Solved papers for VIT Engineering VIT Engineering Solved Paper-2010

done VIT Engineering Solved Paper-2010 Total Questions - 120

• question_answer1) A straight wire carrying current \[i\] is turned into a circular loop. If the magnitude of magnetic moment associated with it in MKS unit is \[M\], the length of wire will be
  A)
   \[\frac{4\pi }{M}\]               
  done clear
  B)
   \[\sqrt{\frac{4\pi M}{i}}\]
  done clear
  C)
   \[\sqrt{\frac{4\pi i}{M}}\]          
  done clear
  D)
   \[\frac{M\pi }{i}\]  
  done clear
  View Answer play_arrow

• question_answer2) The ratio of the amounts of heat developed in the four arms of a balance Wheatstone bridge, when the arms have resistances \[P=100\,\Omega \], \[Q=10\,\Omega \], \[R=300\,\Omega \] and \[S=30\,\Omega \] respectively is
  A)
   3 : 30 : 1 : 10   
  done clear
  B)
   30 : 3 : 10 : 1
  done clear
  C)
   30 : 10 : 1 : 3   
  done clear
  D)
   30 : 1 : 3 : 10  
  done clear
  View Answer play_arrow

• question_answer3) An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from temperature\[20{}^\circ C\]? The temperature of boiling water is\[100{}^\circ C\].
  A)
   12.6 min        
  done clear
  B)
   4.2 min
  done clear
  C)
   6.3 min         
  done clear
  D)
   8.4 min  
  done clear
  View Answer play_arrow

• question_answer4) Magnetic field at the center of a circular loop of area A is B. The magnetic moment of the loop will be
  A)
   \[\frac{B{{A}^{2}}}{{{\mu }_{0}}\pi }\]
  done clear
  B)
   \[\frac{B{{A}^{3/2}}}{{{\mu }_{0}}\pi }\]
  done clear
  C)
   \[\frac{B{{A}^{3/2}}}{{{\mu }_{0}}{{\pi }^{1/2}}}\]
  done clear
  D)
   \[\frac{2B{{A}^{3/2}}}{{{\mu }_{0}}{{\pi }^{1/2}}}\]
  done clear
  View Answer play_arrow

• question_answer5) In Youngs double slit experiment, the spacing between the slits is d and wavelength of light used is \[\text{6000}\overset{\text{o}}{\mathop{\text{A}}}\,\].If the angular width of a fringe formed on a distance screen is \[1{}^\circ \], then value of \[d\] is
  A)
   1 mm           
  done clear
  B)
   0.05 mm
  done clear
  C)
   0.03mm        
  done clear
  D)
   0.01 mm  
  done clear
  View Answer play_arrow

• question_answer6)  An electric dipole consists of two opposite charges   of   magnitude   \[q=1\times {{10}^{-6}}C\] separated by 2.0 cm. The dipole is placed in an external field of\[1\times {{10}^{5}}N{{C}^{-1}}\]. What maximum torque does the field exert on the dipole? How much work must an external agent do to turn the dipole end to end, starring from position of alignment\[(9=0{}^\circ )\]?
  A)
   \[4.4\times {{10}^{6}}N-m,\text{ }3.2\times {{10}^{-4}}J\]
  done clear
  B)
   \[-2\times {{10}^{-3}}N-m,\text{ }-4\times {{10}^{3}}J\]
  done clear
  C)
   \[4\times {{10}^{3}},\text{ }2\times {{10}^{-3}}J\]
  done clear
  D)
   \[2\times {{10}^{-3}}N-m,\text{ }4\times {{10}^{-3}}J\]
  done clear
  View Answer play_arrow

• question_answer7) The electron of hydrogen atom is considered to be revolving round a proton in circular orbit of radius \[{{h}^{2}}/m{{e}^{2}}\] with velocity\[{{e}^{2}}/h\], where\[h=h/2\pi \]. The current \[i\] is
  A)
   \[\frac{4{{\pi }^{2}}m{{e}^{5}}}{{{h}^{2}}}\]        
  done clear
  B)
   \[\frac{4{{\pi }^{2}}m{{e}^{5}}}{{{h}^{3}}}\]
  done clear
  C)
   \[\frac{4{{\pi }^{2}}{{m}^{2}}{{e}^{5}}}{{{h}^{3}}}\]
  done clear
  D)
   \[\frac{4{{\pi }^{2}}{{m}^{2}}{{e}^{2}}}{{{h}^{3}}}\]  
  done clear
  View Answer play_arrow

• question_answer8) In a double slit experiment, 5th dark fringe is formed opposite to one of the slits, the wavelength of light is
  A)
   \[\frac{d{{e}^{2}}}{6D}\]            
  done clear
  B)
   \[\frac{{{d}^{2}}}{9D}\]
  done clear
  C)
   \[\frac{{{d}^{2}}}{15D}\]           
  done clear
  D)
   \[\frac{{{d}^{2}}}{9D}\]
  done clear
  View Answer play_arrow

• question_answer9) Which of the following rays is emitted by a human body?
  A)
   X-rays           
  done clear
  B)
   UV rays
  done clear
  C)
   Visible rays      
  done clear
  D)
   IR rays
  done clear
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• question_answer10) A proton of mass \[1.67\times {{10}^{-27}}kg\] enters a uniform magnetic field of 1 T at point A as shown in figure, with a speed of\[{{10}^{7}}m{{s}^{-1}}\]. The magnetic field is directed normal to the plane of paper downwards. The proton emerges out of the magnetic field at point\[C\], then the distance \[AC\] and the value of angle \[\theta \] will respectively be
  A)
   \[0.7m,\text{ }45{}^\circ \]
  done clear
  B)
   \[0.7\text{ }m,\,\,90{}^\circ \]
  done clear
  C)
   \[0.14\text{ }m,\text{ }90{}^\circ \]
  done clear
  D)
   \[0.14\text{ }m,\text{ }45{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer11) A neutral water molecule\[\text{(}{{\text{H}}_{\text{2}}}\text{O)}\]in its vapour state has an electric dipole moment of magnitude\[6.4\times {{10}^{-30}}C-m\]. How far apart are the molecules centres of positive and negative charges?
  A)
   4m             
  done clear
  B)
   4 mm
  done clear
  C)
   \[4\mu \]m
  done clear
  D)
   4 pm
  done clear
  View Answer play_arrow

• question_answer12) Figure shows a straight wire of length \[l\] carrying current \[i\]. The magnitude of magnetic field produced by the current at point P is
  A)
   \[\frac{\sqrt{2}{{\mu }_{0}}i}{\pi l}\]
  done clear
  B)
   \[\frac{{{\mu }_{0}}i}{4\pi l}\]
  done clear
  C)
   \[\frac{\sqrt{2}{{\mu }_{0}}i}{8\pi l}\]
  done clear
  D)
   \[\frac{{{\mu }_{0}}i}{2\sqrt{2}\pi l}\]  
  done clear
  View Answer play_arrow

• question_answer13) Zener diode is used for
  A)
   producing oscillations in an oscillator
  done clear
  B)
   amplification
  done clear
  C)
   stabilization
  done clear
  D)
   rectification  
  done clear
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• question_answer14) Two light sources are said to be coherent if they are obtained from
  A)
   two independent point sources emitting light of the same wavelength
  done clear
  B)
   a single point source
  done clear
  C)
   a wide source
  done clear
  D)
   two ordinary bulbs emitting light of different wavelengths  
  done clear
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• question_answer15) A small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The number of turns is n and the cross-sectional area of the coil is A. When the coil turns through \[180{}^\circ \] about its diameter, the charge flowing through the coil is Q. The total resistance of the circuit is R. What is the magnitude of the magnetic induction?
  A)
   \[\frac{QR}{nA}\]             
  done clear
  B)
   \[\frac{2QR}{nA}\]
  done clear
  C)
   \[\frac{Qn}{2RA}\]          
  done clear
  D)
   \[\frac{QR}{2nA}\]
  done clear
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• question_answer16) The attenuation in optical fibre is mainly due to
  A)
   absorption
  done clear
  B)
   scattering
  done clear
  C)
   neither absorption nor scattering
  done clear
  D)
   Both [a] and [b]
  done clear
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• question_answer17) An arc of radius r carries charge. The linear density of charge is \[\lambda \] and the arc subtends an angle \[\frac{\pi }{3}\]at the centre. What is electric potential at the centre?
  A)
   \[\frac{\lambda }{4{{\varepsilon }_{0}}}\]              
  done clear
  B)
   \[\frac{\lambda }{8{{\varepsilon }_{0}}}\]
  done clear
  C)
   \[\frac{\lambda }{12{{\varepsilon }_{0}}}\]           
  done clear
  D)
   \[\frac{\lambda }{16{{\varepsilon }_{0}}}\]  
  done clear
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• question_answer18) Sinusoidal carrier voltage of frequency 1.5 MHz and amplitude 50 V is amplitude modulated by sinusoidal voltage of frequency 10 kHz producing 50% modulation. The lower and upper side-band frequencies in kHz are
  A)
   1490, 1510     
  done clear
  B)
   1510,1490
  done clear
  C)
   \[\frac{1}{1490},\frac{1}{1510}\]
  done clear
  D)
   \[\frac{1}{1510},\frac{1}{1490}\]  
  done clear
  View Answer play_arrow

• question_answer19) 50\[\Omega \] and 100\[\Omega \] resistors are connected in series. This connection is connected with a battery of 2.4 V. When a voltmeter of 100\[\Omega \]resistance is connected across 100\[\Omega \] resistor, then the reading of the voltmeter will be
  A)
   1.6 V           
  done clear
  B)
   1.0 V
  done clear
  C)
   1.2 V           
  done clear
  D)
   2.0 V  
  done clear
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• question_answer20) In space charge limited region, the plate current in a diode is 10 mA for plate voltage 150 V. If the plate voltage is increased to 600V, then the plate current will be
  A)
   10 mA          
  done clear
  B)
   40 mA
  done clear
  C)
   80 mA          
  done clear
  D)
   160 mA  
  done clear
  View Answer play_arrow

• question_answer21) Light of wavelength strikes a photo-sensitive surface and electrons are ejected with kinetic energy E. If. the kinetic energy is to be increased to 2E, the wavelength must be changed to \[\lambda \]where
  A)
   \[{{\lambda }^{}}=\frac{\lambda }{2}\]           
  done clear
  B)
   \[{{\lambda }^{}}=2\lambda \]
  done clear
  C)
   \[\frac{\lambda }{2}<{{\lambda }^{}}<\lambda \]         
  done clear
  D)
   \[{{\lambda }^{}}>\lambda \]  
  done clear
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• question_answer22)   The maximum velocity of electrons emitted from a metal surface is\[v\], when frequency of light falling on it is\[f\]. The maximum velocity when frequency becomes \[4f\]is
  A)
   \[2v\]
  done clear
  B)
   \[>2v\]
  done clear
  C)
   \[<2v\]
  done clear
  D)
   between \[2v\] and \[4v\]  
  done clear
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• question_answer23) The collector plate in an experiment on photoelectric effect is kept vertically above the emitter plate. Light source is put on and a saturation photo-current is recorded. An electric field is switched on which has a vertically downward direction, then
  A)
   the photo- current will increase
  done clear
  B)
   the kinetic energy of the electrons will increase
  done clear
  C)
   the slopping potential will decrease
  done clear
  D)
   the threshold wavelength will increase  
  done clear
  View Answer play_arrow

• question_answer24) A cylindrical conductor of radius R carries a current i. The value of magnetic field at a point which is \[\frac{R}{4}\]distance inside from the surface is 10 T. The value of magnetic field at point which is 4R distance outside from the surface
  A)
   \[\frac{4}{3}T\]              
  done clear
  B)
   \[\frac{8}{3}T\]
  done clear
  C)
   \[\frac{40}{3}T\]
  done clear
  D)
   \[\frac{80}{3}T\]  
  done clear
  View Answer play_arrow

• question_answer25) The power of a thin convex lens \[\left( _{a}{{n}_{g}}=1.5 \right)\] is 5.0 D. When it is placed in a liquid of refractive index \[_{a}{{n}_{l}},\] then it behaves as a concave lens of focal length 100 cm. The refractive index of the liquid\[_{a}{{n}_{l}},\]will be
  A)
   5/3             
  done clear
  B)
   4/3
  done clear
  C)
   \[\sqrt{3}\]             
  done clear
  D)
   5/4  
  done clear
  View Answer play_arrow

• question_answer26) Find the value of magnetic field between plates of capacitor at a distance 1 m from centre, where electric field varies by \[{{10}^{10}}V/m\]per second.
  A)
   \[5.56\times {{10}^{-8}}T\]
  done clear
  B)
   \[5.56\times {{10}^{-3}}T\]
  done clear
  C)
   \[\text{5}\text{.56 }\!\!\mu\!\!\text{ T }\!\!~\!\!\text{  }\!\!~\!\!\text{  }\!\!~\!\!\text{  }\!\!~\!\!\text{  }\!\!~\!\!\text{  }\!\!~\!\!\text{  }\!\!~\!\!\text{  }\!\!~\!\!\text{  }\!\!~\!\!\text{ }\]
  done clear
  D)
   \[5.55\text{ }T\]  
  done clear
  View Answer play_arrow

• question_answer27) sing an AC voltmeter the potential difference in the electrical line in a house is read to be 234 V. If line frequency is known to be 50 cycles/s, the equation for the line voltage is
  A)
   \[\text{V }\!\!~\!\!\text{ = 165 sin (100 }\!\!\pi\!\!\text{ t)}\]
  done clear
  B)
   \[\text{V=331 sin}\,\text{(100 }\!\!\pi\!\!\text{ t)}\]
  done clear
  C)
   \[\text{V=220}\,\text{sin}\,\text{(100 }\!\!\pi\!\!\text{ t)}\]
  done clear
  D)
   \[\text{V=440 sin (100 }\!\!\pi\!\!\text{ t)}\]  
  done clear
  View Answer play_arrow

• question_answer28) There are a 25 W - 220 V bulb and a 100 W -220 V line. Which electric bulb will glow more brightly?
  A)
   25 W bulb
  done clear
  B)
   100 W bulb
  done clear
  C)
   Both will have equal incandescence
  done clear
  D)
   Neither 25 W nor 100 W bulb will give light  
  done clear
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• question_answer29) Silver has a work function of 4.7 eV. When ultraviolet light of wavelength 100 nm is incident upon it, potential of 7.7 V is required to stop photoelectrons from reaching the collector plate. The potential required to stop electrons when light of wavelength 200 nm is incident upon silver is
  A)
   1.5 V           
  done clear
  B)
   1.85 V
  done clear
  C)
   1.95 V          
  done clear
  D)
   2.37 V  
  done clear
  View Answer play_arrow

• question_answer30) Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii \[{{R}_{1}}\] and \[{{R}_{2}}\], respectively. The ratio of masses of X and Y is
  A)
   \[\left( {{R}_{1}}/{{R}_{2}} \right)\]         
  done clear
  B)
   \[\left( {{R}_{2}}/{{R}_{1}} \right)\]
  done clear
  C)
   \[{{\left( {{R}_{1}}/{{R}_{2}} \right)}^{2}}\]        
  done clear
  D)
   \[\left( {{R}_{1}}/{{R}_{2}} \right)\]  
  done clear
  View Answer play_arrow

• question_answer31) According to the Bohrs theory of hydrogen atom, the speed of the electron, energy and the radius of its orbit vary with the principal quantum number n, respectively, as
  A)
   \[\frac{1}{n},\frac{1}{{{n}^{2}}},{{n}^{2}}\]
  done clear
  B)
   \[\frac{1}{n},{{n}^{2}}\frac{1}{{{n}^{2}}}\]
  done clear
  C)
   \[{{n}^{2}},\frac{1}{{{n}^{2}}},{{n}^{2}}\]      
  done clear
  D)
   \[n,\frac{1}{{{n}^{2}}},\frac{1}{{{n}^{2}}}\]  
  done clear
  View Answer play_arrow

• question_answer32) In the hydrogen atom, the electron is making\[6.6\times {{10}^{15}}\,\text{rps}\]. If the radius of the orbit is \[0.53\times {{10}^{-10}}m\], then magnetic field produced at the centre of the orbit is
  A)
   140 T          
  done clear
  B)
   12.5 T
  done clear
  C)
   1.4 T            
  done clear
  D)
   0.14 T  
  done clear
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• question_answer33) Two identical light sources \[{{S}_{1}}\] and \[{{S}_{2}}\]emit light of same wavelength\[\lambda \]. These light rays will exhibit interference if
  A)
   their phase differences remain constant
  done clear
  B)
   their phases are distributed randomly
  done clear
  C)
   their light intensities remain constant
  done clear
  D)
   their light intensities change randomly  
  done clear
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• question_answer34) In Meter bridge or Wheatstone bridge for measurement of resistance, the known and the unknown resistances are interchanged. The error so removed is
  A)
   end correction
  done clear
  B)
   index errror
  done clear
  C)
   due to temperature effect
  done clear
  D)
   random error  
  done clear
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• question_answer35) A fish, looking up through the water, sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface of water, the radius of the circle in centimetre is
  A)
   \[\frac{12\,\times \,3}{\sqrt{5}}\]        
  done clear
  B)
   \[12\,\times \,3\,\times \,\sqrt{5}\]
  done clear
  C)
   \[\frac{12\,\times \,3}{\sqrt{7}}\]        
  done clear
  D)
   \[12\,\times \,3\,\times \,\sqrt{7}\]  
  done clear
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• question_answer36) Radio waves diffract around building although light waves do not. The reason is that radio waves
  A)
   travel with speed larger than c
  done clear
  B)
   have much larger wavelength than light
  done clear
  C)
   carry news
  done clear
  D)
   are not electromagnetic waves  
  done clear
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• question_answer37) In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If \[{{a}_{0}}\] is the radius of the ground state orbit, \[m\] is the mass and \[e\] is charge on the electron and \[{{\varepsilon }_{0}}\] is the vacuum permittivity, the speed of the electron is
  A)
   \[0\]             
  done clear
  B)
   \[\frac{e}{\sqrt{{{\varepsilon }_{0}}{{a}_{0}}m}}\]
  done clear
  C)
   \[\frac{e}{\sqrt{4\pi {{\varepsilon }_{0}}{{a}_{0}}m}}\]           
  done clear
  D)
   \[\frac{\sqrt{4\pi {{\varepsilon }_{0}}{{a}_{0}}m}}{e}\]  
  done clear
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• question_answer38) A potential difference of \[2V\] is applied between the opposite faces of a Ge crystal plate of area \[1c{{m}^{2}}\] and thickness 0.5 mm. If the concentration of electrons in Ge is \[2\times {{10}^{19}}/{{m}^{2}}\] and mobilitys of electrons and holes are \[\text{0}\text{.36 }{{\text{m}}^{\text{2}}}{{\text{V}}^{\text{-1}}}{{\text{s}}^{\text{-1}}}\]and \[\text{0}\text{.14 }{{\text{m}}^{\text{2}}}{{\text{V}}^{\text{-1}}}{{\text{s}}^{\text{-1}}}\]respectively, then the current flowing through the plate will be
  A)
   0.25 A
  done clear
  B)
   0.45 A
  done clear
  C)
   0.56 A
  done clear
  D)
   0.64 A
  done clear
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• question_answer39) An AM wave has 1800 W of total power content. For 100% modulation the carrier should have power content equal to
  A)
   1000 W
  done clear
  B)
   1200 W
  done clear
  C)
   1500 W
  done clear
  D)
   1600 W  
  done clear
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• question_answer40) Two light rays having the same wavelength \[\lambda \] in vacuum are in phase initially. Then the first ray travels a path \[{{l}_{1}}\] through a medium of refractive index \[{{n}_{1}}\] while the second ray travels a path of length \[{{l}_{2}}\] through a median of refractive index\[{{n}_{2}}\].   The two waves are then combined to observe interference. The phase difference between the two waves is
  A)
   \[\frac{2\pi }{\lambda }\left( {{l}_{2}}-{{l}_{1}} \right)\]
  done clear
  B)
   \[\frac{2\pi }{\lambda }\left( {{n}_{1}}{{l}_{1}}-{{n}_{2}}{{l}_{2}} \right)\]
  done clear
  C)
   \[\frac{2\pi }{\lambda }\left( {{n}_{2}}{{l}_{2}}-{{n}_{1}}{{l}_{1}} \right)\]
  done clear
  D)
   \[\frac{2\pi }{\lambda }\left( \frac{{{l}_{1}}}{{{n}_{1}}}-\frac{{{l}_{2}}}{{{n}_{2}}} \right)\]
  done clear
  View Answer play_arrow

• question_answer41) The correct formula of the complex tetraammineaquachlorocobalt (III) chloride is
  A)
   \[[Cl({{H}_{2}}O){{(N{{H}_{3}})}_{4}}Co]Cl\]
  done clear
  B)
   \[[CoCl({{H}_{2}}O){{(N{{H}_{3}})}_{4}}]Cl\]
  done clear
  C)
   \[[Co{{(N{{H}_{3}})}_{4}}({{H}_{2}}O)Cl]Cl\]
  done clear
  D)
   \[[CoCl({{H}_{2}}O){{(N{{H}_{3}})}_{4}}]C{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer42) The equivalent conductance at infinite dilution of a weak acid such as HF
  A)
   can be determined by extrapolation of measurements on dilute solutions of \[HCl\],\[HBr\] and \[HI\]
  done clear
  B)
   can be determined by measurement on very dilute HF solutions
  done clear
  C)
   can   best   be   determined   from measurements on dilute solutions of \[NaF\],\[NaCl\] and \[HCl\]
  done clear
  D)
   is an undefined quantity
  done clear
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• question_answer43)  The product A is
  A)
   succinic acid     
  done clear
  B)
   melonic acid
  done clear
  C)
   oxalic acid       
  done clear
  D)
   maleic acid
  done clear
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• question_answer44) For a reaction of type \[A+B\xrightarrow{{}}\] products, it is observed that doubling concentration of A causes the reaction rate to be four times as great, but doubling amount of B does not affect the rate. The unit of rate constant is
  A)
   \[{{s}^{-1}}\]
  done clear
  B)
   \[{{s}^{-1}}\,mol\,\,{{L}^{-1}}\]
  done clear
  C)
   \[{{s}^{-1}}\,mo{{l}^{-1}}\,\,L\]
  done clear
  D)
   \[s\,\,{{s}^{-1}}\,mo{{l}^{-2}}\,\,{{L}^{2}}\]
  done clear
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• question_answer45) A chemical reaction was carried out at 320 K and 300 K. The rate constants were found to be \[{{k}_{1}}\] and \[{{k}_{2}}\] respectively. Then
  A)
   \[{{k}_{2}}=4{{k}_{1}}\]         
  done clear
  B)
   \[{{k}_{2}}=2{{k}_{1}}\]
  done clear
  C)
   \[{{k}_{2}}=0.25{{k}_{1}}\]      
  done clear
  D)
   \[{{k}_{2}}=0.5{{k}_{1}}\]
  done clear
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• question_answer46) The formula of ethyl carbinol is
  A)
   \[C{{H}_{3}}OH\]
  done clear
  B)
   \[C{{H}_{3}}C{{H}_{2}}OH\]
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\]
  done clear
  D)
   \[{{(C{{H}_{3}})}_{3}}COH\]
  done clear
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• question_answer47) Which of the following gives red colour in Victor Meyers test?
  A)
   n-propyl alcohol
  done clear
  B)
   Isopropyl alcohol
  done clear
  C)
   hert-butyl alcohol
  done clear
  D)
   sec-butyl alcohol
  done clear
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• question_answer48) Enthalpy of a compound is equal to its
  A)
   heat of combustion
  done clear
  B)
   heat of formation
  done clear
  C)
   heat of reaction
  done clear
  D)
   heat of solution
  done clear
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• question_answer49) For which one of the following reactions will there be a positive \[\Delta S\]?
  A)
   \[{{H}_{2}}O(g)\xrightarrow{{}}{{H}_{2}}O(l)\]
  done clear
  B)
   \[{{H}_{2}}+{{I}_{2}}\xrightarrow{{}}2HI\]
  done clear
  C)
   \[CaC{{O}_{3}}(s)\xrightarrow{{}}CaO(s)+C{{O}_{2}}(g)\]
  done clear
  D)
   \[{{N}_{2}}(g)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g)\]
  done clear
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• question_answer50) Across the lanthanide series, the basicity of the lanthanide hydroxides
  A)
   increases
  done clear
  B)
   decreases
  done clear
  C)
   first increases and then decreases
  done clear
  D)
   first decreases and then increases
  done clear
  View Answer play_arrow

• question_answer51) When p-nitrobromobenzene reacts with sodium ethoxide, the product obtained is
  A)
   p-nitroanisole
  done clear
  B)
   ethyl phenyl ether
  done clear
  C)
   p-nitrophenetole
  done clear
  D)
   no reaction occurs
  done clear
  View Answer play_arrow

• question_answer52) A radioactive element X emits \[3\alpha \],\[1\beta \] and \[1\gamma \]-particles and forms \[_{76}{{Y}^{235}}\]. Element X is
  A)
   \[_{81}{{X}^{247}}\]         
  done clear
  B)
   \[_{80}{{X}^{247}}\]
  done clear
  C)
   \[_{81}{{X}^{246}}\]       
  done clear
  D)
   \[_{80}{{X}^{246}}\]
  done clear
  View Answer play_arrow

• question_answer53) For the reaction, \[2A(g)+{{B}_{2}}(g)2A{{B}_{2}}(g)\] the equilibrium constant, \[{{K}_{p}}\] at 300 K is 16.0. The value of \[{{K}_{p}}\] for \[A{{B}_{2}}(g)A(g)+1/2{{B}_{2}}(g)\]
  A)
   \[8\]             
  done clear
  B)
   \[0.25\]
  done clear
  C)
   \[0.125\]          
  done clear
  D)
   \[32\]
  done clear
  View Answer play_arrow

• question_answer54) Frenkel defect is generally observed in
  A)
   \[AgBr\]
  done clear
  B)
   \[AgI\]
  done clear
  C)
   \[ZnS\]
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer55) Most crystals show good cleavage because their atoms, ions or molecules are weakly
  A)
   bonded together
  done clear
  B)
   strongly bonded together
  done clear
  C)
   spherically symmetrical
  done clear
  D)
   arranged in planes
  done clear
  View Answer play_arrow

• question_answer56) \[[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]N{{O}_{2}}\]and \[[Co{{(N{{H}_{3}})}_{4}}ClN{{O}_{2}}]Cl\] exhibit which type of isomerism?
  A)
   Geometrical    
  done clear
  B)
   Optical
  done clear
  C)
   Linkage        
  done clear
  D)
   lonisation
  done clear
  View Answer play_arrow

• question_answer57) Which of the following compounds is not coloured?
  A)
   \[N{{a}_{2}}[Cu{{(Cl)}_{4}}]\]
  done clear
  B)
   \[Na[Cd{{(Cl)}_{4}}]\]
  done clear
  C)
   \[{{K}_{4}}[Fe{{(CN)}_{6}}]\]
  done clear
  D)
   \[{{K}_{3}}[Fe{{(CN)}_{6}}]\]
  done clear
  View Answer play_arrow

• question_answer58) Which of the following is a Gattermann aldehyde synthesis?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer59) Aldol is
  A)
   \[\beta \]-hydroxybutyraldehyde
  done clear
  B)
   \[\alpha \]-hydroxybutanal
  done clear
  C)
   \[\beta \]-hydroxypropanal
  done clear
  D)
   None. of the above
  done clear
  View Answer play_arrow

• question_answer60) Nitrobenzene  can  be  converted  into azobenzene by reduction with
  A)
   \[Zn,\,N{{H}_{4}}Cl,\,\Delta \]
  done clear
  B)
   \[Zn/NaOH,\,C{{H}_{3}}OH\]
  done clear
  C)
   \[Zn/NaOH\]
  done clear
  D)
   \[LiAl{{H}_{4}}\], ether
  done clear
  View Answer play_arrow

• question_answer61) The one which is least basic is
  A)
   \[N{{H}_{3}}\]    
  done clear
  B)
   \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]
  done clear
  C)
   \[{{({{C}_{6}}{{H}_{5}})}_{3}}N\]   
  done clear
  D)
   \[{{({{C}_{6}}{{H}_{5}})}_{2}}NH\]
  done clear
  View Answer play_arrow

• question_answer62) Coordination number of \[Ni\] in \[{{[Ni{{({{C}_{2}}{{O}_{4}})}_{3}}]}^{4-}}\]is
  A)
   3                 
  done clear
  B)
   6
  done clear
  C)
   4                  
  done clear
  D)
   5
  done clear
  View Answer play_arrow

• question_answer63) Mg. is an important component of which biomolecule occurring extensively in living world?
  A)
   Haemoglobin   
  done clear
  B)
   Chlorophyll
  done clear
  C)
   Florigen         
  done clear
  D)
   ATP
  done clear
  View Answer play_arrow

• question_answer64) Sterling silver is
  A)
   \[AgN{{O}_{3}}\]
  done clear
  B)
   \[A{{g}_{2}}S\]
  done clear
  C)
   Alloy of 80% \[Ag+20%\,Cu\]
  done clear
  D)
   \[AgCl\]
  done clear
  View Answer play_arrow

• question_answer65) Identify the statement which is not correct regarding \[CuS{{O}_{4}}\]
  A)
   It reacts with \[KI\] to give iodine
  done clear
  B)
   It reacts with \[KCl\] to give \[C{{u}_{2}}C{{l}_{2}}\]
  done clear
  C)
   It reacts with \[NaOH\] and glucose to give\[C{{u}_{2}}O\]
  done clear
  D)
   It gives \[CuO\] on strong heating in air
  done clear
  View Answer play_arrow

• question_answer66) Transition metals usually exhibit highest oxidation states in their
  A)
   chlorides        
  done clear
  B)
   fluorides
  done clear
  C)
   bromides        
  done clear
  D)
   iodides
  done clear
  View Answer play_arrow

• question_answer67) The number of Faradays needed to reduce 4 g equivalents of \[C{{u}^{2+}}\]to \[Cu\] metal will be
  A)
   \[1\]              
  done clear
  B)
   \[2\]
  done clear
  C)
   \[1/2\]            
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer68) Which one of the following cells can convert chemical energy of \[{{H}_{2}}\] and \[{{O}_{2}}\] directly into electrical energy?
  A)
   Mercury cell     
  done clear
  B)
   Daniell cell
  done clear
  C)
   Fuel cell        
  done clear
  D)
   Lead storage cell
  done clear
  View Answer play_arrow

• question_answer69) On treatment of propanone with dilute \[Ba{{(OH)}_{2}}\], the product formed is
  A)
   aldol
  done clear
  B)
   phorone
  done clear
  C)
   propionaldehyde
  done clear
  D)
   4-hydroxy-4-methyl-2-pentanone
  done clear
  View Answer play_arrow

• question_answer70) Which of the following converts \[C{{H}_{3}}CON{{H}_{2}}\]to \[C{{H}_{3}}N{{H}_{2}}\]?
  A)
   \[NaBr\]
  done clear
  B)
   \[NaOBr\]
  done clear
  C)
   \[B{{r}_{2}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer71) Which  metal  aprons  are  worn  by radiographer .to protect him from radiation?
  A)
   Mercury coated apron
  done clear
  B)
   Lead apron
  done clear
  C)
   Copper apron
  done clear
  D)
   Aluminimised apron
  done clear
  View Answer play_arrow

• question_answer72) The standard Gibbs free energy change, \[\Delta {{G}^{o}}\] is related to equilibrium constant, \[{{K}_{P}}\] as
  A)
   \[{{K}_{P}}=-RT\] In \[\Delta {{G}^{o}}\]
  done clear
  B)
   \[{{K}_{P}}={{\left[ \frac{e}{RT} \right]}^{\Delta {{G}^{o}}}}\]
  done clear
  C)
   \[{{K}_{P}}=-\frac{\Delta G}{RT}\]
  done clear
  D)
   \[{{K}_{P}}={{e}^{-\Delta {{G}^{o}}/RT}}\]
  done clear
  View Answer play_arrow

• question_answer73) The yield of the product in the reaction \[{{A}_{2}}(g)+2B(g)C(g)+Q\,\,kJ\] would be higher at
  A)
   high temperature and high pressure
  done clear
  B)
   high temperature and low pressure
  done clear
  C)
   low temperature and high pressure
  done clear
  D)
   low temperature and low pressure
  done clear
  View Answer play_arrow

• question_answer74) In which of the following case, does the reaction go farthest to completion?
  A)
   \[K={{10}^{2}}\]         
  done clear
  B)
   \[K=10\]
  done clear
  C)
   \[K={{10}^{-2}}\]         
  done clear
  D)
    \[K=1\]
  done clear
  View Answer play_arrow

• question_answer75) Formation of cyanohydrin-from a ketone is an example of
  A)
   electrophilic addition
  done clear
  B)
   nucleophilic addition
  done clear
  C)
   nucleophilic substitution
  done clear
  D)
   electrophilic substitution
  done clear
  View Answer play_arrow

• question_answer76) Glycerol on treatment with oxalic acid at \[{{110}^{o}}C\] forms
  A)
   formic acid      
  done clear
  B)
   allyl alcohol
  done clear
  C)
   \[C{{O}_{2}}\] and \[CO\]     
  done clear
  D)
   acrolein
  done clear
  View Answer play_arrow

• question_answer77) The activity of an old piece of wood is just 25% of the fresh piece of wood. If \[{{t}_{1/2}}\] of C-14 is 6000 yr, the age of piece of wood is
  A)
   \[6000\text{ }yr\]        
  done clear
  B)
   \[3000\text{ }yr\]
  done clear
  C)
   \[9000\text{ }yr\]
  done clear
  D)
   \[12000\text{ }yr\]
  done clear
  View Answer play_arrow

• question_answer78) The radius of \[N{{a}^{+}}\] is 95 pm and that of \[C{{l}^{-}}\] ion is 181 pm. Hence, the coordination number of \[N{{a}^{+}}\] will be
  A)
   4                
  done clear
  B)
   6
  done clear
  C)
   8               
  done clear
  D)
   unpredictable
  done clear
  View Answer play_arrow

• question_answer79) The reaction, \[ROH+{{H}_{2}}C{{N}_{2}}\] in the presence of \[HB{{F}_{4}}\], gives the following product
  A)
   \[ROC{{H}_{3}}\]        
  done clear
  B)
   \[RC{{H}_{2}}OH\]
  done clear
  C)
   \[ROHC{{N}_{2}}{{N}_{2}}\]    
  done clear
  D)
   \[RC{{H}_{2}}C{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer80) The fatty acid which shows reducing property is
  A)
   acetic acid       
  done clear
  B)
   ethanoic acid
  done clear
  C)
   oxalic acid      
  done clear
  D)
   formic acid
  done clear
  View Answer play_arrow

• question_answer81) If \[F\] is functions such that \[F(0)=2,\]\[F(1)=3,\]\[F(x+2)=2F(x)-F(x+1)\] for \[x\ge 0,\] than\[F(5)\] is equal to
  A)
   -7
  done clear
  B)
   -3
  done clear
  C)
   17
  done clear
  D)
   13
  done clear
  View Answer play_arrow

• question_answer82) Let\[S\]be a set containing \[n\]elements. Then, number of binary operations on \[S\]is
  A)
   \[{{n}^{n}}\]
  done clear
  B)
   \[{{2}^{{{n}^{2}}}}\]
  done clear
  C)
   \[{{n}^{{{n}^{2}}}}\]
  done clear
  D)
   \[{{n}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer83) The numerically greatest term in the expansion of \[{{(2-5x)}^{11}}\]when \[x=\frac{1}{5},\]is
  A)
   \[55\times {{3}^{9}}\]
  done clear
  B)
   \[55\times {{3}^{6}}\]
  done clear
  C)
   \[45\times {{3}^{6}}\]
  done clear
  D)
   \[45\times {{3}^{9}}\]
  done clear
  View Answer play_arrow

• question_answer84) The number of solutions of the equation\[\sin \,({{e}^{x}})={{5}^{x}}+{{5}^{-x}},\]is
  A)
   0
  done clear
  B)
   1
  done clear
  C)
   2
  done clear
  D)
   infinitely many
  done clear
  View Answer play_arrow

• question_answer85) If \[{{a}^{x}}={{b}^{y}}={{c}^{z}}={{d}^{u}}\]and \[a,b,c,d\]are in GP, then \[x,y,z,u\]are in
  A)
   AP
  done clear
  B)
   GP
  done clear
  C)
   HP
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer86) If z satisfies the equation \[\left| \,z\, \right|-z=1+2i,\]then z is equal to
  A)
   \[\frac{3}{2}+2i\]
  done clear
  B)
   \[\frac{3}{2}-2i\]
  done clear
  C)
   \[2-\frac{3}{2}i\]
  done clear
  D)
   \[2+\frac{3}{2}i\]
  done clear
  View Answer play_arrow

• question_answer87) If \[z=\frac{1-i\sqrt{3}}{1+i\sqrt{3}},\]then arg (z) is
  A)
   \[60{}^\circ \]
  done clear
  B)
   \[120{}^\circ \]
  done clear
  C)
   \[240{}^\circ \]
  done clear
  D)
   \[300{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer88) If \[f(x)=\sqrt{{{\log }_{10}}{{x}^{2}}}.\] The set of all values of \[x\]for which \[f(x)\]is real, is
  A)
   \[[-1,\,1]\]
  done clear
  B)
   \[[1,\,\infty )\]
  done clear
  C)
   \[(-\infty ,\,-1]\]
  done clear
  D)
   \[(-\infty ,\,-1]\cup [1,\infty )\]
  done clear
  View Answer play_arrow

• question_answer89) For what values of m can the expression \[2{{x}^{2}}+mxy+3{{y}^{2}}-5y-2\] be expressed as the product of two linear factors?
  A)
   \[0\]
  done clear
  B)
   \[\pm 1\]
  done clear
  C)
   \[\pm 7\]
  done clear
  D)
   \[49\]
  done clear
  View Answer play_arrow

• question_answer90) If \[B\]is non-singular matrix and\[A\]is a square matrix, then det\[({{B}^{-1}}AB)\]is equal to
  A)
   \[\det \,({{A}^{-1}})\]
  done clear
  B)
   \[\det \,({{B}^{-1}})\]
  done clear
  C)
   \[\det \,(A)\]
  done clear
  D)
   \[\det \,(B)\]
  done clear
  View Answer play_arrow

• question_answer91) If \[f(x),\,g(x)\]and \[h\,(x)\]are three polynomials of degree 2 and \[\Delta (x)=\left| \begin{matrix}    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\ \end{matrix} \right|\] then \[\Delta (x)\]is a polynomial of degree
  A)
   2
  done clear
  B)
   3
  done clear
  C)
   0
  done clear
  D)
   atmost 3
  done clear
  View Answer play_arrow

• question_answer92) The chances of defective screws in three boxes A, B, C are \[\frac{1}{5},\frac{1}{6},\frac{1}{7}\]respectively. A box is selected at random and a screw drawn from it at random is found to be defective, Then, the probability that it came from box A, is
  A)
   \[\frac{16}{29}\]
  done clear
  B)
   \[\frac{1}{15}\]
  done clear
  C)
   \[\frac{27}{59}\]
  done clear
  D)
   \[\frac{42}{107}\]
  done clear
  View Answer play_arrow

• question_answer93) The value of \[\frac{\cos \theta }{1+\sin \theta }\]is equal to
  A)
   \[\tan \left( \frac{\theta }{2}-\frac{\pi }{4} \right)\]
  done clear
  B)
   \[\tan \left( -\frac{\pi }{4}-\frac{\theta }{2} \right)\]
  done clear
  C)
   \[\tan \left( \frac{\pi }{4}-\frac{\theta }{2} \right)\]
  done clear
  D)
   \[\tan \left( \frac{\pi }{4}+\frac{\theta }{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer94) If \[3\sin \theta +5cos\theta =5,\] then the value of \[5\sin \theta -3cos\theta \]is equal to
  A)
   5
  done clear
  B)
   4
  done clear
  C)
   3
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer95) The principal value of \[{{\sin }^{-1}}\left\{ \sin \frac{5\pi }{6} \right\}\]is
  A)
   \[\frac{\pi }{6}\]
  done clear
  B)
   \[\frac{5\pi }{6}\]
  done clear
  C)
   \[\frac{7\pi }{6}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer96) A rod of length \[l\]slides with its ends of two perpendicular lines. Then, the locus of its mid-point is
  A)
   \[{{x}^{2}}+{{y}^{2}}=\frac{{{l}^{2}}}{4}\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}=\frac{{{l}^{2}}}{2}\]
  done clear
  C)
   \[{{x}^{2}}-{{y}^{2}}=\frac{{{l}^{2}}}{4}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer97) The equation of straight line through the intersection of line \[2x+y=1\]and \[3x+2y=5\]and passing through the origin is
  A)
   \[7x+3y=0\]
  done clear
  B)
   \[7x-y=0\]
  done clear
  C)
   \[3x+2y=0\]
  done clear
  D)
   \[x+y=0\]
  done clear
  View Answer play_arrow

• question_answer98) The line joining (5, 0) to \[(10\,\cos \theta ,\,10\sin \theta )\] is divided internally in the ratio 2 : 3 at P. If \[\theta \]varies, then the locus of P is
  A)
   a straight line
  done clear
  B)
   a pair of straight lines
  done clear
  C)
   a circle
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer99) If \[2x+y+k=0\]is a normal to the parabola \[{{y}^{2}}=-8x,\]then the value of k, is
  A)
   8
  done clear
  B)
   16
  done clear
  C)
   24
  done clear
  D)
   32
  done clear
  View Answer play_arrow

• question_answer100) \[\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+.....+\frac{1}{n\,(n+1)} \right]\] is equal to
  A)
   1
  done clear
  B)
   -1
  done clear
  C)
   0
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer101) The condition that the line \[lx+my=1\]may be normal to the curve\[{{y}^{2}}=4ax,\]is
  A)
   \[a{{l}^{3}}-2al{{m}^{2}}={{m}^{2}}\]
  done clear
  B)
   \[a{{l}^{2}}+2al{{m}^{3}}={{m}^{2}}\]
  done clear
  C)
   \[a{{l}^{3}}+2al{{m}^{2}}={{m}^{3}}\]
  done clear
  D)
   \[a{{l}^{3}}+2al{{m}^{2}}={{m}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer102) If \[\int{f(x)dx=f(x),}\] then \[\int{{{\left\{ f(x) \right\}}^{2}}dx}\]is equal to
  A)
   \[\frac{1}{2}{{\left\{ f(x) \right\}}^{2}}\]
  done clear
  B)
   \[{{\left\{ f(x) \right\}}^{3}}\]
  done clear
  C)
   \[\frac{{{\left\{ f(x) \right\}}^{3}}}{3}\]
  done clear
  D)
   \[{{\left\{ f(x) \right\}}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer103) \[\int{{{\sin }^{-1}}\left\{ \frac{(2x+2)}{\sqrt{4{{x}^{2}}+8x+13}} \right\}}\,dx\]is equal to
  A)
   \[(x+1){{\tan }^{-1}}\left( \frac{2x+2}{3} \right)\] \[-\frac{3}{4}\log \left( \frac{4{{x}^{2}}+8x+13}{9} \right)+c\]
  done clear
  B)
   \[\frac{3}{2}{{\tan }^{-1}}\left( \frac{2x+2}{3} \right)\] \[-\frac{3}{4}\log \left( \frac{4{{x}^{2}}+8x+13}{9} \right)+c\]
  done clear
  C)
   \[(x+1){{\tan }^{-1}}\left( \frac{2x+2}{3} \right)\] \[-\frac{3}{2}\log \,(4{{x}^{2}}+8x+13)+c\]
  done clear
  D)
   \[\frac{3}{2}(x+1){{\tan }^{-1}}\left( \frac{2x+2}{3} \right)\] \[-\frac{3}{4}\log \,(4{{x}^{2}}+8x+13)+c\]
  done clear
  View Answer play_arrow

• question_answer104) If the equation of an ellipse is \[3{{x}^{2}}+2{{y}^{2}}+6x-8y+5=0,\] then which of the following are true?
  A)
   \[e=\frac{1}{\sqrt{3}}\]
  done clear
  B)
   centre is \[(-1,\,2)\]
  done clear
  C)
   foci are \[(-1,\,1)\]are \[(-1,\,3)\]
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer105) The equation of the common tangents to the two hyperbolas \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]and \[\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1,\]are
  A)
   \[y=\pm \,\,x\,\,\pm \sqrt{{{b}^{2}}-{{a}^{2}}}\]
  done clear
  B)
   \[y=\pm \,\,x\,\,\pm \sqrt{{{a}^{2}}-{{b}^{2}}}\]
  done clear
  C)
   \[y=\pm \,\,x\,\,\pm \sqrt{{{a}^{2}}+{{b}^{2}}}\]
  done clear
  D)
   \[y=\pm \,\,x\,\,\pm \left( {{a}^{2}}-{{b}^{2}} \right)\]
  done clear
  View Answer play_arrow

• question_answer106) Domain of the function \[f(x)={{\log }_{x}}\cos x,\]is
  A)
   \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)-\{\,1\,\}\]
  done clear
  B)
   \[\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]-\{\,1\,\}\]
  done clear
  C)
   \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer107) Range of the function \[y={{\sin }^{-1}}\left( \frac{{{x}^{2}}}{1+{{x}^{2}}} \right),\]is
  A)
   \[\left( 0,\frac{\pi }{2} \right)\]
  done clear
  B)
   \[\left[ \underset{{}}{\mathop{0,}}\, \right.\left. \frac{\pi }{2} \right)\]
  done clear
  C)
   \[\left( \left. 0,\frac{\pi }{2} \right] \right.\]
  done clear
  D)
   \[\left[ 0,\,\frac{\pi }{2} \right]\]
  done clear
  View Answer play_arrow

• question_answer108) If \[x=\sec \theta -\cos \theta ,\] \[y={{\sec }^{n}}\theta -{{\cos }^{n}}\theta ,\] then \[({{x}^{2}}+4){{\left( \frac{dy}{dx} \right)}^{2}}\]is equal to
  A)
   \[{{n}^{2}}({{y}^{2}}-4)\]
  done clear
  B)
   \[{{n}^{2}}(4-{{y}^{2}})\]
  done clear
  C)
   \[{{n}^{2}}({{y}^{2}}+4)\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer109) If \[y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+.....\infty }}}},\]then \[\frac{dy}{dx}\]is equal to
  A)
   \[\frac{y+x}{{{y}^{2}}-2x}\]
  done clear
  B)
   \[\frac{{{y}^{3}}-x}{2{{y}^{2}}-2xy-1}\]
  done clear
  C)
   \[\frac{{{y}^{3}}+x}{2{{y}^{2}}-x}\]
  done clear
  D)
   None of these
  done clear
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• question_answer110) If \[\int_{1}^{x}{\frac{dt}{\left| \,t\, \right|\sqrt{{{t}^{2}}-1}}}=\frac{\pi }{6},\]then \[x\]can be equal to
  A)
   \[\frac{2}{\sqrt{3}}\]
  done clear
  B)
   \[\sqrt{3}\]
  done clear
  C)
   \[2\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer111) The area bounded by the curve \[y=\left| \,\sin x\, \right|,\]\[x\text{-}\]axis and the lines \[\left| \,x\, \right|=\pi ,\]is
  A)
   2 sq unit
  done clear
  B)
   1 sq unit
  done clear
  C)
   4 sq unit
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer112) The degree of the differential equation of all curves having normal of constant length c is
  A)
   1
  done clear
  B)
   3
  done clear
  C)
   4
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer113) If \[\overrightarrow{a}=2\hat{i}+2\hat{j}+3\hat{k},\] \[\overrightarrow{b}=-\hat{i}+2\hat{j}+\hat{k}\] and \[\overrightarrow{c}=3\hat{i}+\hat{j},\] then \[\overrightarrow{a}+t\,\overrightarrow{b}\] is perpendicular to \[\overrightarrow{c},\]if t is equal to
  A)
   2
  done clear
  B)
   4
  done clear
  C)
   6
  done clear
  D)
   8
  done clear
  View Answer play_arrow

• question_answer114) The distance between the line \[\overrightarrow{r}=2\hat{i}-2\hat{j}+3\hat{k}+\lambda (\hat{i}-\hat{j}+4\hat{k})\] and the plane \[\overrightarrow{r}\cdot (\hat{i}+5\hat{j}+\hat{k})=5,\]is
  A)
   \[\frac{10}{3}\]
  done clear
  B)
   \[\frac{10}{\sqrt{3}}\]
  done clear
  C)
   \[\frac{10}{3\sqrt{3}}\]
  done clear
  D)
   \[\frac{10}{9}\]
  done clear
  View Answer play_arrow

• question_answer115) The equation of sphere concentric with the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y-8z-5=0\]and which passes through the origin is
  A)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y-8z=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6y-8z=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y-8z-6=0\]
  done clear
  View Answer play_arrow

• question_answer116) If the lines \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\] and \[\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}\] intersect, then the value of k, is
  A)
   \[\frac{3}{2}\]
  done clear
  B)
   \[\frac{9}{2}\]
  done clear
  C)
   \[-\frac{2}{9}\]
  done clear
  D)
   \[-\frac{3}{2}\]
  done clear
  View Answer play_arrow

• question_answer117) The two curves \[y={{3}^{x}}\]and \[y={{5}^{x}}\]intersect at an angle
  A)
   \[{{\tan }^{-1}}\left( \frac{\log 3-\log 5}{1+\log 3\,\,\log 5} \right)\]
  done clear
  B)
   \[{{\tan }^{-1}}\left( \frac{\log 3+\log 5}{1-\log 3\,\,\log 5} \right)\]
  done clear
  C)
   \[{{\tan }^{-1}}\left( \frac{\log 3+\log 5}{1+\log 3\,\,\log 5} \right)\]
  done clear
  D)
   \[{{\tan }^{-1}}\left( \frac{\log 3-\log 5}{1-\log 3\,\,\log 5} \right)\]
  done clear
  View Answer play_arrow

• question_answer118) The equation \[\lambda {{x}^{2}}+4xy+{{y}^{2}}+\lambda x+3y+2=0\] represents a parabola, if \[\lambda \] is
  A)
   0
  done clear
  B)
   1
  done clear
  C)
   2
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer119) If two circles \[2{{x}^{2}}+2{{y}^{2}}-3x+6y+k=0\] and \[{{x}^{2}}+{{y}^{2}}-4x+10y+16=0\] cut orthogonally, then the value of k is
  A)
   41
  done clear
  B)
   14
  done clear
  C)
   4
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer120) If \[A\,(-2,\,1),\] \[B\,(2,\,3)\] and \[C\,(-2,\,-4)\] are three points. Then the angle between \[BA\]and \[BC\]is
  A)
   \[{{\tan }^{-1}}\left( \frac{2}{3} \right)\]
  done clear
  B)
   \[{{\tan }^{-1}}\left( \frac{3}{2} \right)\]
  done clear
  C)
   \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\]
  done clear
  D)
   \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]
  done clear
  View Answer play_arrow