Solved papers for VIT Engineering VIT Engineering Solved Paper-2014

done VIT Engineering Solved Paper-2014 Total Questions - 120

• question_answer1) A coil of resistance 10\[\Omega \] and an inductance 5 H is connected to a 100 V battery. The energy stored in the coil is
  A)
  325 erg                 
  done clear
  B)
  125 J
  done clear
  C)
  250 erg                 
  done clear
  D)
  250 J
  done clear
  View Answer play_arrow

• question_answer2) A galvanometer has current range of 15 mA and voltage range 750 mV. To convert this galvanometer into an ammeter of range 25 A, the required shunt is
  A)
  0.8 \[\Omega \]               
  done clear
  B)
  0.93\[\Omega \]
  done clear
  C)
  0.03 \[\Omega \]            
  done clear
  D)
  2.0 \[\Omega \]
  done clear
  View Answer play_arrow

• question_answer3) The daniel cell is balanced on 125 cm length of a potentiometer. Now, the cell is ?short circuited by a resistance of 2\[\Omega \], and the balance is obtained at 100 cm. The internal resistance of the daniel cell is
  A)
  \[\frac{4}{3}\Omega \]                 
  done clear
  B)
  1.50 \[\Omega \]
  done clear
  C)
  1.25\[\Omega \]                              
  done clear
  D)
  0.5 \[\Omega \]
  done clear
  View Answer play_arrow

• question_answer4) Four resistances of 10\[\Omega \], 60\[\Omega \]., 100\[\Omega \]. and 200\[\Omega \]. respectively taken in order are used to form a Wheatstone's bridge. A 15V battery is connected to the ends of a 200\[\Omega \], resistance, the current through it will be
  A)
  \[7.5\times {{10}^{-5}}A\]           
  done clear
  B)
  \[7.5\times {{10}^{-4}}A\]
  done clear
  C)
  \[7.5\times {{10}^{-3}}A\]           
  done clear
  D)
  \[7.5\times {{10}^{-2}}A\]
  done clear
  View Answer play_arrow

• question_answer5) circuit has a self-inductance of 1 H and carries a current of 2A. To prevent sparking, when the circuit is switched off, a capacitor which can withstand 400 V is used. The least capacitance of capacitor connected across the switch must be equal to
  A)
  50 \[\mu F\]                      
  done clear
  B)
  25 \[\mu F\]
  done clear
  C)
  100\[\mu F\]                     
  done clear
  D)
  12.5 \[\mu F\]
  done clear
  View Answer play_arrow

• question_answer6) The output Y of the logic circuit shown in figure is best represented as
  A)
  \[\overset{-}{\mathop{A}}\,++\overline{B.C}\]                
  done clear
  B)
   \[A+\overline{B}.C\]
  done clear
  C)
  \[\overline{A+B.C}\]                     
  done clear
  D)
   \[\overline{A+\overset{-}{\mathop{B}}\,.C}\]
  done clear
  View Answer play_arrow

• question_answer7) A resistor of 6 \[k\Omega \] with tolerance 10% and another resistance of 4 \[k\Omega \] with tolerance 10% are connected in series. The tolerance of the combination is about
  A)
  5%                                         
  done clear
  B)
  10%
  done clear
  C)
  12%                                       
  done clear
  D)
  15% In series combination,                         \[=5000kW\]                          \[=\frac{mgh}{t}\] Error in combination               \[=7.5\times 9.8\times 4.7\]                \[=3454.5kW\]                \[\text{=}\frac{\text{Power used}}{\text{Power consumed}}\text{ }\!\!\times\!\!\text{ 100}\]               \[=\frac{3454.5}{5000}\times 100=69%\]                    = 10
  done clear
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• question_answer8) If we add impurity to a metal those atoms also deflect electrons. Therefore,
  A)
  the electrical and thermal conductivities both increase
  done clear
  B)
  the electrical and thermal conductivities both decrease
  done clear
  C)
  the electrical conductivity increases but thermal conductivity decreases
  done clear
  D)
  the electrical conductivity decrease but thermal conductivity increases
  done clear
  View Answer play_arrow

• question_answer9) A proton and an a-particle, accelerated through the same potential difference, enter a region of uniform magnetic field normally. If the radius of the proton orbit is 10 cm, then radius of a-particle is
  A)
  10 cm                   
  done clear
  B)
  \[10\sqrt{2}cm\]
  done clear
  C)
  20 cm                   
  done clear
  D)
  \[5\sqrt{2}cm\]
  done clear
  View Answer play_arrow

• question_answer10) An ammeter and a voltmeter of resistance R are connected in series to an electric cell of negligible internal resistance. Their reading are A and V respectively. If another resistance R is connected in parallel with the voltmeter, Then
  A)
  both/A and V will increase
  done clear
  B)
  both A and V will decrease
  done clear
  C)
   A will decrease and V will increase
  done clear
  D)
  A will increase and V will decrease
  done clear
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• question_answer11) A neutron is moving with velocity u. It collides head on and elastically with an atom of mass number A. If the initial kinetic energy of the neutron is E , then how much kinetic energy will be retained by the neutron after reflection?
  A)
  \[{{\left( \frac{A}{A+1} \right)}^{2}}E\]                 
  done clear
  B)
   \[\frac{A}{{{\left( A+1 \right)}^{2}}}E\]
  done clear
  C)
   \[{{\left( \frac{A-1}{A+1} \right)}^{2}}E\]                            
  done clear
  D)
  \[\frac{\left( A-1 \right)}{{{\left( A+1 \right)}^{2}}}E\]
  done clear
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• question_answer12) If a magnet is suspended at angle 30° to the magnet meridian, the dip of needle makes angle of 45° with the horizontal, the real dip is
  A)
  \[{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]                 
  done clear
  B)
  \[{{\tan }^{-1}}\left( \sqrt{3} \right)\]
  done clear
  C)
  \[{{\tan }^{-1}}\left( \sqrt{\frac{3}{2}} \right)\]                 
  done clear
  D)
   \[{{\tan }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]
  done clear
  View Answer play_arrow

• question_answer13) Which has more luminous efficiency ?
  A)
  A 40 W bulb
  done clear
  B)
  A 40 W fluorescent tube
  done clear
  C)
  Both have same
  done clear
  D)
  Cannot say
  done clear
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• question_answer14) The resistance of a germanium junction diode whose V- I is shown in figure is\[\left( {{V}_{k}}=0.3V \right).\]
  A)
   5 \[k\Omega \]
  done clear
  B)
   0.2 \[k\Omega \]
  done clear
  C)
  2.3 \[k\Omega \]                             
  done clear
  D)
  \[\left( \frac{10}{2.3} \right)k\Omega \]
  done clear
  View Answer play_arrow

• question_answer15) In hydrogen discharge tube, it is observed that through a given, cross-section \[3.31\times {{10}^{15}}\] electrons are moving from right to left and \[3.12\times {{10}^{5}}\] protons are moving from left to right. The current in the discharge tube and its direction will be
  A)
  2 mA, towards left
  done clear
  B)
  2 mA, towards right
  done clear
  C)
  1 mA, towards right
  done clear
  D)
  2 mA, towards left
  done clear
  View Answer play_arrow

• question_answer16) In a semiconductor, separation between conduction and valence band is of the order of
  A)
  0 eV                                      
  done clear
  B)
  1 eV
  done clear
  C)
  10 eV                                    
  done clear
  D)
  50 eV
  done clear
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• question_answer17) If 1000 droplets each of potential IV and radius r are mixed to form a big drop. Then, the potential of the drop as compared to small droplets, will be
  A)
  1000V                   
  done clear
  B)
  800V
  done clear
  C)
  100V   
  done clear
  D)
  (d) 20V
  done clear
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• question_answer18) A Zener diode, having breakdown voltage equal to 15 V is used in a voltage regulator circuit shown in figure. The current through the diode is
  A)
  10mA
  done clear
  B)
  15mA
  done clear
  C)
  20 mA                  
  done clear
  D)
  5 mA
  done clear
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• question_answer19) The activity of a radioactive sample is measured as \[{{N}_{0}}\]counts per minute at t = 0 and \[{{N}_{0}}/C\] counts per minute at t= 5 min. The time, (in minute) at which the activity reduces to half its value, is
  A)
  \[{{\log }_{e}}\frac{2}{5}\]                          
  done clear
  B)
  \[\frac{5}{{{\log }_{e}}2}\]
  done clear
  C)
  \[5{{\log }_{10}}2\]                         
  done clear
  D)
  \[5{{\log }_{e}}2\]
  done clear
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• question_answer20) If the electron in the hydrogen atom jumps from third orbit to second orbit, the wavelength of the emitted radiation in term of Rydberg constant is
  A)
   \[\frac{6}{5R}\] 
  done clear
  B)
                         \[\frac{36}{5R}\]
  done clear
  C)
   \[\frac{64}{7R}\]                                             
  done clear
  D)
   None of these
  done clear
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• question_answer21) Silver has a work function of 4.7 eV. When ultraviolet light of wavelength 100 nm is incident on it a potential of 7.7 V is required to stop the photoelectrons from reaching the collector plate. How much potential will be required to stop photoelectrons, when light of wavelength 200 nm is incident on it?
  A)
  15.4V 
  done clear
  B)
  2.35V
  done clear
  C)
  3.85V                    
  done clear
  D)
  1.5V
  done clear
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• question_answer22) If the distance of 100 W lamp is increased from a photocell, the saturation current i in the photocell varies with the distance d as
  A)
  \[i\propto {{d}^{2}}\]                    
  done clear
  B)
  \[i\propto d\]
  done clear
  C)
  \[i\propto \frac{1}{d}\]                                
  done clear
  D)
  \[i\propto \frac{1}{{{d}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer23) Following process is known as                 \[hv\leftrightarrow {{e}^{+}}+{{e}^{-}}\]
  A)
  pair production      
  done clear
  B)
  photoelectric effect
  done clear
  C)
   Compton effect      
  done clear
  D)
    Zeeman effect
  done clear
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• question_answer24) During charging a capacitor, variations of potential V of the capacitor with time t is shown as
  A)
                                                              
  done clear
  B)
  
  done clear
  C)
                                                                    
  done clear
  D)
            
  done clear
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• question_answer25) When a resistor of 11\[\Omega \] is connected in series with an electric cell. The current flowing in it is 0.5 A. Instead when a resistor of 5\[\Omega \] is connected to the same electric cell in series, the current increases by 0.4 A. The internal resistance of the cell is
  A)
  1.5\[\Omega \]                
  done clear
  B)
  2\[\Omega \]
  done clear
  C)
  2.5\[\Omega \] 
  done clear
  D)
  3.5\[\Omega \]
  done clear
  View Answer play_arrow

• question_answer26) A battery is charged at a potential of 15 V in 8 h when the current flowing is 10A. The battery on discharge supplies a current of 5A for 15 h. The mean terminal voltage during discharge is 14V. The watt-hour efficiency of battery is
  A)
  80% 
  done clear
  B)
                                         90%
  done clear
  C)
  87.5%                                   
  done clear
  D)
  82.5%  
  done clear
  View Answer play_arrow

• question_answer27)                A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis, where the magnetic induction will be \[\frac{1}{8}\]th to its value at the centre of the coil is
  A)
  \[\frac{R}{\sqrt{3}}\]                     
  done clear
  B)
  \[R\sqrt{3}\]
  done clear
  C)
  \[2\sqrt{3}R\]                   
  done clear
  D)
  \[\frac{2}{\sqrt{3}}R\]
  done clear
  View Answer play_arrow

• question_answer28) The incorrect statement regarding the lines of force of the magnetic field B is
  A)
  magnetic intensity is a measure of lines of force passing through unit area held normal to it
  done clear
  B)
  magnetic lines of force from a close curve
  done clear
  C)
  inside a magnet, its magnetic lines of force move from north pole of a magnetic towards its south pole
  done clear
  D)
  due to a magnetic lines of force never cut each other
  done clear
  View Answer play_arrow

• question_answer29) Two coils have a mutual inductance 0.55 H. The current changes in the first coil according equation \[I={{I}_{0}}\]sin wt. where, \[{{I}_{0}}=10A\] and \[\omega =100\pi \]rad/s. The maximum value of emfin the second coil is
  A)
  \[2\pi \]                                               
  done clear
  B)
  \[5\pi \]
  done clear
  C)
   \[\pi \]                                
  done clear
  D)
  \[4\pi \]
  done clear
  View Answer play_arrow

• question_answer30) An L-C-R circuit contains \[R=50\Omega ,\] L = 1 mH and \[C=0.\mu F.\]The impedance of the circuit will be minimum for a frequency of
  A)
  \[\frac{{{10}^{5}}}{2\pi }Hz\]   
  done clear
  B)
  \[\frac{{{10}^{6}}}{2\pi }Hz\]
  done clear
  C)
  \[2\pi \times {{10}^{5}}Hz\]        
  done clear
  D)
  \[2\pi \times {{10}^{6}}Hz\]
  done clear
  View Answer play_arrow

• question_answer31) An eye can detect \[5\times {{10}^{4}}\]photons per square metre per sec of green light \[\left( \lambda =5000\overset{\circ }{\mathop{\text{A}}}\, \right)\]while the ear can detect \[{{10}^{-13}}W/{{m}^{2}}.\]. The factor by which the eye is more sensitive as a power detector then the ear is close to  
  A)
             5                                            
  done clear
  B)
  10                   
  done clear
  C)
  \[{{10}^{6}}\]                                    
  done clear
  D)
  15   
  done clear
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• question_answer32)                  The amplification factor of a triode is 50. If the grid potential is decreased by 0.20 V. What increase, in plate potential will keep the plate current unchanged?
  A)
   5V                                         
  done clear
  B)
  10V
  done clear
  C)
  0.2 V                                     
  done clear
  D)
   50 V          
  done clear
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• question_answer33)                                       If in a nuclear fission, piece of uranium of mass 5.0 g is lost, the energy obtained in kWh is
  A)
  \[1.25\times {{10}^{7}}\]             
  done clear
  B)
  \[2.25\times {{10}^{7}}\]
  done clear
  C)
  \[3.25\times {{10}^{7}}\]             
  done clear
  D)
  \[0.25\times {{10}^{7}}\]
  done clear
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• question_answer34) Current in the circuit will be
  A)
   \[\frac{5}{40}A\]                            
  done clear
  B)
  \[\frac{5}{50}A\]
  done clear
  C)
   \[\frac{5}{10}A\]                            
  done clear
  D)
   \[\frac{5}{20}A\]
  done clear
  View Answer play_arrow

• question_answer35) An installation consisting of an electric motor driving a water pump left 75 L of water per second to a height of 4.7 m. If the motor consumes a power of 5 kW, then the efficiency of the installation is
  A)
  39%                                       
  done clear
  B)
  69%
  done clear
  C)
  93%                                       
  done clear
  D)
  96%
  done clear
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• question_answer36) The potential difference across the terminals of a battery is 50 V when 11 A current is drawn and 60 V, when 1 A current is drawn. The emf and the internal resistance of the battery are
  A)
  \[62V,2\Omega \]          
  done clear
  B)
  \[63V,1\Omega \]
  done clear
  C)
  \[61V,1\Omega \]   
  done clear
  D)
  \[64V,2\Omega \]
  done clear
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• question_answer37) Beyond which frequency, the ionosphere bands any incident electromagnetic radiation but do not reflect it back towards the earth?
  A)
   50 MHz          
  done clear
  B)
  40 MHz
  done clear
  C)
  30 MHz          
  done clear
  D)
  20 MHz
  done clear
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• question_answer38) A metallic surface ejects electrons. When exposed to green light of intensity I but no photoelectrons are emitted, when exposed to yellow light of intensity 7. It is possible to eject electron from the same surface by
  A)
  yellow light of same intensity which is more than
  done clear
  B)
   green light of any intensity
  done clear
  C)
  red light of any intensity
  done clear
  D)
  None of the above
  done clear
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• question_answer39) An electron moves at right angle to a magnetic field of\[5\times {{10}^{-2}}\] T with a speed of \[6\times {{10}^{7}}\]m/s. If the specific charge of the electron is \[1.7\times {{10}^{11}}C/kg.\]The radius of the circular path will be
  A)
  2.9 cm                  
  done clear
  B)
  3.9 cm
  done clear
  C)
  2.35 cm  
  done clear
  D)
  2 cm
  done clear
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• question_answer40) A solenoid 30 cm long is made by winding 2000 loops of wire on an iron rod whose cross-section is 1.5 cm2. If the relative permeability of the iron is 6000. What is the self-inductance of the solenoid?
  A)
  1.5H      
  done clear
  B)
  2.5H
  done clear
  C)
  3.5H                                      
  done clear
  D)
  0.5H
  done clear
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• question_answer41) The standard molar heat of formation of ethane, \[\text{C}{{\text{O}}_{\text{2}}}\]and water (l) are respectively -21.1, -94.1 and - 68.3 kcal. The standard molar heat of combustion of ethane will be
  A)
  -372 kcal              
  done clear
  B)
  162 kcal
  done clear
  C)
  -240 kcal                              
  done clear
  D)
  183.5 kcal
  done clear
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• question_answer42) The solubility product of \[\text{A}{{\text{g}}_{\text{2}}}\text{Cr}{{\text{O}}_{\text{4}}}\]is \[32\times {{10}^{-12}}.\] What is the concentration of \[\text{CrO}_{\text{4}}^{\text{-}}\] ions in that solution?
  A)
  \[\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{M}\]
  done clear
  B)
  \[\text{16 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{M}\]
  done clear
  C)
  \[\text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{M}\]         
  done clear
  D)
  \[\text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-8}}}\text{M}\]
  done clear
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• question_answer43) The equivalent conductivity of a solution containing 2.54 g of \[CuS{{O}_{4}}\] per L is \[91.0{{W}^{-1}}\]\[c{{m}^{2}}e{{q}^{-1}}.\] Its conductivity would be
  A)
  \[2.9\times {{10}^{-3}}{{\Omega }^{-1}}c{{m}^{-1}}\]
  done clear
  B)
  \[1.8\times {{10}^{-2}}{{\Omega }^{-1}}c{{m}^{-1}}\]
  done clear
  C)
  \[2.4\times {{10}^{-4}}{{\Omega }^{-1}}c{{m}^{-1}}\]
  done clear
  D)
  \[3.6\times {{10}^{-3}}{{\Omega }^{-1}}c{{m}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer44) The half-life of two samples are 0.1 and 08 s. Their respective concentration are 400 and 50 respectively. The order of the reaction is
  A)
  0                                             
  done clear
  B)
  2
  done clear
  C)
  1                                             
  done clear
  D)
  4
  done clear
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• question_answer45) Which sequence of reactions shows correct chemical relation between sodium and its compounds ?
  A)
  \[Na+{{O}_{2}}\to Na{{O}_{2}}\xrightarrow{HCl\left( aq \right)}\]                        \[NaCl\xrightarrow{C{{O}_{2}}}N{{a}_{2}}C{{O}_{3}}\xrightarrow{\Delta }Na\]
  done clear
  B)
  \[Na\xrightarrow{{{O}_{2}}}N{{a}_{2}}O\xrightarrow{{{H}_{2}}O}NaOH\xrightarrow{C{{O}_{2}}}\]                                      \[N{{a}_{2}}C{{O}_{3}}\xrightarrow{\Delta }Na\]
  done clear
  C)
  \[Na+{{H}_{2}}O\to NaOH\xrightarrow{HCl}NaCl\xrightarrow{C{{O}_{2}}}\]                                      \[N{{a}_{2}}C{{O}_{3}}\xrightarrow{\Delta }Na\]?
  done clear
  D)
  \[Na+{{H}_{2}}O\to NaOH\xrightarrow{C{{O}_{2}}}N{{a}_{2}}C{{O}_{3}}\]                                      \[\xrightarrow{HCl}\underset{\left( molten \right)}{\mathop{NaCl}}\,\xrightarrow{Electrolysis}Na\]
  done clear
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• question_answer46) Purest form of iron is
  A)
  pig iron                
  done clear
  B)
   wrought iron
  done clear
  C)
  cast iron              
  done clear
  D)
  steel
  done clear
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• question_answer47) Which has the smallest size?
  A)
  \[N{{a}^{+}}\]                                   
  done clear
  B)
  \[M{{g}^{2+}}\]
  done clear
  C)
  \[A{{l}^{3+}}\]                                  
  done clear
  D)
  \[{{\text{P}}^{\text{5+}}}\]
  done clear
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• question_answer48) In the reaction, \[8Al+3F{{e}_{3}}{{O}_{4}}\to 4A{{l}_{2}}{{O}_{3}}+9Fe\] the number of electrons transferred from the reluctant to the bxidant is
  A)
  8                                             
  done clear
  B)
   4
  done clear
  C)
  16                                          
  done clear
  D)
  24
  done clear
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• question_answer49) The bond angles of \[\text{N}{{\text{H}}_{\text{3}}}\text{,NH}_{\text{4}}^{\text{+}}\] and \[\text{NH}_{\text{2}}^{\text{-}}\] are in the order
  A)
   \[NH_{2}^{-}>N{{H}_{3}}>NH_{4}^{+}\]
  done clear
  B)
  \[NH_{4}^{+}>N{{H}_{3}}>NH_{2}^{-}\]
  done clear
  C)
  \[N{{H}_{3}}>NH_{2}^{-}>NH_{4}^{+}\]
  done clear
  D)
  \[NH>NH_{4}^{+}>NH_{2}^{-}\]
  done clear
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• question_answer50) A gaseous mixture containing He, \[C{{H}_{4}}\]and \[S{{O}_{2}}\] was allowed to effuse through a fine hole then find what molar ratio of gases coming out initially? (Given mixture contains He, \[C{{H}_{4}}\]and  \[S{{O}_{2}}\] in 1 : 2 : 3 mole ratio).
  A)
   \[\sqrt{2}:\sqrt{2} & :3\]             
  done clear
  B)
  2 : 2 : 3
  done clear
  C)
   4 : 4 : 3     
  done clear
  D)
  1:1:3
  done clear
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• question_answer51) According to Bohr's theory, the angular momentum for an electron of 3rd orbit is
  A)
  3 h               
  done clear
  B)
  1.5 h
  done clear
  C)
   9 h               
  done clear
  D)
  \[2\frac{h}{\pi }\]
  done clear
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• question_answer52) 2.76 g of silver carbonate on being strongly heated yields a residue weighing
  A)
  3.54g                    
  done clear
  B)
  3.0g  
  done clear
  C)
  1.36g                    
  done clear
  D)
  2.16g
  done clear
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• question_answer53) The final product (IV) in the sequence of reactions \[\begin{align}   & C{{H}_{3}}CHOH\xrightarrow{PB{{r}_{3}}}I\xrightarrow[Ether]{Mg} \\  & | \\  & C{{H}_{3}} \\ \end{align}\]                              ..
  A)
            \[\begin{align}   & C{{H}_{3}}-CHOC{{H}_{2}}C{{H}_{2}}OH \\  & | \\  & C{{H}_{3}} \\ \end{align}\]
  done clear
  B)
              \[\begin{align}   & C{{H}_{3}}-CHC{{H}_{2}}C{{H}_{2}}Br \\  & | \\  & C{{H}_{3}} \\ \end{align}\]
  done clear
  C)
               \[\begin{align}   & C{{H}_{3}}-CH-C{{H}_{2}}C{{H}_{2}}OH \\  & | \\  & C{{H}_{3}} \\ \end{align}\]
  done clear
  D)
                \[\begin{align}   & C{{H}_{3}}-CHOC{{H}_{2}}C{{H}_{3}} \\  & | \\  & C{{H}_{3}} \\ \end{align}\]
  done clear
  View Answer play_arrow

• question_answer54) \[Ph-C\equiv C-C{{H}_{3}}\xrightarrow{H{{g}^{2+}}/{{H}^{+}}}A,\]
  A)
                                             
  done clear
  B)
  
  done clear
  C)
                                                                                
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer55) Which of the following has an ester linkage?
  A)
  Nylon-66             
  done clear
  B)
  Dacron
  done clear
  C)
  PVC                                       
  done clear
  D)
  Bakelite
  done clear
  View Answer play_arrow

• question_answer56) Which of the following pairs give positive Tollen's test?
  A)
  Glucose, sucrose
  done clear
  B)
  Glucose, fructose
  done clear
  C)
  Hexanal, acetophenone
  done clear
  D)
  Fructose, sucrose
  done clear
  View Answer play_arrow

• question_answer57) Peptisation involves
  A)
  precipitation of colloidal particles
  done clear
  B)
  disintegration of colloidal aggregates
  done clear
  C)
   evaporation of dispersion medium
  done clear
  D)
  impact of molecules of the dispersion medium on the colloidal particles
  done clear
  View Answer play_arrow

• question_answer58) Which of the following has the maximum number of unpaired d-electrons?
  A)
  \[F{{e}^{2+}}\]                 
  done clear
  B)
  \[C{{u}^{+}}\]
  done clear
  C)
   Zn                                         
  done clear
  D)
  \[N{{i}^{3+}}\]
  done clear
  View Answer play_arrow

• question_answer59) Iodine is formed when potassium iodide reacts with a solution of
  A)
  \[ZnS{{O}_{4}}\]                              
  done clear
  B)
  \[CuS{{O}_{4}}\]
  done clear
  C)
  \[{{\left( N{{H}_{4}} \right)}_{2}}S{{O}_{4}}\]                     
  done clear
  D)
  \[N{{a}_{2}}S{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer60) Which of the following does not represent the correct order of the property indicated?
  A)
  \[S{{c}^{3+}}>C{{r}^{3+}}>F{{e}^{3+}}>M{{n}^{3+}}\] ? ionic radii
  done clear
  B)
  \[Sc<Ti<Cr<Mn\] ? density
  done clear
  C)
  \[M{{n}^{2+}}>N{{i}^{2+}}>C{{o}^{2+}}<F{{e}^{2+}}\] ? ionic radii
  done clear
  D)
  \[FeO<CaO<MnO<CuO\] ? basic nature
  done clear
  View Answer play_arrow

• question_answer61) If the elevation in boiling point of a solution of 10 g of solute (mol. wt. = 100) in 100 g of water is \[\Delta {{T}_{b}},\]the ebullioscopic constant of water is
  A)
  10                                          
  done clear
  B)
  100 \[{{T}_{b}}\]
  done clear
  C)
  \[\Delta {{T}_{b}},\]                       
  done clear
  D)
  \[\frac{\Delta {{T}_{b}}}{10}\]
  done clear
  View Answer play_arrow

• question_answer62) Which of the following compounds cannot be prepared singly by the Wurtz reaction?
  A)
  \[{{C}_{2}}{{H}_{6}}\]
  done clear
  B)
  \[{{\left( C{{H}_{3}} \right)}_{2}}CHC{{H}_{3}}\]
  done clear
  C)
  \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\]
  done clear
  D)
  All of the above can be prepared
  done clear
  View Answer play_arrow

• question_answer63) Which of the following oxides is strongly  asic?
  A)
  \[T{{l}_{2}}O\]                  
  done clear
  B)
  \[{{B}_{2}}{{O}_{3}}\]
  done clear
  C)
  \[A{{l}_{2}}{{O}_{3}}\]                  
  done clear
  D)
  \[G{{a}_{2}}{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer64) In Langmuir's model of adsorption of a gas on a solid surface,
  A)
  the rate of dissociation of adsorbed molecules from the surface does not depend on the surface covered
  done clear
  B)
  the adsorption at a single site on the surface may involve multiple molecules at the same time
  done clear
  C)
  the mass of gas striking a given area of surface is proportional to the pressure of the gas
  done clear
  D)
  the mass of gas striking a given area of surface is independent of the pressure of the gas
  done clear
  View Answer play_arrow

• question_answer65) How many sigma and pi-bonds are there in the. molecule        of        dicyanoethene (CN?CH\[\equiv \]CH?CN)?
  A)
  3 sigma and 3 pi
  done clear
  B)
  5 sigma and 2 pi
  done clear
  C)
  7 sigma and 5 pi
  done clear
  D)
  2 sigma and 3 pi
  done clear
  View Answer play_arrow

• question_answer66) What will be the order of reactivity of the following carbonyl compounds with Grignard's reagent?
  A)
                                                                                     I > II > III > IV                                     
  done clear
  B)
  IV > III > II > I
  done clear
  C)
   II > I > IV > III
  done clear
  D)
  III > II > I > IV
  done clear
  View Answer play_arrow

• question_answer67)   The final product ?C?  in the above reaction is
  A)
                                                                                  
  done clear
  B)
  
  done clear
  C)
                                                                         
  done clear
  D)
                       
  done clear
  View Answer play_arrow

• question_answer68) Which of the following isomerism is shown by ethyl acetoacetate?
  A)
  Geometrical isomerism
  done clear
  B)
  Keto-enol tautomerism
  done clear
  C)
  Enantiomerism
  done clear
  D)
  Diastereoisomerism
  done clear
  View Answer play_arrow

• question_answer69) The final product obtained in the reaction,
  A)
                                                                    
  done clear
  B)
                
  done clear
  C)
                                                                   
  done clear
  D)
                                          
  done clear
  View Answer play_arrow

• question_answer70) Among the following the strongest nucleophile is
  A)
  \[{{C}_{2}}{{H}_{5}}SH\]
  done clear
  B)
  \[C{{H}_{3}}CO{{O}^{-}}\]
  done clear
  C)
  \[C{{H}_{3}}N{{H}_{2}}\]
  done clear
  D)
  \[NCCH_{2}^{-}\]
  done clear
  View Answer play_arrow

• question_answer71) Which set has different class of compounds?
  A)
  Tranquillizers-Equanil, heroin, valium
  done clear
  B)
  Antiseptics-Bithional, dettol, boric acid
  done clear
  C)
  Analgesics-Naproxen, morphine, aspirin
  done clear
  D)
  Bactericidal-Penicillin, aminoglycosides, of loxacin
  done clear
  View Answer play_arrow

• question_answer72) The sodium extract, of an organic compound on acidification with acetic acid and addition of lead acetate solution gives a black precipitate. The organic compound contains
  A)
  nitrogen                              
  done clear
  B)
  halogen
  done clear
  C)
  sulphur                
  done clear
  D)
  phosphorus
  done clear
  View Answer play_arrow

• question_answer73) The volume strength of 1.5 N \[{{H}_{2}}{{O}_{2}}\]solution is
  A)
  16.8L                     
  done clear
  B)
   8.4 L
  done clear
  C)
  4.2 L                      
  done clear
  D)
   5.2 L
  done clear
  View Answer play_arrow

• question_answer74) \[MnO_{4}^{-}+8{{H}^{+}}+5{{e}^{-}}\to M{{n}^{2+}}+4{{H}_{2}}O;\]                                                \[{{E}^{\circ }}=1.51V\] \[Mn{{O}_{2}}+4{{H}^{+}}+2{{e}^{-}}\to M{{n}^{2+}}+2{{H}_{2}}O'\]                         \[{{E}^{\circ }}=1.23V{{E}^{\circ }}_{MnO_{4}^{-}|Mn{{O}_{2}}}is\]
  A)
   1.70 V                  
  done clear
  B)
   0.91 V
  done clear
  C)
   1.37 V                  
  done clear
  D)
  0.548 V
  done clear
  View Answer play_arrow

• question_answer75) A metal has bcc structure and the edge length of its unit cell is 3.04\[\overset{\circ }{\mathop{\text{A}}}\,\]. The volume of the unit cell in cm 3 will be
  A)
  \[1.6\times {{10}^{21}}c{{m}^{3}}\]     
  done clear
  B)
  \[2.81\times {{10}^{-23}}c{{m}^{3}}\]
  done clear
  C)
  \[6.02\times {{10}^{-23}}c{{m}^{3}}\]  
  done clear
  D)
  \[6.6\times {{10}^{-24}}c{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer76) Among \[{{\left[ Fe{{\left( {{H}_{2}}O \right)}_{6}} \right]}^{3+}},\]\[{{\left[ Fe{{\left( CN \right)}_{6}} \right]}^{3-}},\] \[{{\left[ Fe{{\left( Cl \right)}_{6}} \right]}^{3-}}\]species, the hybridisation state of the Fe atom are, respectively.
  A)
   \[{{d}^{2}}s{{p}^{3}},{{d}^{2}}s{{p}^{3}},s{{p}^{2}}{{d}^{2}}\]
  done clear
  B)
  \[s{{p}^{3}}{{d}^{2}},{{d}^{2}}s{{p}^{3}},{{d}^{2}}s{{p}^{3}}\]
  done clear
  C)
  \[s{{p}^{3}}{{d}^{2}},{{d}^{2}}s{{p}^{3}},s{{p}^{3}}{{d}^{2}}\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer77) Which of the following hydrogen bonds are strongest in vapour phase?
  A)
  HF.......... HF
  done clear
  B)
  HF.......... HCI
  done clear
  C)
  HCI.......... HCI
  done clear
  D)
  HF.......... HI
  done clear
  View Answer play_arrow

• question_answer78) The rate constant for forward reaction and backward reaction of hydrolysis of ester are \[1.1\times {{10}^{-2}}\] and \[1.5\times {{10}^{-3}}\]per   minute respectively. Equilibrium constant for the reaction is      \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}+{{H}_{2}}O\rightleftharpoons C{{H}_{3}}COOH+{{C}_{2}}{{H}_{5}}OH\]
  A)
  33.7                                       
  done clear
  B)
  7.33
  done clear
  C)
  5.33                                       
  done clear
  D)
   33.3
  done clear
  View Answer play_arrow

• question_answer79) 19.85 mL of 0.1 N NaOH reacts with 20 mL of HCI solution for complete neutralisation. The molarity of HCI solution is
  A)
  9.9                                         
  done clear
  B)
  0.99
  done clear
  C)
   0.099                   
  done clear
  D)
  0.0099
  done clear
  View Answer play_arrow

• question_answer80) An /-shell containing 6 unpaired electrons can Exchange
  A)
  6 electrons                         
  done clear
  B)
  9 electrons
  done clear
  C)
  12 electrons                      
  done clear
  D)
  15 electrons
  done clear
  View Answer play_arrow

• question_answer81)                   If the vertices of a triangle are A (0, 4, 1). B (2,3, -1) AND C (4, 5, 0), then the orthocentre of \[\Delta ABC,\] is
  A)
  (4, 5, 0)                
  done clear
  B)
  (2, 3, -1)
  done clear
  C)
  (-2, 3, -1)                             
  done clear
  D)
   (2, 0, 2)
  done clear
  View Answer play_arrow

• question_answer82) The equation of normal to the curve \[y={{\left( 1+x \right)}^{y}}+{{\sin }^{-1}}\left( {{\sin }^{2}}x \right)\] at x = 0 is
  A)
   x + y = 1
  done clear
  B)
   x ? y = 1
  done clear
  C)
   x + y = - 1                           
  done clear
  D)
   x ? y = - 1
  done clear
  View Answer play_arrow

• question_answer83) The value of c from the Lagrange?s mean value theorem for which \[f\left( x \right)=\sqrt{25-{{x}^{2}}}\] in [1, 5], is
  A)
  5                                             
  done clear
  B)
  1
  done clear
  C)
  \[\sqrt{15}\]                                      
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer84) If \[\text{A=}\left[ _{\text{5}}^{\text{3}}_{\text{7}}^{\text{4}} \right],\] then A. (adj A) is equal to
  A)
  A                                            
  done clear
  B)
  |A|
  done clear
  C)
  A|. l                                      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer85) If there is an error of k% in measuring the edge of a cube, then the per cent rear in estimating its volume is
  A)
  k                                             
  done clear
  B)
  3k
  done clear
  C)
  \[\frac{k}{3}\]                                   
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer86) If the system of equation x + ky ? z = 0, 3x ? ky ? z = 0 and x ? 3y + z = 0, has non-zero solution, then k is equal to
  A)
  -1                                           
  done clear
  B)
  0
  done clear
  C)
  1             
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer87) If the points (1, 2, 3) and (2, -1, 0) lie on the opposite sides of the plane 2x + 3y ? 2z = k, then
  A)
  k < 1      
  done clear
  B)
  k > 2
  done clear
  C)
   k < 1 or k > 2                     
  done clear
  D)
  1 < k < 2
  done clear
  View Answer play_arrow

• question_answer88) If \[\text{ }\!\!\Delta\!\!\text{ }\left( \text{x} \right)\left| \begin{matrix}    \text{1} & \text{cosx} & \text{1-cosx}  \\    \text{1+sinx} & \text{cosx} & \text{1+sinx-cosx}  \\    \text{sinx} & \text{sinx} & \text{1}  \\ \end{matrix} \right|\], then \[\int_{0}^{\pi /4}{\Delta }\left( x \right)dx\] is equal to
  A)
  \[\frac{1}{4}\]                                   
  done clear
  B)
  \[\frac{1}{2}\]
  done clear
  C)
   0                                            
  done clear
  D)
  \[-\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer89) Let f? (x), be differentiable \[\forall x.\] If f(1) = - 2 and \[f'\left( x \right)\ge 2\forall x\in \] [ 1, 6], then
  A)
  f(6) < 8                 
  done clear
  B)
  \[f\left( 6 \right)\ge 8\]
  done clear
  C)
  \[f\left( 6 \right)\ge 5\]                
  done clear
  D)
  \[f\left( 6 \right)\le 5\]
  done clear
  View Answer play_arrow

• question_answer90) If  \[{{\text{ }\!\!\Delta\!\!\text{ }}_{\text{r}}}\text{=}\left| \begin{matrix}    \text{2r-1} & ^{\text{m}}{{\text{C}}_{\text{r}}} & \text{1}  \\    {{\text{m}}^{\text{2}}}\text{-1} & {{\text{2}}^{\text{m}}} & \text{m+1}  \\    \text{si}{{\text{n}}^{\text{2}}}\left( {{\text{m}}^{\text{2}}} \right) & \text{si}{{\text{n}}^{\text{2}}}\left( \text{m} \right) & \text{si}{{\text{n}}^{\text{2}}}\left( \text{m+1} \right)  \\ \end{matrix} \right|\text{,}\] then value of \[\sum\limits_{r=0}^{m}{{{\Delta }_{r}}}\] is
  A)
  1                                             
  done clear
  B)
   0
  done clear
  C)
   2                                            
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer91) Two  lines   \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\] and   \[\frac{x-3}{1}=\frac{y-k}{2}=z\]  intersect at a point, if k is equal to
  A)
  \[\frac{2}{9}\]                                   
  done clear
  B)
  \[\frac{1}{2}\]
  done clear
  C)
   \[\frac{9}{2}\]  
  done clear
  D)
  \[\frac{1}{6}\]   
  done clear
  View Answer play_arrow

• question_answer92) The minimum value of \[\frac{x}{\log x}\] is
  A)
  e            
  done clear
  B)
  \[\frac{1}{e}\]
  done clear
  C)
  \[{{e}^{2}}\]                                      
  done clear
  D)
  \[{{e}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer93) The triangle formed by the tangent to the curve \[f\left( x \right)={{x}^{2}}+bx-b\] at the point (1, 1) and the coordinate axes lies in the first quadrant. If its area is 2, then the value of b is
  A)
  -1                                           
  done clear
  B)
  3
  done clear
  C)
  -3           
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer94) The statement \[\left( p\Rightarrow q \right)\Leftrightarrow \left( \sim p\wedge q \right)\] is a
  A)
  tautology                            
  done clear
  B)
  contradiction
  done clear
  C)
   Neither (a) nor (b)         
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer95) If x + i \[y=\frac{3}{2+\cos \theta +i\sin \theta },\] then \[{{x}^{2}}+{{y}^{2}}\]is equal to
  A)
  3x ? 4                   
  done clear
  B)
  4x ? 3
  done clear
  C)
  4x + 3                   
  done clear
  D)
  None of these  
  done clear
  View Answer play_arrow

• question_answer96) The negation of \[\left( \sim p\wedge q \right)\vee \left( p\wedge \sim q \right)\]is
  A)
  \[\left( p\vee \sim q \right)\vee \left( \sim p\vee q \right)\]
  done clear
  B)
  \[\left( p\vee \sim q \right)\wedge \left( \sim p\vee q \right)\]
  done clear
  C)
  \[\left( p\wedge \sim q \right)\wedge \left( \sim p\vee q \right)\]
  done clear
  D)
  \[\left( p\wedge \sim q \right)\wedge \left( p\vee \sim q \right)\]
  done clear
  View Answer play_arrow

• question_answer97) The normals  at three points O,Q and  R of the parabola meet at (h, k). The centroid of the lies on
  A)
  x = 0                                      
  done clear
  B)
  y = 0
  done clear
  C)
   x = -a                   
  done clear
  D)
  y = a
  done clear
  View Answer play_arrow

• question_answer98) The minimum area of the triangle formed by any tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] with the coordinate axes is
  A)
  \[{{a}^{2}}+{{b}^{2}}\]                  
  done clear
  B)
   \[\frac{{{\left( a+b \right)}^{2}}}{2}\]
  done clear
  C)
  ab                                          
  done clear
  D)
   \[\frac{{{\left( a-b \right)}^{2}}}{2}\]
  done clear
  View Answer play_arrow

• question_answer99) If the line lx + my ? n = 0  will be a normal to the hyperbola, then \[\frac{{{a}^{2}}}{{{l}^{2}}}-\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{\left( {{a}^{2}}+{{b}^{2}} \right)}^{2}}}{k},\] where k is equal to
  A)
  n                                            
  done clear
  B)
  \[{{n}^{2}}\]
  done clear
  C)
  \[{{n}^{3}}\]                                      
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer100) If \[\cos \alpha +i\sin \alpha ,b=\cos \beta +i\sin \beta ,\]\[c=\cos \gamma +i\sin \gamma \] and \[\frac{b}{c}+\frac{c}{a}+\frac{a}{b}=1,\]then \[\cos \left( \beta -\gamma  \right)+\cos \left( \gamma -\alpha  \right)+\cos \left( \alpha -\beta  \right)\] is equal to
  A)
  \[\frac{3}{2}\]                                   
  done clear
  B)
  \[-\frac{3}{2}\]
  done clear
  C)
  0                                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer101) If  \[\left| z+4 \right|\le 3,\] then the greatest and the least value of |z + 1| are
  A)
  -1, 6                                      
  done clear
  B)
  6, 0
  done clear
  C)
  6, 3                                        
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer102) The angle between lines joining the origin to the point of intersection of the line \[\sqrt{3}x+y=2\] and the curve \[{{y}^{2}}-{{x}^{2}}=4\] is
  A)
  \[{{\tan }^{-1}}\frac{2}{\sqrt{3}}\]                           
  done clear
  B)
  \[\pi /6\]
  done clear
  C)
  \[{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]                 
  done clear
  D)
  \[\pi /2\]
  done clear
  View Answer play_arrow

• question_answer103) If the area of the triangle on the complex plane formed by the points z, z + iz and iz is 200, then the value of 3 |z| must be equal to
  A)
  20                                          
  done clear
  B)
  40
  done clear
  C)
   60                                         
  done clear
  D)
  80
  done clear
  View Answer play_arrow

• question_answer104) Equation  of the chord of the hyperbola \[25{{x}^{2}}-16{{y}^{2}}=400\] which is bisected at the point (6, 2) is
  A)
  6x ? 7y = 418     
  done clear
  B)
  75x ? 16y = 418
  done clear
  C)
  25x ? 4y = 400   
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer105) If a plane meets the coordinate axes at A, B and C such that the centroid of the triangle is (1, 2, 4) then equation of the plane is
  A)
  x + 2y + 4z = 12 
  done clear
  B)
  4x + 2y + z = 12
  done clear
  C)
   x + 2y + 4z = 3  
  done clear
  D)
  4x + 2y + z = 3
  done clear
  View Answer play_arrow

• question_answer106) The volume of the tetrahedron included between the plane  3x + 4y ? 5z ? 60 = 0 and the coordinate planes is
  A)
  60                                          
  done clear
  B)
  600
  done clear
  C)
  720                                        
  done clear
  D)
  400
  done clear
  View Answer play_arrow

• question_answer107) \[\int_{0}^{2\pi }{\left( \sin x|\sin x| \right)}\]dx  is equal to
  A)
  0                                             
  done clear
  B)
  4
  done clear
  C)
  8                                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer108) The value of \[\int_{0}^{\sqrt{2}}{[{{x}^{2}}]dx,}\] where [.] is the greatest integer function is
  A)
  \[2-\sqrt{2}\]
  done clear
  B)
  \[2+\sqrt{2}\]
  done clear
  C)
  \[\sqrt{2}-1\]                    
  done clear
  D)
  \[\sqrt{2}-2\]
  done clear
  View Answer play_arrow

• question_answer109) If l (m. n) = \[\int_{0}^{1}{{{t}^{m}}{{\left( 1+t \right)}^{n}}dt,}\] then the expression for l (m, n) in terms of l (m +  n + 1) is
  A)
  \[\frac{{{2}^{n}}}{m+1}-\frac{n}{m+1}.l\left( m+1,n+1 \right)\]
  done clear
  B)
  \[\frac{n}{m+1}.l\left( m+1,n-1 \right)\]
  done clear
  C)
  \[\frac{2n}{m+1}+\frac{n}{m+1}l.\left( m+1,n-1 \right)\]
  done clear
  D)
  \[\frac{m}{n+1}.l\left( m+1,n-1 \right)\]
  done clear
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• question_answer110) The area in the first quadrant between \[{{x}^{2}}+{{y}^{2}}={{\pi }^{2}}\] and y = sin x is
  A)
  \[\frac{{{\pi }^{3}}-8}{4}\]
  done clear
  B)
  \[\frac{{{\pi }^{3}}}{4}\]
  done clear
  C)
  \[\frac{{{\pi }^{3}}-16}{4}\]                         
  done clear
  D)
  \[\frac{{{\pi }^{3}}-8}{2}\]
  done clear
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• question_answer111) The area bounded by \[y=x{{e}^{|x|}}\] and lines |x| = 1, y = 0 is
  A)
  4 sq units                            
  done clear
  B)
  6 sq units
  done clear
  C)
  1 sq units                            
  done clear
  D)
  2 sq units
  done clear
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• question_answer112) The solution of \[\frac{dy}{dx}=\frac{{{x}^{2}}+{{y}^{2}}+1}{2xy},\] satisfying y(1) = 0 is given by
  A)
  hyperbola          
  done clear
  B)
  circle
  done clear
  C)
  ellipse                  
  done clear
  D)
  parabola
  done clear
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• question_answer113) If  \[x.\frac{dy}{dx}+y=x.\frac{f\left( xy \right)}{f'\left( xy \right)},\] then f(xy) is equal to
  A)
  \[k.{{e}^{\frac{{{x}^{2}}}{2}}}\]
  done clear
  B)
  \[k.{{e}^{{{y}^{2}}/2}}\]
  done clear
  C)
  \[k.{{e}^{{{x}^{2}}}}\]                   
  done clear
  D)
  \[k.{{e}^{\frac{xy}{2}}}\]
  done clear
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• question_answer114) The differential equation of the rectangular hyperbola, where axes are the asymptotes of the  hyperbola, is
  A)
  \[y\frac{du}{dx}=x\]                      
  done clear
  B)
  \[x\frac{du}{dx}=-y\]
  done clear
  C)
  \[x\frac{dy}{dx}=y\]                      
  done clear
  D)
  xdy + ydx = c
  done clear
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• question_answer115) The length of longer diagonal of the parallelogram constructed on 5a+2b and a -3b, if it is given that \[\left| a \right|=2\sqrt{2},\left| b \right|=3\]and the angle between a and b is \[\frac{\pi }{4},\] is
  A)
  15                                          
  done clear
  B)
  \[\sqrt{113}\]
  done clear
  C)
  \[\sqrt{593}\]   
  done clear
  D)
  \[\sqrt{369}\]
  done clear
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• question_answer116) If \[r=\alpha b\times c+\beta c\times a+\gamma a\times b\]and [a b c] =2, then \[\alpha +\beta +\gamma \] is equal to
  A)
  \[r.[b\times c+c\times a+a\times b]\]
  done clear
  B)
  \[\frac{1}{2}r.\left( a+b+c \right)\]
  done clear
  C)
  2r. (a + b + c)
  done clear
  D)
  4
  done clear
  View Answer play_arrow

• question_answer117) If a, b, c are three non-coplanar vectors and p, q, r are reciprocal vectors, then (isl + mb + nc)  (lp + mq + nr) is equal to
  A)
  l + m + n              
  done clear
  B)
  \[{{l}^{3}}+{{m}^{3}}+{{n}^{3}}\]
  done clear
  C)
  \[{{l}^{2}}+{{m}^{2}}+{{n}^{2}}\]              
  done clear
  D)
  None of these
  done clear
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• question_answer118) If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form \[{{7}^{n}}+{{7}^{m}}\] is divisible by 5, equals to
  A)
  \[\frac{1}{4}\]           
  done clear
  B)
  \[\frac{1}{2}\]
  done clear
  C)
  \[\frac{1}{8}\]                                   
  done clear
  D)
  \[\frac{1}{3}\]
  done clear
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• question_answer119) Let X denote the sum of the numbers  obtained when two fair dice are rolled. The variance and standard deviation of X are
  A)
  \[\frac{31}{6}and\sqrt{\frac{31}{6}}\]
  done clear
  B)
  \[\frac{35}{6}and\sqrt{\frac{35}{6}}\]
  done clear
  C)
  \[\frac{17}{6}and\sqrt{\frac{17}{6}}\]
  done clear
  D)
  \[\frac{31}{6}and\sqrt{\frac{35}{6}}\]
  done clear
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• question_answer120) A four-digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is
  A)
  zero                      
  done clear
  B)
  \[\frac{1}{3}\]
  done clear
  C)
  \[\frac{1}{4}\]                  
  done clear
  D)
   None of these
  done clear
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