  done clear
  B)
   \[2a\]
  done clear
  C)
   \[3a\]                                  
  done clear
  D)
   \[4a\]
  done clear
  View Answer play_arrow

• question_answer151)     The equations of tangents to the ellipse \[9{{x}^{2}}+16{{y}^{2}}=144\]which pass through the point \[(2,3)\]are
  A)
   \[y=3,y=x+5\]  
  done clear
  B)
   \[y=3,x=3\]
  done clear
  C)
   \[x=2,\text{ }y=x+5\]   
  done clear
  D)
   \[y=3,\text{ }y=-x+5\]
  done clear
  View Answer play_arrow

• question_answer152)     Let                                                                                                                           and\[e\]be the eccentricities of a hyperbola and its conjugate, then\[\frac{1}{{{e}^{2}}}+\frac{1}{e{{}^{2}}}\]is equal to
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   2                                            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer153)     If\[f(x)\]is an even differentiable function on R, then\[f(x)\]is
  A)
   an even function
  done clear
  B)
   an odd function
  done clear
  C)
   cant say
  done clear
  D)
   cant be determined
  done clear
  View Answer play_arrow

• question_answer154)     The inverse of the function\[f(x)=\frac{{{10}^{x}}-{{10}^{-x}}}{{{10}^{x}}+{{10}^{-x}}}\]is
  A)
   \[{{\log }_{10}}(2-x)\]                   
  done clear
  B)
   \[\frac{1}{2}{{\log }_{10}}\left( \frac{1+x}{1-x} \right)\]
  done clear
  C)
   \[\frac{1}{2}{{\log }_{10}}(2x-1)\]           
  done clear
  D)
   \[\frac{1}{4}{{\log }_{10}}\left( \frac{2x}{2-x} \right)\]
  done clear
  View Answer play_arrow

• question_answer155)     The value of the\[\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}}\]is equal to
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   \[e\]                                    
  done clear
  D)
   \[{{e}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer156)     If\[f(x)={{e}^{x}}g(x),g(0)=2,g(0)=1,\]then\[f(0)\]is equal to
  A)
   1                                            
  done clear
  B)
   3
  done clear
  C)
   2                                            
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer157)     The slope of the tangent to the curve \[x={{t}^{2}}+3t-8,\text{ }y=2{{t}^{2}}-2t-5\]at the point \[(2,-1)\]is
  A)
   \[\frac{22}{7}\]                               
  done clear
  B)
   \[\frac{6}{7}\]
  done clear
  C)
   \[-\frac{6}{7}\]                                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer158)     The function\[f(x)={{\cot }^{-1}}x+x\]increases in the interval
  A)
   \[(1,\infty )\]                                   
  done clear
  B)
   \[(-1,\infty )\]
  done clear
  C)
   \[(-\infty ,\infty )\]                        
  done clear
  D)
   \[(0,\infty )\]
  done clear
  View Answer play_arrow

• question_answer159)     The  maximum  slope  of the  curve \[y=-{{x}^{3}}+3{{x}^{2}}+2x-27\]is
  A)
   5                                            
  done clear
  B)
   \[-5\]
  done clear
  C)
   \[\frac{1}{5}\]                                  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer160)     The integral\[\int{{{\sin }^{3}}x}{{\cos }^{3}}x\,dx\]is equal to
  A)
   \[\frac{1}{32}\left[ -\frac{3}{2}\cos 2x+\frac{1}{6}\cos 6x \right]+c\]
  done clear
  B)
   \[\frac{1}{32}\left[ -\frac{3}{2}\sin 2x+\frac{1}{6}\sin 6x \right]+c\]
  done clear
  C)
   \[-\frac{1}{32}\left[ -\frac{3}{2}\cos 2x+\frac{1}{6}\sin 6x \right]+c\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer161)     The value of\[\int{\frac{{{e}^{x}}\,dx}{\sqrt{5-4{{e}^{x}}-{{e}^{2x}}}}}\]is equal to
  A)
   \[{{\tan }^{-1}}\left( \frac{{{e}^{x}}+2}{3} \right)+c\]
  done clear
  B)
   \[{{\sin }^{-1}}\left( \frac{{{e}^{x}}+2}{3} \right)+c\]
  done clear
  C)
   \[{{\cos }^{-1}}\left( \frac{{{e}^{x}}+2}{3} \right)+c\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer162)     \[\int_{0}^{1}{\frac{({{x}^{\alpha }}-1)dx}{\log x}}\]equals
  A)
   \[\frac{1}{\alpha +1}\]                 
  done clear
  B)
   \[\frac{1}{\alpha -1}\]
  done clear
  C)
   \[\alpha -1\]                                     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer163)     Solution of\[{{e}^{(dy/dx)}}=x+1;y(0)=5\]is
  A)
  \[y=x\text{ }log(x+1)-x-log(x+1)+5\]
  done clear
  B)
  \[y=x\text{ }log(x+1)+x+log(x+1)+5\]
  done clear
  C)
   \[y=x\text{ }log(x+1)-x+log(x+1)+5\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer164)     For any vector\[\overrightarrow{a},|\overrightarrow{a}\times \hat{i}{{|}^{2}}+|\overrightarrow{a}\times \hat{j}{{|}^{2}}+|\overrightarrow{a}\times \hat{k}{{|}^{2}}\]is equal to
  A)
   \[|\overrightarrow{a}{{|}^{2}}\]                                             
  done clear
  B)
   \[2|\overrightarrow{a}{{|}^{2}}\]
  done clear
  C)
   \[3|\overrightarrow{a}{{|}^{2}}\]                          
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer165)     The shortest distance between the lines \[\overrightarrow{r}=(4\hat{i}-\hat{j})+\lambda (\hat{i}+2\hat{j}-3\hat{k})\]and \[\overrightarrow{r}=(\hat{i}-\hat{j}+2\hat{k})+\mu (2\hat{i}+4\hat{j}-5\hat{k})\]is equal to
  A)
   \[\frac{6}{\sqrt{10}}\]                  
  done clear
  B)
   \[\frac{6}{\sqrt{5}}\]
  done clear
  C)
   \[\frac{6}{5}\]                                  
  done clear
  D)
   \[\frac{3}{5}\]
  done clear
  View Answer play_arrow

• question_answer166)     If A and B are two independent events such that\[P(\overline{A}\cap B)=\frac{2}{15}\]and\[P(A\cap \overline{B})=\frac{1}{6},\]then P is
  A)
   \[\frac{1}{5}\]                                  
  done clear
  B)
   \[\frac{5}{6}\]
  done clear
  C)
   \[\frac{4}{5}\]                                  
  done clear
  D)
   \[\frac{7}{6}\]
  done clear
  View Answer play_arrow

• question_answer167)     Maximum and minimum values of\[6\text{ }sin\text{ }x\text{ }cos\text{ }x+4\text{ }cos\text{ }2x\]are respectively
  A)
   5 and\[-5\]
  done clear
  B)
  \[2\sqrt{13}\]and\[-2\sqrt{13}\]
  done clear
  C)
   10 and\[-10\]                   
  done clear
  D)
   \[\frac{5}{2}\]and\[-\frac{5}{2}\]
  done clear
  View Answer play_arrow

• question_answer168)     In a\[\Delta ABC,\]if \[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\]and the side\[a=2,\]then area of the triangle is
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   \[\frac{\sqrt{3}}{2}\]                                    
  done clear
  D)
   \[\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer169)     The equation\[{{\sin }^{-1}}x-{{\cos }^{-1}}x={{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]has
  A)
   no solution
  done clear
  B)
   unique solution
  done clear
  C)
   infinite number of solutions
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer170)     A tower subtends an angle a at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b ft just above A is P. Then, height of the tower is
  A)
   \[b\text{ }tan\text{ }\alpha \text{ }cot\text{ }\beta \]                  
  done clear
  B)
   \[b~cot\text{ }\alpha \text{ }tan\text{ }\beta \]
  done clear
  C)
   \[b\text{ }tan\text{ }\alpha \text{ }tan\text{ }\beta \]                  
  done clear
  D)
   \[b\text{ }cot\text{ }\alpha \text{ }cot\text{ }\beta \]
  done clear
  View Answer play_arrow