Solved papers for VIT Engineering VIT Engineering Solved Paper-2015

done VIT Engineering Solved Paper-2015 Total Questions - 120

• question_answer1) Equal charges q each are placed at the vertices of an equilateral triangle of side r. The magnitude of electric field intensity at any vertex is
  A)
  \[\frac{2q}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\]                  
  done clear
  B)
  \[\frac{q}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\]
  done clear
  C)
  \[\frac{\sqrt{3}q}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\]    
  done clear
  D)
  \[\frac{\sqrt{2}q}{4\pi {{\varepsilon }_{0}}.{{r}^{2}}}\]
  done clear
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• question_answer2) Two points masses, m each carrying charges -q and +g are attached to the ends of a massless rigid non-conducting wire of length ?L?. When this arrangement is placed in a |      uniform electric field, then it deflects       through an angle i. The minimum time      needed by rod to align itself along the field is
  A)
   \[2\pi \sqrt{\frac{mL}{qE}}\]                     
  done clear
  B)
   \[\frac{\pi }{2}\sqrt{\frac{mL}{2qE}}\]
  done clear
  C)
  \[\pi \sqrt{\frac{2mL}{qE}}\]                      
  done clear
  D)
  \[\pi \sqrt{\frac{3mL}{qE}}\]
  done clear
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• question_answer3) A condenser of capacitance C is fully charged by a 200V supply. It is then discharged through a small coil of resistance wire embedded in' thermally insulated block of specific heat 250 J/kg-K and of mass 100 g. If the temperature of the block rises by 0.4 K, then the value of C is
  A)
  300 \[\mu F\]                    
  done clear
  B)
  200 \[\mu F\]
  done clear
  C)
  400 \[\mu F\]                    
  done clear
  D)
  500 \[\mu F\]
  done clear
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• question_answer4)            The capacitance of a parallel plate capacitor with air as medium is 3\[\mu F\], As a dielectric is introduced between the plates, the capacitance becomes 15\[\mu F\]. The permittivity of the  medium in \[{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\] is
  A)
  \[8.15\times {{10}^{-11}}\]        
  done clear
  B)
  \[0.44\times {{10}^{-10}}\]
  done clear
  C)
  \[15.2\times {{10}^{12}}\]           
  done clear
  D)
  \[1.6\times {{10}^{-14}}\]
  done clear
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• question_answer5) The masses of three copper wires are in the ratio 2:3:5 and their lengths are in the ratio 5:3:2.Then, the ratio of their electrical resistances is
  A)
  1:9:15                   
  done clear
  B)
  2:3:5
  done clear
  C)
  5:3:2                     
  done clear
  D)
  125:30:8
  done clear
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• question_answer6) A 30V-90W lamp is operated on a 120 V DC line. A resistor is connected in series with the lamp in order to glow it properly. The value of resistance is
  A)
  10\[\Omega \]  
  done clear
  B)
  30\[\Omega \]   
  done clear
  C)
  20\[\Omega \]                                 
  done clear
  D)
  40\[\Omega \]
  done clear
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• question_answer7) In a potentiometer experiment, the balancing length of a cell is 560 cm. When an external resistance of 10 \[\Omega \] is connected in parallel to the cell, the balancing length changes by 60 cm. The internal resistance of a cell is
  A)
  1.4\[\Omega \]                
  done clear
  B)
  1.6\[\Omega \]
  done clear
  C)
  0.12\[\Omega \]              
  done clear
  D)
  1.2\[\Omega \]
  done clear
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• question_answer8) Two sources of equal emf are connected to a resistance R. The internal resistance of these sources are \[{{r}_{1}}\]and \[{{r}_{2}}\]\[\left( {{r}_{1}}>{{r}_{2}} \right).\]If the potential difference across the source having internal Resistance  \[{{r}_{2}}\] is zero, then
  A)
  \[R=\frac{{{r}_{1}}{{r}_{2}}}{{{r}_{2}}-{{r}_{1}}}\]                              
  done clear
  B)
  \[R={{r}_{2}}\left( \frac{r{{+}_{1}}{{r}_{2}}}{{{r}_{2}}-{{r}_{1}}} \right)\]
  done clear
  C)
  \[R=\frac{{{r}_{1}}{{r}_{2}}}{{{r}_{2}}+{{r}_{1}}}\]                             
  done clear
  D)
   \[R={{r}_{2}}-{{r}_{1}}\]
  done clear
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• question_answer9) An electron of mass \[9.0\times {{10}^{-31}}\]kg under the action of a magnetic field moves in a circle of radius 2 cm at a speed of \[3\times {{10}^{6}}m/s.\]If a proton of mass \[1.8\times {{10}^{27}}\]kg was to move in a circle of same radius in the same magnetic field, then its speed will become
  A)
  \[1.5\times {{10}^{3}}m/s\]       
  done clear
  B)
  \[3\times {{10}^{6}}m/s\]
  done clear
  C)
  \[6\times {{10}^{4}}m/s\]           
  done clear
  D)
  \[2\times {{10}^{6}}m/s\]    
  done clear
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• question_answer10)            A horizontal rod of mass 0.01kg and length 10 cm is placed on a frictionless plane inclined at an angle 60° with the horizontal and with the length of rod parallel to the edge of the inclined plane. A uniform magnetic field is applied vertically downwards. If the current through the rod is 1.73 A, then the value of magnetic field induction B for which the rod remains stationary 'on the inclined plane is
  A)
  1 T         
  done clear
  B)
  3 T
  done clear
  C)
  2.5 T                      
  done clear
  D)
  4 T
  done clear
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• question_answer11) 1. A current of 2 A is flowing in the sides of an equilateral triangle of side 9 cm. The magnetic field at the centroid of the triangle is
  A)
  \[1.66\times {{10}^{-5}}T\]         
  done clear
  B)
  \[1.22\times {{10}^{-4}}T\]
  done clear
  C)
  \[1.33\times {{10}^{-5}}T\]         
  done clear
  D)
  \[1.44\times {{10}^{-4}}T\]
  done clear
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• question_answer12) The direction of magnetic field dB due to current element dl at a distance r is the direction of
  A)
  \[\text{r }\!\!\times\!\!\text{ dl}\]                         
  done clear
  B)
  \[\text{dl}\times \text{r}\]  
  done clear
  C)
  \[\left( r/d \right)\overset{\hat{\ }}{\mathop{r}}\,\]                      
  done clear
  D)
  dl
  done clear
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• question_answer13) A galvanometer with a scale divided into 100 equal divisions has a current sensitivity of 10 divisions per milliampere and a voltage sensitivity of 2 divisions per millivolt. The galvanometer resistance will be
  A)
  4 \[\Omega \]                   
  done clear
  B)
  5\[\Omega \]
  done clear
  C)
  3 \[\Omega \]                   
  done clear
  D)
  7\[\Omega \]
  done clear
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• question_answer14) The earth is considered as a short magnet with its centre coinciding with the geometric centre of earth. The angle of dip \[\phi \] related to the magnetic latitude \[\lambda \] as
  A)
  \[\tan \phi =\frac{1}{2\tan \alpha }\]      
  done clear
  B)
  \[\tan \lambda =2\tan \phi \]
  done clear
  C)
  \[\tan \lambda =2\tan \phi \]       
  done clear
  D)
  \[\tan \phi =2\tan \lambda \]
  done clear
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• question_answer15) Which of the following statement related to hysteresis loop is incorrect?
  A)
  The curve of B against H for a ferromagnetic material is called hysteresis loop
  done clear
  B)
  The area of B-H curve is a measure of power dissipated per cycle per unit area of the specimen
  done clear
  C)
  Coercitivity is a measure of the magnetic field required to destroy the residual magnetism of ferromagnetic material
  done clear
  D)
  The retentivity of a specimen is the measure of magnetic field remaining in the specimen when the magnetising field is removed
  done clear
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• question_answer16) A magnetic needle lying parallel to the       magnetic field requires W units of work to      turn it through an angle 45°. The torque       required to maintain the needle in this       position will be   
  A)
  \[\sqrt{2}W\]                    
  done clear
  B)
  \[\frac{1}{\sqrt{3}W}\]                   
  done clear
  C)
  \[\left( \sqrt{2}-1 \right)W\]                      
  done clear
  D)
   \[\frac{W}{\left( \sqrt{2}-1 \right)}\]      
  done clear
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• question_answer17) An induced emf has
  A)
  a direction same as field direction
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  B)
  a direction opposite to the field direction
  done clear
  C)
  no direction of its own
  done clear
  D)
  None of the above
  done clear
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• question_answer18) A coil of area \[5c{{m}^{2}}\] having 20 turns is placed in a uniform magnetic field of  \[{{10}^{3}}\]gauss. The normal to the plane of coil makes an angle 30° with the magnetic field. The flux through the coil is
  A)
  \[6.67\times {{10}^{-4}}wb\]     
  done clear
  B)
  \[3.2\times {{10}^{-5}}wb\]
  done clear
  C)
  \[5.9\times {{10}^{-4}}wb\]       
  done clear
  D)
  \[8.65\times {{10}^{-4}}wb\]
  done clear
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• question_answer19) The current graph for resonance in LC circuit is
  A)
                                                                           
  done clear
  B)
  
  done clear
  C)
                                                                   
  done clear
  D)
  
  done clear
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• question_answer20) The value of inductance L for which the current is maximum in series LCR circuit with \[C=10\mu F\] and (0=1000 rad/s
  A)
  10 mH                                  
  done clear
  B)
   50 mH
  done clear
  C)
  200 mH                
  done clear
  D)
   100 mH     
  done clear
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• question_answer21)              A ray of light is incident on a plane mirror at an angle of 30°. At what angle with the horizontal must a plane mirror be placed so that the reflected ray becomes vertically upwards?
  A)
  40°                         
  done clear
  B)
  20°    
  done clear
  C)
  30°                         
  done clear
  D)
  60°
  done clear
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• question_answer22) A compound microscope having magnifying      power 35 with its eye-piece of focal length       10 cm. Assume that the final image is at least      distance of distinct vision then the      magnification produced by the objective is
  A)
  -4                                           
  done clear
  B)
  5     
  done clear
  C)
  10                                          
  done clear
  D)
  -10
  done clear
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• question_answer23) The refractive index for a prism is given as  \[\mu =\cot \frac{A}{2}.\]Then, angle of minimum deviation in terms of angle of prism is
  A)
  90°-A                                    
  done clear
  B)
  2A
  done clear
  C)
  180°-A                                  
  done clear
  D)
  180°-2A
  done clear
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• question_answer24) Two convex lenses of power 2D and 5D are separated by a distance \[\frac{1}{3}m.\]. The power of optical system formed is
  A)
  + 2 D                     
  done clear
  B)
  - 2 D   
  done clear
  C)
  - 3 D                      
  done clear
  D)
  + 3 D
  done clear
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• question_answer25) Two light rays having the same wavelength in vacuum are in phase initially. Then, the first ray travels a path \[{{L}_{1}}\]through a medium of refractive index \[{{\mu }_{1}}\] while the second ray travels a path \[{{L}_{2}}\] through a medium of refractive index \[{{\mu }_{2}}.\] The two waves are then combined to observe interference. The phase difference between the two waves is
  A)
   \[\frac{2\pi }{\lambda }\left( \frac{{{L}_{1}}}{{{\mu }_{1}}}-\frac{{{L}_{2}}}{{{\mu }_{2}}} \right)\]            
  done clear
  B)
  \[\frac{2\pi }{\lambda }\left( {{L}_{2}}-{{L}_{1}} \right)\]
  done clear
  C)
  \[\frac{2\pi }{\lambda }\left( {{\mu }_{2}}{{L}_{1}}-{{\mu }_{1}}{{L}_{2}} \right)\]              
  done clear
  D)
   \[\frac{2\pi }{\lambda }\left( {{\mu }_{1}}{{L}_{1}}-{{\mu }_{2}}{{L}_{2}} \right)\]             
  done clear
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• question_answer26) Two polaroids are kept crossed to each other. If one of them is rotated an angle 60°, the percentage of incident light now transmitted . through the system is
  A)
  10%                       
  done clear
  B)
  20%   
  done clear
  C)
  25%                       
  done clear
  D)
  12.5%
  done clear
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• question_answer27) An electromagnetic wave propagating along north lies its electric field vertically upward. The magnetic field vector points towards
  A)
  downward                         
  done clear
  B)
  east                 
  done clear
  C)
  north                    
  done clear
  D)
  south
  done clear
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• question_answer28) Pick out the wrong statement.
  A)
  Gauss's law of magnetism is given by \[\oint{B.ds=0}\]
  done clear
  B)
  An EM wave is a wave radiated by a charge at rest and propagates through electric field only
  done clear
  C)
  A time varying electric field is a source of changing magnetic field
  done clear
  D)
  Faraday's law of EM induction is \[\oint{E.dl=-\frac{d{{\phi }_{B}}}{dt}}\]
  done clear
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• question_answer29) When--sunlight is scattered by atmospheric    atoms and molecules the amount of      scattering of light of wavelength 880nm is A.     Then, the amount of scattering of light of wavelength 330 nm is approximately
  A)
  10 A                      
  done clear
  B)
  20 A  
  done clear
  C)
  40 A                      
  done clear
  D)
  50.5 A
  done clear
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• question_answer30) The ratio of volume occupied by an atom to the volume of the nucleus is
  A)
  \[{{10}^{5}}:1\]                                
  done clear
  B)
  \[{{10}^{20}}:1\]
  done clear
  C)
  \[{{10}^{15}}:1\]                              
  done clear
  D)
  \[1:{{10}^{15}}\]
  done clear
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• question_answer31) When a hydrogen atom is raised from ground energy level to excited energy level, then
  A)
  potential energy increases and kinetic energy  decreases
  done clear
  B)
  kinetic energy increases and potential energy  decreases
  done clear
  C)
  Both KE and PE increase
  done clear
  D)
  Both KE and PE decrease
  done clear
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• question_answer32) The half life for a-decay of uranium \[_{\text{92}}{{\text{U}}^{\text{228}}}\] is \[4.47\times {{10}^{8}}\] yr. If a rock contains 60% of      original \[_{\text{92}}{{\text{U}}^{\text{228}}}\] atoms, then its age is [take log 6 =0.778, log 2=0.3]
  A)
  \[1.2\times {{10}^{7}}yr\]            
  done clear
  B)
  \[3.3\times {{10}^{8}}yr\]
  done clear
  C)
  \[4.2\times {{10}^{9}}yr\]            
  done clear
  D)
  \[6.5\times {{10}^{9}}yr\] Given \[\left( \frac{2E}{{{r}_{1}}+{{r}_{2}}+R} \right){{r}^{2}}\]               \[E-\frac{2E}{\left( {{r}_{1}}+{{r}_{2}}+R \right)}{{r}_{2}}=0\] \[{{r}_{1}}+{{r}_{2}}+R=2{{r}_{2}}\]            \[R={{r}_{2}}-{{r}_{1}}\] Apply logarithm on both sides           \[~n\log 2=\log 10log6\] \[\therefore \]     \[Bqv=\frac{m{{v}^{2}}}{r}\]            \[{{m}_{e}}{{v}_{e}}={{m}_{p}}{{v}_{p}}\] So     \[{{v}_{p}}=\left( \frac{{{m}_{e}}}{{{m}_{p}}} \right){{v}_{e}}=\left( \frac{9\times {{10}^{-31}}}{1.8\times {{10}^{-27}}} \right)3\times {{10}^{6}}\]           \[{{v}_{p}}=1.5\times {{10}^{3}}m/s\]
  done clear
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• question_answer33) A nuclear transformation is given by \[Y\left( n,\alpha  \right){{\to }_{3}}L{{i}^{7}}.\] The nucleus, of element Y is
  A)
  \[_{5}B{{e}^{11}}\]                         
  done clear
  B)
  \[_{5}B{{e}^{10}}\]   
  done clear
  C)
  \[_{5}B{{e}^{9}}\]                           
  done clear
  D)
  \[_{5}{{C}^{12}}\]
  done clear
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• question_answer34) The angular momentum of an electron in Bohr's hydrogen atom whose energy is -3.4 eV, is
  A)
  \[\frac{5h}{2\pi }\]                         
  done clear
  B)
  \[\frac{h}{2\pi }\]    
  done clear
  C)
   \[\frac{h}{\pi }\]                             
  done clear
  D)
  \[\frac{2h}{3\pi }\]
  done clear
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• question_answer35) When the momentum of a photon is changed by an amount p' then the corresponding change in the de-Broglie wavelength is found to be 0.20%. Then, the original momentum of the photon was
  A)
  300 p'                   
  done clear
  B)
  500 p'  
  done clear
  C)
  400 p'                   
  done clear
  D)
  100 p'
  done clear
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• question_answer36) Suppose a beam of electrons with each electron having energy \[{{E}_{0}}\] incident on a metal surface kept in an evacuated chamber. Then,     
  A)
  electrons can be emitted with any energy with a maximum of \[{{E}_{0}}\]
  done clear
  B)
  no electrons will be emitted as only photons can,  emit electrons
  done clear
  C)
  electrons can be emitted but all with an energy \[{{E}_{0}}\]
  done clear
  D)
  electrons can be emitted with any energy with a maximum of \[{{E}_{0}}-\phi ,\]where being work function                                              
  done clear
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• question_answer37) An n-type semiconductor is               
  A)
  neutral
  done clear
  B)
  positively charged
  done clear
  C)
  negatively charged
  done clear
  D)
  negatively or positively charged depending on the amount of impurity added
  done clear
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• question_answer38) In the half wave rectifier circuit operating with   50 Hz   mains   frequency.   The fundamental frequency in the ripple will be
  A)
  100 Hz                  
  done clear
  B)
  20Hz
  done clear
  C)
  50 Hz                                    
  done clear
  D)
  25 Hz
  done clear
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• question_answer39) The input resistance of a common emitter amplifier is 330 \[\Omega \]. and the load resistance is \[5k\Omega .\]. A change of base current is \[15\mu A\]results in the change of collector current by 1 mA. The voltage gain of amplifier is
  A)
  1000                                      
  done clear
  B)
  10001
  done clear
  C)
  1010                                      
  done clear
  D)
  1100
  done clear
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• question_answer40) To get an output y = 0 from the circuit shown in the figure, the input C must be                    
  A)
  0                                             
  done clear
  B)
  1
  done clear
  C)
  either 0 or 1                       
  done clear
  D)
  None of these
  done clear
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• question_answer41) Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction,  \[{{C}_{6}}{{H}_{6}}\left( g \right)+3{{H}_{2}}\left( g \right)\to {{C}_{6}}{{H}_{12}}\left( g \right)\] A mixture of \[{{C}_{6}}{{H}_{6}}\] and excess \[{{H}_{2}}\] has a pressure of 60mm of Hg in an unknown volume. After the gas had been passed over a nickel catalyst and all the benzene converted to cyclohexane, the pressure of the gas was 30 mm of Hg in the same volume at the same temperature. The fraction of \[{{C}_{6}}{{H}_{6}}\] (by volume) present in the original volume is
  A)
   1/3                       
  done clear
  B)
  1/4   
  done clear
  C)
  1/5                        
  done clear
  D)
  1/6
  done clear
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• question_answer42) An alloy of copper, silver and gold is found to have copper atom constituting the ccp lattice. If silver atom occupy the edge centres and gold atom is present at body centred, the alloy has a formula
  A)
  \[\text{C}{{\text{u}}_{\text{4}}}\text{A}{{\text{g}}_{\text{2}}}\text{Au}\]          
  done clear
  B)
  \[\text{C}{{\text{u}}_{\text{4}}}\text{A}{{\text{g}}_{4}}\text{Au}\]
  done clear
  C)
  \[\text{C}{{\text{u}}_{\text{4}}}\text{A}{{\text{g}}_{3}}\text{Au}\]                       
  done clear
  D)
  \[\text{CuAgAu}\]
  done clear
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• question_answer43) Given, \[\text{ }\!\!\Delta\!\!\text{ }{{\text{G}}^{\text{o}}}\text{=-nF}{{\text{E}}^{\text{o}}}_{\text{cell}}\] and \[\text{ }\!\!\Delta\!\!\text{ }{{\text{G}}^{\text{o}}}\text{=-RT}\]In k. The value of n = 2 will be given by the slope of which line in the figure                               
  A)
                  OA                                         
  done clear
  B)
  OB
  done clear
  C)
  OC                                         
  done clear
  D)
  OD
  done clear
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• question_answer44) The false statements among the following are I. A primary carbocation is less stable than E a tertiary carbocation. II. A secondary propyl carbocation is less stable than allyl carbocation. III. A tertiary free radical is more stable than a primary free radical,                     IV. Isopropyl carbanion is more stable than ethyl carbanion.                       
  A)
  I and II                 
  done clear
  B)
  II and III                
  done clear
  C)
  I and IV                
  done clear
  D)
  II and IV
  done clear
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• question_answer45) A colourless water soluble solid A on heating gives equimolar quantities of B and C. B gives dense white fumes with HCl and C does so with \[N{{H}_{3}}\]. B gives brown precipitate with Nessler's reagent and C gives white precipitate with nitrates of \[A{{g}^{+}},P{{b}^{+}}\]and \[H{{g}^{+}}\]. A is
  A)
  \[\text{N}{{\text{H}}_{\text{4}}}\text{Cl}\]                        
  done clear
  B)
  \[\text{N}{{\text{H}}_{\text{4}}}\text{C}{{\text{O}}_{\text{3}}}\]
  done clear
  C)
  \[\text{N}{{\text{H}}_{\text{4}}}\text{N}{{\text{O}}_{2}}\]                        
  done clear
  D)
  \[FeS{{O}_{4}}\]
  done clear
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• question_answer46) The IUPAC name of             
  A)
  4-ethyl-5,6,7,9-tetramethyldeca-2. 9-diene        
  done clear
  B)
   7-ethyl-2,4,5,6-tetramethyldeca-1, 8-diene     
  done clear
  C)
  7-ethyl-2,4,5,6-tetramethyldeca-1, 7-diene
  done clear
  D)
   7?(1?propenly)-2,3,4,5-tetramethyl non 1-ene
  done clear
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• question_answer47) Caffeine has a molecular weight of 194 u. If it contains 28.9% by mass of nitrogen, number       of atom of nitrogen in cue molecular of        caffeine is
  A)
   4        
  done clear
  B)
  6
  done clear
  C)
  2                                             
  done clear
  D)
  3
  done clear
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• question_answer48) A compound X on heating gives a colourless gas. The residue is dissolved in water to obtain Y. Excess \[C{{O}_{2}}\] is passed through aqueous solution of V when Z is formed. Z on gentle heating gives back X. The compound X is
  A)
  \[\text{Ca}{{\left( \text{HC}{{\text{O}}_{\text{3}}} \right)}_{\text{2}}}\]              
  done clear
  B)
  \[\text{CaC}{{\text{O}}_{3}}\]
  done clear
  C)
  \[\text{NaHC}{{\text{O}}_{\text{3}}}\]                 
  done clear
  D)
  \[\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]
  done clear
  View Answer play_arrow

• question_answer49) Which two sets of reactants best represents the amphoteric character of\[Zn{{\left( OH \right)}_{2}}\]? Set I   \[Zn{{\left( OH \right)}_{2}}\left( s \right)\] and \[\overset{-}{\mathop{O}}\,H\](a q) Set 11 \[Zn{{\left( OH \right)}_{2}}\left( s \right)\] and \[{{H}_{2}}O\left( I \right)\] Set III \[Zn{{\left( OH \right)}_{2}}\left( s \right)\] and \[{{H}^{+}}\left( aq \right)\] Set IV \[Zn{{\left( OH \right)}_{2}}\left( s \right)\]and \[N{{H}_{3}}\](a q)
  A)
  III and II               
  done clear
  B)
  I and III
  done clear
  C)
  IV and I                
  done clear
  D)
  II and IV
  done clear
  View Answer play_arrow

• question_answer50) \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{-N}{{\text{O}}_{\text{2}}}\xrightarrow[\text{N}{{\text{H}}_{\text{4}}}\text{Cl}]{\text{Zn dust}}\text{A}\xrightarrow[\text{conc}\text{.HCl}]{\text{cold}}\text{B}\]A and B respectively are
  A)
          
  done clear
  B)
        
  done clear
  C)
        
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer51) Point out-incorrect stability order
  A)
  \[{{\left[ \text{Cu}{{\left( \text{N}{{\text{H}}_{\text{3}}} \right)}_{\text{4}}} \right]}^{\text{2+}}}\text{}{{\left[ \text{Cu}{{\left( \text{en} \right)}_{\text{2}}} \right]}^{\text{2+}}}\text{}{{\left[ \text{Cu}\left( \text{trien} \right) \right]}^{\text{2+}}}\]
  done clear
  B)
  \[{{\left[ Fe{{\left( {{\text{H}}_{2}}\text{O} \right)}_{6}} \right]}^{\text{3+}}}\text{}{{\left[ Fe{{\left( N{{O}_{2}} \right)}_{6}} \right]}^{3-}}\text{}{{\left[ Fe{{\left( N{{H}_{3}} \right)}_{6}} \right]}^{\text{3+}}}\]
  done clear
  C)
  \[{{\left[ Co{{\left( {{\text{H}}_{2}}\text{O} \right)}_{6}} \right]}^{\text{3+}}}\text{}{{\left[ Rh{{\left( {{H}_{2}}O \right)}_{6}} \right]}^{3+}}\text{}{{\left[ lr{{\left( {{H}_{2}}O \right)}_{6}} \right]}^{\text{3+}}}\]
  done clear
  D)
  \[{{\left[ Cr{{\left( \text{N}{{\text{H}}_{3}} \right)}_{6}} \right]}^{\text{+}}}\text{}{{\left[ Cr{{\left( N{{H}_{3}} \right)}_{6}} \right]}^{2+}}\text{}{{\left[ Cr{{\left( N{{H}_{3}} \right)}_{6}} \right]}^{\text{3+}}}\]
  done clear
  View Answer play_arrow

• question_answer52) Consider the following changes \[M\left( s \right)\to M\left( g \right)\]                         ...(1) \[M\left( g \right)\to {{M}^{2+}}\left( g \right)+2{{e}^{-}}\]           ...(2) \[M\left( g \right)\to {{M}^{+}}\left( g \right)+{{e}^{-}}\]                   ...(3) \[{{M}^{+}}\left( g \right)\to {{M}^{2+}}\left( g \right)+2{{e}^{-}}\]              ...(4) \[M\left( g \right)\to {{M}^{2+}}\left( g \right)+2{{e}^{-}}\]                ...(5) The second ionisation energy of M could be determined from the energy values associated with
  A)
  1+2+4                                   
  done clear
  B)
  2+3-4
  done clear
  C)
  1+5-3                                    
  done clear
  D)
  5-3
  done clear
  View Answer play_arrow

• question_answer53) In benzene, the triple bond consists of
  A)
  one sp-sp sigma bond and two p-p pi bonds
  done clear
  B)
   two sp-sp sigma bonds and one p-p pi bond
  done clear
  C)
   one \[s{{p}^{2}}-s{{p}^{2}}\]sigma bond, one p-p pi bond
  done clear
  D)
   one \[s{{p}^{2}}-s{{p}^{2}}\]sigma bond, one \[s{{p}^{2}}-s{{p}^{2}}\]pi bond and one p-p pi bond
  done clear
  View Answer play_arrow

• question_answer54) In keto-enol tautomerism of dicarbonyl compounds, the enol-form is preferred in contrast to the keto-form, this is due to
  A)
  presence of carbonyl group on each side of \[-C{{H}_{2}}-group\]
  done clear
  B)
  resonance stabilisation of enol form
  done clear
  C)
  presence of methylene group
  done clear
  D)
   rapid chemical exchange
  done clear
  View Answer play_arrow

• question_answer55) An organic compound having carbon, hydrogen and sulphur contains 4% of sulphur. The minimum molecular weight of the compound is
  A)
  200                                        
  done clear
  B)
  400
  done clear
  C)
  600                                        
  done clear
  D)
  800
  done clear
  View Answer play_arrow

• question_answer56) Which one of the following is a case of negative adsorption?
  A)
  Acetic acid solution in contact with animal charcoal.
  done clear
  B)
  Dilute KQ solution in contact with blood charcoal.
  done clear
  C)
  Concentration KCI solution in contact with blood charcoal.
  done clear
  D)
  \[{{H}_{2}}\]gas in contact with charcoal at 300 K.
  done clear
  View Answer play_arrow

• question_answer57) The concentrations of the reactant A in the reaction \[A\to B\] at different times are given Below

  Concentration (M)	Time (Minutes)
  0.069	0
  0.052	17
  0.035	34
  0.018	51

  The rate constant of the reaction according to the correct order of reaction is
  A)
  0.001 M/min     
  done clear
  B)
  \[0.001{{\min }^{-1}}\]
  done clear
  C)
  \[0.001\min /M\]            
  done clear
  D)
  \[0.001{{M}^{-1}}{{\min }^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer58) The ratio of slopes of \[{{K}_{\max }}vs\] V and \[{{V}_{0}}\] vs v curves in the photoelectric effects gives (v = frequency, \[{{K}_{\max }}\] = maximum kinetic energy, \[{{v}_{o}}\] = stopping potential)
  A)
  the ratio of Planck's constant of electronic charge
  done clear
  B)
  work function
  done clear
  C)
  Planck's constant
  done clear
  D)
  charge of electron
  done clear
  View Answer play_arrow

• question_answer59) With excess of water, both \[{{\text{P}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] and \[\text{PC}{{\text{l}}_{\text{5}}}\] give
  A)
  \[{{\text{H}}_{\text{3}}}\text{P}{{\text{O}}_{\text{3}}}\]                            
  done clear
  B)
  \[{{\text{H}}_{\text{3}}}\text{P}{{\text{O}}_{2}}\] 
  done clear
  C)
  \[{{\text{H}}_{\text{3}}}\text{P}{{\text{O}}_{4}}\]                          
  done clear
  D)
  \[{{H}_{4}}{{P}_{2}}{{O}_{7}}\]
  done clear
  View Answer play_arrow

• question_answer60) The dissolution of \[\text{Al}{{\left( \text{OH} \right)}_{\text{3}}}\]by a solution of NaOH results in the formation of
  A)
  \[{{\left[ \text{A}{{\left( {{\text{H}}_{\text{2}}}\text{O} \right)}_{\text{4}}}{{\left( \text{OH} \right)}_{\text{2}}} \right]}^{\text{+}}}\]    
  done clear
  B)
  \[{{\left[ \text{A}{{\left( {{\text{H}}_{\text{2}}}\text{O} \right)}_{3}}{{\left( \text{OH} \right)}_{3}} \right]}^{\text{+}}}\]
  done clear
  C)
  \[{{\left[ \text{A}{{\left( {{\text{H}}_{\text{2}}}\text{O} \right)}_{2}}{{\left( \text{OH} \right)}_{4}} \right]}^{-}}\]   
  done clear
  D)
  \[\left[ \text{A}{{\left( {{\text{H}}_{\text{2}}}\text{O} \right)}_{6}}{{\left( \text{OH} \right)}_{3}} \right]\]
  done clear
  View Answer play_arrow

• question_answer61) Which of the following does not exist?
  A)
  \[Kl+{{l}_{2}}\to K{{l}_{3}}\]
  done clear
  B)
  \[KF+{{F}_{2}}\to K{{F}_{3}}\]
  done clear
  C)
  \[K{{B}_{r}}+lC{{l}_{2}}\to K\left[ BrlCl \right]\]
  done clear
  D)
  \[KF+Br{{F}_{3}}\to K\left[ Br{{F}_{4}} \right]\]
  done clear
  View Answer play_arrow

• question_answer62) If the ionisation energy and electron affinity of an element are 275 and 86 kcal \[mo{{l}^{-1}}\]respectively, then the electronegativity of the element on the Mulliken scale is
  A)
  2.8     
  done clear
  B)
  0.0     
  done clear
  C)
  4.0                         
  done clear
  D)
  2.6
  done clear
  View Answer play_arrow

• question_answer63) Which of the following sets of reactants is used for preparation of paracetamol from phenol?
  A)
  \[\text{HN}{{\text{O}}_{\text{3}}}\text{,}{{\text{H}}_{\text{2}}}\text{/Pd,}{{\left( \text{C}{{\text{H}}_{\text{3}}}\text{CO} \right)}_{\text{2}}}\text{O}\]
  done clear
  B)
  \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{,}{{\text{H}}_{\text{2}}}\text{/Pd,}{{\left( \text{C}{{\text{H}}_{\text{3}}}\text{CO} \right)}_{\text{2}}}\text{O}\]
  done clear
  C)
  \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}{{\text{N}}_{\text{2}}}\text{Cl,SnC}{{\text{l}}_{\text{2}}}\text{/HCl,}{{\left( \text{C}{{\text{H}}_{\text{3}}}\text{CO} \right)}_{\text{2}}}\text{O}\]
  done clear
  D)
  \[\text{B}{{\text{r}}_{\text{2}}}\text{/}{{\text{H}}_{\text{2}}}\text{O,Zn/HCl,}{{\left( \text{C}{{\text{H}}_{\text{3}}}\text{CO} \right)}_{\text{2}}}\text{O}\]
  done clear
  View Answer play_arrow

• question_answer64) A certain compound gives negative test with ninhydrin and positive test with Benedict's solution. The compound is
  A)
  a protein           
  done clear
  B)
   a monosaccharide
  done clear
  C)
  a lipid                  
  done clear
  D)
   an amino acid
  done clear
  View Answer play_arrow

• question_answer65) Super glue or crazy glue is
  A)
  poly (methyl methacrylate)
  done clear
  B)
  poly (ethyl acrylate)
  done clear
  C)
   poly (methyl a-cyanoacrylate)
  done clear
  D)
  poly ( ethyl methacrylate)
  done clear
  View Answer play_arrow

• question_answer66) X and V respectively are
  A)
  picric acid, 2,4, 6-tribromopheno!
  done clear
  B)
  5-hitrophenol acid, 5-bromosalicylic acid
  done clear
  C)
  o-nitrophenol, o-bromophenol
  done clear
  D)
   3,5-dinitrosalicylicacid,3,5- dibromosalicylicacid
  done clear
  View Answer play_arrow

• question_answer67) In the cannizzaro reaction given below\[2Ph-CHO\xrightarrow{O{{H}^{-}}}\]\[Ph-C{{H}_{2}}-OH+PhCO_{2}^{-}\]the slowest step is
  A)
  the attack of \[\overline{O}H\] at the carbonyl group         
  done clear
  B)
   the transfer of hydride ion to the carbonyl group 
  done clear
  C)
  the abstraction of a proton from the carboxylic acid
  done clear
  D)
   the deprotonation of \[Ph-C{{H}_{2}}OH\]
  done clear
  View Answer play_arrow

• question_answer68) The reaction of l-bromo-3-chlorocyclobutane with metallic sodium in dioxane under reflux conditions gives
  A)
          
  done clear
  B)
           
  done clear
  C)
         
  done clear
  D)
        
  done clear
  View Answer play_arrow

• question_answer69) Identify Z in the following reaction sequence \[\begin{align}   & C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\xrightarrow[160-{{180}^{\circ }}C]{Conc.{{H}_{2}}S{{O}_{4}}}X \\  & \downarrow  \\  & Y\xrightarrow[\begin{smallmatrix}  \left( i \right)Alc.KOH \\  (ii)NaN{{H}_{2}} \end{smallmatrix}]{}Z \\ \end{align}\]
  A)
  \[C{{H}_{3}}-CH\left( N{{H}_{2}} \right)-C{{N}_{2}}N{{H}_{2}}\]
  done clear
  B)
  \[C{{H}_{3}}-CHOH-C{{H}_{2}}OH\]
  done clear
  C)
   \[C{{H}_{3}}-C\left( OH \right)=C{{H}_{2}}\]
  done clear
  D)
  \[C{{H}_{3}}-C\equiv CH\]
  done clear
  View Answer play_arrow

• question_answer70) Which of the following reactions is used to prepare isobutane?
  A)
  Wurtz reaction of \[{{C}_{2}}{{H}_{5}}Br\]
  done clear
  B)
  Hydrolysis of n-butylmagnesium iodide
  done clear
  C)
  Reduction of propanol with red phosphorus and HI
  done clear
  D)
  Decarboxylation of 3-methylbutanoic acid
  done clear
  View Answer play_arrow

• question_answer71) When copper is treated with a certain concentration of nitric acid/nitric oxide and nitrogen dioxide are liberated in equal volumes according to the equation, \[_{X}Cu+yHN{{O}_{3}}\to Cu{{\left( N{{O}_{3}} \right)}_{2}}+NO+N{{O}_{2}}+{{H}_{2}}O\]The coefficients o X and y are respectively
  A)
  2 and 3                 
  done clear
  B)
  2 and 6
  done clear
  C)
  1 and 3                 
  done clear
  D)
  3 and 8
  done clear
  View Answer play_arrow

• question_answer72) A saturated solution of H2S in 0.1 M HCl at       25°C contains \[{{S}^{2-}}\]ion concentration of        \[{{10}^{-23}}\] mol \[{{L}^{-1}}\]. The solubility product of some sulphides  are  \[CuS={{10}^{-44}},\]\[FeS={{10}^{-14}},\]\[MnS={{10}^{-15}},\]\[CdS={{10}^{-25}}.\]If 0.01 M solution of these salts in 1M HCl are saturated with \[{{H}_{2}}S,\]which of these will be precipitated?
  A)
  AIl                          
  done clear
  B)
  All except MnS
  done clear
  C)
  All except MnS and FeS
  done clear
  D)
  Only CuS
  done clear
  View Answer play_arrow

• question_answer73) Consider the water gas equilibrium reaction,     \[C\left( s \right)+{{H}_{2}}O\left( g \right)\rightleftharpoons CO\left( g \right)+{{H}_{2}}\left( g \right)\] Which of the following statements is true at equilibrium?
  A)
  If the amount of C(s) is increased, less water would be formed
  done clear
  B)
  If the amount of C(s) is increased, more CO and \[{{H}_{2}}\] would be formed
  done clear
  C)
  If the pressure on the system is increased by halving the volume, more water would be formed
  done clear
  D)
  If the pressure on the system is increased by halving the volume, more CO and \[{{H}_{2}}\] would be formed
  done clear
  View Answer play_arrow

• question_answer74) The chemical composition of slag formed during the smelting process in the extraction of copper is
  A)
  \[C{{u}_{2}}O+FeS\]
  done clear
  B)
  \[FeSi{{O}_{3}}\]
  done clear
  C)
  \[CuFe{{S}_{2}}\]
  done clear
  D)
  \[C{{u}_{2}}S+FeO\]
  done clear
  View Answer play_arrow

• question_answer75) \[\text{X C}{{\text{l}}_{\text{2}}}\left( excess \right)+\text{Y C}{{\text{l}}_{\text{2}}}\to \text{X C}{{\text{l}}_{\text{4}}}+Y\downarrow \] \[\text{Y O}\xrightarrow[>{{400}^{\circ }}C]{\Delta }\frac{1}{2}{{O}_{2}}+Y\] Ore  of Y would be,
  A)
  siderite                
  done clear
  B)
  malachite
  done clear
  C)
  hornsiiver                           
  done clear
  D)
  cinnabar
  done clear
  View Answer play_arrow

• question_answer76) For the given reaction, \[{{H}_{2}}\left( g \right)+C{{l}_{2}}\left( g \right)\to 2{{H}^{+}}\left( aq \right)+2C{{l}^{-}}\left( aq \right);\]                                           \[\Delta {{G}^{\circ }}=-262.4kJ\] The value of free energy of formation\[\left( \Delta {{G}^{\circ }}f \right)\] for the ion \[C{{l}^{-1}}\left( aq \right),\] therefore  will be
  A)
  \[-131.2kJmo{{l}^{-1}}\]               
  done clear
  B)
  \[+131.2kJmo{{l}^{-1}}\]
  done clear
  C)
  \[\text{-262}\text{.4kJmo}{{\text{l}}^{\text{-1}}}\]
  done clear
  D)
  \[\text{+262}\text{.4kJmo}{{\text{l}}^{\text{-1}}}\]
  done clear
  View Answer play_arrow

• question_answer77) The molarity of \[\text{N}{{\text{O}}_{\text{3}}}^{\text{-}}\]     in the solution after 2L of 3M \[AgN{{O}_{3}}\] is mixed with 3L of 1M \[\text{BaC}{{\text{l}}_{\text{2}}}\] is
  A)
  1.2M                     
  done clear
  B)
  1.8 M
  done clear
  C)
   0.5 M                   
  done clear
  D)
  0.4 M
  done clear
  View Answer play_arrow

• question_answer78) Amongest\[\text{NO}_{\text{3}}^{\text{-}}\text{,AsO}_{\text{3}}^{\text{3-}}\text{,CO}_{\text{3}}^{\text{2-}}\text{,ClO}_{\text{3}}^{\text{-}}\text{,SO}_{\text{3}}^{\text{2-}}\] and \[BO_{3}^{3-},\]the non-planar species are
  A)
  \[CO_{3}^{2-},SO_{3}^{2-}\] and  \[BO_{3}^{2-}\]
  done clear
  B)
  \[ASO_{3}^{3-},ClO_{3}^{-}\] and \[SO_{3}^{2-}\]
  done clear
  C)
  \[NO_{3}^{-},CO_{3}^{2-}\] and \[BO_{3}^{3-}\]
  done clear
  D)
  \[SO_{3}^{2-},NO_{3}^{-}\] and  \[BO_{3}^{3-}\]
  done clear
  View Answer play_arrow

• question_answer79)  A and B respectively are
  A)
       
  done clear
  B)
        
  done clear
  C)
        
  done clear
  D)
        
  done clear
  View Answer play_arrow

• question_answer80) A certain metal when irradiated by light \[\left( r=3.2\times {{10}^{16}}Hz \right)\] emits photoelectrons with twice kinetic energy as did photoelectrons when the same metal is irradiated by light \[\left( r=2.0\times {{10}^{16}}Hz \right).\]The \[{{V}_{0}}\] of metal is
  A)
  \[1.2\times {{10}^{14}}Hz\]        
  done clear
  B)
  \[8\times {{10}^{15}}Hz\]
  done clear
  C)
  \[1.2\times {{10}^{16}}Hz\]        
  done clear
  D)
  \[4\times {{10}^{12}}Hz\]
  done clear
  View Answer play_arrow

• question_answer81) If the matrix \[\text{A=}\left[ \begin{matrix}    \text{1} & \text{3} & \text{1}  \\    \text{-1} & \text{2} & \text{-3}  \\    \text{0} & \text{1} & \text{2}  \\ \end{matrix} \right]\text{,}\]  then adj (adj A) is equal to
  A)
            \[\left[ \begin{matrix}    \text{12} & \text{36} & \text{12}  \\    \text{-12} & \text{24} & \text{-36}  \\    \text{0} & \text{12} & \text{24}  \\ \end{matrix} \right]\]
  done clear
  B)
            \[\left[ \begin{matrix}    \text{12} & \text{26} & \text{-12}  \\    \text{24} & 36 & \text{-36}  \\    \text{0} & \text{12} & \text{-24}  \\ \end{matrix} \right]\]
  done clear
  C)
              \[\left[ \begin{matrix}    \text{12} & \text{-12} & 36  \\    \text{24} & -24 & \text{-36}  \\    \text{0} & \text{12} & \text{24}  \\ \end{matrix} \right]\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer82) Which of the following options is not the asymptote of the curve \[\text{3}{{\text{x}}^{\text{3}}}\text{+2}{{\text{x}}^{\text{2}}}\text{y-7x}{{\text{y}}^{\text{2}}}\text{+2}{{\text{y}}^{\text{3}}}\text{-14xy+7}{{\text{y}}^{\text{2}}}\text{+4x+5y=0?}\]
  A)
  \[\text{y=}\frac{\text{-1}}{\text{2}}\text{ }\!\!\times\!\!\text{ -}\frac{\text{5}}{\text{6}}\]                        
  done clear
  B)
  \[y=x-\frac{7}{6}\]
  done clear
  C)
  \[y=2x+\frac{3}{7}\]                      
  done clear
  D)
  \[y=3x-\frac{3}{2}\]
  done clear
  View Answer play_arrow

• question_answer83) If N is a set of natural numbers, then under binary operation a.b = a + b, (N,.) is
  A)
  quasi-group                       
  done clear
  B)
  semi-group
  done clear
  C)
  monoid               
  done clear
  D)
  group
  done clear
  View Answer play_arrow

• question_answer84) \[\int{\frac{dx}{\cos x+\sqrt{3}\sin x}}\]  equal
  A)
  \[\frac{\text{1}}{\text{2}}\text{logtan}\left( \frac{\text{x}}{\text{2}}\text{+}\frac{\text{ }\!\!\pi\!\!\text{ }}{\text{12}} \right)\text{+C}\]
  done clear
  B)
  \[\frac{\text{1}}{3}\text{logtan}\left( \frac{\text{x}}{\text{2}}-\frac{\text{ }\!\!\pi\!\!\text{ }}{\text{12}} \right)\text{+C}\]
  done clear
  C)
  \[\text{logtan}\left( \frac{\text{x}}{\text{2}}+\frac{\text{ }\!\!\pi\!\!\text{ }}{6} \right)\text{+C}\]
  done clear
  D)
  \[\frac{1}{2}\text{logtan}\left( \frac{\text{x}}{\text{2}}-\frac{\text{ }\!\!\pi\!\!\text{ }}{6} \right)\text{+C}\]
  done clear
  View Answer play_arrow

• question_answer85) If (2, 7, 3) is one end of a diameter of the sphere \[{{\text{x}}^{\text{2}}}\text{+}{{\text{y}}^{\text{2}}}\text{+}{{\text{z}}^{\text{2}}}\text{-6x-12y-2z+20=0}\], then the coordinates of the other end of the diameter are
  A)
  (-2, 5, -1)                             
  done clear
  B)
  (4, 5, 1)
  done clear
  C)
   (2, -5, 1)                             
  done clear
  D)
  (4, 5, -1)
  done clear
  View Answer play_arrow

• question_answer86) The two lines x = my + n,   z = py + q  and x = m? y + n?, z = p? y + q? are perpendicular to each other, if
  A)
  \[mm'+pp'=1\] 
  done clear
  B)
  \[\frac{m}{m'}+\frac{p}{p'}=-1\]
  done clear
  C)
  \[\frac{m}{m'}+\frac{p}{p'}=1\]                
  done clear
  D)
  \[mm'+pp'=-1\]
  done clear
  View Answer play_arrow

• question_answer87) A tetrahedron has vertices at O(0, 0, 0), A(1, -2, 1), B (-2, 1, 1) and C (1, -1, 2). Then the angle between the faces OAB and ABC will be
  A)
  \[{{\cos }^{-1}}\left( \frac{1}{2} \right)\]                               
  done clear
  B)
  \[{{\cos }^{-1}}\left( \frac{-1}{6} \right)\]
  done clear
  C)
  \[{{\cos }^{-1}}\left( \frac{-1}{3} \right)\]             
  done clear
  D)
  \[{{\cos }^{-1}}\left( \frac{1}{4} \right)\]
  done clear
  View Answer play_arrow

• question_answer88) If a line segment OP makes angles of \[\frac{\pi }{4}\] and with X-axis and Y-axis, respectively. Then the direction cosines are
  A)
  \[\frac{1}{\sqrt{2}},\frac{\sqrt{3}}{2},\frac{1}{\sqrt{2}}\]              
  done clear
  B)
  \[\frac{1}{\sqrt{2}},\frac{1}{2},\frac{1}{\sqrt{2}}\]
  done clear
  C)
  \[1,\sqrt{3},1\]                 
  done clear
  D)
  \[1,\frac{1}{\sqrt{3}},1\]
  done clear
  View Answer play_arrow

• question_answer89) If p, q, r are simple propositions with truth values T, F, T, then the truth value of \[\left( \sim p\vee q \right)\wedge \sim r\Rightarrow p\] is
  A)
  true      
  done clear
  B)
  false
  done clear
  C)
   true, if r is false               
  done clear
  D)
  true, if q is true
  done clear
  View Answer play_arrow

• question_answer90) On the interval [0, 1], the function with \[{{\text{X}}^{\text{25}}}{{\left( \text{1-x} \right)}^{\text{75}}}\] takes its maximum value at the point
  A)
  0                                             
  done clear
  B)
  \[\frac{1}{4}\]
  done clear
  C)
  \[\frac{1}{2}\]                                   
  done clear
  D)
  \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer91) If\[|z|\ge 3,\]then the least value of\[\left| z+\frac{1}{4} \right|\]is
  A)
  \[\frac{11}{2}\]                                
  done clear
  B)
  \[\frac{11}{4}\]
  done clear
  C)
  3                                             
  done clear
  D)
  \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer92) The normal at the point \[\left( \text{at}_{\text{1}}^{\text{2}}\text{,2a}{{\text{t}}_{\text{1}}} \right)\] on the parabola meets the parabola again in the point \[\left( \text{at}_{2}^{\text{2}}\text{,2a}{{\text{t}}_{2}} \right),\]  then
  A)
  \[{{\text{t}}_{\text{2}}}\text{=-}{{\text{t}}_{\text{1}}}\text{+}\frac{\text{2}}{{{\text{t}}_{\text{1}}}}\]                                  
  done clear
  B)
  \[{{\text{t}}_{\text{2}}}\text{=-}{{\text{t}}_{\text{1}}}-\frac{\text{2}}{{{\text{t}}_{\text{1}}}}\]
  done clear
  C)
  \[{{\text{t}}_{\text{2}}}\text{=}{{\text{t}}_{\text{1}}}-\frac{\text{2}}{{{\text{t}}_{\text{1}}}}\]                 
  done clear
  D)
  \[{{\text{t}}_{\text{2}}}\text{=}{{\text{t}}_{\text{1}}}+\frac{\text{2}}{{{\text{t}}_{\text{1}}}}\]
  done clear
  View Answer play_arrow

• question_answer93) If \[a=\hat{i}-\hat{j}+2\hat{k}\] and \[b=2\hat{i}+\hat{j}+\hat{k},\] then the angle \[\theta \]  between a and b is given by
  A)
  \[{{\tan }^{-1}}\left( 1 \right)\]                 
  done clear
  B)
  \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
  done clear
  C)
  \[{{\sec }^{-1}}\left( 1 \right)\] 
  done clear
  D)
  \[{{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]
  done clear
  View Answer play_arrow

• question_answer94) The area bounded by the curves  y = cos x and y = sin x between the ordinates x = 0 and \[x=\frac{3\pi }{2}\] is
  A)
  \[\left( \text{4}\sqrt{\text{2}}\text{-2} \right)\text{sq units}\]
  done clear
  B)
  \[\left( \text{4}\sqrt{\text{2}}\text{+2} \right)\text{sq units}\]
  done clear
  C)
  \[\left( \text{4}\sqrt{\text{2}}-1 \right)\text{sq units}\]
  done clear
  D)
   \[\left( \text{4}\sqrt{\text{2}}+1 \right)\text{sq units}\]
  done clear
  View Answer play_arrow

• question_answer95) If a, b and c are three non ? coplanar vectors, then (a + b ? c) . \[\left[ \left( a-b \right)\times \left( b-c \right) \right]\] equals
  A)
  0                                             
  done clear
  B)
  \[\text{a}\text{. b }\!\!\times\!\!\text{ c}\]
  done clear
  C)
  \[\text{a}\text{. c }\!\!\times\!\!\text{ b}\]                       
  done clear
  D)
  \[\text{3a}\text{. b }\!\!\times\!\!\text{ c}\]
  done clear
  View Answer play_arrow

• question_answer96) If there is an error of m% in measuring the edge of cube, then the per cent error in estimating its surface area is
  A)
  2 m                                        
  done clear
  B)
  3 m
  done clear
  C)
  1 m                                        
  done clear
  D)
  4 m
  done clear
  View Answer play_arrow

• question_answer97) If the rectangular hyperbola is \[{{x}^{2}}-{{y}^{2}}=64.\] Then,  which of the following  is not correct?
  A)
  The  length of latusrectum is 16
  done clear
  B)
  The eccentricity is \[\sqrt{2}\]
  done clear
  C)
  The asymptotes are parallel to  each other
  done clear
  D)
  The  directrices re \[x=\pm 4\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer98) The equation of tangents to the hyperbola \[3{{x}^{2}}-2{{y}^{2}}=6,\] which is perpendicular to the line x ? 3y = 3, are
  A)
  \[y=-3x\pm \sqrt{15}\]
  done clear
  B)
  \[y=3x\pm \sqrt{6}\]
  done clear
  C)
  \[y=-3x\pm \sqrt{6}\]
  done clear
  D)
  \[y=2x\pm \sqrt{15}\]
  done clear
  View Answer play_arrow

• question_answer99) \[\underset{x\to \pi /4}{\mathop{\lim }}\,\frac{\tan x-1}{\cos 2x}\] is equal to
  A)
  1                                             
  done clear
  B)
  0
  done clear
  C)
   -2                                          
  done clear
  D)
  -1
  done clear
  View Answer play_arrow

• question_answer100) The area of the region bounded by the curves  \[{{x}^{2}}+{{y}^{2}}=9\] and x + y = 3 is
  A)
  \[\frac{9\pi }{4}+\frac{1}{2}\]                    
  done clear
  B)
   \[\frac{9\pi }{4}-\frac{1}{2}\]
  done clear
  C)
  \[9\left( \frac{\pi }{4}-\frac{1}{2} \right)\]            
  done clear
  D)
  \[9\left( \frac{\pi }{4}+\frac{1}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer101) For any three vectors a,b and c,\[[a+b,b+c,c+a]\]is
  A)
  [a,b,c]
  done clear
  B)
  3 [a b c]
  done clear
  C)
  2 [a b c]               
  done clear
  D)
  0
  done clear
  View Answer play_arrow

• question_answer102) \[\int_{0}^{\pi /2}{\sin 2x.\log \tan xdx}\]is equal to
  A)
  0                                             
  done clear
  B)
  2
  done clear
  C)
  4                                             
  done clear
  D)
  7
  done clear
  View Answer play_arrow

• question_answer103) If the mean and variance of a binomial distribution are 4 and 2, respectively. Then, the probability of atleast 7 successes is
  A)
  \[\frac{3}{214}\]                              
  done clear
  B)
  \[\frac{4}{173}\]
  done clear
  C)
  \[\frac{9}{256}\]                              
  done clear
  D)
   \[\frac{7}{231}\]
  done clear
  View Answer play_arrow

• question_answer104) The shortest distance between the lines  \[\frac{\text{x-7}}{\text{3}}\text{=}\frac{\text{y+4}}{\text{-16}}\text{=}\frac{\text{z-6}}{\text{7}}\]and \[\frac{\text{x-10}}{\text{3}}\text{=}\frac{\text{y-30}}{\text{8}}\text{=}\frac{\text{4-z}}{\text{5}}\]  is
  A)
   \[\frac{234}{7}units\]                   
  done clear
  B)
   \[\frac{288}{21}units\]
  done clear
  C)
  \[\frac{221}{3}units\]                    
  done clear
  D)
  \[\frac{234}{21}units\]
  done clear
  View Answer play_arrow

• question_answer105) If a plane passing through the point (2, 2, 1) and is perpendicular to the planes 3x + 2y + 4z + 1 = 0  and  2x + y + 3z + 2 = 0, Then, the equation of the plane is
  A)
   2x ? y ? z ? 1 = 0
  done clear
  B)
   2x + 3y + z ? 1 = 0
  done clear
  C)
   2x + y + z + 3 = 0
  done clear
  D)
  x ? y + z ? 1 = 0
  done clear
  View Answer play_arrow

• question_answer106) From a city population, the probability of selecting a male or smoker is \[\frac{7}{10},\] a male smoker is \[\frac{2}{5}\] and a male, if a smoker is already selected, is \[\frac{2}{3}.\] Then, the probability of
  A)
  selecting a male is \[\frac{3}{2}\]
  done clear
  B)
  selecting a  smoker is \[\frac{1}{5}\]
  done clear
  C)
  selecting anon -  smoker is \[\frac{2}{5}\]
  done clear
  D)
  selecting a smoker, if a male is first selected, is given by \[\frac{8}{5}\]
  done clear
  View Answer play_arrow

• question_answer107) At t = 0, the function \[f\left( t \right)=\frac{\sin t}{t}\] has
  A)
  a minimum        
  done clear
  B)
  a discontinuity
  done clear
  C)
  a point of inflexion         
  done clear
  D)
  a maximum
  done clear
  View Answer play_arrow

• question_answer108) Using Rolle?s theorem the equation \[{{\text{a}}_{\text{0}}}{{\text{x}}^{\text{n}}}\text{+}{{\text{a}}_{\text{1}}}{{\text{x}}^{\text{n-1}}}\text{+}....\text{+}{{\text{a}}_{\text{n}}}\text{=0}\] has atleast one root between 0 and and 1, if
  A)
  \[\frac{{{a}_{0}}}{n}+\frac{{{a}_{1}}}{n-1}+....+{{a}_{n-1}}=0\]
  done clear
  B)
  \[\frac{{{a}_{0}}}{n-1}+\frac{{{a}_{1}}}{n-2}+....+{{a}_{n-2}}=0\]
  done clear
  C)
  \[n{{a}_{0}}+\left( n-1 \right){{a}_{1}}+....+{{a}_{n-1}}=0\]
  done clear
  D)
  \[\frac{{{a}_{0}}}{n+1}+\frac{{{a}_{1}}}{n}+.....+{{a}_{n}}=0\]
  done clear
  View Answer play_arrow

• question_answer109) Which of the following inequality is true for x > 0 ?
  A)
  \[\text{log}\left( \text{1+x} \right)\text{}\frac{\text{x}}{\text{1+x}}\text{x}\]
  done clear
  B)
  \[\frac{\text{x}}{\text{1+x}}\text{xlog}\left( 1+x \right)\]
  done clear
  C)
  \[\text{xlog}\left( \text{1+x} \right)\text{}\frac{\text{x}}{\text{1+x}}\]
  done clear
  D)
  \[\frac{\text{x}}{\text{1+x}}\text{log}\left( \text{1+x} \right)\text{x}\]
  done clear
  View Answer play_arrow

• question_answer110) The solution of \[\frac{{{\text{d}}^{\text{2}}}\text{x}}{\text{d}{{\text{y}}^{\text{2}}}}\text{-x=k,}\] where k is a non-zero constant, vanishes when y = 0 and tends of finite limit as y  tends to infinity, is
  A)
  \[x=k\left( 1+{{e}^{-y}} \right)\]              
  done clear
  B)
  \[\text{x=k}\left( {{\text{e}}^{\text{y}}}\text{+}{{\text{e}}^{\text{-y}}}\text{-2} \right)\]
  done clear
  C)
  \[\text{x=k}\left( {{\text{e}}^{\text{-y}}}\text{-1} \right)\]                         
  done clear
  D)
  \[\text{x=k}\left( {{\text{e}}^{\text{y}}}\text{-1} \right)\]
  done clear
  View Answer play_arrow

• question_answer111) The differential equation (3x + 4y + 1)dx+(4x + 5y + 1)dy = 0  represents a family of
  A)
  circles                   
  done clear
  B)
  parabolas
  done clear
  C)
  ellipses                
  done clear
  D)
  hyperbolas
  done clear
  View Answer play_arrow

• question_answer112) If \[\Delta \left( r \right)=\left| \begin{matrix}    r & {{r}^{3}}  \\    1 & n\left( n+1 \right)  \\ \end{matrix} \right|,\] then \[\sum\limits_{r=1}^{n}{\Delta \left( r \right)}\] is equal to
  A)
  \[\sum\limits_{r=1}^{n}{{{r}^{2}}}\]                       
  done clear
  B)
  \[\sum\limits_{r=1}^{n}{{{r}^{3}}}\]
  done clear
  C)
  \[\sum\limits_{r=1}^{n}{r}\]                      
  done clear
  D)
  \[\sum\limits_{r=1}^{n}{{{r}^{4}}}\]
  done clear
  View Answer play_arrow

• question_answer113) If A, B, C are three events associated with a random experiment, then\[P\left( A \right)P\left( \frac{B}{A} \right)P\left( \frac{C}{A}\cap B \right)\] is
  A)
  \[P\left( A\cup B\cup C \right)\]              
  done clear
  B)
  \[P\left( A\cap B\cap C \right)\]
  done clear
  C)
  \[P\left( \frac{C}{A}\cap B \right)\]                         
  done clear
  D)
  \[P\left( \frac{B}{A} \right)\]
  done clear
  View Answer play_arrow

• question_answer114) If \[\text{A=}\left[ \begin{matrix}    \text{1} & \text{3} & \text{1}  \\    \text{2} & \text{1} & \text{-1}  \\    \text{3} & \text{0} & \text{1}  \\ \end{matrix} \right]\text{,}\] then rank (A) is equal to
  A)
  4                                             
  done clear
  B)
  1
  done clear
  C)
  2                                             
  done clear
  D)
  3
  done clear
  View Answer play_arrow

• question_answer115) The probability of atleast one double six being thrown in n throws with two ordinary dice is greater than 99% Then, the least numerical value of n is
  A)
  100                                        
  done clear
  B)
  164
  done clear
  C)
  170                                        
  done clear
  D)
  184
  done clear
  View Answer play_arrow

• question_answer116) Find the value of k for which the simultaneous equations x + y + z = 3;  x + 2y + 3z = 4 and x + 4y + kz = 6 will not have a unique solution.
  A)
  4                                             
  done clear
  B)
  1
  done clear
  C)
  3                                             
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer117) If the complex number z lies on a circle with centre at the origin and radius \[\frac{1}{4},\] then the complex number \[-1+8z\] lies on a circle with radius
  A)
  4                                             
  done clear
  B)
  1
  done clear
  C)
  3                                             
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer118) If line \[y=2x+c\] is a normal to the ellipse \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=1,\] then
  A)
  \[c=\frac{2}{3}\]                              
  done clear
  B)
  \[c=\sqrt{\frac{73}{5}}\]
  done clear
  C)
  \[c=\frac{14}{\sqrt{73}}\]
  done clear
  D)
  \[c=\sqrt{\frac{5}{7}}\]
  done clear
  View Answer play_arrow

• question_answer119) If \[{{x}^{2}}+x+1=0,\] then the value of \[\sum\limits_{n=1}^{6}{{{\left( {{x}^{n}}+\frac{1}{{{x}^{n}}} \right)}^{2}}}\]is 13                                          
  A)
  12
  done clear
  B)
  done clear
  C)
  9                                             
  done clear
  D)
  14
  done clear
  View Answer play_arrow

• question_answer120) If p: It rains today, q: I go to school, r: I shall meet any friends and s:  I shall go for a movie, then which of the following is the proportion? If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.
  A)
  \[(\sim p\wedge \sim q)\]\[\Rightarrow \] \[(r\wedge s)\]
  done clear
  B)
  \[\sim (p\wedge q)\]\[\Rightarrow \]\[(r\wedge s)\]
  done clear
  C)
  \[\sim (p\vee q)\]\[\Rightarrow \]\[(r\vee s)\]
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow