Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2014

done BCECE Engineering Solved Paper-2014 Total Questions - 150

• question_answer1) Two quantities X and Y have different dimensions. Which mathematical operation given below is physically meaningful?
  A)
  \[X+Y\]                                
  done clear
  B)
  \[X-Y\]
  done clear
  C)
   \[\frac{X}{Y}\]                                 
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer2) If \[\text{A=3\hat{i}+4\hat{j}}\] and \[\text{B =7\hat{i}+24\hat{j},}\], then the vector having the same magnitude as Band parallel to  A is 
  A)
  \[\text{15\hat{i}+20\hat{j}}\]                    
  done clear
  B)
  \[\text{5\hat{i}-3\hat{j}}\]
  done clear
  C)
  \[\text{15\hat{i}+13\hat{j}}\]                    
  done clear
  D)
  \[\text{5\hat{i}+14\hat{j}}\]
  done clear
  View Answer play_arrow

• question_answer3) The gravitational, field due to a mass distribution is \[E=\frac{k}{{{x}^{3}}}\] in the \[x\] - direction, where k is a constant. The value of gravitational potential at a distance \[x\] is [Taking gravitational potential to be zero at infinity]
  A)
  \[\frac{k}{x}\]                                   
  done clear
  B)
  \[\frac{k}{{{x}^{3}}}\]
  done clear
  C)
  \[\frac{k}{2{{x}^{2}}}\] 
  done clear
  D)
  \[\frac{k}{3{{x}^{3}}}\]
  done clear
  View Answer play_arrow

• question_answer4) Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. If velocity of flow of water in the pipe of 4 cm diameter is X, then velocity in 2 cm diameter is
  A)
  2X                                          
  done clear
  B)
  4X
  done clear
  C)
  6X                                          
  done clear
  D)
  8X
  done clear
  View Answer play_arrow

• question_answer5) Water rises to a height h in a capillary on the surface of the earth in stationary condition. Value of h increases, if this tube is taken
  A)
  on poles
  done clear
  B)
   on sun
  done clear
  C)
  in a lift going upward with acceleration
  done clear
  D)
  in a lift going downward with acceleration
  done clear
  View Answer play_arrow

• question_answer6) Two sound waves having a phase difference of\[\text{6}0{}^\circ \], have a path difference of
  A)
  \[\frac{\lambda }{3}\]                                   
  done clear
  B)
  \[\frac{\lambda }{6}\]
  done clear
  C)
  \[\frac{\lambda }{9}\]                                   
  done clear
  D)
  \[\lambda \]
  done clear
  View Answer play_arrow

• question_answer7) Propagation of sound waves in air is an example of         
  A)
  isothermal process                                               
  done clear
  B)
  isobaric process                                                     
  done clear
  C)
  adiabatic process                                                   
  done clear
  D)
  isochoric process
  done clear
  View Answer play_arrow

• question_answer8) A small laboratory telescope has an objective   lens of focal length 140 cm and an eye-piece of focal length 6 cm. Then, separation between the objective and eye-piece is        
  A)
  140cm                    
  done clear
  B)
  24cm                                                                           
  done clear
  C)
  156cm                    
  done clear
  D)
  146cm                                                                        
  done clear
  View Answer play_arrow

• question_answer9) The ratio of the peak current through the capacitor and supply is known as         
  A)
  resonance current                                                
  done clear
  B)
  dynamic resistance                                               
  done clear
  C)
  Q-factor
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer10) For the given circuit diagram, the equivalent resistance across battery is               
  A)
  5\[\Omega \]
  done clear
  B)
              10\[\Omega \]
  done clear
  C)
  20\[\Omega \]                                 
  done clear
  D)
  15\[\Omega \]
  done clear
  View Answer play_arrow

• question_answer11) The specific resistance of a wire is \[\rho \], its volume is 3m3 and its resistance is \[3\Omega \], then its length will be
  A)
  \[\frac{3}{\sqrt{\rho }}\]                                              
  done clear
  B)
  \[\frac{\sqrt{3}}{\rho }\]
  done clear
  C)
  \[\frac{5}{\sqrt{\rho }}\]                                              
  done clear
  D)
  \[\frac{\sqrt{5}}{\rho }\]
  done clear
  View Answer play_arrow

• question_answer12) A radio transmitter radiates 1 kW power at a wavelength 198.6 m. How many photons does it emit per second?
  A)
  \[\text{1}{{0}^{\text{1}0}}\]                                      
  done clear
  B)
  \[\text{1}{{0}^{\text{2}0}}\]
  done clear
  C)
  \[\text{1}{{0}^{\text{3}0}}\]                      
  done clear
  D)
  \[\text{1}{{0}^{\text{4}0}}\]
  done clear
  View Answer play_arrow

• question_answer13) For an L-R circuit, the inductive reactance is equal to the resistance R of the circuit. An emf \[E={{E}_{0}}\cos (\omega t)\]is applied to the circuit. Then, the power consumed in the circuit is
  A)
  \[\frac{{{E}_{0}}}{R}\]                                   
  done clear
  B)
  \[\frac{E_{0}^{2}}{4R}\]
  done clear
  C)
  \[\frac{4R}{{{E}_{0}}}\]                                 
  done clear
  D)
  \[\frac{R}{{{E}_{0}}}\]
  done clear
  View Answer play_arrow

• question_answer14) The following truth table corresponds to the logic gate

  A	S	y
  0	0	0
  0	1	1
  1	0	1
  1	1	1

  A)
  NAND                  
  done clear
  B)
  AND
  done clear
  C)
  XOR                      
  done clear
  D)
   OR
  done clear
  View Answer play_arrow

• question_answer15) The corresponding truth table for the function Z of X and Y represented by given figure is
  A)
                 

  X	Y	Z
  0	0	0
  0	1	0
  1	0	1
  1	1	1

  done clear
  B)
                   

  X	Y	Z
  0	0	1
  0	1	1
  1	0	0
  1	1	0

                 
  done clear
  C)

  X	Y	Z
  0	0	1
  0	1	0
  1	0	1
  1	1	0

  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer16) Thermal conductivity of a material in CGS  system is 0.4. In steady state, the rate of flow of heat is\[\text{1}0\text{ cal}/\text{s}-\text{c}{{\text{m}}^{\text{2}}}\].The thermal gradient will be
  A)
  \[\text{5}{}^\circ \text{C}/\text{cm}\]                  
  done clear
  B)
  \[\text{15}{}^\circ \text{C}/\text{cm}\]
  done clear
  C)
  \[\text{25}{}^\circ \text{C}/\text{cm}\]                
  done clear
  D)
  \[\text{5}0{}^\circ \text{C}/\text{cm}\]
  done clear
  View Answer play_arrow

• question_answer17) Shape of graph between speed and kinetic energy of the body is
  A)
  hyperbola                          
  done clear
  B)
  straight line
  done clear
  C)
  parabola     
  done clear
  D)
  circle
  done clear
  View Answer play_arrow

• question_answer18) For a common emitter circuit amplifier, the load resistance of the output circuit is 500 times the resistance of the input circuit. If \[\alpha \text{ }=\text{ }0.\text{98}\], then, current gain is
  A)
  0.98                       
  done clear
  B)
  50     
  done clear
  C)
  98                          
  done clear
  D)
  49
  done clear
  View Answer play_arrow

• question_answer19) A water pump of power 2kW is installed in a home. Then, the amount of water (in litres) it can raise in one minute to a height of 10m is [Take\[g=10m/{{s}^{2}}\]]
  A)
  200 L
  done clear
  B)
                         1200 L
  done clear
  C)
   800 L                    
  done clear
  D)
  350 L
  done clear
  View Answer play_arrow

• question_answer20) For the given circuit of p - n junction, the potential barrier is
  A)
  raised                   
  done clear
  B)
  lowered
  done clear
  C)
  remains same                   
  done clear
  D)
  data insufficient
  done clear
  View Answer play_arrow

• question_answer21) A man fires a large number of bullets in all directions with same speed \[\upsilon \]. The maximum area on the ground on which these bullets will spread is
  A)
  \[\frac{\pi {{v}^{2}}}{g}\]                             
  done clear
  B)
  \[\frac{{{v}^{2}}}{{{g}^{2}}}\]
  done clear
  C)
  \[\frac{\pi {{v}^{4}}}{{{g}^{2}}}\]                                              
  done clear
  D)
  \[\frac{{{v}^{4}}}{{{g}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer22) Shaft of a motor rotates at a constant angular velocity of 3000 rpm. The radians it has turned through in 1 s is
  A)
  \[\pi \]                                 
  done clear
  B)
  \[10\pi \]
  done clear
  C)
  \[50\pi \]                            
  done clear
  D)
  \[100\pi \]
  done clear
  View Answer play_arrow

• question_answer23) Motion of planets in solar system is an example of conservation of
  A)
  momentum                       
  done clear
  B)
  velocity
  done clear
  C)
  angular momentum       
  done clear
  D)
  energy
  done clear
  View Answer play_arrow

• question_answer24) The radii of two planets are respectively \[{{R}_{1}}\]   and \[{{R}_{2}}\] and their densities are \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\]. Ratio of the accelerations due to gravity at their surfaces is  
  A)
  \[\frac{{{R}_{1}}}{{{R}_{2}}}.\frac{{{\rho }_{1}}}{{{\rho }_{2}}}\]
  done clear
  B)
  \[\frac{{{R}_{2}}}{{{R}_{1}}}.\frac{\rho _{1}^{2}}{{{\rho }_{2}}}\]
  done clear
  C)
  \[\frac{{{R}_{1}}}{{{R}_{2}}}.\frac{{{\rho }_{2}}}{\rho _{1}^{2}}\]                               
  done clear
  D)
  \[1:1\]
  done clear
  View Answer play_arrow

• question_answer25) A tank is filled with water. There is a hole in . the bottom. At the bottom total pressure is 3 aim, then, the velocity of water flowing from h\[\left( \text{1atm }=\text{1}{{0}^{5}}\text{ N}/{{\text{m}}^{\text{2}}} \right)\],then, the velocity of water flowing from hole is
  A)
  10m/s                  
  done clear
  B)
  20m/s
  done clear
  C)
  15m/s                  
  done clear
  D)
  25m/s
  done clear
  View Answer play_arrow

• question_answer26)  A horizontal overhead power line carries a current of 90A in east to west direction. Magnitude of magnetic field due to the  current 1.5 m below the line is
  A)
  \[1.2T\]                                 
  done clear
  B)
  \[1.2\times {{10}^{-10}}T\]
  done clear
  C)
  \[0T\]                                   
  done clear
  D)
  \[1.2\times {{10}^{-5}}T\]           
  done clear
  View Answer play_arrow

• question_answer27) Find the difference of air pressure between  the inside and outside of a soap bubble 5 mm in diameter, if the surface tension is 1.6 N/m.
  A)
  \[\text{256}0\text{ N}/{{\text{m}}^{\text{2}}}\]              
  done clear
  B)
  \[\text{372}0\text{N}/{{\text{m}}^{2}}\]
  done clear
  C)
  \[~\text{12}0\text{8N}/{{\text{m}}^{\text{2}}}~\]          
  done clear
  D)
  \[~\text{95}0\text{N}/{{\text{m}}^{\text{2}}}\]
  done clear
  View Answer play_arrow

• question_answer28) Impulse of a force is equal to the change in
  A)
  mass                                     
  done clear
  B)
  velocity
  done clear
  C)
  momentum                       
  done clear
  D)
  energy
  done clear
  View Answer play_arrow

• question_answer29) A   particle   moves   through   angular displacement \[\theta \] on a circular path of radius r. The linear displacement will be
  A)
  \[2r\sin \left( \frac{\theta }{2} \right)\] 
  done clear
  B)
  \[2r\cos \left( \frac{\theta }{2} \right)\]
  done clear
  C)
  \[2r\tan \left( \frac{\theta }{2} \right)\]                
  done clear
  D)
  \[2r\cot \left( \frac{\theta }{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer30) An electron and a photon have equal energy. Then\[{{E}_{K}}\].the ratio of wavelengths of photon and electron is \[\left( \frac{{{\lambda }_{\text{photon}}}}{{{\lambda }_{\text{electron}}}} \right)\]
  A)
  \[\sqrt{\frac{{{E}_{K}}}{2}}\]                      
  done clear
  B)
  \[\frac{1}{\sqrt{2{{E}_{K}}}}\]
  done clear
  C)
  \[\frac{2}{\sqrt{{{E}_{K}}}}\]                      
  done clear
  D)
  \[\frac{\sqrt{3{{E}_{K}}}}{2}\]
  done clear
  View Answer play_arrow

• question_answer31) In a transistor, forward bias is always smaller than the reverse bias. This is done to
  A)
  maintain constant current supply
  done clear
  B)
  get good output
  done clear
  C)
  avoid excessive heating of transistor
  done clear
  D)
  maintain flow of majority charge carriers
  done clear
  View Answer play_arrow

• question_answer32) Light with an energy flux of \[\text{18W}/\text{c}{{\text{m}}^{\text{2}}}\]falls on a non-reflecting surface at normal incidence, The surface has an area of\[\text{2}0\text{ c}{{\text{m}}^{\text{2}}}\], then the total momentum delivered on the surface during a  span of 30 mm is    
  A)
                            \[2.16\times {{10}^{-3}}kg-m/s\]
  done clear
  B)
  \[1.52\times {{10}^{-5}}kg-m/s\]
  done clear
  C)
   \[8.31\times {{10}^{-8}}kg-m/s\]
  done clear
  D)
  \[18.2\times {{10}^{-6}}kg-m/s\]
  done clear
  View Answer play_arrow

• question_answer33) The Young's modulus of a wire of length L and radius r is \[\text{YN}/{{\text{m}}^{\text{2}}}\]. The length and radius are reduced to \[\frac{L}{6}\] and \[\frac{r}{6},\] then its Young's modulus is
  A)
  \[6Y\]                                   
  done clear
  B)
  \[\frac{Y}{6}\]
  done clear
  C)
  \[Y\]     
  done clear
  D)
  \[3Y\]
  done clear
  View Answer play_arrow

• question_answer34) In a circular coil (1) of radius R, current \[I\] is flowing and in another coil (2) of radius 2R a current \[2I\] is flowing, then the ratio of the magnetic fields produced by the two coils is
  A)
  1: 1                                        
  done clear
  B)
  1:2
  done clear
  C)
  2: 1                                        
  done clear
  D)
  3:1
  done clear
  View Answer play_arrow

• question_answer35) Which of the following statement is true for relative magnetic permeability?
  A)
  It is dimensionless
  done clear
  B)
  It is unit less
  done clear
  C)
  Its value is greater than 1000 tor iron
  done clear
  D)
  All of the above
  done clear
  View Answer play_arrow

• question_answer36) When the self-inductance of the primary and secondary coil is doubled, then the mutual inductance of the two coils is
  A)
  halved
  done clear
  B)
  doubled
  done clear
  C)
  quadrupled
  done clear
  D)
  reduced to one-fourth
  done clear
  View Answer play_arrow

• question_answer37) In a semiconductor diode, the forward voltage is changed from 0.5 V to 0.7V, then the   forward current changes by 1mA. The forward resistance of the diode junction is
  A)
  100 \[\Omega \]              
  done clear
  B)
  50 \[\Omega \]
  done clear
  C)
  200 \[\Omega \]        
  done clear
  D)
  250 \[\Omega \]
  done clear
  View Answer play_arrow

• question_answer38) Moment of inertia of wheel about the axis of 4 rotation is 3 MKS units. Its kinetic energy will be 600 J, if period of rotation is (in seconds)
  A)
  \[\pi \]                                 
  done clear
  B)
  \[\frac{\pi }{5}\]
  done clear
  C)
  \[\frac{\pi }{10}\]            
  done clear
  D)
  \[2\pi \]
  done clear
  View Answer play_arrow

• question_answer39) A galvanometer has a coil resistance of 100 \[\Omega \] It gives a full scale deflection when a current of 1mA is passed through it. The value of resistance which can convert the galvanometer into an ammeter giving full scale deflection for a current of 10 A is
  A)
  \[{{10}^{-4}}\Omega \]                 
  done clear
  B)
  \[{{10}^{-2}}\Omega \]
  done clear
  C)
  \[{{10}^{4}}\Omega \]                  
  done clear
  D)
  \[{{10}^{2}}\Omega \]
  done clear
  View Answer play_arrow

• question_answer40) A siren emits sound of frequency 1000 Hz, it moves away from the observer towards a cliff     with a speed of\[\text{1}0\text{ m}{{\text{s}}^{{{\text{-}}^{\text{1}}}}}\]. Then, the  frequency of sound heard by observer coming directly from the siren is
  A)
  less than 1000 Hz                            
  done clear
  B)
  greater than 1000 Hz
  done clear
  C)
  equal to 1000 Hz
  done clear
  D)
  no sound is heard
  done clear
  View Answer play_arrow

• question_answer41) One surface of a lens is convex and the other  is concave. If the radii of curvatures are \[{{R}_{1}}\] and \[{{R}_{2}}\],then the lens will be convex, if
  A)
  \[{{R}_{1}}<{{R}_{2}}\]  
  done clear
  B)
  \[{{R}_{1}}>{{R}_{2}}\]
  done clear
  C)
  \[{{R}_{1}}={{R}_{2}}\]                  
  done clear
  D)
  None  of these
  done clear
  View Answer play_arrow

• question_answer42) A convex mirror of radius of curvature 1.6 m has an object placed at a distance of 1m from it. The image is formed at a distance of 1
  A)
  \[\frac{18}{3}\]m behind the mirror
  done clear
  B)
  \[\frac{18}{3}\]m infront of the mirror
  done clear
  C)
  \[\frac{4}{9}\] m behind the mirror  
  done clear
  D)
  ?\[\frac{4}{9}\]m in front of the mirror
  done clear
  View Answer play_arrow

• question_answer43) When a radioactive isotope \[_{88}{{R}^{228}}\]decays in 5 series by the emission of \[3\alpha \]-particles and P--\[\beta \]-particles, the mass number of the isotope finally formed is
  A)
  83                                          
  done clear
  B)
  72
  done clear
  C)
  216                                        
  done clear
  D)
  228
  done clear
  View Answer play_arrow

• question_answer44) As shown in the experimental setup, two cells with the same emf E and different internal resistance \[{{r}_{1}}\] and \[{{r}_{2}}\] are connected in series to an external resistance R Value of R so that the potential difference across the first cell be zero, is
  A)
  \[{{r}_{1}}+{{r}_{2}}\]                    
  done clear
  B)
  \[\frac{{{r}_{1}}}{{{r}_{2}}}\]
  done clear
  C)
  \[{{r}_{1}}-{{r}_{2}}\]
  done clear
  D)
  \[{{r}_{1}}{{r}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer45) Two radioactive sources X and Y of half lives 1h and 2 h respectively initially contain the same number of radioactive atoms. At the  end of 2 h, their rates of disintegration are in the ratio of
  A)
  4: 3                        
  done clear
  B)
  3:4    
  done clear
  C)
  1 :2                        
  done clear
  D)
  2 :1
  done clear
  View Answer play_arrow

• question_answer46) A photon will have less energy, if its
  A)
  wavelength is longer
  done clear
  B)
  wavelength is shorter
  done clear
  C)
  amplitude is less    
  done clear
  D)
  data insufficient
  done clear
  View Answer play_arrow

• question_answer47) The current gain of a transistor in a common base arrangement is 0.98. The change in collector current corresponding to a change of 5 mA in emitter current is
  A)
  0.1 mA                 
  done clear
  B)
  0.2mA
  done clear
  C)
  4.9mA                  
  done clear
  D)
  9.2mA                      
  done clear
  View Answer play_arrow

• question_answer48) B. A plano-convex lens has a curved surface of radius of curvature R and refractive index \[\mu \]. If its plane surface is silvered, then, it behaves as a
  A)
  convex lens                       
  done clear
  B)
  convex mirror
  done clear
  C)
  concave lens                     
  done clear
  D)
  concave mirror
  done clear
  View Answer play_arrow

• question_answer49) An electric bulb is made of tungsten filament  of resistance \[R\Omega \]. It is marked 100W and 230 V. Then, the value of R is
  A)
  300 \[\Omega \]                              
  done clear
  B)
  529 \[\Omega \]  
  done clear
  C)
  739 \[\Omega \]                              
  done clear
  D)
  100\[\Omega \]
  done clear
  View Answer play_arrow

• question_answer50) Which of the following are the properties of fuse wire?
  A)
  Made of alloy of tin
  done clear
  B)
  Has a low melting point
  done clear
  C)
  Connected in series with main supply
  done clear
  D)
  All of the above
  done clear
  View Answer play_arrow

• question_answer51) The site of action of insulin is
  A)
  mitochondria                    
  done clear
  B)
  nucleus
  done clear
  C)
  plasma membrane         
  done clear
  D)
  DNA
  done clear
  View Answer play_arrow

• question_answer52) The wave number of the spectral line in the emission spectrum of hydrogen will be equal to \[\frac{8}{9}\] times the Rydberg's constant if the electron jumps from
  A)
  n = 3 t on =1       
  done clear
  B)
  n =10 to n = 1
  done clear
  C)
  n = 9 t on = 1     
  done clear
  D)
   n=2 t on = 1
  done clear
  View Answer play_arrow

• question_answer53) Which one of the following is an artificial sweetening agent?
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer54)          Nitrobenzene on reduction using zinc in alkaline medium results in X. The number of sigma (\[\sigma \]) and pi (\[\pi \]) bonds in X is
  A)
  \[24\sigma ,7\pi \]                         
  done clear
  B)
  \[24\sigma ,6\pi \]
  done clear
  C)
  \[27\sigma ,7\pi \]                         
  done clear
  D)
  \[27\sigma ,6\pi \]
  done clear
  View Answer play_arrow

• question_answer55) Peroxide ion............ (i) has five completely filled anti bonding  molecular orbitals (ii) is diamagnetic (iii) has bond order one (iv) is isoelectronic with neon Which one of these is correct?
  A)
  (ii) and (iii)         
  done clear
  B)
  (i), (ii) and (iv)
  done clear
  C)
  (i), (ii) and (iii)                   
  done clear
  D)
  (i) and (iv)
  done clear
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• question_answer56) Which one of the following conversions involve change in both hybridisation and shape?
  A)
  \[C{{H}_{4}}\to {{C}_{2}}{{H}_{6}}\]        
  done clear
  B)
  \[N{{H}_{3}}\to NH_{4}^{+}\]
  done clear
  C)
   \[B{{F}_{3}}\to BF_{4}^{-}\]      
  done clear
  D)
  \[{{H}_{2}}O\to {{H}_{3}}{{O}^{+}}\]
  done clear
  View Answer play_arrow

• question_answer57) In chromite ore, the oxidation number of iron and chromium are respectively
  A)
  +3, + 2                                  
  done clear
  B)
  +3, +6 
  done clear
  C)
   +2, + 6                 
  done clear
  D)
  +2, + 3        
  done clear
  View Answer play_arrow

• question_answer58) Identify A and B in the following reactions
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer59) Compound A \[({{C}_{3}}{{H}_{6}}O)\]undergoes following reactions to form B and C. Identify A, 5 and C. \[\underset{A}{\mathop{C\xleftarrow{Zn-Hg/HCl}{{C}_{3}}}}\,\underset{B}{\mathop{\underset{A}{\mathop{{{H}_{6}}}}\,O}}\,\xrightarrow{{{I}_{2}}/NaOH}\underset{C}{\mathop{B}}\,\]
  A)
  \[{{H}_{3}}C-\overset{\text{O}}{\mathop{\overset{\text{ }\!\!|\!\!\text{  }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,-C{{H}_{3}}CH{{l}_{3}}C{{H}_{3}}-C{{H}_{2}}-C{{H}_{3}}\]
  done clear
  B)
  \[{{\text{H}}_{\text{2}}}\text{C=}\underset{\text{H}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{-C}{{\text{H}}_{\text{2}}}\text{OHC}{{\text{H}}_{\text{3}}}\text{l}{{\text{H}}_{\text{3}}}\text{C-C}{{\text{H}}_{\text{2}}}\]
  done clear
  C)
  \[\text{-C}{{\text{H}}_{\text{2}}}\text{-OH}\]                 \[{{\text{H}}_{\text{3}}}\text{C-C}{{\text{H}}_{\text{2}}}\text{-CHO CH}{{\text{l}}_{\text{3}}}\text{ }{{\text{H}}_{\text{3}}}\text{C-}\underset{\text{OH}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{H-C}{{\text{H}}_{\text{3}}}\]
  done clear
  D)
                  \[{{\text{H}}_{\text{3}}}\text{C=}\overset{\text{O}}{\mathop{\overset{\text{ }\!\!|\!\!\text{  }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{-C}{{\text{H}}_{\text{3}}}\text{ CH}{{\text{l}}_{\text{3}}}\text{ }{{\text{H}}_{\text{3}}}\text{C-}\underset{\text{OH}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{H-C}{{\text{H}}_{\text{3}}}\]
  done clear
  View Answer play_arrow

• question_answer60) Which one of the following equations represents the variation of viscosity coefficient (\[\eta \]) with temperature (T)?
  A)
  \[\eta =A{{e}^{-E/RT}}\]              
  done clear
  B)
  \[\eta =A{{e}^{E/RT}}\]
  done clear
  C)
  \[\eta =A{{e}^{-E/kT}}\]              
  done clear
  D)
  \[\eta =A{{e}^{-E/T}}\]
  done clear
  View Answer play_arrow

• question_answer61) Which property among the following is same for both hydrogen and deuterium molecules?
  A)
  Bond energy       
  done clear
  B)
  Melting point
  done clear
  C)
  Boiling point        
  done clear
  D)
  Bond length
  done clear
  View Answer play_arrow

• question_answer62)  Given that \[\text{dE }=\text{ TdS }-\text{ pdV}\] and \[\text{H }=\text{ E }+\text{ pV}\]. Which one of the following relations is true?
  A)
  \[~\text{dH}=\text{ TdS }-\text{ Vdp}\]    
  done clear
  B)
  \[~\text{dH}=\text{SdT}+\text{ Vdp}\]
  done clear
  C)
  \[\text{dH}=-\text{SdT}-\text{Vdp}\]    
  done clear
  D)
  \[\text{dH }=\text{ dE }-\text{ pdV}\]
  done clear
  View Answer play_arrow

• question_answer63) What is the bond angle in \[\text{Cl}{{\text{O}}_{\text{2}}}\text{(OClO)}\]?
  A)
  \[~\text{9}0{}^\circ \]                                   
  done clear
  B)
  \[\text{118}{}^\circ \]    
  done clear
  C)
  \[\text{1}0\text{5}{}^\circ \]                      
  done clear
  D)
  \[\text{111}{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer64) A system is allowed to move from state A to B following path ACB by absorbing 80 J of heat energy. The work done by the system is 30 J.  The work done by the system in reaching state B from A is 10 J through path ADB. Which statements are correct? (i) Increase in internal energy from state A tc state B is 50 J. (ii) If path ADB is followed to reach state B, \[\Delta E=50J\]. (iii)  If work done by the system in path AB is 20J,the heat absorbed during path AB = 70 J. (iv)  The value \[{{E}_{C}}-{{E}_{A}}\]is equal to \[{{E}_{D}}-{{E}_{B}}\]. (v) Heat absorbed by the system to reach B from A through path ADD is 60 J.
  A)
  \[\text{I,V}\]                    
  done clear
  B)
  \[\text{I,III,V}\]
  done clear
  C)
  \[\text{I, II, III, V}\]                        
  done clear
  D)
  \[\text{I,IV,V}\]
  done clear
  View Answer play_arrow

• question_answer65)  Identify the order in which the spin only magnetic moment (in BM) increases for the following four ions \[\text{I}.\text{ F}{{\text{e}}^{\text{2+}}}\]                                        \[\text{II}\text{.T}{{\text{i}}^{\text{2+}}}\] \[\text{III}\text{.C}{{\text{u}}^{\text{2+}}}\]                                      \[\text{IV}\text{.}{{\text{V}}^{\text{2+}}}\]
  A)
  \[\text{I,II, IV, III}\]                        
  done clear
  B)
  \[\text{IV,I, II, III}\]
  done clear
  C)
  \[\text{III,IV, I, II}\]                        
  done clear
  D)
  \[\text{III,II, IV, I}\]
  done clear
  View Answer play_arrow

• question_answer66) Which one of the following statements is not correct?
  A)
  Moissan boron is amorphous
  done clear
  B)
  The reaction between boron and concentrated \[\text{HN}{{\text{O}}_{\text{3}}}\]gives \[{{\text{N}}_{\text{2}}}\text{O}\]
  done clear
  C)
  Amorphous boron on heating with oxygen forms \[{{\text{B}}_{\text{2}}}{{\text{O}}_{\text{3}}}\]
  done clear
  D)
  Boron is a non-conductor of electricity
  done clear
  View Answer play_arrow

• question_answer67) In photoelectric effect, if the energy required to overcome the attractive forces on the electron, (work functions) of Li, Na and Rb are\[\text{2}.\text{41 eV}\], \[\text{2}.\text{3}0\text{ eV}\] and \[\text{2}.0\text{9 eV}\] respectively, the work function of 'K' could approximately be in eV.
  A)
  2.52                                       
  done clear
  B)
  2.20
  done clear
  C)
  2.35                                       
  done clear
  D)
  2.01
  done clear
  View Answer play_arrow

• question_answer68) The oxoacid of sulphur which contains two sulphur atoms in different oxidation states is
  A)
  pyrosulphurous acid
  done clear
  B)
  hyposulphurous acid
  done clear
  C)
   pyrosulphuric add
  done clear
  D)
  persutphuric acid
  done clear
  View Answer play_arrow

• question_answer69) The correct sequence of reactions to convert p-nitrophenol into quinol involves
  A)
  reduction, diazotization and hydrolysis
  done clear
  B)
  hydrolysis, diazotization and reduction
  done clear
  C)
  hydrolysis, reduction and diazotization
  done clear
  D)
  diazotization, reduction and hydrolysis
  done clear
  View Answer play_arrow

• question_answer70) The compound obtained when acetaldehyde reacts with dilute aqueous sodium hydroxide exhibits
  A)
  geometrical isomerism
  done clear
  B)
  optical isomerism
  done clear
  C)
   neither optical nor geometrical isomerism
  done clear
  D)
   both optical and geometrical isomerism
  done clear
  View Answer play_arrow

• question_answer71) An oxygen containing organic compound  upon oxidation forms a carboxylic acid as the only organic product with its molecular mass higher by 14 units. The organic compound is
  A)
  an aldehyde                      
  done clear
  B)
  a orimary alcohol
  done clear
  C)
  a secondary alcohol       
  done clear
  D)
  a ketone
  done clear
  View Answer play_arrow

• question_answer72) A buffer solution contains 0.1 mole of sodium acetate in \[\text{1}000\text{ c}{{\text{m}}^{\text{3}}}\]of 0.1 M acetic acid. To the above buffer solution, 0.1 mole of sodium acetate is further added and dissolved. The pH of the resulting buffer is equal to
  A)
  \[p{{K}_{a}}-\log 2\]                      
  done clear
  B)
  \[p{{K}_{a}}\]
  done clear
  C)
  \[p{{K}_{a}}+2\]              
  done clear
  D)
  \[p{{K}_{a}}+\log 2\]
  done clear
  View Answer play_arrow

• question_answer73) Which one of the following is wrongly matched?
  A)
  \[{{\text{ }\!\![\!\!\text{ Cu(N}{{\text{H}}_{\text{3}}}{{\text{)}}_{\text{4}}}\text{ }\!\!]\!\!\text{ }}^{\text{2+}}}\] -Square planar
  done clear
  B)
  \[\text{ }\!\![\!\!\text{ Ni(CO}{{\text{)}}_{\text{4}}}\text{ }\!\!]\!\!\text{ }\] - Neutral ligand
  done clear
  C)
  \[\text{ }\!\![\!\!\text{ Fe(CN)}_{6}^{3-}\text{ }\!\!]\!\!\text{ }\]   - \[\text{ }\!\![\!\!\text{ Fe(CN)}_{6}^{3-}\text{ }\!\!]\!\!\text{ s}{{\text{p}}^{3}}{{d}^{2}}\]
  done clear
  D)
  \[{{\text{ }\!\![\!\!\text{ Co(en}{{\text{)}}_{3}}\text{ }\!\!]\!\!\text{ }}^{3+}}\]- Follows EAN rule
  done clear
  View Answer play_arrow

• question_answer74) The activation energy for a reaction at the temperature T K was found to be 2. 303 RT J \[\text{mo}{{\text{l}}^{\text{-1}}}\]. The ratio of the rate constant to Arrhenius factor is
  A)
  \[\text{1}{{0}^{\text{-1}}}\]                                       
  done clear
  B)
  \[\text{1}{{0}^{\text{-2}}}\]
  done clear
  C)
  \[\text{2}\times \text{1}{{0}^{\text{-3}}}\]                         
  done clear
  D)
  \[\text{2}\times \text{1}{{0}^{\text{-2}}}\]
  done clear
  View Answer play_arrow

• question_answer75) Match the following

  Column I	Column II
  (A) Potential of hydrogen electrode at pH =10 (B) \[C{{u}^{2+}}|Cu\] (C) \[Zn|Z{{n}^{2+}}\] (D) \[\frac{2.303RT}{F}\]	(I) 0.76V (II) 0.059 (III) -0.591 V (IV) 0.337V (V) -0.76V

            A             B             C             D
  A)
                                  (III)         (I)           (II)          (V)
  done clear
  B)
                  (II)          (v)          (I)           (IV)
  done clear
  C)
                  (III)         (IV)        (I)           (II)
  done clear
  D)
                  (V)          (I)           (IV)        (II)
  done clear
  View Answer play_arrow

• question_answer76) The formal charges of \[{{\text{N}}_{\text{(1)}}}\text{,}{{\text{N}}_{\text{(2)}}}\]and O atoms in are respectively
  A)
  \[+1,-1,0\]                          
  done clear
  B)
  \[-1,+1,0\]
  done clear
  C)
  \[+1,+1,0\]                         
  done clear
  D)
  \[-1,-1,0\]
  done clear
  View Answer play_arrow

• question_answer77) g of silver gets distributed between \[\text{1}0\text{ c}{{\text{m}}^{\text{3}}}\]of molten zinc and \[\text{1}00\text{ c}{{\text{m}}^{\text{3}}}\]of molten lead at\[\text{8}00{}^\circ \text{ C}\]. The percentage of silver in the zinc layer is approximately
  A)
  89                          
  done clear
  B)
  91     
  done clear
  C)
  97                          
  done clear
  D)
  94
  done clear
  View Answer play_arrow

• question_answer78) Carbon can reduce ferric oxide to iron at a temperature above 983 K because
  A)
   carbon monoxide formed is thermodynamically less stable than ferric oxide
  done clear
  B)
   carbon has a higher affinity towards oxidation than iron
  done clear
  C)
  free energy change for the formation of carbon  dioxide is less negative than that for ferric oxide
  done clear
  D)
  iron has a higher affinity towards oxygen than carbon
  done clear
  View Answer play_arrow

• question_answer79) Which one of the following is the ratio of the  lowering of vapour pressure of 0.1 M aqueous solutions of \[\text{BaC}{{\text{l}}_{2}}\], \[\text{NaCl}\] and \[\text{A}{{\text{l}}_{2}}{{(S{{O}_{4}})}_{3}}\] respectively?
  A)
  3 : 2 : 5                 
  done clear
  B)
  5 : 2 : 3  
  done clear
  C)
  5 : 3 : 2                                 
  done clear
  D)
  2 : 3 : 5
  done clear
  View Answer play_arrow

• question_answer80) In which one of the following, does the given amount of chlorine exert the least pressure in a vessel of capacity \[\text{1 d}{{\text{m}}^{\text{3}}}\]at 273 K?
  A)
   0.0355 g 
  done clear
  B)
  0.071 g
  done clear
  C)
  \[\text{6}.0\text{23 }\times \text{1}{{0}^{\text{21}}}\]molecules
  done clear
  D)
  0.02 mol
  done clear
  View Answer play_arrow

• question_answer81) 19 g of a mixture containing \[\text{NaHC}{{\text{O}}_{\text{3}}}\]and \[N{{a}_{2}}C{{O}_{3}}\]on complete heating liberated 1.12 L of \[C{{O}_{2}}\] at STP. The weight of the remaining solid was 15.9 g. What is the weight (in g) of \[N{{a}_{2}}C{{O}_{3}}\]in the mixture before heating?
  A)
  8.4                                         
  done clear
  B)
  15.9
  done clear
  C)
  4.0                                         
  done clear
  D)
  1.6
  done clear
  View Answer play_arrow

• question_answer82) Match the following

  Column I	Column II
  (A) Acetaldehyde, Vinyl alcohol (B) Eclipsed and staggered ethane (C) (+) 2-butanol, (-) 2- butanol (D) Methyl-n- propylamine and diethylamine	1. Enantiomers 2. Tautomers 3. Chain isomers 4. Conformational isomers  5. Metamers

  A)
  A     B      C      D                 1     4      3       5
  done clear
  B)
                  2     4      1       5
  done clear
  C)
                  5     1      4       2
  done clear
  D)
                   5     1      3      2
  done clear
  View Answer play_arrow

• question_answer83) With respect to chlorobenzene, which of the following statements is not correct?
  A)
  \[\text{Cl}\] is ortho/para directing
  done clear
  B)
  \[\text{Cl}\] exhibits +M effect                   
  done clear
  C)
   \[\text{Cl}\] is ring deactivating
  done clear
  D)
  \[\text{Cl}\] is meta directing
  done clear
  View Answer play_arrow

• question_answer84) The product(s) formed when \[{{H}_{2}}{{O}_{2}}\] reacts with disodium hydrogen phosphate is
  A)
  \[{{P}_{2}}{{O}_{5}}.N{{a}_{3}}P{{O}_{4}}\]         
  done clear
  B)
  \[N{{a}_{2}}HP{{O}_{4}}.{{H}_{2}}{{O}_{2}}\]
  done clear
  C)
  \[Na{{H}_{2}}P{{O}_{4}},{{H}_{2}}O\]    
  done clear
  D)
  \[N{{a}_{2}}HP{{O}_{4}}.{{H}_{2}}O\]
  done clear
  View Answer play_arrow

• question_answer85)  The correct sequence of steps involved in the mechanism of Cannizzaro's reaction is
  A)
  nucleophilic attack, transfer of \[{{\text{H}}^{\text{-}}}\] and transfer of \[{{\text{H}}^{+}}\]
  done clear
  B)
  transfer of \[{{\text{H}}^{-}}\], transfer of \[{{\text{H}}^{+}}\] and nucleophilic attack
  done clear
  C)
  transfer of \[{{\text{H}}^{+}}\] , nucleophilic attack and transfer of \[{{\text{H}}^{-}}\]
  done clear
  D)
  electrophilic attack by \[\text{O}{{\text{H}}^{-}}\], transfer of \[{{\text{H}}^{-}}\] and
  done clear
  View Answer play_arrow

• question_answer86) What is Z in the following reactions? \[\text{BC}{{\text{l}}_{\text{3}}}\text{+}{{\text{H}}_{\text{2}}}\xrightarrow[\text{45}{{\text{0}}^{\text{o}}}\text{-C}]{\text{Cu-Al}}\text{X+HCl}\] \[\text{X}\xrightarrow{\text{methylation}}Z\]
  A)
  \[(C{{H}_{3}})B{{H}_{2}}\]           
  done clear
  B)
  \[(C{{H}_{3}}){{B}_{2}}{{H}_{2}}\]
  done clear
  C)
  \[{{(C{{H}_{3}})}_{3}}{{B}_{2}}{{H}_{3}}\]             
  done clear
  D)
  \[{{(C{{H}_{3}})}_{6}}{{B}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer87) The empirical formula of a non-electrolyte is\[\text{C}{{\text{H}}_{\text{2}}}\text{O}\]. A solution containing 6g of the compound exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The molecular formula of the compound is
  A)
  \[{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{4}}}{{\text{O}}_{\text{2}}}\]                
  done clear
  B)
  \[{{\text{C}}_{3}}{{\text{H}}_{6}}{{\text{O}}_{3}}\]
  done clear
  C)
  \[{{\text{C}}_{5}}{{\text{H}}_{10}}{{\text{O}}_{5}}\]                       
  done clear
  D)
  \[{{\text{C}}_{4}}{{\text{H}}_{8}}{{\text{O}}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer88) \[{{E}_{1}},{{E}_{2}},{{E}_{3}}\]are the emf values of the three galvanic cells respectively. (i) \[\text{Zn }\!\!|\!\!\text{ Zn}_{\text{1M}}^{\text{2+}}\text{ }\!\!|\!\!\text{  }\!\!|\!\!\text{ Cu}_{\text{0}\text{.1M}}^{\text{2+}}\text{ }\!\!|\!\!\text{ Cu}\]                     (ii) \[Zn|Zn_{1M}^{2+}||Cu_{1M}^{2+}|Cu\] (iii) \[Zn|Zn_{0.1M}^{2+}||Cu_{1M}^{2+}|Cu\] Which one of the following is true?
  A)
  \[{{E}_{2}}>{{E}_{3}}>{{E}_{1}}\]              
  done clear
  B)
  \[{{E}_{3}}>{{E}_{2}}>{{E}_{1}}\]
  done clear
  C)
  \[{{E}_{1}}>{{E}_{2}}>{{E}_{3}}\]              
  done clear
  D)
  \[{{E}_{1}}>{{E}_{3}}>{{E}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer89) In Kjeldahl's method, ammonia from 5 got food neutralizes \[\text{3}0\text{ c}{{\text{m}}^{\text{3}}}\] of 0.1 N acid. The percentage of nitrogen in the food is
  A)
   0.84                      
  done clear
  B)
  8.4      
  done clear
  C)
  16.8                       
  done clear
  D)
  1.68
  done clear
  View Answer play_arrow

• question_answer90) Which one of the following has the most nucleophilic nitrogen?
  A)
                                         
  done clear
  B)
         
  done clear
  C)
                                                               
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer91)     \[\text{C}{{\text{H}}_{\ }}_{\text{3}}\text{C}{{\text{H}}_{\text{2}}}\text{Br}\xrightarrow[\text{ }\!\!\Delta\!\!\text{ }]{\text{aq}\text{.KOH}}\text{A}\xrightarrow[\text{ }\!\!\Delta\!\!\text{ }]{\text{KMn}{{\text{O}}_{\text{4}}}\text{/}{{\text{H}}^{\text{+}}}}\] \[\text{B}\xrightarrow[\text{ }\!\!\Delta\!\!\text{ }]{\text{N}{{\text{H}}_{\text{3}}}}\text{C}\xrightarrow[\text{alkali}]{\text{B}{{\text{r}}_{\text{2}}}}\text{D, }\!\!'\!\!\text{ D }\!\!'\!\!\text{ }\]is
  A)
  \[\text{C}{{\text{H}}_{\text{3}}}\text{Br}\]                        
  done clear
  B)
  \[\text{C}{{\text{H}}_{\text{3}}}\text{CON}{{\text{H}}_{\text{2}}}\]
  done clear
  C)
  \[\text{C}{{\text{H}}_{\text{3}}}\text{N}{{\text{H}}_{\text{2}}}\]                            
  done clear
  D)
  \[CHB{{r}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer92) The enthalpy changes for the following processes are listed below        \[\text{C}{{\text{l}}_{\text{2}}}\text{(g)}\to \text{2Cl(g),242}\text{.3 kJ mo}{{\text{l}}^{\text{-1}}}\] \[{{\text{I}}_{\text{2}}}\text{(g)}\to \text{2I(g),151}\text{.0 kJ mo}{{\text{l}}^{\text{-1}}}\] \[\text{ICl(g)}\to \text{I(g)+Cl(g),211}\text{.3 kJ mo}{{\text{l}}^{\text{-1}}}\] \[{{\text{I}}_{\text{2}}}\text{(g)}\to {{\text{I}}_{\text{2}}}\text{(g),62}\text{.76 kJ mo}{{\text{l}}^{\text{-1}}}\] Given that the standard states for iodine and chlorine are\[{{I}_{2}}(s)\] and \[C{{l}_{2}}(g),\] the standard enthalpy for the formation of \[ICl(g)\] is
  A)
  \[-\text{14}.\text{6 kJ mo}{{\text{l}}^{\text{-1}}}\]      
  done clear
  B)
  \[-\text{16}.\text{8 kJ mo}{{\text{l}}^{\text{-1}}}\]
  done clear
  C)
  \[+\text{16}.\text{8 kJ mo}{{\text{l}}^{-}}^{\text{1}}\]    
  done clear
  D)
  \[+\text{244}.\text{8 kJ mo}{{\text{l}}^{\text{-1}}}\]
  done clear
  View Answer play_arrow

• question_answer93) \[\text{2}.\text{5 mL}\] of \[\frac{2}{5}M\] weak monoacidic base\[({{K}_{b}}=1\times {{10}^{-12}}\text{ at 2}{{\text{5}}^{\circ }}C)\] is titrated with \[\frac{2}{15}M\] \[\text{HCl}\] in water at\[\text{25}{}^\circ \text{C}\]. The concentration of \[{{\text{H}}^{\text{+}}}\] at equivalence point is\[({{K}_{\omega }}=1\times {{10}^{-14}}\text{ at 2}{{\text{5}}^{\circ }}C)\]
  A)
  \[\text{3}.\text{7}\times \text{1}0{{-}^{\text{13}}}\text{M}\]                   
  done clear
  B)
  \[3.2\times {{10}^{-7}}M\]
  done clear
  C)
  \[3.2\times {{10}^{-2}}M\]                          
  done clear
  D)
  \[2.2\times {{10}^{-2}}M\]
  done clear
  View Answer play_arrow

• question_answer94) Three reactions involving \[{{\text{H}}_{\text{2}}}\text{PO}_{\text{4}}^{\text{-}}\] are given below \[\text{I}\text{.}\] \[{{\text{H}}_{\text{3}}}\text{P}{{\text{O}}_{\text{4}}}\text{+}{{\text{H}}_{\text{2}}}\text{O}\to {{\text{H}}_{\text{3}}}{{\text{O}}^{\text{+}}}\text{+}{{\text{H}}_{\text{2}}}\text{PO}_{\text{4}}^{\text{-}}\] \[\text{II}\text{. }{{\text{H}}_{2}}\text{PO}_{4}^{-}\text{+}{{\text{H}}_{\text{2}}}\text{O}\to \text{HPO}_{4}^{2-}\text{+}{{\text{H}}_{3}}{{\text{O}}^{+}}\] \[\text{III}\text{. }{{\text{H}}_{\text{2}}}\text{PO}_{\text{4}}^{\text{-}}\text{+O}{{\text{H}}^{\text{-}}}\to {{\text{H}}_{\text{3}}}\text{P}{{\text{O}}_{\text{4}}}\text{+}{{\text{O}}^{\text{2-}}}\] In which of the above does H^O^ act as an acid?
  A)
  II only                   
  done clear
  B)
  I and II  
  done clear
  C)
  III only                                 
  done clear
  D)
  l only
  done clear
  View Answer play_arrow

• question_answer95) The correct IUPAC name of tartaric acid is
  A)
  1,  4-dicarboxy-2. 3-dihydroxyethane
  done clear
  B)
  \[\text{ }\!\!\alpha\!\!\text{ , }\!\!\alpha\!\!\text{  }\!\!'\!\!\text{ }\] -dihydroxybutane-1. 4-dioic acid
  done clear
  C)
  1, 4-dihydroxybutane-2, 3-dioic acid
  done clear
  D)
  2, 3-dihydroxybutane-1, 4-dioic acid
  done clear
  View Answer play_arrow

• question_answer96)          Correct order of stability is
  A)
  \[\text{I}>\text{IV}>\text{II}>\text{III}\]  
  done clear
  B)
  \[\text{I}>\text{II}>\text{III}>\text{IV}\]
  done clear
  C)
  \[\text{I}>\text{II}>\text{IV}>\text{III}\]             
  done clear
  D)
  \[\text{I}>\text{III}>\text{IV}>\text{II}\]
  done clear
  View Answer play_arrow

• question_answer97) Match the Column I and II and pick the correct  Matching from the codes given below.

  Column 1	Column II
  A. Polycyclic aromatic hydrocarbons B. Dioxins C. IR active molecules D. Peroxy acetyl nitrate	1. Global warming 2. Photochemical 3. Carcinogens 4. Waste incineration

  A)
  A     B      C      D                 3      4      1       2
  done clear
  B)
                  4      3      2       1
  done clear
  C)
                  3      4      2       1
  done clear
  D)
                   1      2      3      4
  done clear
  View Answer play_arrow

• question_answer98) 48.          Consider the following statements. I. \[\text{La}{{\left( \text{OH} \right)}_{\text{3}}}\]is the least basic among hydroxides of lanthanides. II. \[Z{{r}^{4+}}\]and \[\text{H}{{\text{f}}^{\text{4+}}}\]possess almost the same ionic radii. III. \[C{{e}^{4+}}\] can act as an oxidising agent. Which of the above is/are true?
  A)
  l and III                
  done clear
  B)
  II and III
  done clear
  C)
  II only                   
  done clear
  D)
  l and II
  done clear
  View Answer play_arrow

• question_answer99) Concentrated hydrochloric acid when kept in  open air sometimes produces a cloud of white fumes. The explanation for it is that
  A)
  concentrated hydrochloric acid emits strongly smelling HC1 gas all the time
  done clear
  B)
   oxygen in air reacts with the emitted HCl gas to form a could of chlorine gas
  done clear
  C)
  strong affinity of HCl gas for moisture in air results in forming of droplets of liquid solution which appears like a cloudy smoke
  done clear
  D)
  due to strong affinity for water, concentrated hydrochloric acid pulls moisture of air towards itself. This moisture forms droplets of water and hence, the cloud.
  done clear
  View Answer play_arrow

• question_answer100)  Compartments A and B have the following    combinations solution                       

  Column 1	Column II
  I. \[\text{0}\text{.1M KCl}\] II. \[\text{0}\text{.1 }\!\!%\!\!\text{ (m/V)NaCl}\] III. \[\text{18g}{{\text{L}}^{-1}}\] glucose IV. \[\text{20 }\!\!%\!\!\text{  (m/V)}\]	\[\text{0}\text{.2 M KCl}\] \[\text{10 }\!\!%\!\!\text{ (m/V)NaCl}\] \[34.2g{{L}^{-1}}\]sucrose \[\text{10 }\!\!%\!\!\text{ (m/V)}\]glucose

  Indicate the number of solutions which is/are isotonic
  A)
                                  I only                    
  done clear
  B)
  III only
  done clear
  C)
                                  IV only                 
  done clear
  D)
  II only
  done clear
  View Answer play_arrow

• question_answer101) The value of \[\int_{{}}^{{}}{\frac{dx}{(1+{{x}^{2}})\sqrt{1-{{x}^{2}}}}}\] is *-correct-answer-description-* Let \[\int_{{}}^{{}}{\frac{dx}{(1+{{x}^{2}})\sqrt{1-{{x}^{2}}}}}\] Put \[x=\frac{1}{t}\Rightarrow dx=-\frac{1}{{{t}^{2}}}dt\] Then, \[l=\int_{{}}^{{}}{\frac{-dt}{{{t}^{2}}\left( 1+\frac{1}{{{t}^{2}}} \right)\sqrt{1-{{\left( \frac{1}{t} \right)}^{2}}}}}\] \[=-\int_{{}}^{{}}{\frac{tdt}{({{t}^{2}}+1)\sqrt{{{t}^{2}}-1}}}\]                 Again put \[{{\text{t}}^{\text{2}}}\text{-1 = }{{\text{z}}^{\text{2 }}}\Rightarrow \text{t dt = z dz}\]                 Then  , \[\text{l = -}\int_{{}}^{{}}{\frac{\text{z dz}}{\text{(}{{\text{z}}^{\text{2}}}\text{+2) z}}}\]                 \[=-\int_{{}}^{{}}{\frac{1}{{{z}^{2}}+2}}dz\]                 \[=-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{z}{\sqrt{2}} \right)+C\]                 \[=-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sqrt{{{t}^{2}}-1}}{\sqrt{2}} \right)+C\]                 \[=-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sqrt{1-{{x}^{2}}}}{\sqrt{2}x} \right)+C\]
  A)
  \[-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sqrt{1-{{x}^{2}}}}{\sqrt{2x}} \right)+C\]
  done clear
  B)
  \[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sqrt{1-{{x}^{2}}}}{\sqrt{2x}} \right)+C\]
  done clear
  C)
  \[-{{\tan }^{-1}}\left( \frac{\sqrt{1-{{x}^{2}}}}{\sqrt{2x}} \right)+C\]
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer102) The value of \[\int_{0}^{\pi }{e{{\sin }^{{{2}_{x}}}}{{\cos }^{3}}xdx}\]is
  A)
   -1                          
  done clear
  B)
  0       
  done clear
  C)
  1                             
  done clear
  D)
  \[\pi \]
  done clear
  View Answer play_arrow

• question_answer103) The area bounded by \[y={{\sin }^{-1}}x,x=\frac{1}{\sqrt{2}}\] and \[X-\]axis is
  A)
  \[\frac{1}{\sqrt{2}}+1\]                
  done clear
  B)
  \[1-\frac{1}{\sqrt{2}}\]
  done clear
  C)
  \[\frac{\pi }{4\sqrt{2}}\]                               
  done clear
  D)
  \[\frac{\pi }{4\sqrt{2}}+\frac{1}{\sqrt{2}}-1\]
  done clear
  View Answer play_arrow

• question_answer104) The solution of the differential equation \[\frac{dy}{dx}={{e}^{x-y}}({{e}^{x}}-{{e}^{y}})\]
  A)
  \[{{e}^{y}}=({{e}^{x}}+1)+C{{e}^{-{{e}^{x}}}}\]
  done clear
  B)
  \[{{e}^{y}}=({{e}^{x}}-1)+C\]
  done clear
  C)
  \[{{e}^{y}}=({{e}^{x}}-1)+C{{e}^{-{{e}^{x}}}}\]
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer105) Let a, b and c be non-zero vectors such that no two are collinear and \[(a\times b)\times c=\frac{1}{3}\]\[b||c|\]\[|a.\] If  \[\theta \] is the acute angle between the vectors b and c, then sin \[\theta \] is equal to
  A)
   \[\frac{2\sqrt{2}}{3}\]  
  done clear
  B)
  \[\frac{\sqrt{2}}{3}\]
  done clear
  C)
  \[\frac{2}{3}\]                                   
  done clear
  D)
  \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer106) On the interval [0,1], the function\[{{x}^{25}}{{(1-x)}^{75}}\] takes its maximum value at the point
  A)
  0                                             
  done clear
  B)
  \[\frac{1}{4}\]
  done clear
  C)
  \[\frac{1}{2}\]                                   
  done clear
  D)
  \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer107) The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases when the side is 10 cm, is
  A)
  \[\sqrt{3}c{{m}^{2}}/s\]
  done clear
  B)
  \[10c{{m}^{2}}/s\]
  done clear
  C)
  \[10\sqrt{3}c{{m}^{2}}/s\]
  done clear
  D)
  \[\frac{10}{\sqrt{3}}c{{m}^{2}}/s\]
  done clear
  View Answer play_arrow

• question_answer108) The slope of the normal to the curve\[x=1-a\sin \theta ,y=b{{\cos }^{2}}\theta \] at \[\theta =\frac{\pi }{2}\]is
  A)
  \[\frac{a}{2b}\]                                
  done clear
  B)
  \[\frac{2a}{b}\]
  done clear
  C)
  \[\frac{a}{b}\]                                  
  done clear
  D)
  \[\frac{-a}{2b}\]
  done clear
  View Answer play_arrow

• question_answer109) The    angle    between    the    line \[\frac{3x-1}{3}=\frac{y+3}{-1}=\frac{5-2z}{4}\]and   the   plane\[3x-3y-6z=10\] is equal to
  A)
  \[\frac{\pi }{6}\]                                              
  done clear
  B)
  \[\frac{\pi }{4}\]
  done clear
  C)
  \[\frac{\pi }{3}\]                                              
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer110) The equation of the plane meets the axes in A, and C such that the centroid of the \[\Delta \]ABC is\[\left( \frac{1}{3},\frac{1}{3},\frac{1}{3} \right),\] is given by
  A)
  \[x+y+z=1\]                       
  done clear
  B)
  \[x+y+z=2\]
  done clear
  C)
  \[\frac{x}{3}+\frac{y}{3}+\frac{z}{3}=3\]               
  done clear
  D)
  \[x+y+z=\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer111) The probability that a student get success in a competition is \[\frac{3}{4}\]. The probability that exactly 2 out of 4 students get success, is
  A)
  \[\frac{9}{41}\]                                
  done clear
  B)
  \[\frac{25}{128}\]
  done clear
  C)
  \[\frac{1}{5}\]                                   
  done clear
  D)
  \[\frac{27}{128}\]
  done clear
  View Answer play_arrow

• question_answer112) In a certain town, 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is
  A)
  10000                   
  done clear
  B)
  20000
  done clear
  C)
  30000                   
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer113) The function \[f:R\to R\] is defined by \[f\left( x \right)={{3}^{-x}}\]. Observe the following statements I. \[f\] is one-one. II. \[f\] is onto. III.\[f\] s a decreasing function. Out of these, true statements are
  A)
  I, III           
  done clear
  B)
  II, Ill
  done clear
  C)
   l, ll                         
  done clear
  D)
  All of these    
  done clear
  View Answer play_arrow

• question_answer114)       1f \[\left| z-\frac{4}{z} \right|=2\], then the maximum value of \[|z|\] is  equal to
  A)
  \[\sqrt{3}+1\]                   
  done clear
  B)
  \[\sqrt{5}+1\]
  done clear
  C)
  \[2\]                                     
  done clear
  D)
  \[2+\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer115) If P, Q, R and S are represented by the complex numbers  \[4+i,\] \[1+6i,\] \[-4+3i,\] \[-1-2i\] respectively, then PQRS is a     
  A)
  rectangle            
  done clear
  B)
  square
  done clear
  C)
  rhombus             
  done clear
  D)
  parallelogram
  done clear
  View Answer play_arrow

• question_answer116) If\[x={{\log }_{\alpha }}bc,\] \[y={{\log }_{b}}ca\]and \[z={{\log }_{c}}ab\], then the value of\[\frac{1}{1+x}+\frac{1}{1+y}+\frac{1}{1+z}\] will be
  A)
  x + y + z               
  done clear
  B)
  1
  done clear
  C)
  ab + bc + ca       
  done clear
  D)
  abc
  done clear
  View Answer play_arrow

• question_answer117) If\[\alpha \] and \[\beta \]are the roots of \[{{x}^{\text{2}}}+5x+\text{ 4 }=\text{ }0,\] then equation whose roots are \[\frac{\alpha +2}{3}\] and \[\frac{\beta +2}{3}\], is
  A)
  \[9{{x}^{2}}+3x+2=0\]                   
  done clear
  B)
  \[9{{x}^{2}}-\text{ }3x+2\text{ }=0\]
  done clear
  C)
  \[9{{x}^{2}}+\text{ }3x-2\text{ }=\text{ }0\]        
  done clear
  D)
  \[9{{x}^{2}}-\text{ }3x+\text{ }2\text{ }=0\]
  done clear
  View Answer play_arrow

• question_answer118) If one of the roots of equation \[{{x}^{2}}+ax\text{ }+\text{3 }=\text{ }0\]  is 3 and one of the roots of the equation \[~{{x}^{2}}+ax+\text{ }b=0\] is three times the other root, then the value of b is
  A)
   3                                            
  done clear
  B)
  4      
  done clear
  C)
  2                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer119) If sum of the series \[\sum\limits_{n=0}^{\infty }{{{r}^{n}}=S}\]for \[|r|<1,\] then sum of the series \[\sum\limits_{n=0}^{\infty }{{{r}^{2n}}}\]is
  A)
  \[{{S}^{2}}\]                                      
  done clear
  B)
  \[\frac{{{S}^{2}}}{2S+1}\]
  done clear
  C)
  \[\frac{2S}{{{S}^{2}}-1}\]                             
  done clear
  D)
  \[\frac{{{S}^{2}}}{2S-1}\]
  done clear
  View Answer play_arrow

• question_answer120) The term independent of \[x\] in the expansion of \[{{\left( x-\frac{1}{x} \right)}^{4}}{{\left( x+\frac{1}{x} \right)}^{3}}\]is
  A)
  -3                                           
  done clear
  B)
  0
  done clear
  C)
  3                                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer121) The value of \[\left( \frac{^{50}{{C}_{0}}}{1}+\frac{^{50}{{C}_{2}}}{3}+.....+\frac{^{50}{{C}_{50}}}{51} \right)\] is
  A)
  \[\frac{{{2}^{50}}}{51}\]                                               
  done clear
  B)
  (b) \[\frac{{{2}^{50}}-1}{51}\]
  done clear
  C)
  \[\frac{{{2}^{50}}-1}{50}\]                           
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer122) If \[\left| \begin{matrix}    {{x}^{2}}+x & 3x-1 & -x+3  \\    2x+1 & 2+{{x}^{2}} & {{x}^{3}}-3  \\    x-3 & {{x}^{2}}+4 & 3x  \\ \end{matrix} \right|\] \[={{a}_{0}}+{{a}_{1}}x\] \[+{{a}_{2}}{{x}^{2}}+.....+{{a}_{7}}{{x}^{7}},\]then the value of \[{{a}_{0}}\] is
  A)
  25
  done clear
  B)
  24
  done clear
  C)
  23
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer123) Let A be a square matrix, all of whose en are integers. Then, which one of the follow! true?
  A)
  If det\[\left( \text{A} \right)=\pm \text{ 1},\], then\[{{A}^{-1}}\] need not exist
  done clear
  B)
  lf det, \[\left( \text{A} \right)=\pm \text{ 1},\] then \[{{A}^{-1}}\] exists but all its entrie not necessarily integers
  done clear
  C)
  lf det \[\text{(A)}\ne \pm 1,\] then \[{{A}^{-1}}\]exists and all its entrie non-integers
  done clear
  D)
  If det\[\left( \text{A} \right)=\pm \text{ 1,}\], then\[{{A}^{-1}}\] exists and all its entries ?integers
  done clear
  View Answer play_arrow

• question_answer124) If      \[\sin A-\sqrt{6}\cos A=\sqrt{7}\cos A,\]then \[\cos A+\sqrt{6}\sin A\]is equal to
  A)
  \[\sqrt{\text{6}}\text{sinA}\]                      
  done clear
  B)
  \[-\sqrt{\text{7}}\text{sinA}\]
  done clear
  C)
  \[\sqrt{6}\cos A\]                             
  done clear
  D)
  \[\sqrt{7}\cos A\]
  done clear
  View Answer play_arrow

• question_answer125) 25.          The maximum value of \[4{{\sin }^{2}}x-12\sin x+7\] is
  A)
  25                                          
  done clear
  B)
   4
  done clear
  C)
  Does not exist  
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer126) The number of values of \[x\] in \[[0,2\pi ]\]satisfying  the equation \[3\text{ }\cos \text{ }2x-10\text{ }\cos \text{ }x\text{ }+\text{ }7\text{ }=\text{ }0\] is
  A)
  1                                             
  done clear
  B)
  2      
  done clear
  C)
  3                                             
  done clear
  D)
  4
  done clear
  View Answer play_arrow

• question_answer127) \[\tan \left[ \frac{\pi }{4}+\frac{1}{2}{{\cos }^{-1}}\left( \frac{a}{b} \right) \right]+\tan \left[ \frac{\pi }{4}-\frac{1}{2}{{\cos }^{-1}}\left( \frac{a}{b} \right) \right]\]is equal to
  A)
  \[\frac{2a}{b}\]                                
  done clear
  B)
  \[\frac{2b}{a}\]
  done clear
  C)
  \[\frac{a}{b}\]                                  
  done clear
  D)
  \[\frac{b}{a}\]
  done clear
  View Answer play_arrow

• question_answer128) If in a \[\Delta \text{ABC}\], the altitudes from the vertices A, B and C on opposite sides are in HP, then sin A, sin B, sin C are in
  A)
  HP
  done clear
  B)
  arithoietic-geometric progression
  done clear
  C)
  AP
  done clear
  D)
  GP
  done clear
  View Answer play_arrow

• question_answer129) In a\[\Delta \Alpha \Beta C\], if\[{{r}_{1}}=2{{r}_{2}}=3{{r}_{3}},\], then
  A)
  \[\frac{a}{b}=\frac{4}{5}\]                           
  done clear
  B)
  \[\frac{a}{b}=\frac{5}{4}\]
  done clear
  C)
  \[a+b-2c=0\]     
  done clear
  D)
  \[2a=b+c\]
  done clear
  View Answer play_arrow

• question_answer130) The base of a cliff is circular. From the extremities of a diameter of the base, angles  of elevation of the top of the cliff are \[\text{3}0{}^\circ \] and\[\text{6}0{}^\circ \]. If the height of the cliff be 500 m, then diameter of the base of the cliff is
  A)
  \[\frac{2000}{\sqrt{3}}m\]                          
  done clear
  B)
  \[\frac{1000}{\sqrt{3}}m\]
  done clear
  C)
  \[\frac{2000}{\sqrt{2}}m\]                          
  done clear
  D)
  \[1000\sqrt{3}m\]
  done clear
  View Answer play_arrow

• question_answer131) The intercepts on the straight line \[y=mx\] by the lines y = 2 and y = 6 is less than 5, then m belongs to
  A)
  \[\left] -\frac{4}{3},\frac{4}{3} \right[\]                 
  done clear
  B)
  \[\left] \frac{4}{3},\frac{3}{8} \right[\]
  done clear
  C)
   \[\left. \left] -\infty ,\frac{-4}{3}, \right[\cup  \right]\frac{4}{3},\infty \left[ \begin{align}   &  \\  &  \\ \end{align} \right.\]
  done clear
  D)
  \[\left] \frac{4}{3},\infty  \right[\]
  done clear
  View Answer play_arrow

• question_answer132) Let A (2, -3) and B (-2,1) be vertices of a \[\Delta \text{ABC}\]. If the centroid of this triangle moves on the line\[2x\text{ }+\text{ }3y\text{ }=\text{1}\], then the locus of the vertex C is the line
  A)
  2x + 3y = 9          
  done clear
  B)
   2x - 3y = 7         
  done clear
  C)
  3x+2y=5                              
  done clear
  D)
  3x-2y=3
  done clear
  View Answer play_arrow

• question_answer133) A straight line through the point (2, 2) intersects the lines \[\sqrt{3}x+y=0\] and \[\sqrt{3x}-y=0\]at the points A and B. The equation of the line AB, so that the \[\Delta \text{OAB}\] is equilateral, is       
  A)
  x-2=0                                    
  done clear
  B)
  \[y-2=0\]
  done clear
  C)
  x + y - 4 = 0         
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer134) If \[(a,{{a}^{2}})\] falls inside the angle made by the lines \[y=\frac{x}{2},x>0\]and\[y=3x,x>0,\], then a belongs to
  A)
  \[(3,\infty )\]                    
  done clear
  B)
  \[\left( \frac{1}{2},3 \right)\]
  done clear
  C)
  \[\left( -3,-\frac{1}{2} \right)\]                  
  done clear
  D)
  \[\left( 0,\frac{1}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer135) The locus of a point which moves so that the ratio of the length of the tangents to the circles \[{{x}^{2}}+{{y}^{2}}+4x+3=0\]and \[{{x}^{2}}{{y}^{2}}-6x\]\[+5=0\] is 2 : 3, is
  A)
  \[~5{{x}^{2}}+\text{ }5{{y}^{2}}-\text{ }60x\text{ }+\text{ }7\text{ }=\text{ }0\]
  done clear
  B)
  \[~5{{x}^{2}}+\text{ }5{{y}^{2}}\text{+ }60x\text{ }+\text{ }7\text{ }=\text{ }0\]
  done clear
  C)
  \[~5{{x}^{2}}+\text{ }5{{y}^{2}}\text{+ }60x\text{ }+\text{ 12 }=\text{ }0\]
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer136) The   circles   \[{{x}^{2}}+{{y}^{2}}-\text{ }5x+6y+\text{ 15 }=\text{ }0\]  and \[{{x}^{2}}+{{y}^{2}}-2x+6y+\text{6}=0\]touch each other
  A)
  internally            
  done clear
  B)
  externally
  done clear
  C)
   Do not say anything      
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer137) An ellipse has OB as semi-minor axis, F and F' are its foci and the\[\angle FBF'\]is a right angle. Then, the eccentricity of the ellipse is
  A)
  \[\frac{1}{\sqrt{3}}\]                                     
  done clear
  B)
  \[\frac{1}{4}\]
  done clear
  C)
  \[\frac{1}{2}\]                                   
  done clear
  D)
  \[\frac{1}{\sqrt{2}}\]
  done clear
  View Answer play_arrow

• question_answer138) If t is a parameter, then \[x=a\left( t+\frac{1}{t} \right)\] and\[y=b\left( t-\frac{1}{t} \right)\]represent
  A)
  an ellipse            
  done clear
  B)
  a circle
  done clear
  C)
  a pair of straight lines
  done clear
  D)
  a hyperbola
  done clear
  View Answer play_arrow

• question_answer139) The locus of a point \[P(\alpha ,\beta )\] moving under the condition that the line \[y=ax+\beta \] is a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is
  A)
  a hyperbola                       
  done clear
  B)
  a parabola
  done clear
  C)
  a circle                 
  done clear
  D)
  an ellipse     
  done clear
  View Answer play_arrow

• question_answer140) If two tangents drawn from a point P to the  parabola \[{{y}^{2}}=4x\] are at right angles, then the locus of P is     
  A)
            x=1                                        
  done clear
  B)
  2x+1=0           
  done clear
  C)
  x=-1                                      
  done clear
  D)
  2x-1=0
  done clear
  View Answer play_arrow

• question_answer141) Equation of the ellipse whose foci are (2, 2) and (4, 2) and the major axis is of length 10, is
  A)
  \[\frac{{{(x+3)}^{2}}}{24}+\frac{{{(y+2)}^{2}}}{25}=1\]
  done clear
  B)
  \[\frac{{{(x-3)}^{2}}}{24}+\frac{{{(y-2)}^{2}}}{25}=1\]
  done clear
  C)
  \[\frac{{{(x+3)}^{2}}}{24}+\frac{{{(y+2)}^{2}}}{24}=1\]
  done clear
  D)
  \[\frac{{{(x-3)}^{2}}}{25}+\frac{{{(y-2)}^{2}}}{24}=1\]
  done clear
  View Answer play_arrow

• question_answer142) If \[f(x)={{\log }_{{{x}^{2}}}}({{\log }_{e}}x),\] then \[f'\text{ }\left( x \right)at\text{ }x\text{ }=e\] is
  A)
  1                                             
  done clear
  B)
  e
  done clear
  C)
  \[\frac{1}{2e}\]  
  done clear
  D)
  0
  done clear
  View Answer play_arrow

• question_answer143) If ; \[y={{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+......\infty }}},\] \[\frac{dy}{dx}\], is equal to
  A)
  \[\frac{2xy}{2y-{{x}^{2}}}\]         
  done clear
  B)
  \[\frac{xy}{y+{{x}^{2}}}\]
  done clear
  C)
  \[\frac{xy}{y-{{x}^{2}}}\]                             
  done clear
  D)
  \[\frac{2x}{2+\frac{{{x}^{2}}}{y}}\]
  done clear
  View Answer play_arrow

• question_answer144) \[\underset{x\to 0}{\mathop{\lim }}\,\left[ \frac{{{e}^{x}}-{{e}^{\sin x}}}{x-\sin x} \right]\]is equal to
  A)
  -1                                           
  done clear
  B)
  0
  done clear
  C)
  1                                             
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer145)  If \[f'(2)=6,f'(1)=4,\], then \[\underset{h\to 0}{\mathop{\lim }}\,\frac{f(2h+2+{{h}^{2}})-f(2)}{f(h-{{h}^{2}}+1)-f(1)}\] is equal to
  A)
  3                                             
  done clear
  B)
  \[-\frac{3}{2}\]
  done clear
  C)
  \[\frac{3}{2}\]                                   
  done clear
  D)
  Does not exist
  done clear
  View Answer play_arrow

• question_answer146) The value of k for which the function\[f(x)\left\{ \underset{k,}{\mathop{\frac{1-\cos 4x}{8{{x}^{2}}}}}\, \right.,\begin{matrix}    x\ne 0  \\    x=0  \\ \end{matrix}\]is continuous at \[x=\text{ }0\], is
  A)
  \[k=0\]
  done clear
  B)
  \[k=1\]
  done clear
  C)
  \[k=-1\]
  done clear
  D)
  None of the above      
  done clear
  View Answer play_arrow

• question_answer147) The set of points, where the function \[f(x)=|x-1|{{e}^{x}}\]is differentiable, is
  A)
  R                                            
  done clear
  B)
  \[R-\{1\}\]
  done clear
  C)
  \[R-\{-1\}\]                        
  done clear
  D)
  \[R-\{0\}\]
  done clear
  View Answer play_arrow

• question_answer148) Suppose p points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points  is
  A)
  \[{{p}^{3}}+3{{p}^{2}}\]               
  done clear
  B)
  \[\frac{1}{2}{{p}^{3}}({{p}^{3}}+p)\]
  done clear
  C)
  \[\frac{{{p}^{2}}}{2}(5p-3)\]                       
  done clear
  D)
  \[{{p}^{2}}(4p-3)\]
  done clear
  View Answer play_arrow

• question_answer149) The mode of the binomial distribution for  which mean and standard deviation are 10 and \[\sqrt{5}\] respectively, is
  A)
  7                                             
  done clear
  B)
  8
  done clear
  C)
  9                                             
  done clear
  D)
  10
  done clear
  View Answer play_arrow

• question_answer150) The period of the function \[f(x)=\sin \left( \sin \frac{x}{5} \right)\]is
  A)
  \[2\pi \]                                               
  done clear
  B)
  \[\frac{2\pi }{5}\]
  done clear
  C)
  \[10\pi \]            
  done clear
  D)
  \[5\pi \]
  done clear
  View Answer play_arrow