Solved papers for Manipal Engineering Manipal Engineering Solved Paper-2012

done Manipal Engineering Solved Paper-2012 Total Questions - 240

• question_answer1) Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is
  A)
  \[\sqrt{8}\]                                        
  done clear
  B)
  \[\sqrt{2/17}\]
  done clear
  C)
  \[\sqrt{1/8}\]    
  done clear
  D)
         \[\sqrt{32/17}\]
  done clear
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• question_answer2) A man, standing between two cliffs, claps his hands and starts hearing a series of echoes at intervals of one second. If the speed of sound in air is\[340\,\,m{{s}^{-1}}\], the distance between the cliffs is
  A)
   680 m                                  
  done clear
  B)
   1700 m
  done clear
  C)
   340 m                  
  done clear
  D)
          1620 m
  done clear
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• question_answer3) A beam of light of wavelength 600 nm from a source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fring is
  A)
   2.4 cm                                 
  done clear
  B)
   2.4 mm
  done clear
  C)
   1.2 mm          
  done clear
  D)
          1.2 cm
  done clear
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• question_answer4) A thin plano-convex lens acts like a concave mirror of focal length 0.2 m when silvered from its plane surface. The refractive index of the material of the lens is 1.5. The radius of curvature of the convex surface of the lens will be
  A)
   0.1 m                   
  done clear
  B)
   0.75 m
  done clear
  C)
   0.4 m                   
  done clear
  D)
          0.2 m
  done clear
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• question_answer5) A balloon is rising vertically up with a velocity of\[29\,\,m{{s}^{-1}}\]. A stone is dropped from it and it reaches the ground in\[10\,\,s\]. The height of the balloon when the stone was dropped from it is \[(g=9.8m{{s}^{-1}})\]
  A)
   400 m                                  
  done clear
  B)
   150 m
  done clear
  C)
   100 m                  
  done clear
  D)
          200 m
  done clear
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• question_answer6) In a Youngs double slit experiment, the separation between the two slits is 0.9 mm and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, the wavelength of the monochromatic source of light used is
  A)
   450 nm               
  done clear
  B)
   400 nm
  done clear
  C)
   500 nm         
  done clear
  D)
          600 nm
  done clear
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• question_answer7) A count rate meter shows a count of 240 per minute from a given radioactive source. One hour later the meter shows a count rate of 30 per minute. The half-life of the source is
  A)
   80 min                                 
  done clear
  B)
   120 min
  done clear
  C)
   20 min                 
  done clear
  D)
          30 min
  done clear
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• question_answer8) Two conductors of the same material have their diameters in the ratio\[1:2\]and their lengths in the ratio\[2:1\]. If the temperature difference between their ends is the same, then the ratio of amounts of heat conducted per second through them will be
  A)
   4 : 1                                      
  done clear
  B)
   1 : 4
  done clear
  C)
   8 : 1                      
  done clear
  D)
          1 : 8
  done clear
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• question_answer9) An ideal gas heat engine operates in a Carnots cycle between\[{{227}^{o}}C\]and\[{{127}^{o}}C\]. It absorbs\[6\times {{10}^{4}}J\]at high temperature. The amount of heat converted into work is
  A)
  \[1.6\times {{10}^{4}}J\]                              
  done clear
  B)
  \[1.2\times {{10}^{4}}J\]
  done clear
  C)
  \[4.8\times {{10}^{4}}J\]              
  done clear
  D)
         \[3.5\times {{10}^{4}}J\]
  done clear
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• question_answer10) Effective capacitance between\[A\]and\[B\]in the figure shown is (all capacitances are in\[\mu F\])
  A)
  \[\frac{3}{14}\mu F\]                    
  done clear
  B)
  \[\frac{14}{3}\mu F\]
  done clear
  C)
  \[21\,\,\mu F\]
  done clear
  D)
         \[23\,\,\mu F\]
  done clear
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• question_answer11) When the bob of a simple pendulum swings, the work done by tension in the string is
  A)
   > 0                                        
  done clear
  B)
   < 0
  done clear
  C)
   zero                     
  done clear
  D)
          maximum
  done clear
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• question_answer12) For a particle executing simple harmonic motion, the kinetic energy\[K\]is given by\[K={{K}_{0}}{{\cos }^{2}}\omega t\]. The maximum value of potential energy is
  A)
  \[{{K}_{0}}\]                                      
  done clear
  B)
   zero
  done clear
  C)
  \[{{K}_{0}}/2\]  
  done clear
  D)
          not obtainable
  done clear
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• question_answer13) A particle is moving along a circular path of radius\[5m\]with a uniform speed\[5m{{s}^{-1}}\]. What will be the average acceleration when the particle completes half revolution?
  A)
   Zero                                     
  done clear
  B)
  \[10\,\,m{{s}^{-2}}\]
  done clear
  C)
  \[10\pi \,\,m{{s}^{-2}}\]               
  done clear
  D)
         \[\frac{10}{\pi }\,\,m{{s}^{-2}}\]
  done clear
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• question_answer14) \[ECE\]of copper is\[3.3\times {{10}^{-7}}kg/C\]. If\[100\,\,kWh\] energy is consumed at\[33\,\,V\]in a copper voltameter, then mass of copper liberated is
  A)
   3.6 kg                                  
  done clear
  B)
   3.3 kg
  done clear
  C)
   1 kg                      
  done clear
  D)
          1 mg
  done clear
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• question_answer15) In non-resonant circuit, what will be the nature of the circuit for frequencies higher than the resonant frequency?
  A)
   Resistive            
  done clear
  B)
          Capacitive
  done clear
  C)
          Inductive           
  done clear
  D)
          None of these
  done clear
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• question_answer16) A spot of light S rotates in a horizontal plane with a constant angular velocity of\[0.1\,\,rad/s\]. The spot of light P moves along the wall at a distance of\[3m\]from\[S\]. The velocity of spot\[P\], where\[\theta ={{45}^{o}}\], is
  A)
  \[~0.5\,\,m/s\]                
  done clear
  B)
  \[0.6\,\,m/s\]
  done clear
  C)
  \[0.7\,\,m/s\]          
  done clear
  D)
         \[0.8\,\,m/s\]
  done clear
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• question_answer17) A balloon contains\[500\,\,{{m}^{3}}\]of Heat\[{{27}^{o}}C\]and 1 atmospheric pressure. The volume of Heat\[-{{3}^{o}}C\]and\[0.5\]atmospheric pressure will be
  A)
  \[700\,\,{{m}^{3}}\]                       
  done clear
  B)
  \[900\,\,{{m}^{3}}\]
  done clear
  C)
  \[1000\,\,{{m}^{3}}\]     
  done clear
  D)
         \[500\,\,{{m}^{3}}\]
  done clear
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• question_answer18) Which of the following is different from others?
  A)
   Wavelength                     
  done clear
  B)
   Velocity
  done clear
  C)
   Frequency       
  done clear
  D)
          Amplitude
  done clear
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• question_answer19) The breaking force for a wire of diameter\[D\]of a material is\[F\]. The breaking force for a wire of the same material of radius\[D\]is
  A)
  \[F\]                                     
  done clear
  B)
  \[2F\]
  done clear
  C)
  \[\frac{F}{4}\]                   
  done clear
  D)
         \[4F\]
  done clear
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• question_answer20) If pressure of a gas contained in a closed vessel is increased by\[0.4%\]when heated by\[{{1}^{o}}C\], its initial temperature must be
  A)
  \[250\,\,K\]                       
  done clear
  B)
  \[{{250}^{o}}C\]
  done clear
  C)
  \[2500\,\,K\]         
  done clear
  D)
         \[{{25}^{o}}C\]
  done clear
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• question_answer21) In an electromagnetic wave, the electric and magnetizing fields are\[100\,\,V/m\]and\[0.265\,\,A/m\]. The maximum energy flow is
  A)
  \[26.5\,\,W/{{m}^{2}}\]               
  done clear
  B)
  \[36.5\,\,W/{{m}^{2}}\]
  done clear
  C)
  \[46.7\,\,W/{{m}^{2}}\]
  done clear
  D)
         \[765\,\,W/{{m}^{2}}\]
  done clear
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• question_answer22) A bullet of mass\[10\,\,g\]is fired from a gun of mass\[1\,\,kg\]with recoil velocity of gun is\[5m/s\]. The muzzle velocity will be
  A)
   30 km/min        
  done clear
  B)
   60 km/min
  done clear
  C)
   30 m/s          
  done clear
  D)
          500 m/s
  done clear
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• question_answer23) Work done by air when it expands from\[50\,\,L\] to\[150\,\,L\]at a constant pressure of 2 atmosphere is
  A)
  \[2\times {{10}^{4}}J\]                  
  done clear
  B)
  \[2\times 100J\]
  done clear
  C)
  \[2\times {{10}^{11}}J\]
  done clear
  D)
         \[2\times {{10}^{15}}J\]
  done clear
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• question_answer24) In an electron gun, the control grid is given a negative potential, relative to cathode in order to
  A)
   accelerate the electrons
  done clear
  B)
   decrease\[KE\]of electrons
  done clear
  C)
   repel the electrons
  done clear
  D)
   decelerate the electrons
  done clear
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• question_answer25) In an LCR circuit having\[L=8H,\,\,C=0.5\mu F\]and \[R=100\Omega \]in series, the resonance frequency in\[rad/s\]is
  A)
  \[600\]                                 
  done clear
  B)
  \[200\]
  done clear
  C)
  \[250/\pi \]        
  done clear
  D)
         \[500\]
  done clear
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• question_answer26) Power of a lens is\[-4\,\,D\]and for second lens, power is\[+2D;\]the total power of the couple is
  A)
  \[-2\,\,D\]                          
  done clear
  B)
  \[6\,\,D\]
  done clear
  C)
  \[-6\,\,D\]          
  done clear
  D)
         \[-8\,\,D\]
  done clear
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• question_answer27) In which one of the following regions of the electromagnetic spectrum will the vibrational motion of molecules give rise to absorption?
  A)
   Ultraviolet         
  done clear
  B)
   Microwave
  done clear
  C)
   Infrared         
  done clear
  D)
          Radio wave
  done clear
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• question_answer28) During inelastic collision of two particles
  A)
  \[{{(KE)}_{final}}={{(KE)}_{initial}}\]
  done clear
  B)
  \[{{(KE)}_{final}}\]must be greater than\[{{(KE)}_{initial}}\]
  done clear
  C)
   \[{{(KE)}_{final}}\]must be less than\[{{(KE)}_{initial}}\]
  done clear
  D)
   \[{{(KE)}_{final}}\]must be greater or less than\[{{(KE)}_{initial}}\]
  done clear
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• question_answer29) Two gases are at absolute temperatures\[300\,\,K\]and\[350\,\,K\]respectively. The ratio of average kinetic energy of their molecules is
  A)
  \[6:7\]                                  
  done clear
  B)
  \[36:49\]
  done clear
  C)
  \[7:6\]                  
  done clear
  D)
         \[343:216\]
  done clear
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• question_answer30) The current in a coil changes from\[0\]to\[2A\]in\[0.05\,\,s\]. If the induced emf is\[80\,\,V\], the self-inductance of the coil is,
  A)
  \[1\,\,H\]                                            
  done clear
  B)
  \[0.5\,\,H\]
  done clear
  C)
  \[1.5\,\,H\]        
  done clear
  D)
         \[2\,\,H\]
  done clear
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• question_answer31) Equal volumes of monoatomic and diatomic gases at the same temperature are given equal quantities of heat. Then,
  A)
   the temperature of diatomic gas will be more
  done clear
  B)
   the temperature of monoatomic gas will be more
  done clear
  C)
   the temperature of both will be zero
  done clear
  D)
   nothing can be said
  done clear
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• question_answer32) A copper wire and a steel wire of the same diameter and length are joined end to end and a force is applied which stretches their combined length by 1 cm. Then, the two wires will have
  A)
   the same stress and strain
  done clear
  B)
   the same stress but different strains
  done clear
  C)
   the same strain but different stresses
  done clear
  D)
   different stresses and strains
  done clear
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• question_answer33) The length of the seconds pendulum is decreased by 0.3 cm when it is shifted to Chennai from London. If the acceleration due to gravity at London is \[981\,\,cm/{{s}^{2}}\], the acceleration due to gravity at Chennai is
  A)
  \[981\,\,cm/{{s}^{2}}\]       
  done clear
  B)
  \[978\,\,cm/{{s}^{2}}\]
  done clear
  C)
  \[984\,\,cm/{{s}^{2}}\]       
  done clear
  D)
         \[975\,\,cm/{{s}^{2}}\]
  done clear
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• question_answer34) How does, the electric field\[(E)\]between the plates of a charged cylindrical capacitor vary, with the distance r from the axis of the cylinder?
  A)
  \[E\propto \frac{1}{{{r}^{2}}}\]                 
  done clear
  B)
  \[E\propto \frac{1}{r}\]
  done clear
  C)
  \[E\propto {{r}^{2}}\]                    
  done clear
  D)
  \[E\propto r\]
  done clear
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• question_answer35) A thin bar magnet of length\[2L\]is bent at the mid-point so that the angle between them is\[{{60}^{o}}C\]. The new length of the magnet is
  A)
  \[\sqrt{2}L\]                                      
  done clear
  B)
  \[\sqrt{3}L\]
  done clear
  C)
  \[2\,\,L\]                             
  done clear
  D)
         \[L\]
  done clear
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• question_answer36) A capacitor is connected to a cell of emf E and some internal resistance\[r\]. The potential difference across the
  A)
   cell is\[E\]                          
  done clear
  B)
   cell is\[<E\]
  done clear
  C)
   capacitor is\[<E\] 
  done clear
  D)
     capacitor is\[>E\]
  done clear
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• question_answer37) The radius of the smallest electron orbit in hydrogen-like ion is\[(0.51\times {{10}^{-10}}/4)m\], then it is
  A)
   hydrogen atom               
  done clear
  B)
  \[H{{e}^{+}}\]
  done clear
  C)
  \[L{{i}^{2+}}\]                   
  done clear
  D)
         \[B{{e}^{3+}}\]
  done clear
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• question_answer38) de-Broglie wavelength of a body of mass\[1\,\,kg\]moving with velocity of\[2000\,\,m/s\]is
  A)
  \[3.32\times {{10}^{-27}}\overset{\text{o}}{\mathop{\text{A}}}\,\]       
  done clear
  B)
  \[1.5\times {{10}^{7}}\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  C)
  \[0.55\times {{10}^{-22}}\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  D)
          None of these
  done clear
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• question_answer39) A voltmeter of resistance\[998\Omega \]is connected across a cell of emf\[2\,\,V\]and internal resistance\[2\Omega \]. The potential difference across the voltmeter is
  A)
  \[1.99\,\,V\]                      
  done clear
  B)
  \[3.5\,\,V\]
  done clear
  C)
  \[5\,\,V\]                            
  done clear
  D)
         \[6\,\,V\]
  done clear
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• question_answer40) If a person with a spring balance and a body hanging from it goes up and up in an aeroplane, then the reading of the weight of the body as indicated by the spring balance will
  A)
   goes on increasing
  done clear
  B)
   goes on decreasing
  done clear
  C)
   first increase and then decrease
  done clear
  D)
   remains the same
  done clear
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• question_answer41) A mass\[3m\], initially at rest at the origin explodes into three fragments of equal mass. Two of the fragments have speed\[v\]each and move perpendicular to each other. The third fragment will move with a speed
  A)
  \[\frac{v}{\sqrt{2}}\]                                     
  done clear
  B)
  \[\frac{v}{2}\]
  done clear
  C)
  \[v\]                     
  done clear
  D)
         \[v\sqrt{2}\]
  done clear
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• question_answer42) A nucleus X initially at rest, undergoes alpha decay according to the equation                 \[_{92}{{X}^{A}}{{\to }_{Z}}{{Y}^{228}}+\alpha \] Then, the value of\[A\]and\[Z\]are
  A)
  \[94,\,\,230\]                    
  done clear
  B)
  \[232,\,\,90\]
  done clear
  C)
  \[190,\,\,32\]    
  done clear
  D)
         \[230,\,\,94\]
  done clear
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• question_answer43) The energy gap between the valence band and the conduction band for a material .is\[6\,\,eV\]. The material is
  A)
   an insulator
  done clear
  B)
   a metal
  done clear
  C)
   an intrinsic semiconductor
  done clear
  D)
   a superconductor
  done clear
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• question_answer44) When the inputs of a two input logic gate are 0 and 0, the output is 1. When the inputs are 1 and 0 the output is 0. The logic gate is of the type,
  A)
   AND      
  done clear
  B)
                          NAND
  done clear
  C)
   NOR                     
  done clear
  D)
          OR
  done clear
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• question_answer45) If a transistor biased in the common-emitter mode, the emitter current is
  A)
   much smaller than base current
  done clear
  B)
   much larger than base current
  done clear
  C)
   nearly equal to the base current
  done clear
  D)
   much smaller than the collector current
  done clear
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• question_answer46) A sound has an intensity of\[2\times {{10}^{-8}}\,\,W/{{m}^{2}}\]. Its intensity level in decibels is\[({{\log }_{10}}2=0.3)\]
  A)
   23                                         
  done clear
  B)
   3
  done clear
  C)
   43                         
  done clear
  D)
          4.3
  done clear
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• question_answer47) A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of\[{{240}^{o}}\]. Then, the number of images observable is
  A)
   3                                            
  done clear
  B)
   5
  done clear
  C)
   7                            
  done clear
  D)
          9
  done clear
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• question_answer48) If\[1\,\,A\]of current is passed through\[CuS{{O}_{4}}\]solution for\[10\,\,s\], the number of copper atoms deposite at the cathode will be about
  A)
  \[1.6\times {{10}^{20}}\]             
  done clear
  B)
  \[8\times {{10}^{19}}\]
  done clear
  C)
  \[3.1\times {{10}^{19}}\]        
  done clear
  D)
         \[6.2\times {{10}^{19}}\]
  done clear
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• question_answer49) Two points\[A\]and\[B\]are situated at distance\[x\]and\[2x\]respectively from the nearer pole of a magnet\[2\,\,cm\]long. The ratio of magnetic field at\[A\]and\[B\]is
  A)
   4 : 1 exactly      
  done clear
  B)
   4 : 1 approximately
  done clear
  C)
   8 : 1 exactly      
  done clear
  D)
          8 : 1 approximately
  done clear
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• question_answer50) Electromagnetic waves travel only through
  A)
   material medium
  done clear
  B)
   vacuum
  done clear
  C)
   oscillating electric and magnetic fields
  done clear
  D)
   oscillating electric and magnetic fields whose directions are perpendicular to each other
  done clear
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• question_answer51) The ratio of magnetic moments of two short magnets which give null deflection in\[\tan B\]position at\[12\,\,cm\]and\[18\,\,cm\]from the centre of a deflection magnetometer is
  A)
   2 : 3                                      
  done clear
  B)
   8 : 27
  done clear
  C)
   27 : 8                    
  done clear
  D)
          4 : 9
  done clear
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• question_answer52) A\[220\,\,V\]main supply is connected to a resistance of\[100k\Omega \]. The effective current is
  A)
  \[2.2\,\,mA\]                    
  done clear
  B)
  \[2.2\sqrt{2}mA\]
  done clear
  C)
  \[\frac{2.2}{\sqrt{2}}mA\]           
  done clear
  D)
          None of these
  done clear
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• question_answer53) Two bodies of different masses\[{{m}_{1}}\]and\[{{m}_{2}}\]have equal momenta. Their kinetic energies\[{{E}_{1}}\]and\[{{E}_{2}}\]are in the ratio
  A)
  \[\sqrt{{{m}_{1}}}:\sqrt{{{m}_{2}}}\]                      
  done clear
  B)
  \[{{m}_{1}}:{{m}_{2}}\]
  done clear
  C)
  \[{{m}_{2}}:{{m}_{1}}\]
  done clear
  D)
         \[m_{1}^{2}:m_{2}^{2}\]
  done clear
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• question_answer54) When the light enters from air to glass, for which Colour the angle of deviation is maximum?
  A)
   Red                                      
  done clear
  B)
   Yellow
  done clear
  C)
   Blue                     
  done clear
  D)
          Violet
  done clear
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• question_answer55) Two    waves    are    represented    by\[{{y}_{1}}=A\sin (kx-\omega t)\]and\[{{y}_{2}}=A\cos (kx-\omega t)\]. The amplitude of resultant wave is
  A)
  \[4\,\,A\]                                            
  done clear
  B)
  \[2\,\,A\]
  done clear
  C)
  \[\sqrt{2}A\]                     
  done clear
  D)
         \[A\]
  done clear
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• question_answer56) An atom of mass M which is in the state of rest emits a photon of wavelength\[\lambda \]. As a result, the atom will deflect with the kinetic energy equal to (\[h\]is Plancks constant)
  A)
  \[\frac{{{h}^{2}}}{M{{\lambda }^{2}}}\]                
  done clear
  B)
  \[\frac{1}{2}\frac{{{h}^{2}}}{M{{\lambda }^{2}}}\]
  done clear
  C)
  \[\frac{h}{M\lambda }\]                              
  done clear
  D)
         \[\frac{1}{2}\frac{h}{M\lambda }\]
  done clear
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• question_answer57) If the angular momentum of any rotating body increases by 200%, then the increase in its kinetic energy is
  A)
  \[400%\]                             
  done clear
  B)
  \[800%\]
  done clear
  C)
  \[200%\]             
  done clear
  D)
         \[100%\]
  done clear
  View Answer play_arrow

• question_answer58) A cylindrical tank has a hole of\[1\,\,c{{m}^{2}}\]in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of\[70\,\,c{{m}^{2}}/s\], then the maximum height up to which water can rise in the tank is
  A)
   2.5 cm                                 
  done clear
  B)
   5 cm
  done clear
  C)
   10 cm                  
  done clear
  D)
          0.25 cm
  done clear
  View Answer play_arrow

• question_answer59) X-rays and y-rays of the same energies may be distinguished by
  A)
   their velocity
  done clear
  B)
   their ionizing power
  done clear
  C)
   their intensity
  done clear
  D)
   method of production
  done clear
  View Answer play_arrow

• question_answer60) Which of the following materials is non-crystalline?
  A)
   Copper                               
  done clear
  B)
   Sodium chloride
  done clear
  C)
   Wood                  
  done clear
  D)
          Diamond
  done clear
  View Answer play_arrow

• question_answer61) The vapour density of\[{{N}_{2}}{{O}_{4}}\]at a certain temperature is 30. What is the percentage dissociation of\[{{N}_{2}}{{O}_{4}}\]at this temperature?
  A)
  46%                                       
  done clear
  B)
  53%
  done clear
  C)
  75%                       
  done clear
  D)
         92%
  done clear
  View Answer play_arrow

• question_answer62) Four different colloids have the following gold number, which one has the most effective action?
  A)
  5                                             
  done clear
  B)
  10
  done clear
  C)
  15                          
  done clear
  D)
         13
  done clear
  View Answer play_arrow

• question_answer63) In which of the following case, increase in concentration of ion cause increase in\[{{E}_{cell}}\]?
  A)
  \[Pt({{H}_{2}})|{{H}^{+}}(aq)\]
  done clear
  B)
  \[Pt|Quinhydrone|{{H}^{+}}(aq)\]
  done clear
  C)
  \[Ag|A{{g}^{+}}(aq)\]
  done clear
  D)
  \[Ag,\,\,AgCl|C{{l}^{-}}(aq)\]
  done clear
  View Answer play_arrow

• question_answer64) The relative lowering of vapour pressure of an aqueous solution containing a non-volatile solute is 0.0125. The molality of the solution is
  A)
  0.70                       
  done clear
  B)
         0.30
  done clear
  C)
  0.125                    
  done clear
  D)
         0.07
  done clear
  View Answer play_arrow

• question_answer65) Which of the following is known as Glaubers salt?
  A)
  \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\cdot 5{{H}_{2}}O\]            
  done clear
  B)
  \[N{{a}_{2}}S{{O}_{4}}\cdot 10{{H}_{2}}O\]
  done clear
  C)
  \[N{{a}_{2}}C{{O}_{3}}\cdot 10{{H}_{2}}O\]
  done clear
  D)
         \[Na(N{{H}_{4}})HP{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer66) \[PhCHClBr\xrightarrow{tBu{{O}^{-}}}Carbene\] In the above reaction which of the following will be most probable?
  A)
  \[_{\bullet }^{\bullet }CHBr\]                    
  done clear
  B)
  \[_{\bullet }^{\bullet }CHCl\]
  done clear
  C)
  \[_{\bullet }^{\bullet }CPhBr\]  
  done clear
  D)
         \[_{\bullet }^{\bullet }CPhCl\]
  done clear
  View Answer play_arrow

• question_answer67) Which of the following alcohol is unable to turn orange colour of chromic acid to green?
  A)
  \[1{}^\circ \]alcohol                       
  done clear
  B)
  \[2{}^\circ \]alcohol
  done clear
  C)
  \[3{}^\circ \]alcohol       
  done clear
  D)
         Allyl alcohol
  done clear
  View Answer play_arrow

• question_answer68) Which of the following test is performed by carbohydrates?
  A)
  Biuret test          
  done clear
  B)
  Nitroprusside test
  done clear
  C)
  Ninhydrin test    
  done clear
  D)
         Molischs test
  done clear
  View Answer play_arrow

• question_answer69) Which of the following is not used as propellant?
  A)
  Hydrazine           
  done clear
  B)
  UDMH
  done clear
  C)
  MMH                   
  done clear
  D)
         Phenyl hydrazine
  done clear
  View Answer play_arrow

• question_answer70) Which of the following species have the same number of electrons in its outermost as well as penultimate shell?
  A)
  \[C{{l}^{-}}\]      
  done clear
  B)
  \[{{O}^{2-}}\]
  done clear
  C)
  \[N{{a}^{+}}\]                   
  done clear
  D)
         \[M{{g}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer71) Which of the following is the formula of Sorels cement?
  A)
  \[KCl\cdot MgC{{l}_{2}}\cdot 6{{H}_{2}}O\]
  done clear
  B)
  \[MgC{{l}_{2}}\cdot 5MgO\cdot x{{H}_{2}}O\]
  done clear
  C)
  \[CaS{{O}_{4}}\cdot 2{{H}_{2}}O\]
  done clear
  D)
  \[MgC{{O}_{3}}\cdot CaC{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer72) \[{{S}_{\text{(rhombic)}}}+{{O}_{2}}(g)\xrightarrow{{}}S{{O}_{2}}(g),\]                                                 \[\Delta H=-297.5\,\,kJ\] \[{{S}_{(monoclinic)}}+{{O}_{2}}(g)\xrightarrow{{}}S{{O}_{2}}(g),\]                                                 \[\Delta H=-300\,\,kJ\] The data can predict that
  A)
  rhombic sulphur is yellow in colour
  done clear
  B)
  monoclinic sulphur has metallic lusture
  done clear
  C)
  monoclinic sulphur is more stable
  done clear
  D)
  \[\Delta {{H}_{transition}}\]of\[{{S}_{R}}\]to\[{{S}_{M}}\]is endothermic
  done clear
  View Answer play_arrow

• question_answer73) Which of the following is a measurement of water pollution?
  A)
  PSC                                       
  done clear
  B)
  PCB
  done clear
  C)
  BOD                      
  done clear
  D)
         COD
  done clear
  View Answer play_arrow

• question_answer74) The half-life period of a first order process is 1.6 min. It will be 90% complete in
  A)
  5.3 min                
  done clear
  B)
  10.6 min
  done clear
  C)
  43.3mm         
  done clear
  D)
         99.7 min
  done clear
  View Answer play_arrow

• question_answer75) Which of the following is tetrabasic acid?
  A)
  Orthophosphorus acid
  done clear
  B)
  Orthophosphoric acid
  done clear
  C)
  Metaphosphoric acid
  done clear
  D)
  Pyrophosphoric acid
  done clear
  View Answer play_arrow

• question_answer76) . Which of the following order for bond angles is correct?
  A)
  \[B{{F}_{3}}<N{{H}_{3}}<P{{F}_{3}}<CI{{F}_{3}}\]
  done clear
  B)
  \[B{{F}_{3}}<N{{F}_{3}}<P{{F}_{3}}<CI{{F}_{3}}\]
  done clear
  C)
  \[CI{{F}_{3}}<P{{F}_{3}}<N{{F}_{3}}<B{{F}_{3}}\]
  done clear
  D)
  \[B{{F}_{3}}\approx N{{F}_{3}}<P{{F}_{3}}<CI{{F}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer77) The triad of the nuclei that is isotonic, is
  A)
  \[_{6}{{C}^{14}},\,{{\,}_{7}}{{N}^{14}},\,{{\,}_{9}}{{N}^{19}}\]
  done clear
  B)
  \[_{6}{{C}^{14}},\,{{\,}_{7}}{{N}^{15}},\,{{\,}_{9}}{{F}^{17}}\]
  done clear
  C)
  \[_{6}{{C}^{14}},\,{{\,}_{7}}{{N}^{14}},\,{{\,}_{9}}{{F}^{17}}\]
  done clear
  D)
         \[_{6}{{C}^{12}},\,{{\,}_{7}}{{N}^{14}},\,{{\,}_{9}}{{F}^{19}}\]
  done clear
  View Answer play_arrow

• question_answer78) The oxidation number of cobalt in\[K[Co{{(CO)}_{4}}]\]is
  A)
  \[-1\]                                    
  done clear
  B)
  \[-3\]
  done clear
  C)
  \[+1\]                   
  done clear
  D)
         \[+3\]
  done clear
  View Answer play_arrow

• question_answer79) Out of\[Cu,\,\,Ag,\,\,Fe\]and\[Zn\], the metal which can displace all others from their salt solution, is
  A)
  \[Zn\]                                   
  done clear
  B)
  \[Cu\]
  done clear
  C)
  \[Ag\]                  
  done clear
  D)
         \[Fe\]
  done clear
  View Answer play_arrow

• question_answer80) Which of the following has magic number of neutrons?
  A)
  \[_{13}A{{l}^{27}}\]                        
  done clear
  B)
  \[_{26}F{{e}^{56}}\]
  done clear
  C)
  \[_{83}B{{i}^{209}}\]      
  done clear
  D)
         \[_{92}{{U}^{238}}\]
  done clear
  View Answer play_arrow

• question_answer81) If\[{{K}_{a}}\]of\[HCN=4\times {{10}^{-10}}\], then the\[pH\]of\[2.5\times {{10}^{-1}}\]molar\[HCN(aq)\]is
  A)
  1                                             
  done clear
  B)
  2.5
  done clear
  C)
  4                             
  done clear
  D)
         5
  done clear
  View Answer play_arrow

• question_answer82) A coffee cup calorimeter initially contains\[125g\]of water at a temperature of\[{{24.2}^{o}}C\]. After adding of\[10.5g\]of\[KBr\], the temperature becomes\[{{21.1}^{o}}C\]. The heat of solution is
  A)
  \[40\,\,J/g\]                      
  done clear
  B)
  \[117\,\,J/g\]
  done clear
  C)
  \[167.7\,\,J/g\]
  done clear
  D)
         \[420.05\,\,J/g\]
  done clear
  View Answer play_arrow

• question_answer83) What product is formed when cyclohexanone is oxidised?
  A)
  \[HOOC\cdot {{(C{{H}_{2}})}_{4}}\cdot COOH\]
  done clear
  B)
  \[C{{H}_{3}}C{{H}_{2}}COOH\]
  done clear
  C)
  \[C{{H}_{3}}{{(C{{H}_{2}})}_{4}}\cdot COOH\]
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer84) The reaction \[C{{H}_{3}}CN+4H\xrightarrow{Na/{{C}_{2}}{{H}_{5}}OH}C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\]is known as
  A)
  Hofmanns bromamide reaction
  done clear
  B)
  Mendius reaction
  done clear
  C)
  Perkins reaction
  done clear
  D)
  Sabatier reaction
  done clear
  View Answer play_arrow

• question_answer85) Action of\[B{{r}_{2}}\]on cyclopentene gives
  A)
  cyclopentyl bromide
  done clear
  B)
  1, 2 - dibromo cyclopentane
  done clear
  C)
  cyclopentyl dibromide
  done clear
  D)
  no reaction
  done clear
  View Answer play_arrow

• question_answer86) In a face-centred cubic arrangement of\[A\]and\[B\]atoms whose\[A\]atoms are at the corner of the unit cell and\[B\]atoms at the face-centre, one of\[A\]atom is missing from one corner in the unit cell. The simplest formula of the compound is
  A)
  \[{{A}_{24}}{{B}_{7}}\]                  
  done clear
  B)
  \[{{A}_{7}}{{B}_{24}}\]
  done clear
  C)
  \[{{A}_{7}}{{B}_{4}}\]                    
  done clear
  D)
         \[A{{B}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer87) Beryllium shows diagonal relationship with
  A)
  \[B\]                                     
  done clear
  B)
  \[Mg\]
  done clear
  C)
  \[Al\]                    
  done clear
  D)
         \[Na\]
  done clear
  View Answer play_arrow

• question_answer88) A compound has the molecular formula\[{{X}_{4}}{{O}_{6}}\]. If\[10g\]of\[{{X}_{4}}{{O}_{6}}\]has\[5.72\,\,g\,\,X\], then calculate atomic mass of\[X\]
  A)
  32 amu                                
  done clear
  B)
  64 amu
  done clear
  C)
  67 amu                
  done clear
  D)
         98 amu
  done clear
  View Answer play_arrow

• question_answer89) Which of the following is Rinmanns green?
  A)
  \[ZnO\]                               
  done clear
  B)
  \[ZnS+BaS{{O}_{4}}\]
  done clear
  C)
  \[ZnS{{O}_{4}}\cdot 7{{H}_{2}}O\]
  done clear
  D)
         \[ZnO\cdot CaO\]
  done clear
  View Answer play_arrow

• question_answer90) For the valence electron in copper, the four quantum numbers are
  A)
  \[n=4,\,\,l=0,\,\,m=0,\,\,s=\frac{1}{2}\]
  done clear
  B)
  \[n=4,\,\,l=0,\,\,m=+2,\,\,s=\frac{1}{2}\]
  done clear
  C)
  \[n=4,\,\,l=1,\,\,m=+2,\,\,s=\frac{1}{2}\]
  done clear
  D)
  \[n=4,\,\,l=1,\,\,m=0,\,\,s=\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer91) Geometry of\[B{{F}_{3}}\]is
  A)
  trigonal planar                  
  done clear
  B)
  pentagonal
  done clear
  C)
  trihedral         
  done clear
  D)
         tetrahedral
  done clear
  View Answer play_arrow

• question_answer92) Which of the following will represent the normality of 10%\[(w/V)\]acetic acid?
  A)
  \[1.66\,\,N\]                     
  done clear
  B)
  \[16.6\,\,N\]
  done clear
  C)
  \[3.32\,\,N\]           
  done clear
  D)
         \[33.2\,\,N\]
  done clear
  View Answer play_arrow

• question_answer93) The oxidation number of sulphur in\[{{H}_{2}}{{S}_{2}}{{O}_{8}}\]is
  A)
  +2                                          
  done clear
  B)
  +4
  done clear
  C)
  +6                          
  done clear
  D)
         +7
  done clear
  View Answer play_arrow

• question_answer94) Which of the following reaction requires catalyst?
  A)
  \[S+{{O}_{2}}\xrightarrow{{}}S{{O}_{2}}\]
  done clear
  B)
  \[C+{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}\]
  done clear
  C)
  \[2S{{O}_{2}}+{{O}_{2}}\xrightarrow{{}}2S{{O}_{3}}\]
  done clear
  D)
  All of the above
  done clear
  View Answer play_arrow

• question_answer95) \[{{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)+22\,\,kcal\] The activation energy for the forward reaction is 50 kcal. What is the activation energy for the backward reaction?
  A)
  \[72\text{ }kcal\]             
  done clear
  B)
  \[28\text{ }kcal\]
  done clear
  C)
  \[-72\text{ }kcal\]         
  done clear
  D)
         \[-28\text{ }kcal\]
  done clear
  View Answer play_arrow

• question_answer96) Malonic acid and succinic acid are distinguished by
  A)
  heating
  done clear
  B)
                         \[NaHC{{O}_{3}}\]
  done clear
  C)
  both (a) and (b) 
  done clear
  D)
        None of these
  done clear
  View Answer play_arrow

• question_answer97) When chloroform is treated with chlorine in the presence of sunlight, it yields
  A)
  urotropine         
  done clear
  B)
  pyrene
  done clear
  C)
  chloropicrin      
  done clear
  D)
         chloritone
  done clear
  View Answer play_arrow

• question_answer98)  Which of the following areand?
  A)
  Both are  
  done clear
  B)
  Both are
  done clear
  C)
  respectively.
  done clear
  D)
  respectively.
  done clear
  View Answer play_arrow

• question_answer99) Which of the following will explain synthesis of RNA?
  A)
  Translation         
  done clear
  B)
  Coagulation
  done clear
  C)
  Transcription     
  done clear
  D)
         Replication
  done clear
  View Answer play_arrow

• question_answer100) Which of the following is a narrow spectrum antibiotics?
  A)
   Penicillin G       
  done clear
  B)
  Dettol
  done clear
  C)
  Aspirin           
  done clear
  D)
         Analgin
  done clear
  View Answer play_arrow

• question_answer101) When aniline reacts with oil of bitter almonds, condensation takes place and benzyl derivatives are formed. These are known as
  A)
  Millons base     
  done clear
  B)
  Schiffs reagent
  done clear
  C)
  Benedict reagent
  done clear
  D)
         Schiffs base
  done clear
  View Answer play_arrow

• question_answer102)  Which of the following is correct about\[(A),\,\,(B)\]and\[(C)\]?
  A)
  A, B and C are anomers
  done clear
  B)
  A and C are anomers
  done clear
  C)
  A, B and C are metamers
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer103) The\[IUPAC\]name ofis
  A)
  bicyclo (2, 1, 0) pentane
  done clear
  B)
  1, 2-cyclopropyl cyclobutane
  done clear
  C)
  1, 2-methylene cyclobutane
  done clear
  D)
  cyclopentane (4, 3) annulene
  done clear
  View Answer play_arrow

• question_answer104) In the conversion of ethanol into methanol which of the following reagents will be used?
  A)
  \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}/{{H}_{2}}S{{O}_{4}}\]        
  done clear
  B)
  \[NaOH+CaO\]
  done clear
  C)
  \[C{{l}_{2}}+aq.KOH\]
  done clear
  D)
         All of these
  done clear
  View Answer play_arrow

• question_answer105) PDI for natural polymers is generally close to
  A)
  zero                                      
  done clear
  B)
  1
  done clear
  C)
  10                          
  done clear
  D)
         100
  done clear
  View Answer play_arrow

• question_answer106) Which of the following is diamagnetic?
  A)
  \[{{H}_{2}}\]                                      
  done clear
  B)
  \[H_{2}^{-}\]
  done clear
  C)
  \[H_{2}^{+}\]                    
  done clear
  D)
         \[He_{2}^{+}\]
  done clear
  View Answer play_arrow

• question_answer107) Which of the following is a property of non-metal?
  A)
  Electronegativity
  done clear
  B)
  Basic nature of oxide
  done clear
  C)
  Reducing property
  done clear
  D)
  Low ionisation potential
  done clear
  View Answer play_arrow

• question_answer108) One mole of ice is converted into water at\[273\text{ }K\]. The entropies of\[{{H}_{2}}O(s)\]and\[{{H}_{2}}O(l)\]are\[38.20\]and\[60.01\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\]respectively. The enthalpy change for the conversion is
  A)
  \[3\,\,kJ\,\,mo{{l}^{-1}}\]                            
  done clear
  B)
  \[4\,\,kJ\,\,mo{{l}^{-1}}\]
  done clear
  C)
  \[5\,\,kJ\,\,mo{{l}^{-1}}\]            
  done clear
  D)
         \[6\,\,kJ\,\,mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer109) Complete the following reaction,                 \[{{P}_{4}}+NaOH+{{H}_{2}}O\xrightarrow{{}}?\]
  A)
  \[P{{H}_{3}}+N{{a}_{2}}HP{{O}_{2}}\]
  done clear
  B)
  \[P{{H}_{3}}+Na{{H}_{2}}P{{O}_{2}}\]
  done clear
  C)
  \[{{H}_{3}}P{{O}_{4}}+NaO\]     
  done clear
  D)
  \[P{{H}_{3}}+N{{a}_{2}}P{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer110) The elevation in boiling point would be highest for
  A)
  \[0.08\,\,M\,\,BaC{{l}_{2}}\]      
  done clear
  B)
  \[0.15\,\,M\,\,KCl\]
  done clear
  C)
  \[0.10\,\,M\]Glucose
  done clear
  D)
         \[0.06\,\,M\,\,Ca{{(N{{O}_{3}})}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer111) What is the magnetic moment of\[{{[Fe{{F}_{6}}]}^{3-}}\]?
  A)
  2 BM                                     
  done clear
  B)
  5.9 BM
  done clear
  C)
  7BM                      
  done clear
  D)
         35 BM
  done clear
  View Answer play_arrow

• question_answer112) In the given reaction, identify compound\[C\]?
  A)
   
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer113) The ratio of rate of diffusion of hydrogen and helium gas is
  A)
  \[1:1.4\]              
  done clear
  B)
  \[1:1\]
  done clear
  C)
  \[1.4:1\]              
  done clear
  D)
         \[1:2\]
  done clear
  View Answer play_arrow

• question_answer114) The reaction, known as
  A)
  substitution reaction
  done clear
  B)
  addition reaction
  done clear
  C)
  elimination reaction
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer115) Which of the following is responsible for hardness of water?
  A)
  \[CaHC{{O}_{3}}\]                           
  done clear
  B)
  \[CaC{{l}_{2}}\]
  done clear
  C)
  Both (a) and (b) 
  done clear
  D)
        None of these
  done clear
  View Answer play_arrow

• question_answer116) Which of the following is differ in nature from others?
  A)
  Vasopressin                      
  done clear
  B)
  Thyroid
  done clear
  C)
  Oxytocin         
  done clear
  D)
  Insulin
  done clear
  View Answer play_arrow

• question_answer117) Indigo is an example of
  A)
  vat dye                
  done clear
  B)
  mordant dye
  done clear
  C)
  azo dye          
  done clear
  D)
         phthalein dye
  done clear
  View Answer play_arrow

• question_answer118) Solder is an alloy of lead with
  A)
  \[Cu\]                                  
  done clear
  B)
  \[Fe\]
  done clear
  C)
  \[Sn\]                   
  done clear
  D)
  \[Zn\]
  done clear
  View Answer play_arrow

• question_answer119) An aqueous solution contains following ions: \[Hg_{2}^{2+},\,\,H{{g}^{2+}},\,\,P{{b}^{2+}}\]and\[C{{d}^{2+}}\].On adding\[HCl\], which of these will precipitate?
  A)
  \[H{{g}_{2}}C{{l}_{2}}\]
  done clear
  B)
         \[PbC{{l}_{2}}\]
  done clear
  C)
  \[H{{g}_{2}}C{{l}_{2}}\]and\[PbC{{l}_{2}}\]
  done clear
  D)
         \[HgC{{l}_{2}}\]and\[PbC{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer120) Which of the following molecules/species are aromatic in nature?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer121) The sum of the series\[1+\frac{{{2}^{2}}}{2!}+\frac{{{3}^{2}}}{3!}+\frac{{{4}^{2}}}{4!}+...\]is
  A)
  \[2e\]   
  done clear
  B)
  \[3e\]
  done clear
  C)
  \[2e-1\]               
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer122) If\[f(x)={{x}^{2}}+2bx+2{{c}^{2}}\]and\[g(x)=-{{x}^{2}}+2cx+{{b}^{2}}\] are such that\[f(x)>\max g(x)\], then relation between\[b\]and \[c\]is
  A)
   no relation                        
  done clear
  B)
  \[0<c<\frac{b}{2}\]
  done clear
  C)
  \[|c|<\sqrt{2}|b|\]       
  done clear
  D)
         \[|c|\,\,>\sqrt{2}|b|\]
  done clear
  View Answer play_arrow

• question_answer123) If\[\left| \frac{{{z}_{1}}}{{{z}_{2}}} \right|=1\]and\[({{z}_{1}}{{z}_{2}})=0\], then
  A)
  \[{{z}_{1}}={{z}_{2}}\]                   
  done clear
  B)
  \[{{\left| {{z}_{2}} \right|}^{2}}={{z}_{1}}{{z}_{2}}\]
  done clear
  C)
  \[{{z}_{1}}{{z}_{2}}=1\] 
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer124) If\[\cos A=m\cos B\], and \[\cot \frac{A+B}{2}=\lambda \tan \frac{B-A}{2}\], then\[\lambda \]is
  A)
  \[\frac{m}{m-1}\]                           
  done clear
  B)
  \[\frac{m+1}{m}\]
  done clear
  C)
  \[\frac{m+1}{m-1}\]      
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer125) In a triangle, the angle are in\[AP\]and the lengths of the two larger sides are 10 and 9, respectively, then the length of the third side can be
  A)
  \[5\pm \sqrt{6}\]                            
  done clear
  B)
  \[0.7\]
  done clear
  C)
  \[15-\sqrt{6}\]  
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer126) The complex number\[z=x+iy\]which satisfy the equation\[\left| \frac{z-5i}{z+5i} \right|=1\], lie on
  A)
   the x-axis
  done clear
  B)
   the straight line\[y=5\]
  done clear
  C)
   a circle passing through the origin
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer127) If\[x>1,\,\,y>1,\,\,z>1\]are in\[GP\], then\[\frac{1}{1+\ln x}\],\[\frac{1}{1+\ln y}\],\[\frac{1}{1+\ln z}\]are in
  A)
  \[AP\]                                  
  done clear
  B)
   HP
  done clear
  C)
  \[GP\]                  
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer128) If\[\frac{{{e}^{x}}}{1-x}={{B}_{0}}+{{B}_{1}}x+{{B}_{2}}{{x}^{2}}+...+{{B}_{n}}{{x}^{n}}+...\], then \[{{B}_{n}}-{{B}_{n-1}}\]equals
  A)
  \[\frac{1}{n!}\]                 
  done clear
  B)
  \[\frac{1}{(n-1)!}\]
  done clear
  C)
  \[\frac{1}{n!}-\frac{1}{(n-1)!}\] 
  done clear
  D)
         \[1\]
  done clear
  View Answer play_arrow

• question_answer129) lf\[f(x)=\left\{ \begin{matrix}    \frac{\sin [x]}{[x]}, & [x]\ne 0  \\    0, & [x]=0  \\ \end{matrix} \right.\] where\[[x]\]denotes the greatest integer less than or equal to\[x\], then\[\underset{x\to 0}{\mathop{\lim }}\,f(x)\]equals
  A)
  \[1\]                                     
  done clear
  B)
  \[0\]
  done clear
  C)
  \[-1\]                    
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer130) If\[y(t)\]is a solution of\[(1+t)\frac{dy}{dt}-ty=1\]and\[y(0)=-1\], then\[y(1)\]equal to
  A)
  \[-\frac{1}{2}\]                                 
  done clear
  B)
  \[e+\frac{1}{2}\]
  done clear
  C)
  \[e-\frac{1}{2}\]              
  done clear
  D)
         \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer131) The locus of the mid-points of the chord of the circle\[{{x}^{2}}+{{y}^{2}}=4\]which subtends a right angle at the origin, is
  A)
  \[x+y=2\]                           
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}=1\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}=2\]             
  done clear
  D)
         \[x+y=1\]
  done clear
  View Answer play_arrow

• question_answer132) From a point A common tangents are drawn to the circle\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}/2\]and parabola\[{{y}^{2}}=4ax\]. The area of the quadrilateral formed by the common tangents to the chord of contact of the parabola is
  A)
  \[\frac{15{{a}^{3}}}{4}\]sq units               
  done clear
  B)
  \[\frac{15{{a}^{2}}}{4}\]sq units
  done clear
  C)
  \[\frac{7{{a}^{2}}}{4}\]sq units  
  done clear
  D)
         \[\frac{{{a}^{2}}}{4}\]sq units
  done clear
  View Answer play_arrow

• question_answer133) Let\[\omega =-\frac{1}{2}+i\frac{\sqrt{3}}{2}\], then value of the determinant\[\left| \begin{matrix}    1 & 1 & 1  \\    1 & -1-{{\omega }^{2}} & {{\omega }^{2}}  \\    1 & {{\omega }^{2}} & \omega   \\ \end{matrix} \right|\]is
  A)
  \[3\omega \]                                    
  done clear
  B)
  \[3\omega (\omega -1)\]
  done clear
  C)
  \[3{{\omega }^{2}}\]                     
  done clear
  D)
         \[3\omega (1-\omega )\]
  done clear
  View Answer play_arrow

• question_answer134) The harmonic mean of the root of the equation\[(5+\sqrt{2}){{x}^{2}}-(4+\sqrt{5})x+8+2\sqrt{5}=0\]is
  A)
   2                            
  done clear
  B)
   4
  done clear
  C)
   6               
  done clear
  D)
                          8
  done clear
  View Answer play_arrow

• question_answer135) Domain of the function\[\log |{{x}^{2}}-9|\]is
  A)
  \[R\]                                     
  done clear
  B)
  \[R-[-3,\,\,3]\]
  done clear
  C)
  \[R-\{-3,\,\,3\}\]              
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer136) Let\[f:R\to R\]be such that\[f(1)=3\]and\[f(1)=6\]. Then,\[\underset{x\to 0}{\mathop{\lim }}\,{{\left[ \frac{f(1+x)}{f(1)} \right]}^{1/x}}\]equals
  A)
  \[1\]                                     
  done clear
  B)
  \[{{e}^{1/2}}\]
  done clear
  C)
  \[{{e}^{2}}\]                      
  done clear
  D)
         \[{{e}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer137) The value of\[[\mathbf{a}\,\,\mathbf{a}+\mathbf{b}\,\,\mathbf{a}+\mathbf{b}+\mathbf{c}]\]is
  A)
  \[{{[\mathbf{abc}]}^{2}}\]          
  done clear
  B)
  \[[\mathbf{abc}]\]
  done clear
  C)
  \[2[\mathbf{abc}]\]       
  done clear
  D)
         \[3[\mathbf{abc}]\]
  done clear
  View Answer play_arrow

• question_answer138) If\[\mathbf{a}=-\mathbf{i}+2\mathbf{j}-\mathbf{k}\],\[\mathbf{b}=\mathbf{i}+\mathbf{j}-3\mathbf{k}\]and\[\mathbf{c}=-4\mathbf{i}-\mathbf{k}\], then\[\mathbf{a}\times (\mathbf{b}\times \mathbf{c})+(\mathbf{a}\cdot \mathbf{b})\mathbf{c}\]
  A)
  \[5\mathbf{i}+5\mathbf{j}-15\mathbf{k}\]                        
  done clear
  B)
  \[0\]
  done clear
  C)
  \[12\mathbf{j}+4\mathbf{k}\]  
  done clear
  D)
         \[-3\mathbf{i}+6\mathbf{j}-3\mathbf{k}\]
  done clear
  View Answer play_arrow

• question_answer139) If\[I(m,\,\,n)=\int_{0}^{1}{{{t}^{m}}}{{(1+t)}^{n}}dt\], then the expression for\[I(m,\,\,n)\]in terms of\[I(m+1,\,\,n-1)\]is
  A)
  \[\frac{{{2}^{n}}}{m+1}-\frac{n}{m+1}I(m+1,\,\,n-1)\]
  done clear
  B)
  \[\frac{n}{m+1}I(m+1,\,\,n-1)\]
  done clear
  C)
  \[\frac{{{2}^{n}}}{m+1}+\frac{n}{m+1}I(m+1,\,\,n-1)\]
  done clear
  D)
  \[\frac{m}{m+1}I(m+1,\,\,n-1)\]
  done clear
  View Answer play_arrow

• question_answer140) The\[\Delta PQR\]is inscribed in the circle\[{{x}^{2}}+{{y}^{2}}=25.\] If\[Q\]and\[R\]have coordinates (3, 4) and (-4, 3), respectively. Then,\[\angle QPR\]is equal to
  A)
  \[\frac{\pi }{2}\]                              
  done clear
  B)
  \[\frac{\pi }{3}\]
  done clear
  C)
  \[\frac{\pi }{4}\]                              
  done clear
  D)
         \[\frac{\pi }{6}\]
  done clear
  View Answer play_arrow

• question_answer141) The equation of directrix of the parabola\[{{y}^{2}}+4y+4x+2=0\]is
  A)
  \[x=-1\]                               
  done clear
  B)
  \[x=1\]
  done clear
  C)
  \[x=-\frac{3}{2}\]            
  done clear
  D)
         \[x=\frac{3}{2}\]
  done clear
  View Answer play_arrow

• question_answer142) If\[a>2b>0\], then positive value of\[m\]for which \[y=mx-b\sqrt{1+{{m}^{2}}}\]is a common tangent to\[{{x}^{2}}+{{y}^{2}}={{b}^{2}}\]and\[{{(x-a)}^{2}}+{{y}^{2}}={{b}^{2}}\]is
  A)
  \[\frac{2b}{\sqrt{{{a}^{2}}-4{{b}^{2}}}}\]                              
  done clear
  B)
  \[\frac{\sqrt{{{a}^{2}}-4{{b}^{2}}}}{2b}\]
  done clear
  C)
  \[\frac{2b}{a-2b}\]         
  done clear
  D)
         \[\frac{b}{a-2b}\]
  done clear
  View Answer play_arrow

• question_answer143) If\[\alpha \in \left[ 0,\,\,\frac{\pi }{2} \right)\], then\[\sqrt{{{x}^{2}}+x}+\frac{{{\tan }^{2}}\alpha }{\sqrt{{{x}^{2}}+x}}\]is always greater than or equal to
  A)
  \[2\tan \alpha \]                              
  done clear
  B)
  \[1\]
  done clear
  C)
  \[2\]                     
  done clear
  D)
         \[{{\sec }^{2}}\alpha \]
  done clear
  View Answer play_arrow

• question_answer144) If an edge of a cube measure 2 m with a possible error of 0.5 cm. Find the corresponding error in the calculated volume of the cube
  A)
  \[0.6\,\,{{m}^{3}}\]                        
  done clear
  B)
  \[0.06\,\,{{m}^{3}}\]
  done clear
  C)
  \[0.006\,\,{{m}^{3}}\]   
  done clear
  D)
         \[0.0006\,\,{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer145) Let/be twice differentiable function satisfying \[f(1)=1,\,\,f(2)=4,\,\,f(3)=9\],then
  A)
  \[f(x)=2,\,\,\forall \,\,x\in R\]
  done clear
  B)
  \[f(x)=5=f(x)\]. For some\[x\in (1,\,\,3)\]
  done clear
  C)
   there exists atleast one\[x\in (1,\,\,3)\]such that\[f(x)=2\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer146) The order of the differential equation whose general solution is given by                 \[y=({{C}_{1}}+{{C}_{2}})\cos (x+{{C}_{3}})-{{C}_{4}}{{e}^{x+{{C}_{5}}}}\] where,\[{{C}_{1}},\,\,{{C}_{2}},\,\,{{C}_{3}},\,\,{{C}_{4}},\,\,{{C}_{5}}\]are arbitrary constants, is
  A)
   5                                            
  done clear
  B)
   4
  done clear
  C)
   3                            
  done clear
  D)
          2
  done clear
  View Answer play_arrow

• question_answer147) Evaluate\[\int{(\sqrt{\tan x}+\sqrt{\cot x})\,\,dx}\]
  A)
  \[\sqrt{2}{{\tan }^{-1}}(\sqrt{\tan x}-\sqrt{\cot x})+C\]
  done clear
  B)
  \[\frac{2}{\sqrt{2}}{{\tan }^{-1}}x+C\]
  done clear
  C)
  \[\sqrt{2}{{\tan }^{-1}}\left( \frac{\sqrt{\tan x}-\sqrt{\cot x}}{\sqrt{2}} \right)+C\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer148) In an election, number of candidates exceeds the number to be elected by 2. A man can vote in 56 ways. Then, the number of candidates is
  A)
   5                                            
  done clear
  B)
   6
  done clear
  C)
   7                            
  done clear
  D)
          8
  done clear
  View Answer play_arrow

• question_answer149) The  curve  described  parametrically by \[x={{t}^{2}}+t+1,\,\,y={{t}^{2}}-t+1\]represents
  A)
   a pair of straight lines
  done clear
  B)
   an ellipse
  done clear
  C)
   a parabola
  done clear
  D)
   a hyperbola
  done clear
  View Answer play_arrow

• question_answer150) Tangent is drawn to ellipse\[\frac{{{x}^{2}}}{27}+\frac{{{y}^{2}}}{1}=1\]at\[(3\sqrt{3}\cos \theta ,\,\,\sin \theta )\], where\[\left( \theta \in \left( 0,\,\,\frac{\pi }{2} \right) \right)\]. Then, the value of\[\theta \]such that the sum of intercept on axes made by this tangent is minimum, is
  A)
  \[\frac{\pi }{3}\]                                              
  done clear
  B)
  \[\frac{\pi }{6}\]
  done clear
  C)
  \[\frac{\pi }{8}\]                              
  done clear
  D)
         \[\frac{\pi }{4}\]
  done clear
  View Answer play_arrow

• question_answer151) Suppose\[a,\,\,b,\,\,c\]are in\[AP\] and\[{{a}^{2}},\,\,{{b}^{2}},\,\,{{c}^{2}}\]are in\[GP\]. If\[a<b<c\]and\[a+b+c=\frac{3}{2}\], then the value of\[a\]is
  A)
  \[\frac{1}{2\sqrt{2}}\]                   
  done clear
  B)
  \[\frac{1}{2\sqrt{3}}\]
  done clear
  C)
  \[\frac{1}{2}-\frac{1}{\sqrt{3}}\]               
  done clear
  D)
         \[\frac{1}{2}-\frac{1}{\sqrt{2}}\]
  done clear
  View Answer play_arrow

• question_answer152) The function\[f(x)=\frac{\ln (1+ax)-\ln (1-bx)}{x}\]is not defined at\[x=0\]. The value which should be assigned to\[f\]at\[x=0\]so that it is continuous at\[x=0\],is
  A)
  \[a-b\]                 
  done clear
  B)
  \[a+b\]
  done clear
  C)
  \[a-b\]                 
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer153) Domain of definition of function\[f(x)=\sqrt{{{\sin }^{-1}}(2x)+\frac{\pi }{6}}\]for real-valued of\[x\], is
  A)
  \[\left[ -\frac{1}{4},\,\,\frac{1}{2} \right]\]                          
  done clear
  B)
  \[\left[ -\frac{1}{2},\,\,\frac{1}{2} \right]\]
  done clear
  C)
  \[\left[ -\frac{1}{2},\,\,\frac{1}{9} \right]\]          
  done clear
  D)
         \[[0,\,\,\pi ]\]
  done clear
  View Answer play_arrow

• question_answer154) If\[x\,\,dy=y(dx+y\,\,dy)\],\[y(1)=1\]and\[y(x)>0\]. Then,\[y(-3)\]is equal to
  A)
   3                                            
  done clear
  B)
   2
  done clear
  C)
   1                                            
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer155) Evaluate\[\int{\frac{(x-1){{e}^{x}}}{{{(x+1)}^{3}}}dx}\]
  A)
  \[0\]
  done clear
  B)
  \[\frac{{{(x+1)}^{2}}}{{{e}^{x}}}+C\]
  done clear
  C)
  \[\frac{{{e}^{x}}}{{{(x+1)}^{2}}}+C\]
  done clear
  D)
  \[\frac{{{e}^{x}}}{{{(x-1)}^{2}}}+{{(x+1)}^{2}}+C\]
  done clear
  View Answer play_arrow

• question_answer156) If\[a={{\log }_{2}}3,\,\,b={{\log }_{2}}5,\,\,c={{\log }_{7}}2\], then\[{{\log }_{140}}63\]in terms of\[a,\,\,b,\,\,c\]is
  A)
  \[\frac{2ac+1}{2a+abc+1}\]                        
  done clear
  B)
  \[\frac{2ac+1}{2a+c+a}\]
  done clear
  C)
  \[\frac{2ac+1}{2c+ab+a}\]           
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer157) Local maximum value of the function\[\frac{{{\log }_{e}}x}{x}\]is
  A)
  \[1\]     
  done clear
  B)
  \[e\]
  done clear
  C)
  \[\frac{1}{e}\]                  
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer158) \[A+iB\]form of\[\frac{(\cos x+i\sin x)(\cos y+i\sin y)}{(\cot u+i)(1+i\tan v)}\]is
  A)
  \[\sin u\cos v[\cos (x+y-u-v)\]\[+i\sin (x+y-u-v)]\]
  done clear
  B)
  \[\sin u\cos v[\cos (x+y+u+v)\]\[+i\sin (x+y+u+v)]\]
  done clear
  C)
  \[\sin u\cos v[\cos (x+y+u+v)\]\[-i\sin (x+y+u+v)\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer159) In the set\[{{Q}^{+}}\]of all positive rational numbers, the operation\[*\]is defined by the formula\[a+b=\frac{ab}{6}\]. Then, the inverse of\[9\]with respect to\[*\]is
  A)
  \[4\]                                     
  done clear
  B)
  \[3\]
  done clear
  C)
  \[\frac{1}{9}\]                   
  done clear
  D)
         \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer160) If\[\alpha +\beta +\gamma =\pi \],   then   the   value   of\[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta -{{\sin }^{2}}\gamma \]is equal to
  A)
  \[2\sin \alpha \]                               
  done clear
  B)
  \[2\sin \alpha cos\beta sin\gamma \]
  done clear
  C)
  \[2\sin \alpha \sin \beta \cos \gamma \]
  done clear
  D)
  \[2\sin \alpha \sin \beta \sin \gamma \]
  done clear
  View Answer play_arrow

• question_answer161) If in\[\Delta \,\,ABC\] \[\frac{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos C}{c}=\frac{a}{bc}+\frac{b}{ac}\], then\[{{b}^{2}}+{{c}^{2}}\]is equal to
  A)
  \[{{a}^{2}}\]                                      
  done clear
  B)
  \[ac\]
  done clear
  C)
  \[bc\]                   
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer162) In any\[\Delta \,\,ABC\], the least value of\[\left( \frac{{{\sin }^{2}}A+\sin A+1}{\sin A} \right)\].
  A)
  \[3\]                                     
  done clear
  B)
  \[\sqrt{3}\]
  done clear
  C)
  \[9\]                     
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer163) Let\[\lambda \]and\[\alpha \]be real                 \[\lambda x+\sin \alpha \cdot y+\cos \alpha \cdot z=0\],                 \[x+\cos \alpha \cdot y+\sin \alpha \cdot z=0\],                 \[-x+\sin \alpha \cdot y-\cos \alpha \cdot z=0\] has a non-trivial solution. If\[\lambda =1\], then all the values of a is equals
  A)
  \[n\pi +\frac{\pi }{2}\]                  
  done clear
  B)
  \[n\pi +\frac{\pi }{4},\,\,n\pi \]
  done clear
  C)
  \[n\pi +\frac{\pi }{2}\]  
  done clear
  D)
         \[n\pi +\frac{\pi }{4},\,\,\frac{\pi }{4}\]
  done clear
  View Answer play_arrow

• question_answer164) If the roots of the equation                 \[{{x}^{2}}-2ax+{{a}^{2}}+a-3=0\] are real and less than 3, then
  A)
  \[a<2\]                
  done clear
  B)
  \[2\le a\le 3\]
  done clear
  C)
  \[3<a\le 4\]       
  done clear
  D)
         \[a>4\]
  done clear
  View Answer play_arrow

• question_answer165) If\[{{z}_{1}}\]and\[{{z}_{2}}\]are two complex numbers such that\[|{{z}_{1}}|\,\,=\,\,|{{z}_{2}}|+|{{z}_{1}}-{{z}_{2}}|\], then
  A)
  \[\operatorname{Im}\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=0\]                              
  done clear
  B)
  \[\operatorname{Re}\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=0\]
  done clear
  C)
  \[\operatorname{Re}\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=\operatorname{Im}\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)\]
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer166) The number of five digits numbers that can be formed without any restriction is
  A)
   990000                
  done clear
  B)
   10000
  done clear
  C)
   90000                  
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer167) The middle term in the expansion of\[{{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}}+2 \right)}^{n}}\]is
  A)
  \[\frac{n}{{{[(n/2)!]}^{2}}}\]
  done clear
  B)
  \[-\frac{(2n!)}{{{[(n/2)!]}^{2}}}\]
  done clear
  C)
  \[\frac{1\cdot 3\cdot 5...(2n+1)}{n!}{{2}^{n}}\]
  done clear
  D)
  \[\frac{(2n)!}{{{(n!)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer168) The value of\[\sin ({{22}^{o}}30)\]is
  A)
  \[\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}\]
  done clear
  B)
                        \[\sqrt{\sqrt{2}-1}\]
  done clear
  C)
  \[\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}\]    
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer169) If\[\frac{\pi }{2}<\theta <\frac{3\pi }{2}\], then the value of\[\sqrt{\frac{1-\sin \theta }{1+\sin \theta }}\]is equal to
  A)
  \[-\sec \theta +\tan \theta \]    
  done clear
  B)
  \[\sec \theta +\tan \theta \]
  done clear
  C)
  \[\sec \theta -\tan \theta \]   
  done clear
  D)
                          None of these
  done clear
  View Answer play_arrow

• question_answer170) If\[\int{\frac{{{2}^{x}}}{\sqrt{1-{{4}^{x}}}}dx=k{{\sin }^{-1}}({{2}^{x}})+C}\], then\[k\]is equal to
  A)
  \[\log 2\]                            
  done clear
  B)
  \[\frac{1}{2}\log 2\]
  done clear
  C)
  \[\frac{1}{2}\]                   
  done clear
  D)
         \[\frac{1}{\log 2}\]
  done clear
  View Answer play_arrow

• question_answer171) The area of the region bounded by\[y=-1\],\[y=2,\,\,x={{y}^{3}}\]and\[x=0\]is
  A)
  \[\frac{17}{4}sq\,\,units\]
  done clear
  B)
                         \[\frac{1}{4}sq\,\,unit\]
  done clear
  C)
  \[4\,\,sq\,\,units\]         
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer172) The mid-point of the line joining the common points of the line\[2x-3y+8=0\]and\[{{y}^{2}}=8x\]is
  A)
  \[(3,\,\,2)\]                        
  done clear
  B)
  \[(5,\,\,6)\]
  done clear
  C)
  \[(4,\,\,-1)\]      
  done clear
  D)
         \[(2,\,\,-3)\]
  done clear
  View Answer play_arrow

• question_answer173) The value of\[{{\cos }^{2}}{{48}^{o}}-{{\sin }^{2}}{{12}^{o}}\]is
  A)
  \[\frac{\sqrt{5}+1}{8}\]
  done clear
  B)
  \[\frac{\sqrt{5}-1}{8}\]
  done clear
  C)
  \[\frac{\sqrt{5}+1}{16}\]              
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer174) The number of solutions of\[{{\sin }^{2}}\theta +3\cos \theta =3\]in\[[-\pi ,\,\,\pi ]\], is
  A)
   4            
  done clear
  B)
                   2                
  done clear
  C)
   0            
  done clear
  D)
                          None of these
  done clear
  View Answer play_arrow

• question_answer175) The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the angle of elevation of its top changes from\[{{30}^{o}}\]to\[{{60}^{o}}\], is
  A)
  \[25\sqrt{3}m\]               
  done clear
  B)
  \[25\,\,m\]
  done clear
  C)
  \[25\sqrt{4}m\]
  done clear
  D)
         \[\frac{25}{\sqrt{3}}\,\,m\]
  done clear
  View Answer play_arrow

• question_answer176) If\[\underset{x\to \infty }{\mathop{\lim }}\,\left( \frac{{{x}^{3}}+1}{{{x}^{2}}+1}-(ax+b) \right)=2\], then
  A)
  \[a=1,\,\,b=1\]                 
  done clear
  B)
  \[a=1,\,\,b=2\]
  done clear
  C)
  \[a=1,\,\,b=-2\]               
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer177) If\[f(x)=\left\{ \begin{matrix}    \frac{|x+2|}{{{\tan }^{-1}}(x+2)}, & x\ne -2  \\    2, & x=-2  \\ \end{matrix} \right.\], then\[f(x)\]is
  A)
   continuous at\[x=-2\]
  done clear
  B)
   not continuous at\[x=-2\]
  done clear
  C)
   differentiable at\[x=-2\]
  done clear
  D)
   continuous but not derivable at\[x=-2\].
  done clear
  View Answer play_arrow

• question_answer178) Let\[P\]be any point on the curve\[{{x}^{2/3}}+{{y}^{2/3}}={{a}^{2/3}}.\] Then, the length of the segment of the tangent between the coordinate axes of length
  A)
  \[3a\]                                   
  done clear
  B)
  \[4a\]
  done clear
  C)
  \[5a\]                   
  done clear
  D)
         \[a\]
  done clear
  View Answer play_arrow

• question_answer179) The motion of a particle along a straight line is described by the function\[x={{(2t-3)}^{2}}\], where\[x\]is in metre and \[t\] is in second. Then, the velocity of the particle at origin is
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   2                            
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer180) The value of\[\cos \frac{2\pi }{7}+\cos \frac{4\pi }{7}+\cos \frac{6\pi }{7}\]is
  A)
  \[1\]                                     
  done clear
  B)
  \[-1\]
  done clear
  C)
  \[\frac{1}{2}\]                   
  done clear
  D)
         \[-\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer181) The maximum value of\[3\cos \theta +4\sin \theta \]is
  A)
  \[-5\]                                    
  done clear
  B)
  \[5\]
  done clear
  C)
  \[25\]                   
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer182) Which of the following is not a statement?
  A)
   Every set is a finite set
  done clear
  B)
   8 is less than 6
  done clear
  C)
   Where are you going
  done clear
  D)
   The sum of interior angles of a triangle is\[{{180}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer183) The least positive remainder when\[123\times 125\times 127\]is divided by\[124\]is
  A)
   4                                            
  done clear
  B)
   120
  done clear
  C)
   121                       
  done clear
  D)
          130
  done clear
  View Answer play_arrow

• question_answer184) The vertex connectivity of any tree is
  A)
   one                                      
  done clear
  B)
   two
  done clear
  C)
   three                   
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer185) A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is
  A)
   216                                       
  done clear
  B)
   240
  done clear
  C)
   600                       
  done clear
  D)
          3125
  done clear
  View Answer play_arrow

• question_answer186) Given positive integers\[r>1,\,\,n>2\]and the coefficient of\[(3r)\text{th}\]and\[(r+2)\text{th}\]terms in the binomial expansion of\[{{(1+x)}^{2n}}\]are equal, then
  A)
  \[n=2r\]                              
  done clear
  B)
  \[n=2r+1\]
  done clear
  C)
  \[n=3r\]              
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer187) The number of solutions of\[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\]is
  A)
   3                                            
  done clear
  B)
   1
  done clear
  C)
   2                            
  done clear
  D)
          0
  done clear
  View Answer play_arrow

• question_answer188) The value of\[\lim \frac{\int_{0}^{{{x}^{2}}}{{{\cos }^{2}}t\,\,dt}}{x\sin x}\]is
  A)
   2                                            
  done clear
  B)
   1
  done clear
  C)
   0                            
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer189) The value of\[\int_{2}^{3}{\frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}}}dx\]is
  A)
   1                                            
  done clear
  B)
   1/2
  done clear
  C)
   2                            
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer190) The solution of differential equation\[({{e}^{x}}+1)y\,\,dy=(y+1){{e}^{x}}\,\,dx\]is
  A)
  \[({{e}^{x}}+1)(y+1)=C{{e}^{y}}\]
  done clear
  B)
  \[({{e}^{x}}+1)|(y+1)|=C{{e}^{-y}}\]
  done clear
  C)
  \[({{e}^{x}}+1)(y+1)=\pm C{{e}^{y}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer191) The equation of the circle passing through (1, 1) and   the   points   of   intersection   of\[{{x}^{2}}+{{y}^{2}}+13x-3y=0\]and\[11x+\frac{1}{2}y+\frac{25}{2}=0\]is
  A)
  \[4{{x}^{2}}+4{{y}^{2}}-30x-10y=15\]
  done clear
  B)
  \[4{{x}^{2}}+4{{y}^{2}}-30x-13y-25=0\]
  done clear
  C)
  \[4{{x}^{2}}+4{{y}^{2}}-17x-10y+25=0\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer192) The equation of the common tangent to the curves\[{{y}^{2}}=8x\]and\[xy=-1\]is
  A)
  \[3y=9x+2\]
  done clear
  B)
  \[y=2x+1\]
  done clear
  C)
  \[2y=x+8\]
  done clear
  D)
  \[y=x+2\]
  done clear
  View Answer play_arrow

• question_answer193) If\[k\]be the perimeter of the\[\Delta \,\,ABC\], then\[b{{\cos }^{2}}\frac{C}{2}+c{{\cos }^{2}}\frac{B}{2}\]is equal to
  A)
  \[k\]                                     
  done clear
  B)
  \[2k\]
  done clear
  C)
  \[\frac{k}{2}\]                   
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer194) Let\[f(x)\]be a positive function. Let                 \[{{I}_{1}}=\int_{1-k}^{k}{xf\{x(1-x)\}\,\,dx}\],                 \[{{I}_{2}}=\int_{k-1}^{k}{f\{x(1-x)\}\,\,dx}\], where\[2k-1>0\], then\[\frac{{{I}_{1}}}{{{I}_{2}}}\]is
  A)
  \[2\]                                     
  done clear
  B)
  \[k\]
  done clear
  C)
  \[\frac{1}{2}\]                   
  done clear
  D)
         \[1\]
  done clear
  View Answer play_arrow

• question_answer195) If P is a variable point on the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\] with\[AA\]as major axis. Then, the maximum value of the area of the\[\Delta \,\,APA\]is
  A)
  \[ab\,\,sq\,\,unit\]                         
  done clear
  B)
  \[2\,\,ab\,\,sq\,\,unit\]
  done clear
  C)
  \[\frac{ab}{2}sq\,\,unit\]             
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer196) In a\[\Delta \,\,ABC\], if\[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\]the side\[a=2\], then area of the triangle is
  A)
  \[1\,\,sq\,\,unit\]                           
  done clear
  B)
  \[2\,\,sq\,\,units\]
  done clear
  C)
  \[\frac{\sqrt{3}}{2}sq\,\,units\]
  done clear
  D)
         \[\sqrt{3}\,\,sq\,\,units\]
  done clear
  View Answer play_arrow

• question_answer197) The area bounded by the curves\[y=|x|-1\]and\[y=-|x|+1\]is
  A)
  \[1\,\,sq\,\,unit\]           
  done clear
  B)
         \[2\,\,sq\,\,units\]
  done clear
  C)
  \[2\sqrt{2}sq\,\,units\]                
  done clear
  D)
  \[4\,\,sq\,\,units\]
  done clear
  View Answer play_arrow

• question_answer198) The value of the expression\[\sqrt{3}\cos ec{{20}^{o}}-\sec {{20}^{o}}\]is equal to
  A)
  \[2\]                                     
  done clear
  B)
  \[\frac{2\sin {{20}^{o}}}{\sin {{40}^{o}}}\]
  done clear
  C)
  \[4\]                     
  done clear
  D)
         \[\frac{4\sin {{20}^{o}}}{\sin {{40}^{o}}}\]
  done clear
  View Answer play_arrow

• question_answer199) If in a\[\Delta \,\,PQR\],\[\sin P,\,\,\sin Q,\,\,\sin R\]are in\[AP\], then
  A)
   the altitudes are in\[AP\]
  done clear
  B)
   the altitudes are in\[HP\]
  done clear
  C)
   the medians are in\[GP\]
  done clear
  D)
   the medians are in\[AP\]
  done clear
  View Answer play_arrow

• question_answer200) A man and a woman appears in an interview for two vacancies in the same post. The probability of mans selection is\[\frac{1}{4}\]and that of the womans selection is\[\frac{1}{3}\]. What is the probability that none of them will be selected?
  A)
  \[\frac{1}{2}\]                                   
  done clear
  B)
  \[\frac{1}{12}\]
  done clear
  C)
  \[\frac{1}{4}\]                   
  done clear
  D)
          None of these
  done clear
  View Answer play_arrow

• question_answer201) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.
  A)
   The whole country
  done clear
  B)
   was suffering by
  done clear
  C)
   a financial crisis.
  done clear
  D)
   No error
  done clear
  View Answer play_arrow

• question_answer202) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.
  A)
   I do not know where could he have gone
  done clear
  B)
   so early
  done clear
  C)
   in the morning.
  done clear
  D)
   No error
  done clear
  View Answer play_arrow

• question_answer203) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.
  A)
   I suggest that
  done clear
  B)
   he goes
  done clear
  C)
   to the doctor as soon as he returns from taking the examination.
  done clear
  D)
   No error
  done clear
  View Answer play_arrow

• question_answer204) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.
  A)
   The introduction of tea and coffee
  done clear
  B)
   and such other beverages
  done clear
  C)
   have not been without some effect.
  done clear
  D)
   No error.
  done clear
  View Answer play_arrow

• question_answer205) Directions: In the following questions, some of the sentences have errors and some have none. Find out which part of a sentence has an error. The letter of that part is your answer. If there is no error, your answer is (d) i.e., No error.
  A)
   Inspite of the roadblock
  done clear
  B)
   the guards allowed us
  done clear
  C)
   enter the restricted area to search for our friends
  done clear
  D)
   No error.
  done clear
  View Answer play_arrow

• question_answer206) Directions:  In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Illicit
  A)
   immoral             
  done clear
  B)
   illegal                   
  done clear
  C)
   ineligible            
  done clear
  D)
   illegible
  done clear
  View Answer play_arrow

• question_answer207) Directions:  In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Flair
  A)
   talent                  
  done clear
  B)
   tendency           
  done clear
  C)
          bias                      
  done clear
  D)
          need
  done clear
  View Answer play_arrow

• question_answer208) Directions:  In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Conservation
  A)
   preservation                    
  done clear
  B)
   respiration        
  done clear
  C)
   correction     
  done clear
  D)
   confusion
  done clear
  View Answer play_arrow

• question_answer209) Directions:  In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Abysmal
  A)
   sickening           
  done clear
  B)
   gloomy               
  done clear
  C)
          sad                       
  done clear
  D)
          bottomless
  done clear
  View Answer play_arrow

• question_answer210) Directions:  In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word. Salient
  A)
   valient                
  done clear
  B)
   variant
  done clear
  C)
          prodent          
  done clear
  D)
          prominent
  done clear
  View Answer play_arrow

• question_answer211) Directions: In the following questions, choose the word(s) opposite in meaning to the given word. Suppress
  A)
   stir up                 
  done clear
  B)
   rouse                  
  done clear
  C)
   urge                     
  done clear
  D)
          incite
  done clear
  View Answer play_arrow

• question_answer212) Directions: In the following questions, choose the word(s) opposite in meaning to the given word.                 Loosen
  A)
   fasten                 
  done clear
  B)
   accelerate         
  done clear
  C)
          delay             
  done clear
  D)
          paste
  done clear
  View Answer play_arrow

• question_answer213) Directions: In the following questions, choose the word(s) opposite in meaning to the given word. Rebellion
  A)
   forgiveness                      
  done clear
  B)
   retribution        
  done clear
  C)
          submission       
  done clear
  D)
          domination
  done clear
  View Answer play_arrow

• question_answer214) Directions: In the following questions, choose the word(s) opposite in meaning to the given word. Idiosyncrasy
  A)
   insanity              
  done clear
  B)
   sanity  
  done clear
  C)
   generality      
  done clear
  D)
   singularity
  done clear
  View Answer play_arrow

• question_answer215) Directions: In the following questions, choose the word(s) opposite in meaning to the given word. Sanguine
  A)
   diffident            
  done clear
  B)
   hopeless            
  done clear
  C)
          cynical           
  done clear
  D)
          morose
  done clear
  View Answer play_arrow

• question_answer216) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.
  A)
   prioratise           
  done clear
  B)
   picturise             
  done clear
  C)
          hesitate           
  done clear
  D)
          perforate                          
  done clear
  View Answer play_arrow

• question_answer217) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.
  A)
   mendacous      
  done clear
  B)
   obnoxcious       
  done clear
  C)
          pernicious       
  done clear
  D)
          ferocious
  done clear
  View Answer play_arrow

• question_answer218) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.
  A)
   pennetrate                       
  done clear
  B)
   irritate
  done clear
  C)
          hesitate           
  done clear
  D)
          perforate
  done clear
  View Answer play_arrow

• question_answer219) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.
  A)
   passagway        
  done clear
  B)
   causeway          
  done clear
  C)
   subway         
  done clear
  D)
          straightway
  done clear
  View Answer play_arrow

• question_answer220) Directions: In the following questions, groups of four words are given. In each group, one word is wrongly spelt. Find the misspelt word.
  A)
   rapport               
  done clear
  B)
   support              
  done clear
  C)
          repport          
  done clear
  D)
          purport
  done clear
  View Answer play_arrow

• question_answer221) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. Dont worry about the silly row. It was just a storm in a tea cup.
  A)
   important matter dealt with ease
  done clear
  B)
   hot tea being served
  done clear
  C)
   commotion over a trival matter
  done clear
  D)
   confusion and chaos
  done clear
  View Answer play_arrow

• question_answer222) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. The Rajput warriors set their face against the invader.
  A)
   became enemies           
  done clear
  B)
   turned away from                         
  done clear
  C)
   faced difficulty   
  done clear
  D)
          opposed strongly
  done clear
  View Answer play_arrow

• question_answer223) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. Syria is now currying favour with America.
  A)
   pleasing
  done clear
  B)
   favouring
  done clear
  C)
   obliging
  done clear
  D)
   ingratiating itself with
  done clear
  View Answer play_arrow

• question_answer224) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. Our principal is not a man to mince matters.
  A)
   to confuse issues
  done clear
  B)
   to say something mildly
  done clear
  C)
   to mix everything together
  done clear
  D)
   to be very modest
  done clear
  View Answer play_arrow

• question_answer225) Directions: In the following questions, four alternatives are given for the Idio/Phrase printed in bold in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase. We tend to take for granted the conveniences of modern life.
  A)
   to consider       
  done clear
  B)
   to admit             
  done clear
  C)
          to accept readily
  done clear
  D)
          to care for
  done clear
  View Answer play_arrow

• question_answer226) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. Belief that God is in everything and. That everything is God
  A)
   Atheism             
  done clear
  B)
   Pantheism        
  done clear
  C)
          Scepticism       
  done clear
  D)
          Animism
  done clear
  View Answer play_arrow

• question_answer227) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. A picture of a person or a thing drawn in such a highly exaggerated manner as to cause laughter
  A)
   Cartoon              
  done clear
  B)
   Cacography      
  done clear
  C)
          Cartography     
  done clear
  D)
          Caricature
  done clear
  View Answer play_arrow

• question_answer228) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. The state of being miserable be reft of all possessions
  A)
   Dependant      
  done clear
  B)
   Complacent      
  done clear
  C)
          Destitute        
  done clear
  D)
          Omnipresent
  done clear
  View Answer play_arrow

• question_answer229) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. That which cannot be called back
  A)
   Irresponsible                                  
  done clear
  B)
   Irrevocable                                     
  done clear
  C)
   Irredeemable    
  done clear
  D)
          Incalculable
  done clear
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• question_answer230) Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. One who journeys from place to place
  A)
   Quack                 
  done clear
  B)
   Cannibal             
  done clear
  C)
          Itinerant         
  done clear
  D)
          Courier
  done clear
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• question_answer231) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. We have already done the exercise.
  A)
   Already, the exercise has been done by us
  done clear
  B)
   The exercise has already been done by us
  done clear
  C)
   The exercise had been already done by us
  done clear
  D)
   The exercise is already done by us
  done clear
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• question_answer232) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. The main skills we seek to develop include analysing, interpreting and evaluating ideas.
  A)
   The main skills sought by us to develop include analysing, interpreting and evaluating ideas
  done clear
  B)
   The main skills that we are seeking to be developed include analysing, interpreting and evaluating ideas
  done clear
  C)
   The main skills sought to be developed by us include analysing, interpreting and evaluating ideas
  done clear
  D)
   The main skills include analysing, interpreting and evaluating kleas which are sought by us to develop
  done clear
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• question_answer233) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. Who can question Gandhis integrity?
  A)
   By whom Gandhis integrity can be questioned?
  done clear
  B)
   By whom can Gandhis integrity be questioned?
  done clear
  C)
   Gandhis integrity can be questioned by whom?
  done clear
  D)
   Who could have questioned Gandhis integrity?
  done clear
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• question_answer234) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. He presented me a bouquet on my birthday.
  A)
   A bouquet is presented to me on my birthday by him
  done clear
  B)
   I was presented on my birthday a bouquet by him
  done clear
  C)
   I was presented a bouquet on my birthday by him
  done clear
  D)
   I will be presented a bouquet on my birthday by him
  done clear
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• question_answer235) Directions: In the following questions, a sentence has been given in Active Voice/Passive Voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in Passive Voice/Active Voice. This surface feels smooth.
  A)
   This surface is felt smooth
  done clear
  B)
   This surface is smooth when it is felt
  done clear
  C)
   This surface when felt is smooth
  done clear
  D)
   This surface is smooth as felt
  done clear
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• question_answer236) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). In the desert, the sun is the master, all else resigns before its merciless rays.
  A)
   collapses            
  done clear
  B)
   falls                      
  done clear
  C)
   retires           
  done clear
  D)
          No improvement
  done clear
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• question_answer237) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). I intend to learn French next year.
  A)
   learning              
  done clear
  B)
   learn    
  done clear
  C)
          have learnt      
  done clear
  D)
          No improvement
  done clear
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• question_answer238) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). The police needed him for armed robbery.
  A)
   liked                                    
  done clear
  B)
   was after           
  done clear
  C)
          were looking to 
  done clear
  D)
         No improvement
  done clear
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• question_answer239) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). There is no more room for you in this compartment.
  A)
   no more seat
  done clear
  B)
   no more space
  done clear
  C)
   no more accommodation
  done clear
  D)
   No improvement
  done clear
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• question_answer240) Directions: In the following questions, a part of the sentence is printed bold. Below are given alternatives to the bold part at (a), (b) and (c), which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (d). It is easy to see why cities grew on the river banks
  A)
  along the river banks
  done clear
  B)
  in the river banks
  done clear
  C)
  upon the river banks
  done clear
  D)
  No improvement
  done clear
  View Answer play_arrow