Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2006

done JCECE Engineering Solved Paper-2006 Total Questions - 150

• question_answer1) Which of the following rays can be polarised?
  A)
  Water wave and sound wave
  done clear
  B)
  Sound wave and radio wave
  done clear
  C)
  \[X-\]rays and water wave
  done clear
  D)
  Light wave and \[X-\] ray
  done clear
  View Answer play_arrow

• question_answer2) Quantum nature can prove :
  A)
   interference
  done clear
  B)
   photoelectric effect
  done clear
  C)
    diffraction
  done clear
  D)
    polarisation
  done clear
  View Answer play_arrow

• question_answer3) Which one has highest binding energy per nucleon?
  A)
  \[F{{e}^{56}}\]                                 
  done clear
  B)
  \[L{{i}^{6}}\]
  done clear
  C)
   \[{{U}^{235}}\]                                
  done clear
  D)
   \[C{{a}^{40}}\]
  done clear
  View Answer play_arrow

• question_answer4) Huygen's wave theory can't explain:
  A)
   interference
  done clear
  B)
   photoelectric effect
  done clear
  C)
    diffraction
  done clear
  D)
    all of these
  done clear
  View Answer play_arrow

• question_answer5) If the refractive index of a glass prism is \[\cot (A/2)\] and \[A\] is angle of prism, then angle of minimum deviation is:
  A)
  \[\left( \frac{\pi }{2}-A \right)\]                
  done clear
  B)
  \[\left( 2\pi -\frac{A}{2} \right)\]
  done clear
  C)
   \[\left( \frac{\pi -A}{2} \right)\]                               
  done clear
  D)
   \[(\pi -2A)\]
  done clear
  View Answer play_arrow

• question_answer6) If \[f\] is the frequency when mass m is attached to a spring of spring constant \[k\], then new frequency for this arrangement, is:
  A)
  \[f/2\]                                  
  done clear
  B)
  \[\sqrt{2f}\]
  done clear
  C)
   \[f/\sqrt{2}\]                   
  done clear
  D)
   \[2\sqrt{2f}\]
  done clear
  View Answer play_arrow

• question_answer7) What is equivalent capacitance of the network? Each capacitor has \[1\mu F\] capacitance:
  A)
  \[\frac{1}{3}\mu F\]                       
  done clear
  B)
  \[2\mu F\]
  done clear
  C)
  \[\frac{3}{2}\mu F\]                       
  done clear
  D)
   \[3\mu F\]
  done clear
  View Answer play_arrow

• question_answer8) The two capacitors \[{{C}_{1}}\]and\[{{C}_{2}}\]are charged to potentials \[{{V}_{1}}\] and \[{{V}_{2}}\] then connected in parallel. There will be no flow of energy, if:
  A)
  \[{{C}_{1}}{{V}_{1}}={{C}_{2}}{{V}_{2}}\]                              
  done clear
  B)
  \[{{V}_{1}}={{V}_{2}}\]
  done clear
  C)
   \[{{C}_{1}}={{C}_{2}}\]                 
  done clear
  D)
   \[\frac{{{C}_{1}}}{{{V}_{1}}}=\frac{{{C}_{2}}}{{{V}_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer9) Which is not the unit of electric field?
  A)
  \[\frac{N}{C}\]                                 
  done clear
  B)
  \[\frac{N-m}{C}\]
  done clear
  C)
   \[\frac{V}{m}\]                               
  done clear
  D)
   \[\frac{J}{C\text{-}m}\]
  done clear
  View Answer play_arrow

• question_answer10) If a body moves for \[2\,\,s\] with \[15\,\,m/s\] velocity towards east and then moves with \[5\,\,m/s\] velocity for \[8\,\,s\] towards north, then average velocity is:
  A)
   \[5\,\,m/s\]                      
  done clear
  B)
   \[15\,\,m/s\]
  done clear
  C)
    \[30\,\,m/s\]                  
  done clear
  D)
    \[7.5\,\,m/s\]
  done clear
  View Answer play_arrow

• question_answer11) For monoatomic gas which is correct?
  A)
  \[CV=\frac{3}{5}R\]                        
  done clear
  B)
  \[{{C}_{P}}=\frac{5}{2}R\]
  done clear
  C)
   \[{{C}_{P}}-{{C}_{V}}=2R\]         
  done clear
  D)
   \[\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{3}{5}\]
  done clear
  View Answer play_arrow

• question_answer12) Which is correct relationship for diode?
  A)
                              
  done clear
  B)
  
  done clear
  C)
                              
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer13) In a properly biased transistor:
  A)
   both depletion layers are equally large
  done clear
  B)
   both depletion layers are equally small
  done clear
  C)
   emitter-base depletion layer is large but base-collector depletion layer is small
  done clear
  D)
    emitter-base depletion layer is small but base-collector depletion layer is large
  done clear
  View Answer play_arrow

• question_answer14) A wire has resistance \[20\,\,\Omega \]. If its length is increased three times its initial length, then new resistance is:
  A)
  \[40\Omega \]                                 
  done clear
  B)
  \[80\Omega \]
  done clear
  C)
   \[60\Omega \]                                
  done clear
  D)
   \[180\Omega \]
  done clear
  View Answer play_arrow

• question_answer15) A circular coil of diameter \[d\] is rotated in electric field such that electric flux is changed from zero to maximum value \[\phi \] then, electric field is:
  A)
  \[\frac{\phi }{\pi {{d}^{2}}}\]                                      
  done clear
  B)
  \[\frac{2\phi }{\pi {{d}^{2}}}\]
  done clear
  C)
   \[\frac{4{{d}^{2}}}{\pi {{\phi }^{2}}}\]                                   
  done clear
  D)
   \[\frac{4\phi }{\pi {{d}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer16) Work done in rotating a bar magnet from \[0\] to angle \[\theta \] is:
  A)
  \[MH(1-\cos \theta )\] 
  done clear
  B)
   \[\frac{M}{H}(1-\cos \theta )\]
  done clear
  C)
   \[\frac{M}{H}(\cos \theta -1)\]                
  done clear
  D)
   \[MH(\cos \theta -1)\]
  done clear
  View Answer play_arrow

• question_answer17) If a convex lens of refractive index \[1.44\] is dipped in liquid of refractive index \[1.49\], then it behaves as:
  A)
   concave lens   
  done clear
  B)
   convex lens
  done clear
  C)
    mirror                                
  done clear
  D)
    none of these
  done clear
  View Answer play_arrow

• question_answer18) If a source approaches and recedes from observer with same velocity, the ratio of frequencies (apparent) is \[6:5\], then velocity of source is:\[({{v}_{s}}=330\,\,m/s)\]
  A)
  \[20\,\,m/s\]                    
  done clear
  B)
  \[10\,\,m/s\]
  done clear
  C)
  \[30\,\,m/s\]                    
  done clear
  D)
   \[33\,\,m/s\]
  done clear
  View Answer play_arrow

• question_answer19) If a boy swings in a circle so the minimum and maximum height from ground is\[3\,\,m\]and\[6\,\,m\], then, its maximum velocity is:
  A)
  \[5\sqrt{2}m/s\]                              
  done clear
  B)
   \[2\sqrt{5}m/s\]
  done clear
  C)
   \[3\sqrt{5}m/s\]                             
  done clear
  D)
   \[5\sqrt{3}m/s\]
  done clear
  View Answer play_arrow

• question_answer20) If percentage decrease in radius of earth is \[1%\] without changing its mass, then percentage change in acceleration due to gravity is:
  A)
   \[2%\] decrease             
  done clear
  B)
   \[2%\] increase
  done clear
  C)
    \[1%\] decrease            
  done clear
  D)
    \[1%\] increase
  done clear
  View Answer play_arrow

• question_answer21) A black body radiates at two temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\] such that\[{{T}_{1}}<{{T}_{2}}\]. The frequency corresponding to maximum intensity is:
  A)
   less at\[{{T}_{1}}\]
  done clear
  B)
   more at\[{{T}_{1}}\]
  done clear
  C)
   equally in the two cases
  done clear
  D)
    cannot say
  done clear
  View Answer play_arrow

• question_answer22) If temperature is increased by \[1\,\,K\] at constant volume, then work done on the gas is:
  A)
  \[\frac{5}{2}R\]                                
  done clear
  B)
  \[\frac{3}{2}R\]
  done clear
  C)
   \[zero\]                                              
  done clear
  D)
   \[\frac{1}{2}R\]
  done clear
  View Answer play_arrow

• question_answer23) A body cools from\[{{75}^{o}}C\] to\[{{70}^{o}}C\] in time \[{{t}_{1}}\], from \[{{70}^{o}}C\] to \[{{65}^{o}}C\] in time \[{{t}_{2}}\] and from \[{{65}^{o}}C\] to \[{{60}^{o}}C\] in timer\[3\], then:
  A)
  \[{{t}_{3}}>{{t}_{2}}>{{t}_{1}}\]                
  done clear
  B)
  \[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\]
  done clear
  C)
   \[{{t}_{2}}>{{t}_{1}}={{t}_{3}}\]               
  done clear
  D)
   \[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer24) A gas is at \[{{27}^{o}}C\]. Its volume is doubled keeping pressure constant, then final temperature is:
  A)
  \[{{600}^{o}}C\]                               
  done clear
  B)
  \[327\,\,K\]
  done clear
  C)
  \[{{327}^{o}}C\]                               
  done clear
  D)
   \[{{273}^{o}}C\]
  done clear
  View Answer play_arrow

• question_answer25) If the volume of gas is changed from \[{{V}_{1}}\] to \[{{V}_{2}}\] isothermally, then work done is:
  A)
  \[RT\ln \frac{{{V}_{1}}}{{{V}_{2}}}\]                        
  done clear
  B)
  \[RT\ln \frac{{{V}_{2}}}{{{V}_{1}}}\]
  done clear
  C)
  \[R({{T}_{2}}-{{T}_{1}})\ln \frac{{{V}_{2}}}{{{V}_{1}}}\]  
  done clear
  D)
   \[R({{V}_{2}}-{{V}_{1}})\ln \frac{{{T}_{2}}}{{{T}_{1}}}\]
  done clear
  View Answer play_arrow

• question_answer26) If energy is supplied to a gas is ochorically, increase in internal energy is \[dU\] then:
  A)
  \[dQ=dU+dW\]
  done clear
  B)
  \[dQ=dU-dW\]
  done clear
  C)
   \[dQ=dU\]                        
  done clear
  D)
   \[dQ=-dU\]
  done clear
  View Answer play_arrow

• question_answer27) A nucleus \[_{Z}^{A}X\] emits one a and \[2\beta \] particles, then final nucleus is:
  A)
  \[Y_{Z-2}^{A}\]                                
  done clear
  B)
  \[Y_{Z-4}^{A-4}\]
  done clear
  C)
  \[Y_{Z}^{A-4}\]                                
  done clear
  D)
   \[X_{Z}^{A}\]
  done clear
  View Answer play_arrow

• question_answer28) The fringe width for red light is approximately how many times that for violet light in Young's slit experiment?
  A)
   \[2\] times                        
  done clear
  B)
   \[3\] times
  done clear
  C)
    Equal                                  
  done clear
  D)
    \[1/2\] times
  done clear
  View Answer play_arrow

• question_answer29) A person sees clearly at a distance of \[100\,\,cm\], then power of lens used to see object at \[40\,\,cm\] is:
  A)
  \[3D\]                                  
  done clear
  B)
  \[-3D\]
  done clear
  C)
   \[-1.5D\]                            
  done clear
  D)
   \[+1.5D\]
  done clear
  View Answer play_arrow

• question_answer30) The electric potential \[V\] is given as a function of distance \[x\] (metre) by\[V=(5{{x}^{2}}+10x-4)V\]. Value of electric field at \[x=1\,\,m\] is:
  A)
  \[-23\,\,V/m\]
  done clear
  B)
  \[11\,\,V/m\]
  done clear
  C)
   \[6\,\,V/m\]                     
  done clear
  D)
   \[-20\,\,V/m\]
  done clear
  View Answer play_arrow

• question_answer31) In an image converter tube fluorescent material is bombarded by:
  A)
   visible radiation
  done clear
  B)
   electron radiation
  done clear
  C)
   infrared radiation
  done clear
  D)
    ultra violet radiation
  done clear
  View Answer play_arrow

• question_answer32) A particle executes simple harmonic motion with a frequency\[f\]. The frequency with which its kinetic energy oscillates is:
  A)
  \[f/2\]                                  
  done clear
  B)
  \[f\]
  done clear
  C)
   \[2f\]                                   
  done clear
  D)
   \[4f\]
  done clear
  View Answer play_arrow

• question_answer33) The work done by the centripetal force \[F\] when the body completes one rotation around the circle of radius \[R\] is:
  A)
  \[2\pi RF\]                          
  done clear
  B)
  \[2RF\]
  done clear
  C)
   \[RF\]                                  
  done clear
  D)
   \[zero\]
  done clear
  View Answer play_arrow

• question_answer34) The unit mass having \[\overset{\to }{\mathop{\mathbf{r}}}\,=8\widehat{\mathbf{i}}-4\widehat{\mathbf{j}}\] and \[\overset{\to }{\mathop{\mathbf{v}}}\,=8\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}\] in its angular momentum is:
  A)
   \[64\] unit in \[-\mathbf{\hat{k}}\] direction
  done clear
  B)
   \[64\]unit in \[+\mathbf{\hat{k}}\] direction
  done clear
  C)
    \[64\]unit in \[+\widehat{\mathbf{j}}\] direction
  done clear
  D)
    \[64\]unit in \[+\widehat{\mathbf{i}}\] direction
  done clear
  View Answer play_arrow

• question_answer35) Which is nuclear fusion direction?
  A)
   Hydrogen to helium
  done clear
  B)
   Uranium to krypton
  done clear
  C)
    Hydrogen to water
  done clear
  D)
    Neutron to proton
  done clear
  View Answer play_arrow

• question_answer36) If an \[AC\] produces same heat as that produced by a steady current of \[4\,\,A\], then peak value of current is:
  A)
  \[4\,\,A\]                                            
  done clear
  B)
  \[1.56\,\,A\]
  done clear
  C)
   \[5.6\,\,A\]                       
  done clear
  D)
   \[1.41\,\,A\]
  done clear
  View Answer play_arrow

• question_answer37) In\[LCR\]circuit \[f=\frac{50}{\pi }Hz,\] \[V=50\,\,volt,\]\[R=300\Omega \]. If\[L=1\,\,H\]and\[C=20\,\,\mu C\], then voltage across capacitor is:
  A)
  \[zero\]                                               
  done clear
  B)
  \[20\,\,V\]
  done clear
  C)
   \[30\,\,V\]                        
  done clear
  D)
   \[50\,\,V\]
  done clear
  View Answer play_arrow

• question_answer38) If two forces each of \[2\,\,N\] are inclined at \[{{60}^{o}}\], then resultant force is:
  A)
  \[2\,\,N\]                                           
  done clear
  B)
  \[2\sqrt{5}N\]
  done clear
  C)
  \[3\sqrt{2}N\]                  
  done clear
  D)
   \[4\sqrt{2}N\]
  done clear
  View Answer play_arrow

• question_answer39) A block of mass \[10\,\,kg\] is placed on a rough horizontal surface whose coefficient of friction is 0.5. If a horizontal force of \[100\,\,N\] is applied on it, then acceleration of block will be:
  A)
  \[10\,\,m/{{s}^{2}}\]                     
  done clear
  B)
  \[5\,\,m/{{s}^{2}}\]
  done clear
  C)
   \[15\,\,m/{{s}^{2}}\]                    
  done clear
  D)
   \[0.5\,\,m/{{s}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer40) The potential difference across an instrument in a \[AC\] circuit of frequency \[f\] is \[V\] and the current through it is \[I\] such that \[V=5\cos 2\pi ft\,\,volt\] and \[I=2\sin 2\pi ft\,\,amp\]. The power dissipated in the instrument is:
  A)
  \[zero\]                                               
  done clear
  B)
   \[10\,\,W\]
  done clear
  C)
   \[5\,\,W\]                                         
  done clear
  D)
   \[2.5\,\,W\]
  done clear
  View Answer play_arrow

• question_answer41) If ratio of intensities of interfering waves is \[16:9\], then ratio of maximum to minimum intensity is:
  A)
  \[49:1\]                               
  done clear
  B)
  \[225:81\]
  done clear
  C)
  \[3:1\]                                  
  done clear
  D)
  \[9:1\]
  done clear
  View Answer play_arrow

• question_answer42) The power of a lens, a short sighted person uses is \[-2\,\,D\]. Find the maximum distance of an object which he can see without spectacles:
  A)
  \[25\,\,cm\]                      
  done clear
  B)
  \[50\,\,cm\]
  done clear
  C)
  \[100\,\,cm\]                    
  done clear
  D)
  \[10\,\,cm\]
  done clear
  View Answer play_arrow

• question_answer43) The first overtone frequency of a wave on string of length \[2\,\,m\] is \[250\,\,Hz\]. Then, its velocity is:
  A)
  \[1000\,\,m/s\]                
  done clear
  B)
  \[25\,\,m/s\]
  done clear
  C)
   \[100\,\,cm\]                   
  done clear
  D)
  \[10\,\,cm\]
  done clear
  View Answer play_arrow

• question_answer44) What is the current flowing in arm\[AB\]?
  A)
  \[\frac{35}{4}A\]                             
  done clear
  B)
  \[\frac{13}{7}A\]
  done clear
  C)
  \[\frac{5}{7}A\]                                
  done clear
  D)
  \[\frac{7}{5}A\]
  done clear
  View Answer play_arrow

• question_answer45) A projectile is fired making an angle \[2\theta \] with horizontal with velocity\[4\,\,m/s\]. At any instant it makes an angle \[\theta \], then its velocity is:
  A)
  \[4\cos \theta \]
  done clear
  B)
  \[4(2\cos \theta -\sec \theta )\]
  done clear
  C)
   \[2(\sec \theta +4\cos \theta )\]
  done clear
  D)
   \[4(\sec \theta +\cos \theta )\]
  done clear
  View Answer play_arrow

• question_answer46) If path difference becomes \[(2n-1)\frac{\lambda }{2}\] then:
  A)
   white fringe is formed
  done clear
  B)
   bright fringe is formed
  done clear
  C)
    uniform illumination is obtained
  done clear
  D)
    dark fringe is formed
  done clear
  View Answer play_arrow

• question_answer47) If the intensity of fringe at wavelength\[\lambda \]is\[K\], then its intensity at wavelength \[\lambda /2\] is:
  A)
  \[\frac{K}{2}\]                                  
  done clear
  B)
  \[K\]
  done clear
  C)
   \[zero\]                                              
  done clear
  D)
   \[\sqrt{2}K\]
  done clear
  View Answer play_arrow

• question_answer48) A positively charged particle moving with velocity \[v\] enters a region of space having a uniform magnetic field \[B\]. The particle will experience the large deflecting force, when the angle between \[v\] and \[B\] is:
  A)
  \[{{0}^{o}}\]                                      
  done clear
  B)
  \[{{45}^{o}}\]
  done clear
  C)
   \[{{90}^{o}}\]                                   
  done clear
  D)
   \[{{180}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer49) In a step-up transformer the turn ratio is\[1:8\]. A lead accumulator \[(emf=6\,\,V)\] is connected across the primary coil of the transformer. The voltage across the secondary coil is:
  A)
  \[48\,\,V\]                         
  done clear
  B)
  \[0.75\,\,V\]
  done clear
  C)
   \[14\,\,V\]                                        
  done clear
  D)
   \[zero\]
  done clear
  View Answer play_arrow

• question_answer50) The mass of a lift is\[500\,\,kg\]. When it ascends with an acceleration of \[2m/{{s}^{2}}\] the tension in the cable will be:\[(g=10\,\,m/{{s}^{2}})\]
  A)
  \[6000\,\,N\]                    
  done clear
  B)
  \[5000\,\,N\]
  done clear
  C)
   \[4000\,\,N\]                   
  done clear
  D)
   \[1000\,\,N\]
  done clear
  View Answer play_arrow

• question_answer51) A water molecule can form maximum number of \[H-\]bond which is equal to:
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
   \[3\]                                    
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer52) Bond angle in \[{{H}_{2}}O\] is:
  A)
  \[{{109}^{o}}28'\]                            
  done clear
  B)
  \[{{107}^{o}}10\]
  done clear
  C)
   \[{{104.5}^{o}}\]                             
  done clear
  D)
   \[{{92}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer53) Calamine is:
  A)
  \[ZnS\]                                
  done clear
  B)
  \[PbC{{O}_{3}}\]
  done clear
  C)
  \[ZnC{{O}_{3}}\]                              
  done clear
  D)
  \[MgC{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer54) Which is extremely stable?
  A)
  \[N{{F}_{3}}\]                                   
  done clear
  B)
  \[NC{{l}_{3}}\]
  done clear
  C)
  \[NB{{r}_{3}}\]                 
  done clear
  D)
   \[N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer55) \[C{{H}_{3}}COCl\]does not react with:
  A)
   diethyl ether   
  done clear
  B)
   phenol
  done clear
  C)
    ethanol                             
  done clear
  D)
    aniline
  done clear
  View Answer play_arrow

• question_answer56) In \[S{{O}_{2}}\] hybridisation is:
  A)
  \[sp\]                                   
  done clear
  B)
  \[s{{p}^{3}}\]
  done clear
  C)
   \[ds{{p}^{2}}\]                                
  done clear
  D)
   \[s{{p}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer57) Lowest melting point chloride is:
  A)
  \[LiCl\]                 
  done clear
  B)
  \[NaCl\]
  done clear
  C)
   \[KCl\]                                
  done clear
  D)
   \[CsCl\]
  done clear
  View Answer play_arrow

• question_answer58) Half-life of a substance is\[6\min \]. If its initial amount is\[32\,\,g\], then amount present after \[18\,\,\min \] is:
  A)
  \[4\,\,g\]                                            
  done clear
  B)
  \[8\,\,g\]
  done clear
  C)
  \[16\,\,g\]                                          
  done clear
  D)
   \[2\,\,g\]
  done clear
  View Answer play_arrow

• question_answer59) If calcium acetate and calcium for mate react, then product formed is:
  A)
   acetaldehyde                  
  done clear
  B)
   acetic acid
  done clear
  C)
    formic acid                       
  done clear
  D)
    ethyl for mate
  done clear
  View Answer play_arrow

• question_answer60) Reduction with aluminium isopropoxide in excess of isopropyl alcohol is called Meer we in Pond or f Verley reduction\[(MPV)\]. What will be the firal product when cyclohex-2-enone is selectively reduced in \[MPV\] reaction?
  A)
   Cyclohexanol  
  done clear
  B)
   Cyclohex-2-enol
  done clear
  C)
    Cyclohexanone              
  done clear
  D)
    Benzene
  done clear
  View Answer play_arrow

• question_answer61) If \[pH\] of a solution is\[4\], then \[{{H}^{+}}\] is:
  A)
  \[{{10}^{4}}\]                                    
  done clear
  B)
  \[{{10}^{10}}\]
  done clear
  C)
  \[{{10}^{-4}}\]                                  
  done clear
  D)
   \[{{10}^{-10}}\]
  done clear
  View Answer play_arrow

• question_answer62) When sodium nitrate is heated above\[{{6000}^{o}}C\], then:
  A)
   only \[N{{a}_{2}}O\] is formed
  done clear
  B)
   only \[{{N}_{3}}\] is formed
  done clear
  C)
    only \[{{O}_{2}}\] is formed
  done clear
  D)
    all are formed
  done clear
  View Answer play_arrow

• question_answer63) Which of the following produces \[C{{l}_{2}}\] gas?
  A)
  \[NaCl+HN{{O}_{3}}\]   
  done clear
  B)
  \[Mn{{O}_{2}}+HCl\]
  done clear
  C)
   \[KMn{{O}_{4}}+HCl\] 
  done clear
  D)
  \[HCl+HN{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer64) Which is correctly arranged as increasing size?
  A)
  \[F<O<C<Cl<Br\]
  done clear
  B)
  \[C<O<F<Cl<Br\]
  done clear
  C)
  \[Cl<Br<F<C<O\]
  done clear
  D)
   \[O<F<C<Cl<Br\]
  done clear
  View Answer play_arrow

• question_answer65) \[N{{H}_{3}}\] is absorbed by:
  A)
   ozone                 
  done clear
  B)
   \[CaO\]
  done clear
  C)
   pyrargallol                         
  done clear
  D)
   \[CaC{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer66) \[1.25\,\,g\]\[N{{H}_{3}}\] contains how many atoms?
  A)
  \[{{10}^{23}}\]                                  
  done clear
  B)
  \[2\times {{10}^{23}}\]
  done clear
  C)
  \[6\times {{10}^{13}}\]                 
  done clear
  D)
   \[4\times {{10}^{23}}\]
  done clear
  View Answer play_arrow

• question_answer67) Which of the following has smallest bond angle?
  A)
   Ethane                                
  done clear
  B)
   Ethene
  done clear
  C)
   Ethyne                                
  done clear
  D)
    Ethanol
  done clear
  View Answer play_arrow

• question_answer68) Chloroform in air is oxidised to :
  A)
  \[CC{{l}_{4}}\]                                  
  done clear
  B)
   dichloromethane
  done clear
  C)
    phosgene         
  done clear
  D)
    oxygen
  done clear
  View Answer play_arrow

• question_answer69) Gypsum is:
  A)
  \[CaS{{O}_{4}}\cdot 2{{H}_{2}}O\]          
  done clear
  B)
  \[CaS{{O}_{4}}\cdot \frac{1}{2}{{H}_{2}}O\]
  done clear
  C)
   \[MgS{{O}_{4}}\cdot 2{{H}_{2}}O\]        
  done clear
  D)
  \[CuS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer70) Which is not soluble in water?
  A)
  \[PbS{{O}_{4}}\]              
  done clear
  B)
   \[CdS{{O}_{4}}\]
  done clear
  C)
  \[Bi{{(S{{O}_{4}})}_{2}}\]                             
  done clear
  D)
   \[CuS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer71) Which of the following is colour red?
  A)
  \[C{{u}_{2}}O\]                
  done clear
  B)
  \[CuF\]
  done clear
  C)
  \[Zn{{F}_{2}}\]                 
  done clear
  D)
   \[ZnC{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer72) How many unpaired electrons are present in\[[Cr{{(N{{H}_{3}})}_{5}}]B{{r}_{3}}\]?
  A)
   \[1\]                                    
  done clear
  B)
   \[2\]
  done clear
  C)
    \[3\]                                   
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer73) \[S+\frac{3}{2}{{O}_{2}}\xrightarrow{{}}S{{O}_{3}}\Delta H=2x\],\[S{{O}_{2}}+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}S{{O}_{3}}\Delta H=y\],then heat of formation of \[S{{O}_{2}}\] is:
  A)
  \[2x-y\]                               
  done clear
  B)
  \[2x+y\]
  done clear
  C)
  \[x+y\]                
  done clear
  D)
  \[\frac{2x-y}{2}\]
  done clear
  View Answer play_arrow

• question_answer74) Reagent (catalyst) used in Friedel-Craft's alkylation reaction is:
  A)
  \[AlC{{l}_{3}}\]                 
  done clear
  B)
  \[anhyd.\,\,AlC{{l}_{3}}\]
  done clear
  C)
  \[{{N}_{2}}\]                                     
  done clear
  D)
  \[He\]
  done clear
  View Answer play_arrow

• question_answer75) Catalyst used in making \[{{H}_{2}}S{{O}_{4}}\] in contact process is:
  A)
  \[{{V}_{2}}{{O}_{5}}\]                                   
  done clear
  B)
  \[F{{e}_{2}}{{O}_{3}}\]
  done clear
  C)
  \[C{{r}_{2}}{{O}_{3}}\]                  
  done clear
  D)
  \[Cr{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer76) When acetamide is reacted with \[NaOBr\], then product formed is:
  A)
   ethanamine     
  done clear
  B)
   methanamine
  done clear
  C)
   methanamide                 
  done clear
  D)
   ethanenitrile
  done clear
  View Answer play_arrow

• question_answer77) Isocyanide is prepared by :
  A)
   Friedel Craft's reaction
  done clear
  B)
   Wurtz's reacdon
  done clear
  C)
   Williamson synthesis
  done clear
  D)
   Carbylamine reaction
  done clear
  View Answer play_arrow

• question_answer78) If rate of diffusion of \[C{{H}_{4}}\] is twice than that of a gas\[x\], then its molecular mass is:
  A)
  \[64\,\,g\]                          
  done clear
  B)
  \[16\,\,g\]
  done clear
  C)
  \[32\,\,g\]                                          
  done clear
  D)
  \[8\,\,g\]
  done clear
  View Answer play_arrow

• question_answer79) Which one is not Lewis acid?
  A)
  \[Be{{F}_{2}}\]                 
  done clear
  B)
  \[SnC{{l}_{4}}\]
  done clear
  C)
  \[AlC{{l}_{3}}\]                 
  done clear
  D)
   \[B{{F}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer80) Natural gas mainly consists of:
  A)
   methane           
  done clear
  B)
   butane
  done clear
  C)
   propane                             
  done clear
  D)
   ethane \[+\] octane
  done clear
  View Answer play_arrow

• question_answer81) Phenol is treated with \[Zn\] to form:
  A)
   benzoic acid     
  done clear
  B)
   benzyl alcohol
  done clear
  C)
   benzene                            
  done clear
  D)
   benzoquinone
  done clear
  View Answer play_arrow

• question_answer82) Which one is isoelectronic with\[CO?\]
  A)
  \[N_{2}^{-}\]                                    
  done clear
  B)
  \[N_{2}^{+}\]
  done clear
  C)
  \[C{{N}^{-}}\]                                   
  done clear
  D)
  \[NO\]
  done clear
  View Answer play_arrow

• question_answer83) How much volume of \[1\,\,M\,\,{{H}_{2}}S{{O}_{4}}\] is required to neutralize \[20\,\,mL\] of\[1M\,\,NaOH\]?
  A)
  \[10\,\,mL\]
  done clear
  B)
  \[20\,\,mL\]
  done clear
  C)
  \[5\,\,mL\]                         
  done clear
  D)
  \[15\,\,mL\]
  done clear
  View Answer play_arrow

• question_answer84) Fenton's reagent is:
  A)
  \[SnC{{l}_{2}}+HCl\]                       
  done clear
  B)
  \[AgN{{O}_{3}}+N{{H}_{4}}OH\]
  done clear
  C)
  \[CuS{{O}_{4}}+NaOH\]               
  done clear
  D)
   \[FeS{{O}_{4}}+{{H}_{2}}{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer85) \[C{{u}^{2+}}+Ag\xrightarrow{{}}Cu+A{{g}^{+}}\] oxidation half reaction is:
  A)
  \[C{{u}^{2+}}\to Cu\]                    
  done clear
  B)
  \[Ag\to A{{g}^{+}}\]
  done clear
  C)
   \[Cu\to C{{u}^{2+}}\]                   
  done clear
  D)
    all of these
  done clear
  View Answer play_arrow

• question_answer86) \[{{C}_{4}}{{H}_{10}}O\] has how many isomeric alcohols?
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[3\]                                     
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer87) \[IUPAC\]name of\[C{{H}_{3}}-C\equiv C-HC-{{(C{{H}_{3}})}_{2}}\]is:
  A)
   4-methyl-2-pentyne
  done clear
  B)
   1, 1-dimethyl-2-butyne
  done clear
  C)
   2-methyl-4-pentyne
  done clear
  D)
    4, 4-dimethyl-2-butyne
  done clear
  View Answer play_arrow

• question_answer88) Fehling test is given by:
  A)
   glucose                               
  done clear
  B)
   fructose
  done clear
  C)
   sucrose                              
  done clear
  D)
    all of these
  done clear
  View Answer play_arrow

• question_answer89) Number of isomeric primary amine of molecular formula \[{{C}_{4}}{{H}_{11}}N\] is:
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[3\]                                     
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer90) For reaction\[3X+Y{{X}_{3}}Y\]\[\Delta H=+ve\], amount of \[{{X}_{3}}Y\] can be changed by:
  A)
   changing temperature
  done clear
  B)
   changing pressure
  done clear
  C)
   changing temperature, pressure,
  done clear
  D)
   changing temperature, pressure, adding catalyst
  done clear
  View Answer play_arrow

• question_answer91) Which one is most ionic?
  A)
  \[{{P}_{2}}{{O}_{5}}\]                                    
  done clear
  B)
  \[Mn{{O}_{2}}\]
  done clear
  C)
  \[M{{n}_{2}}{{O}_{7}}\]               
  done clear
  D)
  \[{{P}_{2}}{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer92) Which one gives \[{{I}_{2}}\] on reaction with\[KI?\]
  A)
  \[A{{g}_{2}}S{{O}_{4}}\]                               
  done clear
  B)
  \[CuS{{O}_{4}}\]
  done clear
  C)
  \[PbS{{O}_{4}}\]                              
  done clear
  D)
   \[CdS{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer93) Colour of the solution when \[KI\] reacts with \[B{{r}_{2}}\] is:
  A)
   blue                                     
  done clear
  B)
   black
  done clear
  C)
   red                                       
  done clear
  D)
    no change
  done clear
  View Answer play_arrow

• question_answer94) Finely divided iron combines with \[CO\] to give:
  A)
  \[Fe{{(CO)}_{5}}\]                          
  done clear
  B)
  \[F{{e}_{2}}{{(CO)}_{9}}\]
  done clear
  C)
   \[F{{e}_{3}}{{(CO)}_{12}}\]                        
  done clear
  D)
   \[Fe{{(CO)}_{6}}\]
  done clear
  View Answer play_arrow

• question_answer95) Which of the following is pyramidal?
  A)
  \[PC{{l}_{3}}\]                                  
  done clear
  B)
  \[CO_{3}^{2-}\]
  done clear
  C)
   \[S{{O}_{2}}\]                                  
  done clear
  D)
   \[NO_{3}^{-}\]
  done clear
  View Answer play_arrow

• question_answer96) Which of the following conducts electricity?
  A)
   Crystal\[NaCl\]                
  done clear
  B)
   Diamond
  done clear
  C)
   Molten\[KBr\]                 
  done clear
  D)
   Sulphur
  done clear
  View Answer play_arrow

• question_answer97) Ratio of kinetic energy of hydrogen and helium gas at \[300\,\,K\] is:
  A)
  \[2:1\]                                  
  done clear
  B)
  \[4:5\]
  done clear
  C)
  \[1:1\]                                  
  done clear
  D)
   \[1:2\]
  done clear
  View Answer play_arrow

• question_answer98) Which of the following has highest energy?
  A)
  \[n=2,\,\,l=1\]                  
  done clear
  B)
  \[n=3,\,\,l=2\]
  done clear
  C)
   \[n=3,\,\,l=1\]                 
  done clear
  D)
   \[n=2,\,\,l=0\]
  done clear
  View Answer play_arrow

• question_answer99) Oxidation   state   of   phosphorus   in pyrophosphoric acid is:
  A)
  \[+5\]                                   
  done clear
  B)
  \[+3\]
  done clear
  C)
  \[+4\]                                   
  done clear
  D)
   \[+1\]
  done clear
  View Answer play_arrow

• question_answer100) If the \[75%\] of a first order reaction is complete in\[8\min \], then time taken to decompose \[50%\] of its initial amount is:
  A)
  \[2\min \]                           
  done clear
  B)
  \[4\min \]
  done clear
  C)
   \[12\min \]                       
  done clear
  D)
   \[1\min \]
  done clear
  View Answer play_arrow

• question_answer101) If\[a\ne \beta \]and\[{{\alpha }^{2}}=5\alpha -3,\,\,{{\beta }^{2}}=5\beta -3\]then the equation having \[\alpha /\beta \] and \[\beta /\alpha \] as its roots is:
  A)
  \[3{{x}^{2}}+19x+3=0\]
  done clear
  B)
  \[3{{x}^{2}}-19x+3=0\]
  done clear
  C)
  \[3{{x}^{2}}-19x-3=0\]
  done clear
  D)
  \[{{x}^{2}}-16x+1=0\]
  done clear
  View Answer play_arrow

• question_answer102) If\[y={{(x+\sqrt{1+{{x}^{2}}})}^{n}}\], then\[{{(1+x)}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}\]is
  A)
  \[{{n}^{2}}y\]                                    
  done clear
  B)
  \[-{{n}^{2}}y\]
  done clear
  C)
  \[-y\]                                    
  done clear
  D)
  \[2{{x}^{2}}y\]
  done clear
  View Answer play_arrow

• question_answer103) If\[1,\,\,{{\log }_{3}}\sqrt{({{3}^{1-x}}+2)},\,\,{{\log }_{3}}(4\cdot {{3}^{x}}-1)\]are in \[AP\], then \[x\] equals:
  A)
  \[{{\log }_{3}}4\]                             
  done clear
  B)
  \[1-{{\log }_{3}}4\]
  done clear
  C)
  \[1-{{\log }_{4}}3\]                         
  done clear
  D)
  \[{{\log }_{4}}3\]
  done clear
  View Answer play_arrow

• question_answer104) A problem in mathematics is given to three students \[A,\,\,\,B,\,\,\,C\] and their respective probability of solving the problem is \[\frac{1}{2},\,\,\,\frac{1}{3}\] and\[\frac{1}{4}\]. Probability that the problem is solved, is:
  A)
  \[\frac{3}{4}\]                                   
  done clear
  B)
  \[\frac{1}{2}\]
  done clear
  C)
  \[\frac{2}{3}\]                                   
  done clear
  D)
  \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer105) The angle of elevation of a tower at a point distant \[d\] metres from its base is\[{{30}^{o}}\]. If the tower is \[20\,\,m\] high, then the value of \[d\] is:
  A)
  \[10\sqrt{3}m\]               
  done clear
  B)
  \[\frac{20}{\sqrt{3}}m\]
  done clear
  C)
  \[20\sqrt{3}m\]               
  done clear
  D)
  \[10\,\,m\]
  done clear
  View Answer play_arrow

• question_answer106) \[l,\,\,\,m,\,\,\,n\] are the \[p\text{th}\], \[q\text{th}\] and \[r\text{th}\] terms of a \[GP\] and all positive, then\[\left| \begin{matrix}    \log l & p & 1  \\    \log m & q & 1  \\    \log n & r & 1  \\ \end{matrix} \right|\]equals:
  A)
  \[3\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[1\]                                     
  done clear
  D)
  \[zero\]
  done clear
  View Answer play_arrow

• question_answer107) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}\]is equal to:
  A)
  \[\lambda \]                                      
  done clear
  B)
  \[-1\]
  done clear
  C)
   zero                                     
  done clear
  D)
   does not exist
  done clear
  View Answer play_arrow

• question_answer108) A triangle with vertices\[(4,\,\,0),\,\,(-1,\,\,-1),\,\,(3,\,\,5)\] is:
  A)
   isosceles and right angled
  done clear
  B)
   isosceles but not right angled
  done clear
  C)
   right angled but not isosceles
  done clear
  D)
   neither right angled nor isosceles
  done clear
  View Answer play_arrow

• question_answer109) \[{{\cot }^{-1}}(\sqrt{\cos \alpha })-{{\tan }^{-1}}(\sqrt{\cos \alpha })=x\], then\[\sin x\]is equal to:
  A)
  \[{{\tan }^{2}}\left( \frac{\alpha }{2} \right)\]                     
  done clear
  B)
  \[{{\cot }^{2}}\left( \frac{\alpha }{2} \right)\]
  done clear
  C)
  \[\tan \alpha \]                
  done clear
  D)
  \[\cot \left( \frac{\alpha }{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer110) A plane which passes through the point \[(3,\,\,2,\,\,0)\] and the line\[\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}\]is:
  A)
  \[x-y+z=1\]                        
  done clear
  B)
  \[x+y+z=5\]
  done clear
  C)
  \[x+2y-z=1\]     
  done clear
  D)
  \[2x-y+z=5\]
  done clear
  View Answer play_arrow

• question_answer111) The solution of the equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}\] is:
  A)
  \[\frac{{{e}^{-2x}}}{4}\]                               
  done clear
  B)
  \[\frac{{{e}^{-2x}}}{4}+cx+d\]
  done clear
  C)
  \[\frac{1}{4}{{e}^{-2x}}+c{{x}^{2}}+d\]  
  done clear
  D)
  \[\frac{1}{4}{{e}^{-2x}}+c+d\]
  done clear
  View Answer play_arrow

• question_answer112) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+2} \right)}^{x}}\]is equal to:
  A)
  \[{{e}^{4}}\]                                      
  done clear
  B)
  \[{{e}^{2}}\]
  done clear
  C)
  \[{{e}^{3}}\]                                      
  done clear
  D)
  \[e\]
  done clear
  View Answer play_arrow

• question_answer113) The domain of\[{{\sin }^{-1}}\left[ {{\log }_{3}}\left( \frac{x}{3} \right) \right]\]is:
  A)
  \[[1,\,\,9]\]                                        
  done clear
  B)
  \[[-1,\,\,9]\]
  done clear
  C)
  \[[-9,\,\,1]\]                      
  done clear
  D)
  \[[-9,\,\,-1]\]
  done clear
  View Answer play_arrow

• question_answer114) The value of\[{{2}^{1/4}}\cdot {{4}^{1/8}}\cdot {{8}^{1/16}}...\infty \]is
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[3\]                                     
  done clear
  D)
  \[4\]
  done clear
  View Answer play_arrow

• question_answer115) Fifth term of a \[GP\] is \[2\], then the product of its \[9\] terms is:
  A)
   256                                       
  done clear
  B)
   512
  done clear
  C)
   1024                                     
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer116) \[\int_{0}^{10\pi }{|\sin x|}\,\,dx\]is:
  A)
  \[20\]                                   
  done clear
  B)
  \[8\]
  done clear
  C)
  \[10\]                                   
  done clear
  D)
  \[18\]
  done clear
  View Answer play_arrow

• question_answer117) \[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}x}\,\,dx\], then\[\underset{n\to \infty }{\mathop{\lim }}\,n[{{I}_{n}}+{{I}_{n+2}}]\] equal to:
  A)
  \[\frac{1}{2}\]                                   
  done clear
  B)
  \[1\]
  done clear
  C)
  \[\infty \]                                           
  done clear
  D)
  \[zero\]
  done clear
  View Answer play_arrow

• question_answer118) \[\int_{-\pi }^{\pi }{\frac{2x(1+\sin x)}{1+{{\cos }^{2}}x}}dx\]is:
  A)
  \[\frac{{{\pi }^{2}}}{4}\]                               
  done clear
  B)
  \[{{\pi }^{2}}\]
  done clear
  C)
  \[zero\]                                               
  done clear
  D)
  \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer119) The period of the function\[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\] is:
  A)
  \[\pi \]                                 
  done clear
  B)
  \[\frac{\pi }{2}\]
  done clear
  C)
  \[2\pi \]                                               
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer120) If\[{{x}^{y}}={{e}^{x-y}}\], then\[\frac{dy}{dx}\]is:
  A)
  \[\frac{1+x}{1+\log x}\]                
  done clear
  B)
  \[\frac{1-\log x}{1+\log x}\]
  done clear
  C)
   not defined                      
  done clear
  D)
  \[\frac{\log x}{{{(1+\log x)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer121) The two curves \[{{x}^{3}}-3x{{y}^{2}}+2=0\] and\[3{{x}^{2}}y-{{y}^{3}}-2=0\]
  A)
   cut at right angles
  done clear
  B)
   touch each other
  done clear
  C)
   cut at an angle\[\frac{\pi }{3}\]
  done clear
  D)
   cut at an angle\[\frac{\pi }{4}\]
  done clear
  View Answer play_arrow

• question_answer122) 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_answer123) The greatest value of\[f(x)={{(x+1)}^{1/3}}-{{(x-1)}^{1/3}}\]on\[[0,\,\,1]\]is:
  A)
  \[1\]                                     
  done clear
  B)
  \[2\]
  done clear
  C)
  \[3\]                                     
  done clear
  D)
  \[1/3\]
  done clear
  View Answer play_arrow

• question_answer124) \[\int{\frac{dx}{x({{x}^{n}}+1)}}\]is equal to:
  A)
  \[\frac{1}{n}\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]
  done clear
  B)
  \[\frac{1}{n}\log \left( \frac{{{x}^{n}}+1}{{{x}^{n}}} \right)+c\]
  done clear
  C)
  \[\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer125) The area bounded by the curve \[y=2x-{{x}^{2}}\] and the straight line \[y=-x\] is given by:
  A)
  \[\frac{9}{2}sq\,\,unit\]               
  done clear
  B)
  \[\frac{43}{6}sq\,\,unit\]
  done clear
  C)
  \[\frac{35}{6}sq\,\,unit\]                             
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer126) The differential equation of all non-vertical lines in a plane is:
  A)
  \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\]                          
  done clear
  B)
  \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\]
  done clear
  C)
  \[\frac{dy}{dx}=0\]                        
  done clear
  D)
  \[\frac{dx}{dy}=0\]
  done clear
  View Answer play_arrow

• question_answer127) Given two vectors \[\widehat{\mathbf{i}}-\widehat{\mathbf{j}}\] and \[\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}\] the unit vector coplanar with the two vectors and perpendicular to first is:
  A)
  \[\pm \frac{1}{\sqrt{2}}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}})\]                               
  done clear
  B)
  \[\frac{1}{\sqrt{5}}(2\widehat{\mathbf{i}}+\widehat{\mathbf{j}})\]
  done clear
  C)
  \[\pm \frac{1}{\sqrt{2}}(\widehat{\mathbf{i}}+\widehat{\mathbf{k}})\]                              
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer128) The vector \[\widehat{\mathbf{i}}+x\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}\] is rotated through an angle \[\theta \] and doubled in magnitude, then it becomes\[4\widehat{\mathbf{i}}+(4x-2)\widehat{\mathbf{j}}+2\widehat{\mathbf{k}}\]. The value of is:
  A)
  \[\left\{ -\frac{2}{3},\,\,2 \right\}\]                         
  done clear
  B)
  \[\left\{ \frac{1}{3},\,\,2 \right\}\]
  done clear
  C)
  \[\left\{ \frac{2}{3},\,\,0 \right\}\]                           
  done clear
  D)
  \[\{2,\,\,7\}\]
  done clear
  View Answer play_arrow

• question_answer129) A parallelepiped is formed by planes drawn through the points \[(2,\,\,3,\,\,5)\] and \[(5,\,\,9,\,\,7)\] parallel to the coordinate planes. The length of a diagonal of the parallelepiped to piped is:
  A)
  \[7\]                                     
  done clear
  B)
  \[\sqrt{38}\]
  done clear
  C)
  \[\sqrt{155}\]                   
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer130) The equation of the plane containing the line\[\frac{x-{{x}_{1}}}{l}=\frac{y-{{y}_{1}}}{m}=\frac{z-{{z}_{1}}}{n}\]is\[a(x-{{x}_{1}})+b(y-{{y}_{1}})+c(z-{{z}_{1}})=0\], where:
  A)
  \[a{{x}_{1}}+b{{y}_{1}}+c{{z}_{1}}=0\]
  done clear
  B)
  \[al+bm+cn=0\]
  done clear
  C)
  \[\frac{a}{l}=\frac{b}{m}=\frac{c}{n}\]
  done clear
  D)
   \[l{{x}_{1}}+m{{y}_{1}}+n{{z}_{1}}=0\]
  done clear
  View Answer play_arrow

• question_answer131) \[A\] and \[B\] play a game where each is asked to select a number from \[1\] to\[25\]. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is:
  A)
  \[\frac{1}{25}\]                                
  done clear
  B)
  \[\frac{24}{25}\]
  done clear
  C)
  \[\frac{2}{25}\]                                
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer132) The equation of the 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_answer133) Let \[{{T}_{n}}\] denote the number of triangles which can be formed using the vertices of a regular polygon of \[n\] sides. If\[{{T}_{n+1}}-{{T}_{n}}=21\], then n equals:
  A)
  \[5\]                                     
  done clear
  B)
  \[7\]
  done clear
  C)
  \[6\]                                     
  done clear
  D)
  \[4\]
  done clear
  View Answer play_arrow

• question_answer134) In a triangle \[ABC\], \[\frac{A-B+C}{2}\]is equal to:
  A)
  \[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}\]               
  done clear
  B)
  \[{{c}^{2}}+{{a}^{2}}-{{b}^{2}}\]
  done clear
  C)
  \[{{b}^{2}}-{{c}^{2}}-{{a}^{2}}\]                
  done clear
  D)
  \[{{c}^{2}}-{{a}^{2}}-{{b}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer135) For \[x\in R,\,\,\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x-3}{x+2} \right)}^{x}}\] is equal to:
  A)
  \[e\]                                     
  done clear
  B)
  \[{{e}^{-1}}\]
  done clear
  C)
  \[{{e}^{-5}}\]                                    
  done clear
  D)
  \[{{e}^{5}}\]
  done clear
  View Answer play_arrow

• question_answer136) The in centre of the triangle with vertices \[(1,\,\,\sqrt{3}),\,\,(0,\,\,0)\]and\[(2,\,\,0)\]is:
  A)
  \[\left( 1,\,\,\frac{\sqrt{3}}{2} \right)\]
  done clear
  B)
                  \[\left( \frac{2}{3},\,\,\frac{1}{\sqrt{3}} \right)\]
  done clear
  C)
  \[\left( \frac{2}{3},\,\,\frac{\sqrt{3}}{2} \right)\]                               
  done clear
  D)
  \[\left( 1,\,\,\frac{1}{\sqrt{3}} \right)\]
  done clear
  View Answer play_arrow

• question_answer137) If the vectors \[\overset{\to }{\mathop{\mathbf{a}}}\,,\,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,\] and \[\overset{\to }{\mathop{\mathbf{c}}}\,\] from the sides \[BC,\,\,\,CA\] and \[AB\] respectively, of a triangle \[ABC\], then:
  A)
  \[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=0\]
  done clear
  B)
  \[\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,=0\]
  done clear
  C)
  \[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,=0\]
  done clear
  D)
  \[\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,=0\]
  done clear
  View Answer play_arrow

• question_answer138) If \[\omega \] is an imaginary cube root of unity, then \[{{(1+\omega -{{\omega }^{2}})}^{7}}\]equals:
  A)
  \[128\omega \]                
  done clear
  B)
  \[-128\omega \]
  done clear
  C)
  \[128{{\omega }^{2}}\]                 
  done clear
  D)
  \[-128{{\omega }^{2}}\]
  done clear
  View Answer play_arrow

• question_answer139) \[{{\sin }^{2}}\theta =\frac{4xy}{{{(x+y)}^{2}}}\]is true, if and only if:
  A)
  \[x+y\ne 0\]                      
  done clear
  B)
  \[x=y,\,\,x\ne 0,\,\,y\ne 0\]
  done clear
  C)
  \[x=y\]                
  done clear
  D)
  \[x\ne 0,\,\,y\ne 0\]
  done clear
  View Answer play_arrow

• question_answer140) The radius of the circle passing through the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\] and having its centre at\[(0,\,\,3)\] is:
  A)
  \[4\]                                     
  done clear
  B)
  \[3\]
  done clear
  C)
  \[\sqrt{12}\]                                      
  done clear
  D)
  \[\frac{7}{2}\]
  done clear
  View Answer play_arrow

• question_answer141) If \[(\omega \ne 1)\] is a cubic root of unity, then\[\left| \begin{matrix}    1 & 1+1+{{\omega }^{2}} & {{\omega }^{2}}  \\    1-i & -1 & {{\omega }^{2}}-1  \\    -i & -1+\omega -i & -1  \\ \end{matrix} \right|\]equals:
  A)
  \[zero\]                                               
  done clear
  B)
  \[1\]
  done clear
  C)
  \[i\]                                       
  done clear
  D)
  \[\omega \]
  done clear
  View Answer play_arrow

• question_answer142) Let\[f(2)=4\] and \[f'(2)=4\]. Then\[\underset{x\to 2}{\mathop{\lim }}\,\frac{x\,\,f(2)-2f(x)}{x-2}\]is given by:
  A)
  \[2\]                                     
  done clear
  B)
  \[-2\]
  done clear
  C)
  \[-4\]                                    
  done clear
  D)
  \[3\]
  done clear
  View Answer play_arrow

• question_answer143) Three straight lines \[2x+11y-5=0\],\[24x+7y-20=0\]and\[4x-3y-2=0\]:
  A)
   form a triangle
  done clear
  B)
   are only concurrent
  done clear
  C)
   are concurrent with on line bisecting the angle between the other two
  done clear
  D)
   none of the above
  done clear
  View Answer play_arrow

• question_answer144) A straight line through the point\[(2,\,\,2)\]intersects the line\[\sqrt{3}x+y=0\]and\[\sqrt{3}x-y=0\]at the points\[A\]and\[B\]. The equation to the line\[AB\], so that triangle\[AOB\]is equilateral is:
  A)
  \[x-2=0\]                            
  done clear
  B)
  \[y-2=0\]
  done clear
  C)
  \[x+y-4=0\]                       
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer145) The greatest distance of the point \[P(10,\,\,7)\] from the circle \[{{x}^{2}}+{{y}^{2}}-4x-2y-20=0\] is:
  A)
  \[10\]                                   
  done clear
  B)
  \[15\]
  done clear
  C)
  \[5\]                                     
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer146) The equation of the ellipse whose foci are \[(\pm \,\,2,\,\,0)\]and eccentricity \[\frac{1}{2}\] is:
  A)
  \[\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{16}=1\]                   
  done clear
  B)
  \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1\]
  done clear
  C)
  \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{8}=1\]                      
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer147) The equation of the chord joining two points \[({{x}_{1}},\,\,{{y}_{1}})\] and \[({{x}_{2}},\,\,{{y}_{2}})\] on the rectangular hyperbola \[xy={{c}^{2}}\] is:
  A)
  \[\frac{x}{{{x}_{1}}+{{x}_{2}}}+\frac{y}{{{y}_{1}}+{{y}_{2}}}=1\]
  done clear
  B)
  \[\frac{x}{{{x}_{1}}-{{x}_{2}}}+\frac{y}{{{y}_{1}}-{{y}_{2}}}=1\]
  done clear
  C)
  \[\frac{x}{{{y}_{1}}+{{y}_{2}}}+\frac{y}{{{x}_{1}}+{{x}_{2}}}=1\]
  done clear
  D)
  \[\frac{x}{{{y}_{1}}-{{y}_{2}}}+\frac{y}{{{x}_{1}}-{{x}_{2}}}=1\]
  done clear
  View Answer play_arrow

• question_answer148) Let \[R\] be the resultant of \[P\] and \[Q\] \[\text{and}\] if \[\frac{P}{3}=\frac{Q}{7}=\frac{R}{5}\], the angle between \[P\] and \[R\] is:
  A)
  \[{{\cos }^{-1}}\left( \frac{11}{14} \right)\]                          
  done clear
  B)
  \[{{\cos }^{-1}}\left( -\frac{11}{14} \right)\]
  done clear
  C)
  \[\frac{2\pi }{3}\]                                            
  done clear
  D)
  \[\frac{5\pi }{6}\]
  done clear
  View Answer play_arrow

• question_answer149) Two bodies of different masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are dropped from different heights \[{{h}_{1}}\] and \[{{h}_{2}}\]. The ratio of the time taken by the two bodies to fall through these distances is:
  A)
  \[{{h}_{1}}:{{h}_{2}}\]                   
  done clear
  B)
  \[\sqrt{{{h}_{1}}}:\sqrt{{{h}_{2}}}\]
  done clear
  C)
  \[h_{1}^{2}:h_{2}^{2}\]                
  done clear
  D)
  \[{{h}_{2}}:{{h}_{1}}\]
  done clear
  View Answer play_arrow

• question_answer150) If\[\operatorname{var}(x)=8.25,\,\,\operatorname{var}(y)=33.96\]and\[\operatorname{cov}(x,\,\,y)=10.2\], then the correlation coefficient is:
  A)
  \[0.89\]                               
  done clear
  B)
  \[-0.98\]
  done clear
  C)
  \[0.61\]                               
  done clear
  D)
  \[-0.16\]
  done clear
  View Answer play_arrow