Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2015

done BCECE Engineering Solved Paper-2015 Total Questions - 150

• question_answer1) A ball is thrown from the ground to clear a wall 3 m high at a distance of 6 m and falls 18m away from the wall, the angle of projection of ball is
  A)
  \[{{\tan }^{-1}}\left( \frac{3}{2} \right)\]                               
  done clear
  B)
  \[{{\tan }^{-1}}\left( \frac{2}{3} \right)\]
  done clear
  C)
  \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]                               
  done clear
  D)
  \[{{\tan }^{-1}}\left( \frac{3}{4} \right)\]
  done clear
  View Answer play_arrow

• question_answer2) Consider if the electric flux entering and leaving an enclosed surface respectively are \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\], the electric charge inside the surface will be
  A)
  \[{{\varepsilon }_{0}}({{\phi }_{1}}+{{\phi }_{2}})\]                          
  done clear
  B)
  \[\frac{{{\phi }_{2}}-{{\phi }_{1}}}{{{\varepsilon }_{0}}}\]
  done clear
  C)
  \[\frac{{{\phi }_{1}}-{{\phi }_{2}}}{{{\varepsilon }_{0}}}\]                              
  done clear
  D)
  \[\frac{{{\phi }_{1}}+{{\phi }_{2}}}{{{\varepsilon }_{0}}}\]
  done clear
  View Answer play_arrow

• question_answer3) If the escape speed of a projectile on Earth's surface is \[11.2km{{s}^{-1}}\] and a body is projected out with thrice this speed, then determine the speed of the body far away from the Earth.
  A)
  \[\text{56}.\text{63 km}{{\text{s}}^{\text{-1}}}\]            
  done clear
  B)
  \[\text{33 km}{{\text{s}}^{\text{-1}}}\]
  done clear
  C)
  \[~\text{39 km}{{\text{s}}^{\text{-1}}}\]             
  done clear
  D)
  \[\text{31}.\text{7 km}{{\text{s}}^{\text{-1}}}\]
  done clear
  View Answer play_arrow

• question_answer4) Determine the potential drop between the points A and C in the following circuit. Resistances \[1\Omega \]and \[2\Omega \] are representing the internal resistances of the respective cells.
  A)
  \[\frac{4}{5}V\]                                
  done clear
  B)
  1.75 V
  done clear
  C)
  2.25 V                   
  done clear
  D)
  \[\frac{5}{4}V\]
  done clear
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• question_answer5) A tank is filled with a liquid up to a height H. A small hole is made at the bottom of this tank. Consider \[{{t}_{1}}\] be the time taken to empty first half of the tank and \[{{t}_{2}}\] be the time taken to empty rest half of the tank. Then, determine the ratio \[\frac{{{t}_{1}}}{{{t}_{2}}}.\]
  A)
  \[~\text{1}.\text{33}\]                 
  done clear
  B)
  \[\text{1}.\text{5}\]
  done clear
  C)
  \[\text{2}\]                                        
  done clear
  D)
  \[0.\text{414}\]
  done clear
  View Answer play_arrow

• question_answer6) An electron and a proton enter a magnetic field perpendicularly both have same kinetic energy. Which of the following statements are true?
  A)
  Trajectory of proton is less curved
  done clear
  B)
  Trajectory of electron is less curved
  done clear
  C)
  Both trajectories are equally curved
  done clear
  D)
  Both move on straight line path
  done clear
  View Answer play_arrow

• question_answer7) The coefficient of volume expansion of glycerine is\[49\times {{10}^{-5}}{{K}^{-1}}\]. What is the fractional change in its density for a \[\text{3}0{}^\circ \text{ C}\] rise in temperature?
  A)
  \[\text{1}.\text{5}\times \text{1}{{0}^{\text{-2}}}\]                       
  done clear
  B)
  \[\text{2}\times \text{1}{{0}^{\text{-4}}}\]
  done clear
  C)
  \[\text{3}.\text{5}\times \text{1}{{0}^{\text{-3}}}\]                       
  done clear
  D)
  \[2.5\times {{10}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer8) If a conducting rod of length \[4l\] is rotated about at point O in a uniform magnetic field B directed into the paper and \[DE=\text{ I},EA=3I,\]then
  A)
  \[{{V}_{A}}-{{V}_{E}}=\frac{9}{2}B\omega {{l}^{2}}\]      
  done clear
  B)
  \[{{V}_{E}}-{{V}_{A}}=\frac{9}{2}B\omega {{l}^{2}}\]
  done clear
  C)
  \[{{V}_{D}}-{{V}_{E}}=\frac{B\omega {{l}^{2}}}{2}\]        
  done clear
  D)
  \[{{V}_{A}}-{{V}_{E}}=4B\omega {{l}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer9) An open organ pipe has a fundamental frequency of\[\text{3}00\text{ Hz}\]. The first overtone of a closed organ pipe has the same frequency as the first overtone of organ pipe. How long is each pipe?
  A)
  \[\text{41}.\text{25 cm}\]           
  done clear
  B)
  \[~\text{42}.\text{3 cm}\]
  done clear
  C)
  \[~\text{49}.\text{5 cm}\]                          
  done clear
  D)
  \[~\text{4}0.\text{5 cm}\]
  done clear
  View Answer play_arrow

• question_answer10) In \[L-C-R\] circuit, \[f=\frac{50}{\pi }Hz,\] \[V=50V,\]If \[L=1H\] and \[C=20\mu C\], then the voltage across capacitor is
  A)
  \[~\text{5}0\text{ V}\]                 
  done clear
  B)
  \[\text{2}0\text{ V}\]
  done clear
  C)
  zero                                      
  done clear
  D)
  \[\text{3}0\text{V}\]
  done clear
  View Answer play_arrow

• question_answer11) In a car race, car A takes a time t less than car B at the finish and passes the finishing point with speed v more than that of the car B. Assuming that both the cars starts from rest and travel with constant accelerations \[{{a}_{1}}\] and \[{{a}_{2}}\] respectively. So, the value of \[v\] will be
  A)
  \[(\sqrt{{{a}_{1}}/{{a}_{2}}})t\]                 
  done clear
  B)
  \[(\sqrt{{{a}_{2}}/{{a}_{1}}})t\]
  done clear
  C)
  \[({{a}_{1}}\sqrt{{{a}^{2}}})t\]                   
  done clear
  D)
  \[(\sqrt{{{a}_{1}}{{a}_{2}}})t\]
  done clear
  View Answer play_arrow

• question_answer12) If an equiconvex lens is cut into two halves along (i) \[~XOX'\] and (ii) \[YOY'\]as shown in the figure. Let \[f,f',f''\] be the focal lengths of complete lens of each, in case (i) and of each half in case (ii) respectively. Chooses the correct statement form the following?
  A)
  \[f'=f,f'=f\]        
  done clear
  B)
  \[f'=2f,f''=2f\]
  done clear
  C)
  \[f'=f,f''=2f\]
  done clear
  D)
  \[f'=2f,f''=f\]
  done clear
  View Answer play_arrow

• question_answer13) The bob of a pendulum is released from a horizontal position A as shown in the figure. If the length of the pendulum is\[\text{1}.\text{5 m}\], what is the speed with which the bob arrives at the lower most point B, given that it dissipated 5% of its initial energy against air resistance?
  A)
  \[\text{5 m}/\text{s}\]                 
  done clear
  B)
  5.5 m/s
  done clear
  C)
  \[~\text{5}.\text{3 m}/\text{s}\]                             
  done clear
  D)
  \[~\text{4}.\text{4 m}/\text{s}\]
  done clear
  View Answer play_arrow

• question_answer14) In a photo emissive cell with executing wavelength \[\lambda \], the fastest electron has speed \[v\]. If the exciting wavelength is changed to \[\frac{3\lambda }{4}\], the speed of fastest emitted electron will be
  A)
  greater than \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
  done clear
  B)
  \[v{{\left( \frac{3}{4} \right)}^{1/2}}\]
  done clear
  C)
  \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
  done clear
  D)
  less than  \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
  done clear
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• question_answer15) A ball of mass m moving at a speed \[v\] makes a head on collision with an identical ball at rest. The kinetic energy at the balls after the collision is \[\text{3}/\text{4th}\] of the original. What is the coefficient of restitution?
  A)
  \[1/\sqrt{3}\]                    
  done clear
  B)
  \[1\sqrt{2}\]
  done clear
  C)
  \[\sqrt{2}\]                                        
  done clear
  D)
  \[\sqrt{3}\]
  done clear
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• question_answer16) A   radioactive   material   decays   by simultaneous emission of two particles with half-lives \[\mathbf{1620}\text{ }\mathbf{yr}\] and \[\mathbf{810}\text{ }\mathbf{yr}\] respectively. The time in years after which one-fourth of material remains, is
  A)
  \[\text{1}0\text{8}0\text{yr}~~\]                            
  done clear
  B)
  \[\text{234}0\text{yr}\]
  done clear
  C)
  \[\text{486}0\text{ yr}\]              
  done clear
  D)
  \[~\text{324}0\text{ yr}\]
  done clear
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• question_answer17) A cylinder rolls up an inclined plane at an angle of\[\text{3}0{}^\circ \]. At the bottom of the inclined plane, the centre of mass of the cylinder has speed of\[\text{5 m}/\text{s}\]. How long will it take to return to the bottom?
  A)
  \[~\text{2s}\]                                   
  done clear
  B)
  \[\text{3 s}\]
  done clear
  C)
  \[\text{1}.\text{5s}\]                                    
  done clear
  D)
  4s
  done clear
  View Answer play_arrow

• question_answer18) The current gain in the common emitter amplifier mode of a transistor is 10. The input impedance is\[20k\Omega \], and load of resistance is \[100k\Omega \]. The power gain is
  A)
  \[\text{3}00\]                                   
  done clear
  B)
  \[\text{5}00\]
  done clear
  C)
  \[\text{2}00\]                                   
  done clear
  D)
  \[\text{1}00\]
  done clear
  View Answer play_arrow

• question_answer19) What will be the displacement equation of the simple harmonic motion obtained by combining the motions? \[{{x}_{}}_{1}=2\sin \omega t,\]\[{{x}_{}}_{2}=4\sin \left( \omega t+\frac{\pi }{6} \right)\]and \[{{x}_{3}}=6\sin \left( \omega t+\frac{\pi }{3} \right)\]
  A)
  \[x=10.25\sin (\omega t+\phi )\]             
  done clear
  B)
  \[x=10.25\sin (\omega t-\phi )\]
  done clear
  C)
  \[x=11.25\sin (\omega t+\phi )\]
  done clear
  D)
  \[x=11.25\sin (\omega t-\phi )\]
  done clear
  View Answer play_arrow

• question_answer20) An ammeter A reads \[\text{2 A}\] and the voltmeter \[V\] reads\[\text{2}0\text{ V}\]. The value of resistance R is (assuming finite resistaneces of ammeter and voltmeter)
  A)
  exactly \[10\Omega \]                  
  done clear
  B)
   less than \[10\Omega \]
  done clear
  C)
  more than \[10\Omega \]           
  done clear
  D)
   we cannot definitely say
  done clear
  View Answer play_arrow

• question_answer21) A stream of water flowing horizontally with the speed of \[15m{{s}^{-1}}\] gushes out of a tube of cross-sectional area \[{{10}^{-2}}{{m}^{-2}}\] and hits a vertical wall nearby. What is the force exerted on the wall by the impact or water? Assuming it does not rebound.
  A)
  \[\text{225}0\text{ N}\]               
  done clear
  B)
  2000 N
  done clear
  C)
  \[\text{15}00\text{N}~~\]         
  done clear
  D)
  \[\text{1}000\text{N}\]
  done clear
  View Answer play_arrow

• question_answer22) Two charges \[+6\mu C\]and \[-4\mu C\]are placed \[\text{15 cm}\] apart as shown. At what distances from A to its right, the electrostatic potential is zero?
  A)
  \[\text{4},\text{ 9},\text{ 6}0\]                 
  done clear
  B)
  \[\text{9},\text{ 15},\text{45}\]
  done clear
  C)
  \[\text{2}0,\text{ 3}0,\text{ 4}0\]           
  done clear
  D)
  \[\text{9}.\text{ 45},\]infinity
  done clear
  View Answer play_arrow

• question_answer23) A shell of mass \[0.0\text{2}0\text{ kg}\] is fired by a gun of mass\[\text{1}00\text{ kg}\]. If the muzzle speed of the shell is\[\text{8}0\text{m}{{\text{s}}^{\text{-1}}}\]. What is the recoil speed of the gun?
  A)
  \[\text{1}.\text{6 cm}{{\text{s}}^{\text{-1}}}\]                 
  done clear
  B)
  \[0.\text{5 cm}{{\text{s}}^{\text{-1}}}\]
  done clear
  C)
  \[\text{2 cm}{{\text{s}}^{\text{-1}}}\]                   
  done clear
  D)
  \[\text{3cm}{{\text{s}}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer24) If\[E=100\sin (100t)\] volt and\[I=100\sin \left( 100t+\frac{\pi }{3} \right)mA\]are the instantaneous voltage and current, then the             rms values of voltage and current are respectively;
  A)
  \[\text{7}0.\text{7 V},\text{ 7}0.\text{7 mA}\]
  done clear
  B)
  \[~\text{6}0.\text{9 V},\text{ 69}.\text{3 mA}\]
  done clear
  C)
  \[~\text{9}0.\text{6 V},\text{ 141}.\text{4 mA}\]    
  done clear
  D)
  \[\text{6}0\text{ V},\text{ 7}0\text{ mA}\]
  done clear
  View Answer play_arrow

• question_answer25) If torques of equal magnitudes are applied to a hollow cylinder and a solid sphere both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
  A)
  \[{{\omega }_{1}}>{{\omega }_{2}}\]                     
  done clear
  B)
  \[{{\omega }_{1}}={{\omega }_{2}}\]
  done clear
  C)
  \[{{\omega }_{2}}>{{\omega }_{1}}\]      
  done clear
  D)
  None of these
  done clear
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• question_answer26) The threshold frequency for certain metal is\[3.3\times {{10}^{14}}Hz.\] If light of \[8.2\times {{10}^{14}}Hz\]frequency is incident on the metal, then the cut-off voltage of the photoelectric current will be
  A)
  \[\text{3V}\]                    
  done clear
  B)
  4 V
  done clear
  C)
  \[\text{2 V}\]                                    
  done clear
  D)
  \[~\text{2}.\text{5 V}\]
  done clear
  View Answer play_arrow

• question_answer27) If two simple pendulums first of bob mass \[{{M}_{1}}\] and length \[{{l}_{1}}\], second of bob mass \[{{M}_{2}}\] and length \[{{l}_{2}}\]. Given \[{{M}_{1}}={{M}_{2}}\] and. \[{{l}_{1}}=2{{l}_{2}}\] If the vibrational energies of both are same, then which of the following is correct?
  A)
  Amplitude of B is smaller than A
  done clear
  B)
  Amplitude of B is greater than B
  done clear
  C)
   Amplitude will be same
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer28) A thin film of soap solution \[({{\mu }_{s}}=1.4)\] lies on the top of a glass plate\[({{\mu }_{g}}=1.5)\]. When visible light is incident almost normal to the plate, two adjacent reflection maxima are observed at two wavelengths \[\text{42}0\text{ nm}\] and  \[\text{63}0\text{ nm}\]. The minimum thickness of the soap solution are
  A)
  \[\text{42}0\text{ nm}\]              
  done clear
  B)
  \[~\text{5}00\text{ nm}\]
  done clear
  C)
  \[~\text{45}0\text{ nm}\]                           
  done clear
  D)
  \[\text{49}0\text{ nm}\]
  done clear
  View Answer play_arrow

• question_answer29) An air bubble starts rising from the bottom of a lake. Its diameter is \[\text{3}.\text{6 mm}\] at the bottom and \[\text{4 mm}\] at the surface. The depth of the lake is \[\text{25}0\text{ cm}\] and the temperature at surface is40°C. What is the temperature at the bottom of the lake? Given atmpospheric pressure \[=\text{76 cm}\] of Hg and \[\text{g}=\text{ 98}0\text{ cm}/{{\text{s}}^{\text{2}}}\].
  A)
  \[\text{11}{}^\circ \text{C}\]                     
  done clear
  B)
  \[\text{12}.\text{36}{}^\circ \text{C}\]
  done clear
  C)
  \[\text{13}{}^\circ \text{C13}{}^\circ \text{C}\]                 
  done clear
  D)
  \[\text{1}0.\text{37}{}^\circ \text{C}\]
  done clear
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• question_answer30) If four atoms of hydrogen combine to form an \[_{2}^{4}\] He atom, then the amount of energy released is
  A)
  \[~\text{26}.\text{7 MeV}\]      
  done clear
  B)
  \[\text{25}.\text{3 MeV}\]
  done clear
  C)
  \[~\text{22 MeV}\]                
  done clear
  D)
  \[\text{24}.\text{5 MeV}\]
  done clear
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• question_answer31) A simple harmonic wave of amplitude 8 unit travels along positive x-axis. At any given instant of time, for a particle at a distance of \[\text{1}0\text{ cm}\] from the origin, the displacement is + 6 unit and for a particle at a distance of \[\text{25 cm}\] from the origin, the displacement is\[+\text{ 4 unit}\]. Calculate the wavelength.
  A)
  \[\text{2}00\text{cm}\]                               
  done clear
  B)
  \[\text{23}0\text{ cm}\]
  done clear
  C)
  \[\text{21}0\text{ cm}\]                              
  done clear
  D)
  \[\text{25}0\text{ cm}\]
  done clear
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• question_answer32) When a battery of emf \[\text{8 V}\] with internal resistance \[0.5\Omega \], is charged by a \[\text{12}0\text{V}\] DC supply using a series resistance of\[15.5\Omega ,\], then the terminal voltage of the battery is
  A)
  \[\text{11}.\text{5V}\]  
  done clear
  B)
  \[\text{2}0\text{V}\]   
  done clear
  C)
  \[\text{21}.\text{5 V}\]                                
  done clear
  D)
  \[\text{12}.\text{3 V}\]
  done clear
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• question_answer33) A rigid bar of mass \[\text{15 kg}\] is supported symmetrically by three wires each \[\text{2 m}\] long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the tension.
  A)
  \[\text{12}.\text{6}:\text{ 2}\]                  
  done clear
  B)
  \[\text{1}.\text{31}:\text{1}\]
  done clear
  C)
  \[~\text{4}.\text{65}:\text{ 3}\]               
  done clear
  D)
  \[\text{2}.\text{69}:\text{ 4}\]
  done clear
  View Answer play_arrow

• question_answer34) Figure given below shows a network of four capacitors of capacitance equal to \[{{C}_{1}}=C,{{C}_{2}}=2C,{{C}_{3}}\]\[=3C,{{C}_{4}}\]\[=4C\]are connected to a battery. The ratio of charges on \[{{C}_{2}}\]and \[{{C}_{4}}\] is
  A)
  \[7/4\]                 
  done clear
  B)
  \[7/22\]
  done clear
  C)
  \[3/22\]
  done clear
  D)
  \[4/7\]
  done clear
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• question_answer35) Two trains A and B of length \[\text{4}00\text{ m}\] each are moving on two parallel tracks with a uniform speed of \[\text{72 km}{{\text{h}}^{-1}}\] in the same direction, with A head of speed B. The driver of B decides to overtake A and accelerates by \[\text{1m}/{{\text{s}}^{\text{2}}}\]. if after\[\text{5}0\text{s}\], the guard of B just brushes past the driver of A, what was the original distance between them?
  A)
  \[\text{1}00\text{m}\]                 
  done clear
  B)
  \[\text{115}0\text{m}\]
  done clear
  C)
  \[\text{13}00\text{m}\]                               
  done clear
  D)
  \[\text{125}0\text{m}\]
  done clear
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• question_answer36) If a fully charged capacitor C with initial charge \[{{q}_{0}}\]is connected to a coil of self inductance L at \[t=\text{ }0\]. The time at which the energy is stored equally between the electric field and magnetic field is
  A)
  \[\pi \sqrt{LC}\]                               
  done clear
  B)
  \[\frac{\pi }{4}\sqrt{LC}\]
  done clear
  C)
   \[\frac{\pi }{2}\sqrt{LC}\]                           
  done clear
  D)
  \[\frac{\pi }{6}\sqrt{LC}\]
  done clear
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• question_answer37) A rocket is fired from the Earth towards the Sun. At what distance from the Earth's centre, the gravitational force on the rocket is zero? Mass of the Sun \[=2\times {{10}^{30}}kg\]and mass of the Earth \[=6\times {{10}^{24}}kg.\]
  A)
  \[2.6\times {{10}^{8}}m\]                            
  done clear
  B)
  \[3.2\times {{10}^{8}}m\]
  done clear
  C)
  \[3.9\times {{10}^{9}}m\]                            
  done clear
  D)
  \[2.3\times {{10}^{9}}m\]
  done clear
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• question_answer38) In the figure given below, for an angle of incidence \[\text{45}{}^\circ \] at the top surface, what is the minimum refractive index need to total internal reflection at vertical face?
  A)
  \[\frac{\sqrt{2}+1}{2}\]                
  done clear
  B)
   \[\sqrt{\frac{1}{2}}\]
  done clear
  C)
  \[\sqrt{\frac{3}{2}}\]                                     
  done clear
  D)
  \[\sqrt{2}+1\]
  done clear
  View Answer play_arrow

• question_answer39) A solid cylinder of mass \[\text{2}0\text{ kg}\] rotates about its axis with angular speed\[\text{100 rad }{{\text{s}}^{-1}}\]. The radius of the cylinder is\[0.\text{25 m}\]. What is the . kinetic energy associated with the rotation of cylinder? What is the magnitude of angular momentum of cylinder about its axis?
  A)
  \[62.5T-s\]         
  done clear
  B)
  \[70.4T-s\]
  done clear
  C)
  \[79.6T-s\]                         
  done clear
  D)
  \[60.5T-s\]
  done clear
  View Answer play_arrow

• question_answer40) A change of \[\text{8}.0\text{ mA}\] in the emitter current brings a change of \[7.\text{9 mA}\] in the correct collector current. The values of \[\alpha \] and \[\beta \] are
  A)
  \[0.99,90\]                         
  done clear
  B)
  \[0.96,79\]
  done clear
  C)
  \[0.97,99\]                         
  done clear
  D)
  \[0.99,79\]
  done clear
  View Answer play_arrow

• question_answer41) A stone of mass \[0.\text{25 kg}\] tied to the end of a string is whirled round in a circle of radius 1.5m with speed 40 rev/min in a horizontal plane. What is the tension in the string and what is the maximum speed with which the stone can be whirled around, if the string can withstand a maximum tension of\[~\text{2}00\text{ N}\]?
  A)
  \[\text{6}.\text{6 N, 35m}{{\text{s}}^{\text{-1}}}\]   
  done clear
  B)
  \[\text{6N},\text{37m}{{\text{s}}^{\text{-1}}}\]
  done clear
  C)
  \[~\text{7}.\text{5 N, 46 m}{{\text{s}}^{\text{-1}}}\]                     
  done clear
  D)
  \[\text{8 N},\text{ 38 m}{{\text{s}}^{\text{-1}}}\]
  done clear
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• question_answer42) A straight wire of mass 200 g and length \[\text{1}.\text{5 m}\] carries a current of 2 A. It is suspended in mid air by a uniform horizontal magnetic field B, The magnitude of B (in tesla) is
  A)
  \[0.\text{65}\]                                  
  done clear
  B)
  \[0.\text{55}\]   
  done clear
  C)
  \[0.\text{75}\]                                  
  done clear
  D)
  \[0.\text{45}\]
  done clear
  View Answer play_arrow

• question_answer43) A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and light slider supports a weight of 1.5 x lO2]^. The length of the slider is 30 cm. What is the surface tension of the  film?
  A)
  \[\text{3}\times \text{1}{{0}^{\text{-3}}}\text{N}{{\text{m}}^{\text{-1}}}\]        
  done clear
  B)
  \[\text{2}\times \text{1}{{0}^{\text{-5}}}\text{N}{{\text{m}}^{\text{-1}}}\]
  done clear
  C)
  \[4\times \text{1}{{0}^{\text{-4}}}\text{N}{{\text{m}}^{\text{-1}}}\]     
  done clear
  D)
  \[2.5\times \text{1}{{0}^{\text{-2}}}\text{N}{{\text{m}}^{\text{-1}}}\]
  done clear
  View Answer play_arrow

• question_answer44) At constant pressure, the ratio of increase in volume of an ideal gas per degree rise in kelvin temperature to its original volume is
  A)
  \[{{T}^{2}}\]                                      
  done clear
  B)
  \[\frac{1}{T}\]
  done clear
  C)
  \[{{T}^{3}}\]                                      
  done clear
  D)
  \[T\]
  done clear
  View Answer play_arrow

• question_answer45) The length of a magnet is large compared to its width and breadth. The time period of its oscillation in vibration magnetometer is\[\text{2 s}\]. The magnet is cut along its length into three equal parts and three parts are then palced on each other with their like poles together. The time period of this combination will be
  A)
  \[\frac{2}{3}s\] 
  done clear
  B)
  \[\sqrt{\frac{2}{3}}s\]
  done clear
  C)
  \[\frac{3}{2}s\]                                 
  done clear
  D)
  \[\sqrt{\frac{3}{2}}s\]
  done clear
  View Answer play_arrow

• question_answer46) A body of mass \[\text{1 kg}\] is moving in a vertical circular path of radius\[\text{1 m}\]. The difference between the kinetic energies at its highest and lowest positions is
  A)
  \[\text{4}\sqrt{5}J\]                      
  done clear
  B)
  \[20J\]
  done clear
  C)
  \[10J\]                                 
  done clear
  D)
  \[30J\]
  done clear
  View Answer play_arrow

• question_answer47) If electrical force between two charges is \[\text{2}00\text{ N}\] and we increase \[\text{1}0%\] charge on one of the charges and decrease \[\text{1}0%\] charge on the other, then electrical force between them for the same distance becomes
  A)
  \[\text{2}00\text{ N}\]                                 
  done clear
  B)
  202 N  
  done clear
  C)
  198 N                    
  done clear
  D)
  199 N
  done clear
  View Answer play_arrow

• question_answer48) The acceleration due to gravity on the planet is 9 times the acceleration due to gravity on  planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same on the planet B?
  A)
  6m                         
  done clear
  B)
  2/3m  
  done clear
  C)
   2/9m                   
  done clear
  D)
  18m
  done clear
  View Answer play_arrow

• question_answer49) In hydrogen atom Spectrum, frequency of \[2.7\times {{10}^{15}}Hz\] of EM wave is emitted when transmission takes place from 2 to1. If it moves from 3 to 1, the frequency emitted will be
  A)
  \[3.2\times {{10}^{15}}Hz\]                        
  done clear
  B)
  \[32\times {{10}^{15}}Hz\]
  done clear
  C)
  \[1.6\times {{10}^{15}}Hz\]                        
  done clear
  D)
  \[16\times {{10}^{15}}Hz\]
  done clear
  View Answer play_arrow

• question_answer50) If a ray of light in a denser medium strikes a rarer medium at an angle of incidence\[i\] the angles of reflection and refraction are respectively r and r'. If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is
  A)
  \[{{\sin }^{-1}}(\tan r')\]                               
  done clear
  B)
  \[{{\sin }^{-1}}(\tan r)\]
  done clear
  C)
  \[{{\tan }^{-1}}(\sin i)\]                
  done clear
  D)
  \[{{\cot }^{-1}}(\tan i)\]
  done clear
  View Answer play_arrow

• question_answer51) Consider the following reaction sequence of alkene \[C{{H}_{3}}CH=CHC{{H}_{3}}\xrightarrow{{{O}_{3}}}A\xrightarrow[Zn]{{{H}_{2}}O}B\] The product B is
  A)
  \[C{{H}_{3}}C{{H}_{2}}COC{{H}_{3}}\]   
  done clear
  B)
  \[C{{H}_{3}}COC{{H}_{3}}\]
  done clear
  C)
  \[C{{H}_{3}}CHO\]                         
  done clear
  D)
  \[C{{H}_{3}}C{{H}_{2}}CHO\]
  done clear
  View Answer play_arrow

• question_answer52) Choose the correct statement about the industrial preparation of hydrogen from water gas \[(CO+{{H}_{2}})\].
  A)
  \[{{H}_{2}}\] is removed through occlusion with Pd
  done clear
  B)
  CO and \[{{H}_{2}}\]are fractionally separated using differences in their densities
  done clear
  C)
   CO is removed by absorption in aq. \[\text{C}{{\text{u}}_{\text{2}}}\text{C}{{\text{l}}_{\text{2}}}\] solution
  done clear
  D)
  CO is oxidised to \[\text{C}{{\text{O}}_{2}}\]with steam in the presence of a catalyst followed by absorption of \[C{{O}_{2}}\]in alkali
  done clear
  View Answer play_arrow

• question_answer53) The energy required to excite the electron in  the atom from\[n=1\] to \[n=2,\], when the ionisation enthalpy of hydrogen atom is \[1.312\times {{10}^{6}}J\]/mol will be (in the unit of \[{{10}^{5}}\]).
  A)
  8.53                       
  done clear
  B)
  7.51
  done clear
  C)
  \[8.92\]                               
  done clear
  D)
   9.86
  done clear
  View Answer play_arrow

• question_answer54) An ideal mono-atomic gas follows the path ABCD. Then, the work done during the complete cycle is
  A)
  zero                      
  done clear
  B)
  \[-\frac{1}{2}pV\]
  done clear
  C)
  \[-pV\]                
  done clear
  D)
  \[-2pV\]
  done clear
  View Answer play_arrow

• question_answer55) From the following which pairs give the faster \[{{S}_{N}}2\] reaction?
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer56) The reactivity order of halogenations of alkianes is                                                                 \[{{F}_{2}}>C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}.\] (i) Lower the activation energy for the chain initiation step, more reactive is the halogen. (ii) Lower the activation energy for the first chain o- propagation step, more reactive is the halogen. (iii) Lower the activation energy for the second chain propagation step, more reactive is the halogen. (iv) More negative is the overall heat of the reaction (                                                                                      \[\Delta H_{r}^{\circ }\]  of- halogenation of alkane) more reactive is the halogen.
  A)
  I and II
  done clear
  B)
  I, II and III
  done clear
  C)
  II and IV
  done clear
  D)
  II, III and IV
  done clear
  View Answer play_arrow

• question_answer57) What is the bond angle between \[\text{Cl-O-Cl}\] in\[C{{l}_{2}}{{O}_{7}}\]?
  A)
  \[~\text{1}0\text{9}{}^\circ \]                                   
  done clear
  B)
  \[\text{119}{}^\circ \]   
  done clear
  C)
  \[{{108}^{\circ }}25'\]                     
  done clear
  D)
  \[\text{12}0{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer58) The solubility of fluorides of alkali metals in water is
  A)
  \[~\text{LiF }>\text{ NaF }>\text{ KF }>\text{ RbF }>\text{ CsF}\]
  done clear
  B)
  \[\text{CsF }>\text{ RbF }>\text{ KF }>\text{ NaF }>\text{ LiF}\]
  done clear
  C)
  \[\text{LiF }>\text{ KF }>\text{ NaF }>\text{ CsF }>\text{ RbF}\]
  done clear
  D)
  \[\text{CsF }>\text{ KF }>\text{ NaF }>\text{ RbF }>\text{ LiF}\]
  done clear
  View Answer play_arrow

• question_answer59) Which of the following relation is correct for gaseous and reversible reactions?
  A)
  \[\frac{{{K}_{C}}}{{{K}_{P}}}={{(RT)}^{\Delta {{n}_{g}}}}\]            
  done clear
  B)
  \[\frac{{{K}_{p}}}{{{K}_{x}}}={{(p)}^{\Delta {{n}_{g}}}}\]
  done clear
  C)
  \[\frac{{{K}_{C}}}{{{K}_{x}}}={{(p)}^{-\Delta {{n}_{g}}}}\]             
  done clear
  D)
  \[\frac{{{K}_{C}}}{{{K}_{x}}}={{\left( \frac{p}{RT} \right)}^{\Delta {{n}_{g}}}}\]
  done clear
  View Answer play_arrow

• question_answer60) Consider the following sequence of reactions,
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer61) If the dipole moment of \[\text{HBr}\]is  \[2.60\times {{10}^{-30}}\text{Cm}\]and the interatomic spacing is \[1.41\overset{\text{o}}{\mathop{\text{A}}}\,,\]then the per cent ionic character of \[\text{HBr}\]is
  A)
  \[16.23%\]                         
  done clear
  B)
  \[13.21%\]
  done clear
  C)
  \[11.50%\]         
  done clear
  D)
  \[15.81%\]
  done clear
  View Answer play_arrow

• question_answer62) Consider the following reaction, \[\text{CC}{{\text{l}}_{\text{3}}}\text{CH=C}{{\text{H}}_{\text{2}}}\xrightarrow[{{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}\text{/HOCl}]{\text{NaB}{{\text{O}}_{\text{4}}}}\]Product (P) P is
  A)
  \[\text{CC}{{\text{l}}_{\text{3}}}\underset{\text{OH}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{HC}{{\text{H}}_{\text{2}}}\text{Cl}\]
  done clear
  B)
  \[\text{CC}{{\text{l}}_{\text{3}}}\underset{\text{OH}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{H}\underset{\text{OH}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,{{\text{H}}_{2}}\]
  done clear
  C)
  \[\text{CC}{{\text{l}}_{\text{3}}}\underset{\text{Cl}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{H-C}{{\text{H}}_{2}}OH\]
  done clear
  D)
  \[\text{CC}{{\text{l}}_{\text{3}}}\underset{\text{Cl}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{H-}\underset{\text{Cl}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,{{\text{H}}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer63) Among \[{{\left[ \text{Ni(CN}{{\text{)}}_{\text{4}}} \right]}^{\text{2-}}}\text{,}{{\left[ \text{NiC}{{\text{l}}_{\text{4}}} \right]}^{\text{2-}}}\] and \[\left[ \text{Ni(CO}{{\text{)}}_{\text{4}}} \right]\]
  A)
  \[{{\text{ }\!\![\!\!\text{ NiC}{{\text{l}}_{\text{4}}}\text{ }\!\!]\!\!\text{ }}^{\text{2-}}}\] is square planar and\[{{\text{ }\!\![\!\!\text{ Ni(CN}{{\text{)}}_{\text{4}}}\text{ }\!\!]\!\!\text{ }}^{\text{2-}}},\] \[\text{Ni}{{\left( \text{CO} \right)}_{\text{4}}}\] are tetrahedral
  done clear
  B)
   \[\text{Ni}{{\left( \text{CO} \right)}_{\text{4}}}\] is square planar and\[\left[ \text{Ni}{{\left( \text{CN} \right)}_{\text{4}}} \right]{{\text{2}}^{-}},\] \[{{\left[ \text{NiC}{{\text{l}}_{\text{4}}} \right]}^{\text{2-}}}\] are tetrahedral
  done clear
  C)
   \[{{\left[ \text{Ni(CN}{{\text{)}}_{\text{4}}} \right]}^{\text{2-}}}\] is square planar and\[{{\left[ \text{NiC}{{\text{l}}_{\text{4}}} \right]}^{\text{2-}}},\] \[\text{Ni}{{\left( \text{CO} \right)}_{\text{4}}}\] are tetrahedral
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer64) Match the following Column I with Column II.

  Column 1	Column 11
  A. Acetic acid and methyl formate	1. Ring chain tautomerism
  B. Maleic and fumaric acid	2. Functional isomers
  C.	3. Geometrical isomers
  D.	4. Metamerism

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

• question_answer65) Beryllium gives a compound \[\text{X}\] with the following percentage composition: Be Molecular weight of \[-61%,\,N-37.8%,\,Cl-48%,\,H-8.1%\] \[\text{X}\] is \[\text{148 g mo}{{\text{l}}^{-}}^{\text{1}}\] and that of Be is \[\text{9 g mo}{{\text{l}}^{\text{-1}}}.\] The molecular formula of the compound is
  A)
  \[\text{Be}{{\text{N}}_{\text{4}}}\text{C}{{\text{l}}_{\text{2}}}{{\text{H}}_{\text{12}}}\]
  done clear
  B)
  \[~\text{Be}{{\text{N}}_{\text{2}}}\text{Cl}{{\text{H}}_{6}}\]
  done clear
  C)
  \[\text{Be}{{\text{N}}_{\text{4}}}\text{C}{{\text{l}}_{\text{2}}}{{\text{H}}_{6}}\]
  done clear
  D)
  \[\text{Be}{{\text{N}}_{\text{4}}}\text{Cl}{{\text{H}}_{\text{8}}}\]
  done clear
  View Answer play_arrow

• question_answer66) The increasing dipole moments of the following compounds is                               
  A)
  \[\text{I }<\text{ III }<\text{ IV }<\text{ II}\]    
  done clear
  B)
  \[\text{II}=\text{IV}<\text{III}<\text{I}\]
  done clear
  C)
  \[\text{II=IIVIII}\]
  done clear
  D)
  \[\text{IIIIIIIV}\]
  done clear
  View Answer play_arrow

• question_answer67) Compound A undergoes following reactions to form B and C Black coloured solid (A) \[\xrightarrow{KN{{O}_{3}}+KOH}\] Green coloured solution (B) Green coloured \[\xrightarrow{C{{O}_{2}}}\] Pink solution \[\left( \text{C} \right)\text{ }+\text{ }\left( \text{A} \right)\]  Solution (B) (C) decolourised by \[\text{F}{{\text{e}}^{\text{3}}}^{+}\]Identify A, B and C respectively
  A)
  \[\text{Mn}{{\text{O}}_{\text{2}}}\text{,KMn}{{\text{O}}_{\text{4}}}\text{ and }{{\text{K}}_{\text{2}}}\text{Mn}{{\text{O}}_{\text{4}}}\]
  done clear
  B)
  \[~\text{Mn}{{\text{O}}_{2}}\text{, }{{\text{K}}_{\text{2}}}\text{Mn}{{\text{O}}_{\text{4}}}\text{ and KMn}{{\text{O}}_{\text{4}}}\]
  done clear
  C)
  \[\text{KMn}{{\text{O}}_{\text{4}}},\text{ Mn}{{\text{O}}_{2}}\text{ and }{{\text{K}}_{\text{2}}}\text{Mn}{{\text{O}}_{\text{4}}}\]
  done clear
  D)
  \[\text{KMn}{{O}_{\text{4}}},\text{ }{{\text{K}}_{\text{2}}}\text{Mn}{{\text{O}}_{\text{4}}}\text{ and Mn}{{\text{O}}_{\text{2}}}\]
  done clear
  View Answer play_arrow

• question_answer68) The reaction between nitric oxide \[\left( \text{NO} \right)\] and oxygen to form nitrogen dioxide \[\left( \text{N}{{\text{O}}_{2}} \right)\] is a key step in                 photochemical smog formation \[\text{2NO(g)+}{{\text{O}}_{\text{2}}}\text{(g)}\to \text{2N}{{\text{O}}_{\text{2}}}\text{(g)}\]  The grams of \[\text{N}{{\text{O}}_{\text{2}}}\]are formed by complete by reaction of \[\text{1}.\text{2}0\text{ g}\] of NO is
  A)
  7.2g
  done clear
  B)
  2.3g  
  done clear
  C)
  1.8g  
  done clear
  D)
  4.1 g
  done clear
  View Answer play_arrow

• question_answer69) \[2HC\equiv CH\xrightarrow[+N{{H}_{4}}Cl]{C{{H}_{2}}C{{l}_{2}}}A\xrightarrow[\text{HCl}]{\text{1mol}}B\]Identify the compounds A and B
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer70) At\[\text{8}0{}^\circ \text{ C}\], the vapour pressure of pure liquid A is 520 mm Hg and that of pure liquid B is 1000 mm Hg. If a mixture solution of A and  B boils at \[\text{8}0{}^\circ \text{ C}\] and 1 atm pressure, the amount of A in the mixture is
  A)
  50 mol per cent                
  done clear
  B)
  54 mol per cent
  done clear
  C)
   32 mol per cent               
  done clear
  D)
  44 mol percent
  done clear
  View Answer play_arrow

• question_answer71) The correct increasing order of solubility of the sulphates in water is
  A)
  \[\text{BeS}{{\text{O}}_{\text{4}}}>\text{ MgS}{{\text{O}}_{\text{4}}}>\text{ CaS}{{\text{O}}_{\text{4}}}>\text{ }\] \[\text{SrS}{{\text{O}}_{\text{4}}}\] \[>\text{ BaS}{{\text{O}}_{\text{4}}}\]
  done clear
  B)
  \[\text{BaS}{{\text{O}}_{\text{4}}}\text{ }>\text{ SrS}{{\text{O}}_{\text{4}}}\text{ }>\text{ CaS}{{\text{O}}_{\text{4}}}\text{ }>\text{ MgS}{{\text{O}}_{\text{4}}}\] \[\text{ }>\text{ BeS}{{\text{O}}_{\text{4}}}\]
  done clear
  C)
  \[\text{BaS}{{\text{O}}_{\text{4}}}\text{ }>\text{ CaS}{{\text{O}}_{\text{4}}}\text{ }>\text{ SrS}{{\text{O}}_{\text{4}}}\text{ }>\text{ BeS}{{\text{O}}_{\text{4}}}\] \[\text{ }>\text{ MgS}{{\text{O}}_{\text{4}}}\]
  done clear
  D)
  \[\text{BaS}{{\text{O}}_{\text{4}}}\text{ }>\text{ SrS}{{\text{O}}_{4}}>\text{ MgS}{{O}_{\text{4}}}\text{ }>\] \[\text{CaS}{{\text{O}}_{\text{4}}}\text{ }\] \[~\text{ }>\text{ BeS}{{\text{O}}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer72)  Consider the following reaction,\[\text{ZnC}{{\text{l}}_{\text{2}}}\text{+NaOH}\to \underset{\text{White ppt}\text{.}}{\mathop{B}}\,\to \xrightarrow{NaOH}\underset{\text{soluble}}{\mathop{C}}\,\] Then, the final product C is
  A)
  \[\text{N}{{\text{a}}_{\text{2}}}\text{Zn}{{\text{O}}_{\text{2}}}\]   
  done clear
  B)
  \[\text{Zn}{{\left( \text{OH} \right)}_{\text{2}}}\]
  done clear
  C)
  \[\text{ZnO}\]                                  
  done clear
  D)
  \[\text{ZnS}{{\text{O}}_{\text{4}}}\]
  done clear
  View Answer play_arrow

• question_answer73) The vapour pressure of pure water is 23.5 mm Hg. Then, the vapour pressure of an aqueous solution which contains 5 mass percent of urea is (Molar mass of urea is 60).
  A)
  23mmHg             
  done clear
  B)
  18 mmHg
  done clear
  C)
  31 mmHg            
  done clear
  D)
  35 mmHg
  done clear
  View Answer play_arrow

• question_answer74) Which of the following organic chloro compound shows stereochemical inversion during a \[{{S}_{N}}2\] reaction?
  A)
  \[{{\text{(C}{{\text{H}}_{\text{3}}}\text{)}}_{\text{3}}}\text{CCl}\]        
  done clear
  B)
  \[{{(C{{H}_{3}})}_{2}}CHCl\]
  done clear
  C)
  \[{{\text{(}{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}}\text{)}}_{\text{2}}}\text{CHCl}\]           
  done clear
  D)
  \[\text{C}{{\text{H}}_{\text{3}}}\text{Cl}\]
  done clear
  View Answer play_arrow

• question_answer75) Consider the following reactions, \[\text{C(s)+}{{\text{O}}_{\text{2}}}\text{(g)}\to \text{C}{{\text{O}}_{\text{2}}}\text{(g),}\Delta \text{H}=-94\text{kcal}\] \[\text{2CO(g)}+{{\text{O}}_{\text{2}}}\to \text{2C}{{\text{O}}_{\text{2}}}\text{(g),}\Delta \text{H}=-135.2\text{kcal}\] Then, the heat of formation of \[~\text{CO }\left( \text{g} \right)\] is
  A)
  \[~\text{26}.\text{4 kcal}\]                         
  done clear
  B)
  \[-\text{26}.\text{4 kcal}\]
  done clear
  C)
  \[~\text{41}.\text{2 kcal}\]                         
  done clear
  D)
  \[-\text{41}.\text{2 kcal}\]
  done clear
  View Answer play_arrow

• question_answer76) If the \[p{{K}_{a}}\] of a weak acid HA is 4.80 and the \[p{{K}_{b}}\] of a weak base BOH is 4.78. Then, the pH of an aqueous solution of the corresponding salt, BA will be
  A)
  8.23                       
  done clear
  B)
  9.41    
  done clear
  C)
  7.01                       
  done clear
  D)
  5.91
  done clear
  View Answer play_arrow

• question_answer77) Which one of the following is the correct statement?
  A)
  \[{{B}_{3}}{{N}_{3}}{{H}_{6}}\] He is known as inorganic benzene
  done clear
  B)
  Chlorides of both beryllium and aluminium have bridged chloride structure in gas phase
  done clear
  C)
   Boric acid is a protonic acid
  done clear
  D)
  Beryllium exhibits coordination number of six
  done clear
  View Answer play_arrow

• question_answer78) A nitrogenous substance A is treated with \[\text{HN}{{\text{O}}_{2}}\] and the product formed is further treated with \[\text{NaOH}\] solution which produces blue colouration. Then, A will be
  A)
  \[C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\]         
  done clear
  B)
  \[{{(C{{H}_{3}})}_{2}}CHN{{O}_{2}}\]
  done clear
  C)
  \[C{{H}_{3}}C{{H}_{2}}N{{O}_{2}}\]         
  done clear
  D)
  \[C{{H}_{3}}C{{H}_{2}}ONO\]
  done clear
  View Answer play_arrow

• question_answer79) Argon crystallises in fee arrangement and the density of solid and liquid at is \[\text{1}.\text{59 g}/\text{c}{{\text{m}}^{\text{3}}}\]and\[\text{1}.\text{42 g}/\text{c}{{\text{m}}^{\text{3}}},\], respectively. The percentage of empty space in liquid at is
  A)
  34.84%
  done clear
  B)
                  43.8% 
  done clear
  C)
  23.4%                   
  done clear
  D)
  21.6%
  done clear
  View Answer play_arrow

• question_answer80) Which one of the following is an exothermic reaction?
  A)
  \[{{N}_{2}}(g)+{{O}_{2}}(g)+180.8kJ\to 2NO(g)\]
  done clear
  B)
  \[C(\text{graphite})+2S(s)\to C{{S}_{2}}(l)-91.9kJ\]
  done clear
  C)
  \[{{N}_{2}}(g)+3{{H}_{2}}(g)-92kJ\to 2N{{H}_{3}}(g)\]
  done clear
  D)
  \[\text{C(g)+}{{\text{H}}_{\text{2}}}\text{O(g)}\to \text{CO(g)+}{{\text{H}}_{\text{2}}}\text{(g)-131}\text{.1kJ}\]
  done clear
  View Answer play_arrow

• question_answer81) When\[\text{4A}\] of current is passed through a 1.0 L, 0.10 M\[\text{F}{{\text{e}}^{3+}}(aq)\]) solution for 1 h, it is partly reduced to Fe(s) and partly of. \[F{{e}^{2+}}(aq)\]Identify the incorrect statement.
  A)
   0.10 mole of electrons are required to convert all \[F{{e}^{3+}}\] to \[F{{e}^{2+}}\]
  done clear
  B)
  0.025 mol of Fe(s) will be deposited
  done clear
  C)
  0.075 mol of iron remains as \[\text{F}{{\text{e}}^{2+}}\]
  done clear
  D)
   0.050 mol of iron remains as \[\text{F}{{\text{e}}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer82) Which of the following statement are correct?
  A)
  \[C{{O}_{2}}\] and \[\text{Si}{{\text{O}}_{2}}\] both are gases
  done clear
  B)
  \[C{{O}_{2}}\] is gas and \[Si{{O}_{2}}\] is a liquid
  done clear
  C)
  \[C{{O}_{2}}\] is a gas but \[Si{{O}_{2}}\] is a solid
  done clear
  D)
  Carbon and Si both form oxides of similar properties
  done clear
  View Answer play_arrow

• question_answer83) Identify the product B of the following reactions
  A)
             
  done clear
  B)
  
  done clear
  C)
              
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer84) Give that, \[E_{F{{e}^{2+}}/Fe}^{\circ }=-0.44V,\]\[E_{F{{e}^{2+}}/F{{e}^{3+}}}^{\circ }=-0.77V.\] if \[F{{e}^{2+}},F{{e}^{3+}}\] and Fe solid are kept together, then
  A)
  \[F{{e}^{3+}}\]decreases
  done clear
  B)
  \[F{{e}^{3+}}\]increases
  done clear
  C)
   \[F{{e}^{2+}}\]decreases
  done clear
  D)
  \[F{{e}^{2+}},F{{e}^{3+}}\]remain unchanged
  done clear
  View Answer play_arrow

• question_answer85) Which of the following compound in its anionic form is aromatic?
  A)
  
  done clear
  B)
  
  done clear
  C)
                             
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer86) In terms of Arrhenius equation, \[k=A{{e}^{-{{E}_{a}}RT}}\]the  temperature  dependence  of rate constant (k) of a chemical reaction is written. Then, the activation energy \[({{E}_{a}})\] of the reaction can be calculated by plotting.
  A)
  \[\text{log k vs}\frac{\text{1}}{\text{logT}}\]     
  done clear
  B)
  \[\log \text{k vs }\frac{1}{T}\]
  done clear
  C)
  \[\text{k vsT}\]                
  done clear
  D)
  \[\text{k vs }\frac{1}{\log T}\]
  done clear
  View Answer play_arrow

• question_answer87) Which one of the following electrolytes is most effective for the coagulation of \[\text{Fe}{{\left( \text{OH} \right)}_{\text{3}}}\]Sol?
  A)
                                  \[\text{NaCl}\]                                 
  done clear
  B)
  \[\text{N}{{\text{a}}_{\text{2}}}S{{O}_{\text{4}}}\]
  done clear
  C)
  \[~\text{N}{{\text{a}}_{\text{3}}}\text{P}{{\text{O}}_{\text{4}}}\]                         
  done clear
  D)
  \[\text{A}{{\text{S}}_{\text{2}}}{{\text{S}}_{\text{3}}}\]       
  done clear
  View Answer play_arrow

• question_answer88) \[PhC{{H}_{2}}C{{H}_{3}}\xrightarrow[(ii){{H}_{3}}{{O}^{+}}]{(i)Cr{{O}_{2}}C{{l}_{2}}/CC{{l}_{4}}}PhC{{H}_{2}}CHO\] The above reaction is an example of which name reaction?
  A)
   Rosemond reduction                         
  done clear
  B)
   Bjrch reduction
  done clear
  C)
  Mendius reduction
  done clear
  D)
  Etard reduction
  done clear
  View Answer play_arrow

• question_answer89) Which of the following statement is applicable for Tyndall effect?
  A)
  The diameter of the dispersed particle is much smaller than the wavelength of the light used
  done clear
  B)
  The diameter of the dispersed phase is much smaller than the wavelength of the light used
  done clear
  C)
  The refractive indices of the dispersed phase and the dispersion medium must be same
  done clear
  D)
  The refractive indices of the dispersed phase and the dispersion medium must differ greatly in magnitude
  done clear
  View Answer play_arrow

• question_answer90) Match the following and choose the correct option.                                        

  	Column 1		Column II
  A.	Ribose	1.	Ninhydrin
  B.	Biotin	2.	Nucleic acid
  C.	Enzyme	3.	Vitamin
  D.	Glycine	4.	Globular protein

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

• question_answer91) On reduction of glycolic acid with \[\text{HI}\], the product formed is
  A)
  acetic acid          
  done clear
  B)
  iodo acetic acid
  done clear
  C)
   formic acid                        
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer92) Consider the following reaction, Identify the product B.
  A)
  
  done clear
  B)
  
  done clear
  C)
                
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer93) Arrange the following compounds in the increasing order of their reactivity towards HCN. (i) Acetaldehyde (ii) Acetone (iii) Di ? tert ? butyl ketone (iv) Methyl ?tert ?butyl ketone
  A)
  \[~\text{III }<\text{ II }<\text{ IV }<\text{ I}\]
  done clear
  B)
  \[\text{II }<\text{ I }<\text{ IV }<\text{ II}\]
  done clear
  C)
  \[~\text{IV }<\text{ III }<\text{ II }<\text{ I}\]
  done clear
  D)
  \[~\text{II }<\text{ IV }<\text{ I }<\text{ III}\]
  done clear
  View Answer play_arrow

• question_answer94) The enolic form of acetone contains
  A)
  \[10\sigma -\] bonds, \[2\pi \] - bonds and 1 lone pair
  done clear
  B)
  \[9\sigma \] -bonds, \[2\pi \] bonds and 2 lone pairs
  done clear
  C)
  \[8\sigma \]- bonds, \[2\pi \]-bonds and 2 lone pairs
  done clear
  D)
   \[9\sigma -\]bonds, \[1\pi \]-bond and 2 lone pairs
  done clear
  View Answer play_arrow

• question_answer95) The magnetic moment of \[{{M}^{x+}}\] (atomic number = 25) is \[\sqrt{15}\]BM. Then, the oxidation number \[x\] of M is
  A)
  3                                             
  done clear
  B)
  4
  done clear
  C)
  2                                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer96) When 0.1 M \[\text{NaOH}\] is titrated with 0.1 M, 20 mL HA till the end point, \[{{K}_{a}}(HA)=6\times {{10}^{-6}}\] and degree of dissociation of HA is small as compared to unity. What is the pH of the resulting solution at the end point?
  A)
  6.23                       
  done clear
  B)
  9.22
  done clear
  C)
  7.21                       
  done clear
  D)
  8.95
  done clear
  View Answer play_arrow

• question_answer97) Arrange the following in the decreasing order of basic character. (i) p-toluidine (ii) N, N-dimethyl-p-toluidine (iii) p-nitroaniline (iv) Aniline
  A)
  \[~\text{II }>\text{ III }>\text{ I }>\text{ IV}\]
  done clear
  B)
  \[\text{I }>\text{ II }>\text{ III }>\text{ IV}\]
  done clear
  C)
  \[~\text{II }>\text{ I }>\text{ IV }>\text{ III}\]
  done clear
  D)
  \[~\text{IV }>\text{ III }>\text{ I }>\text{ II}\]
  done clear
  View Answer play_arrow

• question_answer98) What   is   the   enthalpy   of   the disproportionation of \[\text{MgCl}\] if the enthalpy of formation of hypothetical  \[\text{MgCl}\]   is \[-\text{125 kJ}/\text{mol}\] and the =\[MgC{{l}_{2}}\] is\[-\text{ 642 kJ}/\text{mol}\]?
  A)
  \[-\text{ 767 kJ}/\text{mol}\]
  done clear
  B)
  \[~\text{767 kJ}/\text{mol}\]
  done clear
  C)
  \[-\text{392 kJ}/\text{mol}\]
  done clear
  D)
  \[\text{392 kJ}/\text{mol}\]
  done clear
  View Answer play_arrow

• question_answer99) The decreasing order of reactivity towards electrophilic addition of the following is (i) \[\text{CH }=\text{CH}\] (ii) \[\text{C}{{\text{H}}_{\text{2}}}=\text{C}{{\text{H}}_{\text{2}}}\]                 (iii) \[{{\text{H}}_{\text{2}}}\text{C}=\text{CH}\text{Cl}\] (iv) \[\text{H}\underset{\text{Cl}}{\mathop{\underset{|}{\mathop{\text{C}}}\,}}\,=\underset{\text{Cl}}{\mathop{\underset{|}{\mathop{\text{C}}}\,}}\,\text{H}\]
  A)
  \[\text{I }>\text{ II }>\text{ III }>\text{ IV}\]        
  done clear
  B)
  \[~\text{II }>\text{ I }>\text{ III }>\text{ IV}\]
  done clear
  C)
  \[\text{IV }>\text{ 111 }>\text{ I }>\text{ II}\]         
  done clear
  D)
  \[~\text{IV }>\text{ III }>\text{ II }>\text{ I}\]
  done clear
  View Answer play_arrow

• question_answer100) Given the following bond dissociation enthalpies\[\left( \text{kJ mo}{{\text{l}}^{\text{-1}}} \right)\]. \[P\equiv P-490,P-P-209,\] \[N\equiv N-946,\] \[N-N-160\]Compare the enthalpy changes for the process (i) \[2{{P}_{2}}(g)\to {{P}_{4}}(g)\] (ii) \[2{{N}_{2}}(g)\to {{N}_{4}}(g)\] Choose the correct option.
  A)
  \[{{P}_{4}}\] is feasible but \[{{\text{N}}_{\text{4}}}\]is not feasible
  done clear
  B)
  \[{{P}_{4}}\] is not feasible but \[{{\text{N}}_{\text{4}}}\]is feasible
  done clear
  C)
  Both \[{{\text{P}}_{4}}\] and \[{{\text{N}}_{\text{4}}}\]are feasible
  done clear
  D)
  Both \[{{P}_{4}}\] and \[{{\text{N}}_{\text{4}}}\]are not feasible
  done clear
  View Answer play_arrow

• question_answer101) \[\int_{{}}^{{}}{\frac{{{x}^{2}}-2}{{{x}^{3}}\sqrt{{{x}^{2}}-1}}}dx\] is equal to
  A)
  \[\frac{{{x}^{2}}}{\sqrt{{{x}^{2}}-1}}+C\]                             
  done clear
  B)
  \[-\frac{{{x}^{2}}}{\sqrt{{{x}^{2}}-1}}+C\]
  done clear
  C)
  \[\frac{\sqrt{{{x}^{2}}-1}}{{{x}^{2}}}+C\]                             
  done clear
  D)
  \[-\frac{\sqrt{{{x}^{2}}-1}}{{{x}^{2}}}+C\]
  done clear
  View Answer play_arrow

• question_answer102) Let \[f(x)\] be twice differentiable function such that \[f''(0)=2.\] Then,\[\underset{x\to 0}{\mathop{\lim }}\,\frac{2f(x)-3f(2x)+f(4x)}{{{x}^{2}}}\]is equal to
  A)
  6           
  done clear
  B)
  3
  done clear
  C)
  12                                         
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer103) If \[\alpha \]and \[\beta \]are non-real numbers satisfying \[{{x}^{3}}-1=0,\]then the value of \[\left| \begin{matrix}    \lambda +1 & \alpha  & \beta   \\    \alpha  & \lambda +\beta  & 1  \\    \beta  & 1 & \lambda +\alpha   \\ \end{matrix} \right|\] is
  A)
   0                                           
  done clear
  B)
  \[{{\lambda }^{3}}\]
  done clear
  C)
  \[{{x}^{2}}+2bx+4=0\] 
  done clear
  D)
  \[{{x}^{2}}-bx+1=0\]
  done clear
  View Answer play_arrow

• question_answer104) Let \[\alpha \]and \[\beta \]be the roots of  \[{{x}^{2}}+bx+1=0\] Then, the equation whose roots are \[-\left( \alpha +\frac{1}{\beta } \right)\]and \[-\left( \beta +\frac{1}{\alpha } \right),\] is
  A)
  \[{{x}^{2}}=0\]                
  done clear
  B)
  \[{{x}^{2}}+2bx+4=0\]
  done clear
  C)
  \[{{x}^{2}}-2bx+4=0\]
  done clear
  D)
  \[{{x}^{2}}-bx+1=0\]
  done clear
  View Answer play_arrow

• question_answer105) The value of \[^{40}{{C}_{0}}{{+}^{40}}{{C}_{1}}{{+}^{40}}{{C}_{2}}+...{{+}^{40}}{{C}_{20}}\] is
  A)
  \[{{2}^{40}}+\frac{40!}{{{(20!)}^{2}}}\]  
  done clear
  B)
  \[{{2}^{39}}-\frac{1}{2}\times \frac{40!}{{{(20!)}^{2}}}\]
  done clear
  C)
  \[{{2}^{39}}{{+}^{40}}{{C}_{20}}\]                           
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer106) 106.        Let \[f:R\to R\] be a function defined by \[f(x)=\frac{{{x}^{2}}-8}{{{x}^{2}}+2}.\] Then, \[f\] is
  A)
                  one-one but not onto
  done clear
  B)
  one-one and onto
  done clear
  C)
  onto but not one-one
  done clear
  D)
  neither one-one nor onto
  done clear
  View Answer play_arrow

• question_answer107) For all \[n\in N,{{7}^{2n}}-48n-1\] is divisible by
  A)
  25                                         
  done clear
  B)
  26
  done clear
  C)
  1234                     
  done clear
  D)
   2304
  done clear
  View Answer play_arrow

• question_answer108) The period of\[f(x)=\sin \frac{2\pi x}{3}+\cos \frac{\pi x}{2}\] is
  A)
  3                                            
  done clear
  B)
  4
  done clear
  C)
  6                                            
  done clear
  D)
  12
  done clear
  View Answer play_arrow

• question_answer109) If \[f(x)=\left\{ \frac{1-\sin x}{{{(\pi -2x)}^{2}}}.\frac{\log \sin x}{\log (1+{{\pi }^{2}}-4\pi x+{{x}^{2}})'k,} \right\}\] \[x\ne \frac{\pi }{2}\] \[x=\frac{\pi }{2}\]                 Is continuous at \[x=\frac{\pi }{2},\]then \[k\]is equal to
  A)
                  \[-\frac{1}{16}\]                               
  done clear
  B)
  \[-\frac{1}{32}\]
  done clear
  C)
                  \[-\frac{1}{64}\]
  done clear
  D)
  \[-\frac{1}{28}\]
  done clear
  View Answer play_arrow

• question_answer110) If \[y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+...\infty }}}}\],then \[\frac{dy}{dx}\] is equal to
  A)
  \[\frac{y+x}{{{y}^{2}}-2x}\]                       
  done clear
  B)
  \[\frac{{{y}^{3}}-x}{2{{y}^{2}}-2xy-1}\]
  done clear
  C)
  \[\frac{{{y}^{3}}+x}{2{{y}^{2}}-x}\]                        
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer111) A differentiable function \[f(x)\]has a relative minimum at \[x=0\], then the function\[y=f(x)+ax+b\]has a relative minimum at \[x=0\] for
  A)
  all a and All B    
  done clear
  B)
  all b, if \[a=0\]
  done clear
  C)
  all \[b>0\]                          
  done clear
  D)
  all \[a>0\]
  done clear
  View Answer play_arrow

• question_answer112) The probability that atleast one of the events A and B occurs, is 0.6. If A and B occur simultaneously with probability 0.2, then \[p(\bar{A})+P(\bar{B})\] is equal to
  A)
   0.4                          
  done clear
  B)
  0.8    
  done clear
  C)
  1.2  
  done clear
  D)
  1.4
  done clear
  View Answer play_arrow

• question_answer113) The solution of the differential equation\[({{x}^{2}}-y{{x}^{2}})\frac{dy}{dx}+{{y}^{2}}+x{{y}^{2}}=0\] is
  A)
  \[\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+C\]
  done clear
  B)
  \[\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+C\]
  done clear
  C)
  \[\log \left( xy \right)=\frac{1}{x}+\frac{1}{y}+C\]
  done clear
  D)
  \[\log (xy)+\frac{1}{x}+\frac{1}{y}=C\]
  done clear
  View Answer play_arrow

• question_answer114) From 50 students taking examinations in 1 Mathematics, Physics and Chemistry, 37 passed in Mathematics, 24 in Physics and 43 in Chemistry. Atmost 19 passed in Mathematics and Physics, atmost 29 passed in Mathematics and Chemistry and atmost 20 passed in Physics and Chemistry. The largest possible-number that could have passed all three examinations, is
  A)
   11                         
  done clear
  B)
   12    
  done clear
  C)
   13                         
  done clear
  D)
  14
  done clear
  View Answer play_arrow

• question_answer115) The area bounded by the curves \[y=\cos x\]and \[y=\sin x\]between the ordinates \[x\text{ }=\text{ }0\]and \[x=\frac{3\pi }{2}\] is
  A)
  \[4\sqrt{2}-1\]                  
  done clear
  B)
  \[4\sqrt{2}+1\]
  done clear
  C)
  \[4\sqrt{2}-2\]                  
  done clear
  D)
  \[4\sqrt{2}+2\]
  done clear
  View Answer play_arrow

• question_answer116) If \[\frac{\log 3}{x-y}=\frac{\log 5}{y-z}=\frac{1og7}{z-x}\],then \[{{3}^{x+y}}{{.5}^{y+z}}{{.7}^{z+x}}\] is equal to
  A)
   0                                            
  done clear
  B)
  2
  done clear
  C)
  1                                             
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer117) The value of the integral \[\int_{0}^{0.9}{[x-2][x]dx,}\]where \[[\cdot ]\] denotes the greatest integer function, is
  A)
  0.9                         
  done clear
  B)
  0      
  done clear
  C)
  1.8                         
  done clear
  D)
  -0.9
  done clear
  View Answer play_arrow

• question_answer118) A root of the equation \[17{{x}^{2}}+17x\tan \left( 2{{\tan }^{-1}}\frac{1}{5}-\frac{\pi }{4} \right)-10=0\] is
  A)
  \[\frac{10}{17}\]                                              
  done clear
  B)
  \[-1\]
  done clear
  C)
  \[-\frac{7}{17}\]                               
  done clear
  D)
  \[1\]
  done clear
  View Answer play_arrow

• question_answer119) The number of solutions of the equation \[3{{\sin }^{2}}x-7\sin x+2=0\] in the interval \[[0,5\pi ]\] is
  A)
  0                                             
  done clear
  B)
  5     
  done clear
  C)
  6                                             
  done clear
  D)
  10
  done clear
  View Answer play_arrow

• question_answer120) If the mean and SD of a binomial distribution are 20 and 4 respectively, then the number of trials is
  A)
  50                          
  done clear
  B)
  25     
  done clear
  C)
  100                        
  done clear
  D)
  80
  done clear
  View Answer play_arrow

• question_answer121) 1f \[a=\hat{i}+\hat{j},b=2\hat{j}-\hat{k}\]and \[r\times a=b\times a,\] \[r\times b\] \[=a\times b,\]  then a unit vector in the direction of r is
  A)
  \[\frac{1}{\sqrt{11}}(\hat{i}+3\hat{j}-\hat{k})\]
  done clear
  B)
  \[\frac{1}{\sqrt{11}}(\hat{i}-3\hat{j}+\hat{k})\]
  done clear
  C)
  \[\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})\]   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer122) If PQRS is a convex quadrilateral with 3, 4, 5 and 6 points marked on sides PQ, QR, RS and PS respectively, then the number of triangles with vertices on different sides is
  A)
                  220                        
  done clear
  B)
  270    
  done clear
  C)
  342                        
  done clear
  D)
  282
  done clear
  View Answer play_arrow

• question_answer123) From the bottom of a pole of height A, the angle of elevation of the top of a tower is \[\alpha \]. The pole subtends an angle \[\beta \]  at the top of the tower. The height of the tower is
  A)
  \[\frac{h\sin \alpha (\alpha -\beta )}{\sin \beta }\]         
  done clear
  B)
  \[\frac{h\sin \alpha \cos (\alpha +\beta )}{\cos \beta }\]
  done clear
  C)
   \[\frac{h\sin \alpha \cos (\alpha -\beta )}{\sin \beta }\]              
  done clear
  D)
  \[\frac{h\sin \alpha \sin (\alpha +\beta )}{\cos \beta }\]
  done clear
  View Answer play_arrow

• question_answer124) If the mean deviation about the median of the numbers a, 2a, 3a, ... , 50a is 50, then \[|\alpha |\] is equal to
  A)
   2                                            
  done clear
  B)
  3     
  done clear
  C)
  4                                             
  done clear
  D)
   5
  done clear
  View Answer play_arrow

• question_answer125) The equation of a straight line passing through the point of intersection of \[x-y+1=0\]and  \[3x+y-5=0\]  and perpendicular to one of them, is
  A)
   x + y + 3 = 0       
  done clear
  B)
   x - y - 3 = 0
  done clear
  C)
  x-3y-5=0                             
  done clear
  D)
  x-3y+5=0
  done clear
  View Answer play_arrow

• question_answer126) Consider   the   circles   \[{{x}^{2}}+{{(y-1)}^{2}}=9,\] \[{{(x-1)}^{2}}+{{y}^{2}}=25\].They are such that
  A)
  these circles touch each other
  done clear
  B)
  one of these circles lies entirely inside the other
  done clear
  C)
  each of these circles lies outside the other
  done clear
  D)
  they intersect in two points
  done clear
  View Answer play_arrow

• question_answer127) The eccentricity of the hyperbola \[\frac{\sqrt{1999}}{3}({{x}^{2}}-{{y}^{2}})=1\]
  A)
  \[\sqrt{2}\]        
  done clear
  B)
  \[2\]
  done clear
  C)
  \[2\sqrt{2}\]                      
  done clear
  D)
  \[\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer128) The direction ratios of the normal to the n plane passing through the points (1,-2, 3),  (-1, 2,-1)  and  parallel  to  the  line \[\frac{x-2}{2}=\frac{y+1}{3}=\frac{z}{4}\] are proportional to
  A)
  2, 3, 4                   
  done clear
  B)
  4, 0, 7
  done clear
  C)
  -2, 0,-1                 
  done clear
  D)
  2, 0, -1
  done clear
  View Answer play_arrow

• question_answer129) The mid-point of the chord 2x + y -4 = 0 of the parabola \[{{y}^{2}}=4x\]is
  A)
  (5/2,-1)                
  done clear
  B)
  -1,5/2)
  done clear
  C)
  (3/2, -1)               
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer130) If the rate of change of area of a square plate is 13 equal to that of the rate of change of its perimeter, then length of the side is
  A)
  1 unit                    
  done clear
  B)
  2 units
  done clear
  C)
  3 units                  
  done clear
  D)
  4 units
  done clear
  View Answer play_arrow

• question_answer131) The exradii of a triangle, \[{{r}_{1}},{{r}_{2}},{{r}_{3}}\]are in 1A armonic progression, then the sides a, b and c are in
  A)
  HP                                        
  done clear
  B)
  AP
  done clear
  C)
  GP                                           
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer132) The equation of the tangent to the curves x = t cost and y = t sin t at the origin is
  A)
  x = 0                                      
  done clear
  B)
  y = 0
  done clear
  C)
   x + y = 0                              
  done clear
  D)
   x-y = 0
  done clear
  View Answer play_arrow

• question_answer133) 1f |a| < 1 and |b| < 1, then the sum of the series \[a(a+b)+{{a}^{2}}({{a}^{2}}+{{b}^{2}})+{{a}^{3}}({{a}^{3}}+{{b}^{3}})+...\] is    
  A)
  \[\frac{a}{1-a}+\frac{ab}{1-ab}\]             
  done clear
  B)
  \[\frac{{{a}^{2}}}{1-{{a}^{2}}}+\frac{ab}{1-ab}\]
  done clear
  C)
  \[\frac{b}{1-b}+\frac{a}{1-a}\]                 
  done clear
  D)
  \[\frac{{{b}^{2}}}{1-{{b}^{2}}}+\frac{ab}{1-ab}\]
  done clear
  View Answer play_arrow

• question_answer134) If \[x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3},\]then \[xy+yz+zx\]is equal to
  A)
   -1                          
  done clear
  B)
  0       
  done clear
  C)
  1                             
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer135) If A is a square matrix such that \[{{\text{A}}^{\text{2}}}\text{ }=\text{ A}\] and  \[\text{B }=\text{ I }-\text{ A,}\], then \[AB+BA+I-{{(I-A)}^{2}}\] is equal to
  A)
  A                                              
  done clear
  B)
  2A    
  done clear
  C)
  -A                                          
  done clear
  D)
  \[l-A\]
  done clear
  View Answer play_arrow

• question_answer136) The radius of the circle passing through the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\] and having its centre \[(0,3),\] is
  A)
                   4                            
  done clear
  B)
  3      
  done clear
  C)
  \[\sqrt{12}\]                      
  done clear
  D)
  7/2
  done clear
  View Answer play_arrow

• question_answer137) Let \[f(x)={{({{x}^{3}}+2)}^{30}}\] .If \[{{f}^{n}}(x)\] is a polynomial of degree 20, where \[{{f}^{n}}(x)\] denotes the nth order derivative of \[f(x)\] with respect to x, then the value of n is
  A)
  60                          
  done clear
  B)
  40     
  done clear
  C)
  70                          
  done clear
  D)
  50
  done clear
  View Answer play_arrow

• question_answer138) The solution set of the in equation \[\frac{1}{|x|-3}<\frac{1}{2}\] is
  A)
  \[(-\infty ,-5)\cup (5,\infty )\]   
  done clear
  B)
  \[(-3,3)\]
  done clear
  C)
  \[(-\infty ,-5)\cup (-3,3)\cup (5,\infty )\]
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer139) For real \[x\], let \[f(x)={{x}^{3}}+5x+1,\] then
  A)
  f is one-one but not onto R
  done clear
  B)
  f is onto R but not one-one
  done clear
  C)
  f is one-one and onto R
  done clear
  D)
  f is neither one-one nor onto R
  done clear
  View Answer play_arrow

• question_answer140) If  \[{{z}_{1}}\] and \[{{z}_{2}}\] are two complex numbers such that \[\operatorname{Im}\] \[({{z}_{1}}+{{z}_{2}})=0,\]\[\operatorname{Im}\]\[({{z}_{1}}{{z}_{2}})=0,\], then
  A)
                  \[{{z}_{1}}=-{{z}_{2}}\]c               
  done clear
  B)
  \[{{z}_{1}}={{z}_{2}}\]
  done clear
  C)
                  \[{{z}_{1}}={{\bar{z}}_{2}}\]                       
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer141) If                                                                                                        \[f(x)=[x\sin \pi x],\]  then which of the following is incorrect?
  A)
                                                                                                                       \[f(x)\]  is continuous at x = 0
  done clear
  B)
                                                                                                                       \[f(x)\]  is continuous in (-1,0)
  done clear
  C)
  \[f(x)\] is differentiable at x = 1
  done clear
  D)
  \[f(x)\] is differentiable in (-1,1)
  done clear
  View Answer play_arrow

• question_answer142) \[\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\]is logically equivalent to
  A)
  \[\tilde{\ }p\]   
  done clear
  B)
  \[p\]
  done clear
  C)
  \[q\]                                    
  done clear
  D)
  \[-q\]
  done clear
  View Answer play_arrow

• question_answer143) The degree of the differential equation\[x=1+\frac{dy}{dx}+\frac{1}{2!}{{\left( \frac{dy}{dx} \right)}^{2}}+\frac{1}{3!}{{\left( \frac{dy}{dx} \right)}^{3}}+...\]is
  A)
                   3
  done clear
  B)
                  1
  done clear
  C)
                  not defined                       
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer144) The value of\[\int_{{}}^{{}}{\frac{{{\sin }^{2}}x{{\cos }^{2}}x}{{{({{\sin }^{3}}x+{{\cos }^{3}}x)}^{2}}}dx}\] is
  A)
  \[\frac{1}{3(1+{{\tan }^{3}}x)}+C\]          
  done clear
  B)
  \[-\frac{1}{3(1+{{\tan }^{3}}x)}+C\]
  done clear
  C)
  \[\frac{1}{1+{{\tan }^{3}}x}+C\]
  done clear
  D)
  \[-\frac{1}{1+{{\tan }^{3}}x}+C\]
  done clear
  View Answer play_arrow

• question_answer145) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}\] is equal to
  A)
  4                                            
  done clear
  B)
  3
  done clear
  C)
  2            
  done clear
  D)
  \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer146) The equations \[ax+by+c=0\]and \[dx+ey+f=0\]represent the same straight line if and only if
  A)
  \[\frac{a}{d}=\frac{b}{c}\]                          
  done clear
  B)
  \[c=f\]
  done clear
  C)
   \[\frac{a}{d}=\frac{b}{e}=\frac{c}{f}\]                 
  done clear
  D)
  \[a=d,b=e,c=f\]
  done clear
  View Answer play_arrow

• question_answer147) If \[y=\sec ({{\tan }^{-1}}x),\] then \[\frac{dy}{dx}\]at \[x=1\]is equal to
  A)
  \[\frac{1}{\sqrt{2}}\]                                     
  done clear
  B)
  \[\frac{1}{2}\]
  done clear
  C)
  \[1\]                                     
  done clear
  D)
  \[\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer148) If the roots of the equation \[{{x}^{2}}\text{ }-\text{ }px\text{ }+\text{ }q\text{ }=\text{ }0\]differ by unity, then
  A)
  \[{{\text{p}}^{\text{2}}}\text{ }=\text{4q}\]                       
  done clear
  B)
  \[{{p}^{2}}=4q+1\]
  done clear
  C)
  \[{{p}^{2}}=4q-1\]          
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer149) If the SD of a set of observations is 8 and each observation is divided by -2, then the SD of the new set of observations will be
  A)
  -4                                           
  done clear
  B)
  -8
  done clear
  C)
   8                                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer150) If \[2(y-a)\] is the HM between y - x and y - z, then x-a, y-a, z-a are in
  A)
  AP                                         
  done clear
  B)
  GP
  done clear
  C)
  HP                           
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow