Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2010

done CEE Kerala Engineering Solved Paper-2010 Total Questions - 240

• question_answer1) Two resistors of resistances\[200\,k\Omega \]and\[1\,M\Omega \] respectively form a potential divider with outer junctions maintained at potentials of\[+3V\]and\[-15V\]. Then, the potential at the junction between the resistors is
  A)
   \[+1\text{ }V\]                                
  done clear
  B)
   \[-0.6\text{ }V\]
  done clear
  C)
   zero                     
  done clear
  D)
          \[-\,12V\]
  done clear
  E)
   \[+12\text{ }V\]
  done clear
  View Answer play_arrow

• question_answer2) The graph between resistivity and temperature, for a limited range of temperatures, is a straight line for a material like
  A)
   copper          
  done clear
  B)
          nichrome
  done clear
  C)
   silicon                  
  done clear
  D)
          mercury
  done clear
  E)
   gallium arsenide
  done clear
  View Answer play_arrow

• question_answer3) In the circuit shown, the current through the\[5\,\Omega \]resistor is
  A)
   \[\frac{8}{3}A\]                               
  done clear
  B)
          \[\frac{9}{13}A\]
  done clear
  C)
   \[\frac{4}{13}A\]            
  done clear
  D)
          \[\frac{1}{3}A\]
  done clear
  E)
   \[\frac{2}{3}A\]
  done clear
  View Answer play_arrow

• question_answer4) A solenoid has core of a material with relative permeability 500 and its windings carry a current of 1 A. The number of turns of the solenoid is \[500\text{ }{{m}^{-1}}\]. The magnetization of the material is nearly
  A)
   \[2.5\times {{10}^{3}}A{{m}^{-1}}\]
  done clear
  B)
          \[2.5\times {{10}^{5}}A{{m}^{-1}}\]
  done clear
  C)
   \[2.0\times {{10}^{3}}A{{m}^{-1}}\]
  done clear
  D)
   \[2.0\times {{10}^{5}}A{{m}^{-1}}\]
  done clear
  E)
   \[5\times {{10}^{5}}A{{m}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer5) Choose the correct statement
  A)
   A paramagnetic material tends to move from a strong magnetic field to weak magnetic field
  done clear
  B)
   A magnetic material is in the paramagnetic phase below its Curie temperature
  done clear
  C)
   The resultant magnetic moment in an atom of a diamagnetic substance is zero
  done clear
  D)
   Typical domain size of a ferromagnetic material is 1 nm
  done clear
  E)
   The susceptibility of a ferromagnetic material is slightly greater than 1
  done clear
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• question_answer6) A\[2\mu C\]charge moving around a circle with a frequency of\[6.25\times {{10}^{12}}Hz\] produces a magnetic field 6.28 T at the centre of the circle. The radius of the circle is
  A)
   2.25m                  
  done clear
  B)
          0.25m
  done clear
  C)
   13.0m                  
  done clear
  D)
          1.25m
  done clear
  E)
   3.25m
  done clear
  View Answer play_arrow

• question_answer7) A galvanometer of resistance \[100\,\,\Omega \] is converted to a voltmeter of range 10 V by connecting a resistance of\[10\,k\Omega \]. The resistance required to convert the same galvanometer to an ammeter of range 1 A is
  A)
   \[0.4\,\Omega \]            
  done clear
  B)
          \[0.3\,\,\Omega \]
  done clear
  C)
   \[1.2\,\Omega \]           
  done clear
  D)
          \[0.2\,\,\Omega \]
  done clear
  E)
   \[0.1\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer8) Two wires with currents 2A and 1A are enclosed in a circular loop. Another wire with current 3 A is situated outside the loop as shown. Then\[\oint{\overrightarrow{B}}.\overrightarrow{dl}\]around the loop is
  A)
   \[{{\mu }_{0}}\]              
  done clear
  B)
          \[3{{\mu }_{0}}\]
  done clear
  C)
   \[6{{\mu }_{0}}\]                            
  done clear
  D)
          \[2{{\mu }_{0}}\]
  done clear
  E)
   zero
  done clear
  View Answer play_arrow

• question_answer9) An L-C-R series AC circuit is at resonance with 10 V each across L, C and R. If the resistance is halved, the respective voltages across L, C and R are
  A)
   10 V, 10 V and 5 V
  done clear
  B)
   10 V, 10 V and 10 V
  done clear
  C)
   20V, 20V and 5V
  done clear
  D)
   20 V, 20 V and 10 V
  done clear
  E)
   5 V, 5 V and 5 V
  done clear
  View Answer play_arrow

• question_answer10) A 50 Hz AC current of peak value 2 A flows through one of the pair of coils. If the mutual inductance between the pair of coils is 150 mH, then the peak value of voltage induced in the second coil is
  A)
   \[30\,\pi V\]                     
  done clear
  B)
          \[60\,\pi V\]
  done clear
  C)
   \[15\,\pi V\]                     
  done clear
  D)
          \[300\,\pi V\]
  done clear
  E)
   \[3\,\pi V\]
  done clear
  View Answer play_arrow

• question_answer11) A transformer is used to light a 100 W and 110 V lamp from a 220 V main supply. If the main current is 0.5 A, then the efficiency of the transformer is nearly
  A)
   89%                      
  done clear
  B)
          100%
  done clear
  C)
   95%                      
  done clear
  D)
          85%
  done clear
  E)
   91%
  done clear
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• question_answer12) An L-C-R series circuit is at resonance. Then
  A)
   the phase difference between current and voltage is\[{{90}^{o}}\]
  done clear
  B)
   the phase difference between current and voltage is\[{{45}^{o}}\]
  done clear
  C)
   its impedance is purely resistive
  done clear
  D)
   its impedance is zero
  done clear
  E)
   the current is minimum
  done clear
  View Answer play_arrow

• question_answer13) A 100 W bulb produces an electric field of \[2.9\text{ }V{{m}^{-1}}\]at a point 3 m away. If the bulb is replaced by 400 W bulb without distributing other conditions, then the electric field produced at the same point is
  A)
   \[2.9\text{ }V{{m}^{-1}}\]        
  done clear
  B)
          \[3.5\text{ }V{{m}^{-1}}\]
  done clear
  C)
   \[5\text{ }V{{m}^{-1}}\]              
  done clear
  D)
          \[5.8\text{ }V{{m}^{-1}}\]
  done clear
  E)
   \[\text{1}\text{.45 }V{{m}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer14) In the total electromagnetic energy falling on a surface is U, then the total momentum delivered (for complete absorption) is
  A)
   \[\frac{U}{c}\]                                 
  done clear
  B)
   \[cU\]
  done clear
  C)
   \[\frac{U}{{{c}^{2}}}\]                  
  done clear
  D)
          \[{{c}^{2}}U\]
  done clear
  E)
   \[\sqrt{\frac{U}{c}}\]
  done clear
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• question_answer15) The focal lengths of the objective and of the eye-piece of a compound microscope are\[{{f}_{o}}\]and\[{{f}_{e}}\]respectively. If L is the tube length and D, the least distance of distinct vision, then its angular magnification, when the image is formed at infinity, is
  A)
   \[\left( 1-\frac{L}{{{f}_{o}}} \right)\left( \frac{D}{{{f}_{e}}} \right)\]
  done clear
  B)
          \[\left( 1+\frac{L}{{{f}_{o}}} \right)\left( \frac{D}{{{f}_{e}}} \right)\]
  done clear
  C)
   \[\frac{L}{{{f}_{o}}}\left( 1-\frac{D}{{{f}_{e}}} \right)\] 
  done clear
  D)
          \[\frac{L}{{{f}_{o}}}\left( 1+\frac{D}{{{f}_{e}}} \right)\]
  done clear
  E)
   \[\frac{L}{{{f}_{o}}}\left( \frac{D}{{{f}_{e}}} \right)\]
  done clear
  View Answer play_arrow

• question_answer16) The velocity of a moving galaxy is\[300\text{ }km{{s}^{-1}}\] and the apparent change in wavelength of a spectral line emitted from the galaxy is observed as 0.5 nm. Then, the actual wavelength of the spectral line is
  A)
  \[3000\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  B)
         \[5000\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  C)
  \[6000\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  D)
                         \[4500\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  E)
                  \[5500\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  View Answer play_arrow

• question_answer17) An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation between the objective and the eye-piece is 36 cm and the final image is formed at infinity. The focal length\[{{f}_{o}}\]of the objective and\[{{f}_{e}}\]of the eye-piece are respectively
  A)
   45 cm and 9 cm
  done clear
  B)
          50 cm and 10 cm
  done clear
  C)
   7.2 cm and 5 cm
  done clear
  D)
          30 cm and 6 cm
  done clear
  E)
   5 cm and 7.2 cm
  done clear
  View Answer play_arrow

• question_answer18) If the reflected image formed is magnified and virtual, then the mirror system is
  A)
   concave only    
  done clear
  B)
          convex only
  done clear
  C)
   plane                   
  done clear
  D)
          concave or convex
  done clear
  E)
   convex or plane
  done clear
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• question_answer19) A vessel of depth x is half filled with oil of refractive index \[{{\mu }_{1}}\] and the other half is filled with water of refractive index\[{{\mu }_{2}}\]The apparent depth of the vessel when viewed from above is
  A)
   \[\frac{x({{\mu }_{1}}+{{\mu }_{2}})}{2{{\mu }_{1}}{{\mu }_{2}}}\]         
  done clear
  B)
          \[\frac{x\,{{\mu }_{1}}\,{{\mu }_{2}}}{2({{\mu }_{1}}+{{\mu }_{2}})}\]
  done clear
  C)
   \[\frac{x{{\mu }_{1}}{{\mu }_{2}}}{({{\mu }_{1}}+{{\mu }_{2}})}\]           
  done clear
  D)
          \[\frac{2x({{\mu }_{1}}+{{\mu }_{2}})}{{{\mu }_{1}}{{\mu }_{2}}}\]
  done clear
  E)
   \[\frac{4({{\mu }_{1}}+{{\mu }_{2}})x}{{{\mu }_{1}}{{\mu }_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer20) If m is the mass of an electron and c is the speed of light, the ratio of the wavelength of a photon of energy E to that of the electron of the same energy is  
  A)
   \[c\sqrt{\frac{2m}{E}}\]              
  done clear
  B)
          \[\sqrt{\frac{2m}{E}}\]
  done clear
  C)
   \[\sqrt{\frac{2m}{cE}}\]              
  done clear
  D)
          \[\sqrt{\frac{m}{E}}\]
  done clear
  E)
   \[\sqrt{\frac{cm}{E}}\]
  done clear
  View Answer play_arrow

• question_answer21) The set which represents the isotope, isobar and isotone respectively is
  A)
  \[{{(}_{1}}{{H}^{2}}{{,}_{1}}{{H}^{3}}),{{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})\]and\[{{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{2}})\]
  done clear
  B)
   \[{{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{2}}),{{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})\]and\[{{(}_{1}}{{H}^{1}}{{,}_{1}}{{H}^{3}})\]
  done clear
  C)
   \[{{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{3}}),{{(}_{1}}{{H}^{2}}{{,}_{1}}{{H}^{3}})\]and\[{{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})\]
  done clear
  D)
   \[{{(}_{1}}{{H}^{2}}{{,}_{1}}{{H}^{3}}),{{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{3}})\]and\[{{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})\]
  done clear
  E)
   \[{{(}_{1}}{{H}^{1}}{{,}_{1}}{{H}^{3}}),{{(}_{79}}A{{u}^{197}}{{,}_{80}}H{{g}^{198}})\]and\[{{(}_{2}}H{{e}^{3}}{{,}_{1}}{{H}^{3}})\]
  done clear
  View Answer play_arrow

• question_answer22) Two samples X and Y contain equal amount of radioactive substances. If\[\frac{1}{16}\]th of the sample X and\[\frac{1}{256}\]th of the sample V, remain after 8 h, then the ratio of half periods of X and Y is
  A)
   2 : 1                      
  done clear
  B)
          1 : 2
  done clear
  C)
   1 : 4                      
  done clear
  D)
          1 : 16
  done clear
  E)
   4 : 1
  done clear
  View Answer play_arrow

• question_answer23) Radioactive\[_{27}^{60}Co\]is transformed into stable\[_{28}^{60}Ni\]by emitting two\[\gamma -\]rays of energies
  A)
   1.33 MeV and 1.17 MeV in succession
  done clear
  B)
   1.17 MeV and 1.33 MeV in succession
  done clear
  C)
   1.37 MeV and 1.13 MeV in succession
  done clear
  D)
   1.13 MeV and 1.37 MeV in succession
  done clear
  E)
   1.17 MeV and 1.13 MeV in succession
  done clear
  View Answer play_arrow

• question_answer24) A pure semiconductor has equal electron and hole concentration of\[{{10}^{16}}{{m}^{-3}}\]. Doping by indium increases\[{{n}_{h}}\]to\[5\times {{10}^{22}}{{m}^{-3}}\]. Then, the value of \[{{n}_{e}}\] in the doped semiconductor is
  A)
   \[{{10}^{6}}/{{m}^{3}}\]              
  done clear
  B)
          \[{{10}^{22}}/{{m}^{3}}\]
  done clear
  C)
   \[2\times {{10}^{6}}/{{m}^{3}}\]             
  done clear
  D)
          \[{{10}^{19}}/{{m}^{3}}\]
  done clear
  E)
   \[2\times {{10}^{9}}/{{m}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer25) The collector supply voltage is 6 V and the voltage drop across a resistor of\[600\,\Omega \]. in the collector circuit is 0.6 V, in a transistor connected in common emitter mode. If the current gain is 20, the base current is
  A)
   0.25mA               
  done clear
  B)
          0.05mA
  done clear
  C)
   0.12mA               
  done clear
  D)
          0.02mA
  done clear
  E)
   0.07mA
  done clear
  View Answer play_arrow

• question_answer26) A full-wave rectifier circuit with an AC input is shown The output voltage across\[{{R}_{L}}\]is represented as
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  E)
   
  done clear
  View Answer play_arrow

• question_answer27) In the given circuit the current through the battery is
  A)
   0.5 A    
  done clear
  B)
          1 A  
  done clear
  C)
   1.5 A    
  done clear
  D)
          2 A
  done clear
  E)
   2.5 A
  done clear
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• question_answer28) A carrier frequency of 1 MHz and peak value of 10 V is amplitude modulated with a signal frequency of 10 kHz with peak value of 0.5 V. Then the modulation index and the side band frequencies respectively are
  A)
   0.05 and 1 ± 0.010 MHz
  done clear
  B)
   0.5 and 1 ± 0.010 MHz
  done clear
  C)
   0.05 and 1 ± 0.005 MHz
  done clear
  D)
   0.5 and 1 ± 0.005 MHz
  done clear
  E)
   0.05 and 1± 0.100 MHz
  done clear
  View Answer play_arrow

• question_answer29) The maximum line-of-sight distance\[{{d}_{M}}\]between two antennas having heights\[{{h}_{t}}\]and\[{{h}_{R}}\]above the earth is
  A)
   \[\sqrt{R({{h}_{T}}+{{h}_{R}})}\]
  done clear
  B)
          \[\sqrt{2R/({{h}_{T}}+{{h}_{R}})}\]
  done clear
  C)
   \[\sqrt{R{{h}_{T}}}+\sqrt{2R{{h}_{R}}}\]
  done clear
  D)
          \[\sqrt{2R{{h}_{T}}}+\sqrt{2R{{h}_{R}}}\]
  done clear
  E)
   \[\sqrt{2R{{h}_{T}}}+\sqrt{R{{h}_{R}}}\]
  done clear
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• question_answer30) The frequency band used in the downlink of satellite communication is
  A)
   9.5 to 2.5 GHz  
  done clear
  B)
          896 to 901 MHz
  done clear
  C)
   3.7 to 4.2 GHz  
  done clear
  D)
          840 to 935 MHz
  done clear
  E)
   3.7 to 4.2 MHz
  done clear
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• question_answer31) In amplitude modulation, the bandwidth is
  A)
   twice the audio signal frequency
  done clear
  B)
   thrice the audio signal frequency
  done clear
  C)
   thrice the carrier wave frequency
  done clear
  D)
   twice the carrier wave frequency
  done clear
  E)
   sum of audio signal frequency and carrier wave frequency
  done clear
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• question_answer32) The quantities RC and\[\left( \frac{L}{R} \right)\](where R, L and C stand for resistance, inductance and capacitance respectively) have the dimensions of
  A)
   force                   
  done clear
  B)
          linear momentum
  done clear
  C)
   linear acceleration         
  done clear
  D)
   time
  done clear
  E)
   linear velocity
  done clear
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• question_answer33) The number of significant figures in 0.002305 is
  A)
   6                            
  done clear
  B)
          4      
  done clear
  C)
   7                            
  done clear
  D)
          2
  done clear
  E)
   3
  done clear
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• question_answer34) A body travelling with uniform acceleration crosses two points A and B with velocities \[20\,m{{s}^{-1}}\] and \[30\,m{{s}^{-1}}\] respectively. The speed of the body at the mid-point of A and B is nearest to
  A)
   \[25.5\,m{{s}^{-1}}\]       
  done clear
  B)
          \[25\,m{{s}^{-1}}\]
  done clear
  C)
   \[24\text{ }m{{s}^{-1}}\]        
  done clear
  D)
          \[10\sqrt{6}\,m{{s}^{-1}}\]
  done clear
  E)
   \[22\,m{{s}^{-1}}\]
  done clear
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• question_answer35) An aeroplane flies around a square field ABCD of each side 1000 km. Its speed along AB is \[250\text{ }km{{h}^{-1}},\]along BC\[500\text{ }km{{h}^{-1}},\] along CD \[200km{{h}^{-1}},\]and along DA \[100\text{ }km{{h}^{-1}}\]. Its average speed (in\[km{{h}^{-1}}\])over the entire trip is
  A)
   225.5                   
  done clear
  B)
          175.5
  done clear
  C)
   125.5                   
  done clear
  D)
          310.5
  done clear
  E)
   190.5
  done clear
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• question_answer36) Free fall of an object (in vacuum) is a case of motion with
  A)
   uniform velocity
  done clear
  B)
   uniform acceleration
  done clear
  C)
   variable acceleration
  done clear
  D)
   constant momentum
  done clear
  E)
   uniform speed
  done clear
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• question_answer37) The maximum height of a projectile is half of its range on the horizontal. If the velocity of projection is u, its range on the horizontal is
  A)
   \[\frac{2{{u}^{2}}}{5g}\]              
  done clear
  B)
          \[\frac{3{{u}^{2}}}{5g}\]
  done clear
  C)
   \[\frac{{{u}^{2}}}{g}\]                  
  done clear
  D)
          \[\frac{{{u}^{2}}}{5g}\]
  done clear
  E)
   \[\frac{4{{u}^{2}}}{5g}\]
  done clear
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• question_answer38) A stone of mass 2 kg is tied to a string of length 0.5 m. If the breaking tension of the string is 900 N, then the maximum angular velocity, the stone can have in uniform circular motion is
  A)
   \[30\,rad{{s}^{-1}}\]       
  done clear
  B)
          \[20\,rad{{s}^{-1}}\]
  done clear
  C)
   \[10\,rad{{s}^{-1}}\]       
  done clear
  D)
          \[25\,rad{{s}^{-1}}\]
  done clear
  E)
   \[40\,rad{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer39) The position of a particle is given by \[\overrightarrow{r}=2{{t}^{2}}\hat{i}+3t\hat{j}+4\hat{k},\]where t is in second and the coefficients have proper units for\[\overrightarrow{r}\]to be in metre. The\[\overrightarrow{a}(t)\]of the particle at\[t=1\text{ }s\] is
  A)
   \[4\text{ }m{{s}^{-2}}\]along \[\text{y-}\]direction
  done clear
  B)
   \[\text{3 }m{{s}^{-2}}\]along\[x\text{-}\]direction
  done clear
  C)
   \[4\text{ }m{{s}^{-2}}\]along\[x\text{-}\]direction
  done clear
  D)
   \[\text{2 }m{{s}^{-2}}\]along\[\text{z-}\]direction
  done clear
  E)
  \[\text{3 }m{{s}^{-2}}\]along\[\text{z-}\]direction
  done clear
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• question_answer40) A passenger getting down from a moving bus, falls in the direction of the motion of the bus. This is an example for
  A)
   moment of inertia
  done clear
  B)
   second law of motion
  done clear
  C)
   third law of motion
  done clear
  D)
   inertia of rest
  done clear
  E)
   inertia of motion
  done clear
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• question_answer41) A body of mass 6 kg is hanging from another body of mass 10 kg as shown in figure.  This combination is being pulled up by a string with an acceleration of\[2\text{ }m{{s}^{-2}}\]. The tension\[{{T}_{1}}\]is \[(g=10\text{ }m{{s}^{-2}})\]    
  A)
   240 N                   
  done clear
  B)
          150 N
  done clear
  C)
   220 N                   
  done clear
  D)
          192 N
  done clear
  E)
   178N
  done clear
  View Answer play_arrow

• question_answer42) Which one of the following is not a contact force?
  A)
   Viscous force    
  done clear
  B)
          Air resistance
  done clear
  C)
   Friction         
  done clear
  D)
          Buoyant force
  done clear
  E)
   Magnetic force
  done clear
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• question_answer43) A force\[(4\hat{i}+\hat{j}-2\hat{k})N\]acting on a body maintains its velocity at\[(2\hat{i}+2\hat{j}+3\hat{k})m{{s}^{-1}}\]. The power exerted is
  A)
   4W        
  done clear
  B)
                          5W
  done clear
  C)
   2W                       
  done clear
  D)
          8W
  done clear
  E)
   1W
  done clear
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• question_answer44) Energy required to break one bond in DNA is
  A)
   \[{{10}^{-10}}J\]             
  done clear
  B)
          \[{{10}^{-18}}J\]
  done clear
  C)
   \[{{10}^{-7}}J\]                
  done clear
  D)
          \[{{10}^{-20}}J\]
  done clear
  E)
   \[{{10}^{-3}}J\]
  done clear
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• question_answer45) Identify the false statement from the following
  A)
   Work-energy theorem is not independent of Newtons second law
  done clear
  B)
   Work-energy theorem holds in all inertial frames
  done clear
  C)
   Work done by friction over a closed path is zero
  done clear
  D)
   No potential energy can be associated with friction
  done clear
  E)
   Work done is a scalar quantity
  done clear
  View Answer play_arrow

• question_answer46) Three bricks each of length L and mass M are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is
  A)
   \[L/4\]                
  done clear
  B)
         \[L/2\]
  done clear
  C)
   \[(3/2)L\]           
  done clear
  D)
         \[(11/12)L\]
  done clear
  E)
   \[(5/6)L\]
  done clear
  View Answer play_arrow

• question_answer47) A fly wheel of moment of inertia\[3\times {{10}^{2}}kg\text{ }{{m}^{2}}\]is rotating with uniform angular speed of 4.6 \[rad{{s}^{-1}}\]. If a torque of\[6.9\times {{10}^{2}}Nm\]retards the wheel, then the time in which the wheel comes to rest is
  A)
   1.5 s                     
  done clear
  B)
          2 s
  done clear
  C)
   0.5 s                     
  done clear
  D)
          1 s
  done clear
  E)
   2.5 s
  done clear
  View Answer play_arrow

• question_answer48) Moment of inertia of a ring of mass M and radius R about a tangent to the circle of the ring is
  A)
   \[\frac{5}{2}M{{R}^{2}}\]                            
  done clear
  B)
   \[\frac{3}{2}M{{R}^{2}}\]
  done clear
  C)
   \[\frac{1}{2}M{{R}^{2}}\]            
  done clear
  D)
          \[M{{R}^{2}}\]
  done clear
  E)
   \[\frac{7}{2}M{{R}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer49) If the escape velocity of a planet is 3 times that of the earth and its radius is 4 times that of the earth, then the mass of the planet is (Mass of the earth\[=6\times {{10}^{24}}kg\])
  A)
   \[1.62\times {{10}^{22}}kg\]
  done clear
  B)
          \[0.72\times {{10}^{22}}kg\]
  done clear
  C)
   \[2.16\times {{10}^{26}}kg\]
  done clear
  D)
          \[1.22\times {{10}^{22}}kg\]
  done clear
  E)
   \[3.6\times {{10}^{22}}kg\]
  done clear
  View Answer play_arrow

• question_answer50) The total energy of a circularly orbiting satellite is
  A)
   twice the kinetic energy of the satellite
  done clear
  B)
   half the kinetic energy of the satellite
  done clear
  C)
   twice the potential energy of the satellite
  done clear
  D)
   equal to the potential energy of the satellite
  done clear
  E)
   half the potential energy of the satellite
  done clear
  View Answer play_arrow

• question_answer51) If an earth satellite of mass m orbiting at a distance 2 R from the centre of earth has to be transferred into the orbit of radius 3 R, the amount of energy required is (R = radius of earth)
  A)
   \[mgR\]              
  done clear
  B)
          \[\frac{mgR}{3}\]
  done clear
  C)
   \[\frac{mgR}{2}\]           
  done clear
  D)
          \[\frac{mgR}{12}\]
  done clear
  E)
   \[\frac{mgR}{9}\]
  done clear
  View Answer play_arrow

• question_answer52) The compressibility of water is \[6\times {{10}^{-10}}{{N}^{-1}}{{m}^{2}}\]. If one litre is subjected to a pressure of \[4\times {{10}^{7}}N{{m}^{-2}},\]the decrease in its volume is
  A)
   2.4 cc                                   
  done clear
  B)
   10 cc
  done clear
  C)
   24 cc                    
  done clear
  D)
          15 cc
  done clear
  E)
   12 cc
  done clear
  View Answer play_arrow

• question_answer53) Bernoullis principle is not involved in the working/explanation of
  A)
   movement of spinning ball
  done clear
  B)
   carburettes of automobile
  done clear
  C)
   blades of a kitchen mixer
  done clear
  D)
   heart attack
  done clear
  E)
   dynamic lift of an aeroplane
  done clear
  View Answer play_arrow

• question_answer54) Which one of the following statements is correct? In the case of
  A)
   shearing stress there is change in volume
  done clear
  B)
   tensile stress there is no change in volume
  done clear
  C)
   shearing stress there is no change in shape
  done clear
  D)
   hydraulic stress there is no change in volume
  done clear
  E)
   tensile stress there is no change in shape
  done clear
  View Answer play_arrow

• question_answer55) The onset of turbulence in a liquid is determined by
  A)
   Pascals law
  done clear
  B)
   Magnus effect
  done clear
  C)
   Reynolds number
  done clear
  D)
   Bernoullis principle
  done clear
  E)
   Torricellis law
  done clear
  View Answer play_arrow

• question_answer56) The temperature at which oxygen molecules have the same root mean square speed as that of hydrogen molecules at 300 K is
  A)
   600 K                   
  done clear
  B)
          2400 K
  done clear
  C)
   1200 K                 
  done clear
  D)
          300 K
  done clear
  E)
   4800 K
  done clear
  View Answer play_arrow

• question_answer57) Mean free path of a gas molecule is
  A)
   inversely proportional to number of molecules per unit volume
  done clear
  B)
   inversely proportional to diameter of the molecule
  done clear
  C)
   directly proportional to the square root of the absolute temperature
  done clear
  D)
   directly proportional to the molecular mass
  done clear
  E)
   independent of temperature
  done clear
  View Answer play_arrow

• question_answer58) A refrigerator with coefficient of performance \[\frac{1}{3}\]releases 200 J of heat to a hot reservoir. Then the work done on the working substance is
  A)
   \[\frac{100}{3}J\]           
  done clear
  B)
          \[100J\]
  done clear
  C)
   \[\frac{200}{3}J\]           
  done clear
  D)
          \[150J\]
  done clear
  E)
   \[50J\]
  done clear
  View Answer play_arrow

• question_answer59) The heat capacity per mole of water is (R is universal gas constant)
  A)
   \[9R\]                  
  done clear
  B)
          \[\frac{9}{2}R\]
  done clear
  C)
   \[6R\]                  
  done clear
  D)
          \[5R\]
  done clear
  E)
   \[3R\]
  done clear
  View Answer play_arrow

• question_answer60) If the frequency of human heart beat is 1.25 Hz, the number of heart beats in 1 min is
  A)
   80                         
  done clear
  B)
          65
  done clear
  C)
   90                         
  done clear
  D)
          75
  done clear
  E)
   120
  done clear
  View Answer play_arrow

• question_answer61) A   particle   oscillating   under   a   force\[\overrightarrow{F}=-k\overrightarrow{x}-b\overrightarrow{v}\] is a(/c and b are constants)
  A)
   simple harmonic oscillator
  done clear
  B)
   non linear oscillator
  done clear
  C)
   damped oscillator
  done clear
  D)
   forced oscillator
  done clear
  E)
   linear oscillator
  done clear
  View Answer play_arrow

• question_answer62) A mass of 4 kg suspended from a spring of force constant\[800\text{ }N{{m}^{-1}}\]executes simple harmonic oscillations. If the total energy of the oscillator is 4 J, the maximum 1accelerations (in\[m{{s}^{-2}}\]) of the mass is
  A)
   5                            
  done clear
  B)
          15
  done clear
  C)
   45                         
  done clear
  D)
          20
  done clear
  E)
   25
  done clear
  View Answer play_arrow

• question_answer63) The principle of superposition is basic to the phenomenon of
  A)
   total internal reflection
  done clear
  B)
   interference
  done clear
  C)
   reflection
  done clear
  D)
   refraction
  done clear
  E)
   polarization
  done clear
  View Answer play_arrow

• question_answer64) Velocity of sound in air is\[320\text{ }m{{s}^{-1}}\]. A pipe closed at one end has a length of 1 m. Neglecting end correction, the air column in the pipe cannot resonate with sound of frequency
  A)
   80 Hz                   
  done clear
  B)
          240 Hz
  done clear
  C)
   320 Hz                 
  done clear
  D)
          400 Hz
  done clear
  E)
   560 Hz
  done clear
  View Answer play_arrow

• question_answer65) A whistle is blown from the tower of a factory with a frequency of 220 Hz. The apparent frequency of sound heard by a worker moving towards the factory with a velocity of\[30\text{ }m{{s}^{-1}}\] is (velocity of sound\[=330\text{ }m{{s}^{-1}}\])
  A)
   280 Hz                 
  done clear
  B)
          200 Hz
  done clear
  C)
   300 Hz                 
  done clear
  D)
          240 Hz
  done clear
  E)
   330 Hz
  done clear
  View Answer play_arrow

• question_answer66) n identical drops, each of capacitance C and charged to a potential V, coalesce to form a bigger drop. Then the ratio of the energy stored in the big drop to that in each small drop is
  A)
   \[{{n}^{5/3}}:1\]             
  done clear
  B)
          \[{{n}^{4/3}}:1\]
  done clear
  C)
   \[n:1\]                
  done clear
  D)
          \[{{n}^{3}}:1\]
  done clear
  E)
   \[{{n}^{2/3}}:1\]
  done clear
  View Answer play_arrow

• question_answer67) Two charged spherical conductors of radii\[{{R}_{1}}\] and\[{{R}_{2}}\]are connected by a wire. Then the ratio of surface charge densities of the spheres\[{{\sigma }_{1}}/{{\sigma }_{2}}\]is
  A)
   \[{{R}_{1}}/{{R}_{2}}\] 
  done clear
  B)
          \[{{R}_{2}}/{{R}_{1}}\]
  done clear
  C)
   \[\sqrt{({{R}_{1}}/{{R}_{2}})}\] 
  done clear
  D)
          \[R_{1}^{2}/R_{2}^{2}\]
  done clear
  E)
   \[R_{2}^{2}/R_{1}^{2}\]
  done clear
  View Answer play_arrow

• question_answer68) Three capacitors are connected in the arms of a triangle ABC as shown in figure. 5 V is applied between A and B. The voltage between B and C is
  A)
   2 V                        
  done clear
  B)
          1 V
  done clear
  C)
   3 V                        
  done clear
  D)
          1.5 V
  done clear
  E)
   0.5 V
  done clear
  View Answer play_arrow

• question_answer69) Two point charges\[+5\mu C\]and\[-2\mu C\]are kept at a distance of 1 m in free space. The distance between the two zero potential points on the line joining the charges is
  A)
   \[\frac{2}{7}m\]                                              
  done clear
  B)
   \[\frac{2}{3}m\]
  done clear
  C)
   \[\frac{22}{21}m\]         
  done clear
  D)
          \[\frac{20}{21}m\]
  done clear
  E)
   \[\frac{8}{21}m\]
  done clear
  View Answer play_arrow

• question_answer70) A negatively charged oil drop is prevented from falling under gravity by applying a vertical electric field\[100\text{ }V{{m}^{-1}}\]. If the mass of the drop is\[1.6\times {{10}^{-3}}g,\] the number of electrons carried by the drop is\[(g=10\text{ }in{{s}^{-2}})\]
  A)
   \[{{10}^{18}}\]                 
  done clear
  B)
          \[{{10}^{15}}\]
  done clear
  C)
   \[{{10}^{6}}\]                   
  done clear
  D)
          \[{{10}^{9}}\]
  done clear
  E)
   \[{{10}^{12}}\]
  done clear
  View Answer play_arrow

• question_answer71) In the circuit shown, the current through\[8\,\Omega ,\]is same before and after connecting E. The value of E is
  A)
   12V                      
  done clear
  B)
          6V
  done clear
  C)
   4V                         
  done clear
  D)
          2V
  done clear
  E)
   8V
  done clear
  View Answer play_arrow

• question_answer72) An electric bulb rated 500 W at 100 V is used in a circuit having a 200 V supply. The resistance R that must be put in series with the bulb, so that the bulb draws 500 W is
  A)
   \[10\,\Omega ,\]           
  done clear
  B)
          \[15\,\Omega ,\]
  done clear
  C)
   \[2.5\,\Omega ,\]           
  done clear
  D)
          \[25\,\Omega ,\]
  done clear
  E)
   \[20\,\Omega ,\]
  done clear
  View Answer play_arrow

• question_answer73) The decreasing order of acidic character among ethane (I), ethene (II), ethyne (III) and propyne (IV) is
  A)
   (I)  > (II) > (III) > (IV)
  done clear
  B)
   (II) > (III) > (I)   > (IV)
  done clear
  C)
   (III) > (IV) > (II)  > (I)
  done clear
  D)
   (IV) > (III) > (II) > (I)
  done clear
  E)
   (III) > (IV) > (I)   > (II)
  done clear
  View Answer play_arrow

• question_answer74) The alkene that will give the same product with HBr in the absence as well as in the presence of peroxide is
  A)
   2-butene           
  done clear
  B)
   1-butene
  done clear
  C)
   propene        
  done clear
  D)
          1-hexene
  done clear
  E)
   2-methylpropene
  done clear
  View Answer play_arrow

• question_answer75) Hyperconjugation is most useful for stabilising which of the following carbocations?
  A)
   Neo-pentyl      
  done clear
  B)
   Tert-butyl
  done clear
  C)
  \[Iso-\]propyl       
  done clear
  D)
          Ethyl
  done clear
  E)
   Methyl
  done clear
  View Answer play_arrow

• question_answer76) Choose the weakest acid among the following
  A)
  \[{{F}_{3}}CCOOH\]
  done clear
  B)
   \[F-C{{H}_{2}}COOH\]
  done clear
  C)
   \[C{{H}_{3}}COOH\]
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}COOH\]
  done clear
  E)
   \[{{(C{{H}_{3}})}_{2}}CH-COOH\]
  done clear
  View Answer play_arrow

• question_answer77) The isomerism that arises due to restricted bond rotation is
  A)
   metamerism
  done clear
  B)
   optical isomerism
  done clear
  C)
   position isomerism
  done clear
  D)
   geometrical isomerism
  done clear
  E)
   functional isomerism
  done clear
  View Answer play_arrow

• question_answer78) The IUPAC name of the following compound, \[[{{(C{{H}_{3}})}_{2}}CH-C{{H}_{2}}-CH=CH-CH=CH-\underset{\begin{smallmatrix}  | \\  {{C}_{2}}{{H}_{5}} \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{3}}\]is        
  A)
   1, 1, 7, 7-tetramethyl-2, 5-octadiene
  done clear
  B)
   2, 8-dimethyl-3, 6-decadiene
  done clear
  C)
   1, 5-diisopropyl-1, 4-hexadiene
  done clear
  D)
   3, 9-dimethyl-4, 6-decadiene
  done clear
  E)
   2, 8-dimethyl-4, 6-decadiene
  done clear
  View Answer play_arrow

• question_answer79) Chlorination of benzene in the presence of halogen carrier is an example of
  A)
   aromatic nucleophilic substitution
  done clear
  B)
   aromatic electrophilic substitution
  done clear
  C)
   aromatic nucleophilic addition
  done clear
  D)
   aromatic electrophilic addition
  done clear
  E)
   free radical substitution
  done clear
  View Answer play_arrow

• question_answer80) Aryl halides doesnt undergo nucleophilic substitution   reactions   under   ordinary conditions because of

  1. approach of nucleophile is retarded

  2. carbon  carrying  halogen  atoms   is\[s{{p}^{3}}-\]hybridised

  3. the substrate molecule is destabilised due to resonance

  4. partial double bond character between carbon and halogen

  A)
   2 and 4 only      
  done clear
  B)
   1 and 4 only
  done clear
  C)
   2 and 3 only    
  done clear
  D)
          2, 3 and 4 only
  done clear
  E)
   1 and 3 only
  done clear
  View Answer play_arrow

• question_answer81) Aldehydes that do not undergo aldol condensation are

  1. propanal

  2. trichloroethanal

  3. methanal

  4. ethanal

  5. benzaldehyde

  A)
   3 and 4 only      
  done clear
  B)
   3 and 5 only
  done clear
  C)
   1, 2 and 3 only  
  done clear
  D)
          2, 3 and 5 only
  done clear
  E)
   5 only
  done clear
  View Answer play_arrow

• question_answer82) Which compound among the following give/s positive iodoform test? 1. Ethanol                            2. Ethanal 3. 1-butanol                        4. 2-butanol 5. Phenyl ethanal
  A)
   1, 2 and 5           
  done clear
  B)
   1, 3 and 4
  done clear
  C)
   1, 2 and 3      
  done clear
  D)
          2, 4 and 5
  done clear
  E)
   1, 2 and 4
  done clear
  View Answer play_arrow

• question_answer83) Amine that cannot be prepared by Gabriel phthalimide synthesis is
  A)
   aniline                                 
  done clear
  B)
   benzylamine
  done clear
  C)
   methylamine    
  done clear
  D)
          iso-butylamine
  done clear
  E)
   tertiary butylamine
  done clear
  View Answer play_arrow

• question_answer84) Which of the following is the least basic amine?
  A)
   Ethylamine       
  done clear
  B)
   Diethylamine
  done clear
  C)
   Aniline                
  done clear
  D)
          Benzylamine
  done clear
  E)
   Methylamine
  done clear
  View Answer play_arrow

• question_answer85) Which of the following bases is not present in DNA?
  A)
   Uracil                                   
  done clear
  B)
   Adenine
  done clear
  C)
   Thymine        
  done clear
  D)
          Guanine
  done clear
  E)
   Cytosine
  done clear
  View Answer play_arrow

• question_answer86) Lactose is made of
  A)
  \[\alpha -\]D-glucose only
  done clear
  B)
  \[\alpha -\]D-glucose and\[\beta -\]D-glucose
  done clear
  C)
  \[\alpha -\]D-galactose and\[\beta -\]D-glucose
  done clear
  D)
  \[\beta -\]D-galactose and\[\beta -\]D-glucose
  done clear
  E)
  \[\beta -\]D-galactose and\[\beta -\]D-glucose
  done clear
  View Answer play_arrow

• question_answer87) The artificial sweetener containing chlorine that has the appearance and taste as that of sugar and stable at cooking temperature is
  A)
   aspartame        
  done clear
  B)
   saccharin
  done clear
  C)
   sucrolose       
  done clear
  D)
          alitame
  done clear
  E)
   bithionol
  done clear
  View Answer play_arrow

• question_answer88) Cetyltrimethyl ammonium bromide is a popular
  A)
   anionic detergent
  done clear
  B)
   cationic detergent
  done clear
  C)
   non-ionic detergent
  done clear
  D)
   sweetener
  done clear
  E)
   antioxidant
  done clear
  View Answer play_arrow

• question_answer89) The number of electrons, neutrons and protons in a species are equal to 10, 8 and 8 respectively. The proper symbol of the species is
  A)
   \[_{8}^{16}O\]                                
  done clear
  B)
   \[_{8}^{18}O\]
  done clear
  C)
   \[_{10}^{18}Ne\]          
  done clear
  D)
          \[_{8}^{16}{{O}^{-}}\]
  done clear
  E)
   \[_{8}^{16}{{O}^{2-}}\]
  done clear
  View Answer play_arrow

• question_answer90) A 600 W mercury lamp emits monochromatic radiation of wavelength 331.3 nm. How many photons are emitted from the lamp per second? (\[h=6.626\times {{10}^{-34}}Js;\]velocity   of   light\[=3\times {{10}^{8}}m{{s}^{-1}}\])
  A)
   \[1\times {{10}^{19}}\]                                
  done clear
  B)
   \[1\times {{10}^{20}}\]
  done clear
  C)
   \[1\times {{10}^{21}}\]                
  done clear
  D)
          \[1\times {{10}^{23}}\]
  done clear
  E)
   \[1\times {{10}^{22}}\]
  done clear
  View Answer play_arrow

• question_answer91) The shortest wavelength in hydrogen spectrum of Lyman series when\[{{R}_{H}}=109678\] \[c{{m}^{-1}},\]is
  A)
  \[1002.7\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  B)
  \[1215.67\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  C)
  \[1127.30\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  D)
         \[911.7\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  E)
   \[1234.7\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  View Answer play_arrow

• question_answer92) Which of the following statements is false?
  A)
  \[{{H}_{2}}\]molecule has\[1\sigma \]bond
  done clear
  B)
  \[HCl\]molecule has\[1\sigma \]bond
  done clear
  C)
   Water molecule has\[2\sigma \]bonds and two lone pairs
  done clear
  D)
   Ethylene molecule has\[5\sigma \]bonds and In bond
  done clear
  E)
   Acetylene molecule has\[3\pi \]bonds and\[3\sigma \] bonds
  done clear
  View Answer play_arrow

• question_answer93) \[{{N}_{2}}\]and\[{{O}_{2}}\]are converted to monopositive cations\[N_{2}^{+}\]and\[O_{2}^{+}\]respectively. Which is incorrect?
  A)
   In\[N_{2}^{+},\]the\[NN\]bond is weakened
  done clear
  B)
   In\[O_{2}^{+},\]the bond order increases
  done clear
  C)
   In\[O_{2}^{+},\] paramagnetism decreases
  done clear
  D)
  \[N_{2}^{+}\]becomes diamagnetic
  done clear
  E)
   Both\[{{O}_{2}},O_{2}^{+}\]are paramagnetic
  done clear
  View Answer play_arrow

• question_answer94) A netural molecule\[X{{F}_{3}}\]has a zero dipole moment. The element X is most likely
  A)
   chlorine              
  done clear
  B)
   boron
  done clear
  C)
   nitrogen        
  done clear
  D)
          carbon
  done clear
  E)
   bromine
  done clear
  View Answer play_arrow

• question_answer95) 56 g of nitrogen and 96 g of oxygen are mixed isothermalty and at a total pressure of 10 atm. The partial pressures of oxygen and nitrogen (in atm) are respectively
  A)
   4, 6                                       
  done clear
  B)
   5, 5                
  done clear
  C)
   2, 8                       
  done clear
  D)
          8, 2
  done clear
  E)
   6, 4
  done clear
  View Answer play_arrow

• question_answer96) How much time (in hours) would it take to distribute one Avogadro number of wheat grains, if\[{{10}^{20}}\]grains are distributed each second?
  A)
   0.1673                                 
  done clear
  B)
   1.673
  done clear
  C)
   16.73                   
  done clear
  D)
          167.3
  done clear
  E)
   1673
  done clear
  View Answer play_arrow

• question_answer97) The first\[({{\Delta }_{i}}{{H}_{1}})\]and second\[({{\Delta }_{i}}{{H}_{2}})\]ionisation enthalpies (in\[kJ\text{ }mo{{l}^{-1}}\]) and the\[({{\Delta }_{eg}}H)\]electron gain enthalpy (in\[kJ\text{ }mo{{l}^{-1}}\]) of the elements I, II, III, IV and V are given below

  Element	\[{{\Delta }_{i}}{{H}_{1}}\]	\[{{\Delta }_{i}}{{H}_{2}}\]	\[{{\Delta }_{eg}}H\]
  I	520	7300	\[-\,60\]
  II	419	3051	\[-\,48\]
  III	1681	3374	\[-\,328\]
  IV	1008	1846	\[-\,295\]
  V	2372	5251	\[+\,48\]

  The most reactive metal and the least reactive non-metal of these are respectively
  A)
   l and V                                
  done clear
  B)
   V and II
  done clear
  C)
   II and V               
  done clear
  D)
          IV and V
  done clear
  E)
   V and III
  done clear
  View Answer play_arrow

• question_answer98) Which of the following undergoes reduction with hydrogen peroxide in alkaline medium?
  A)
   \[M{{n}^{2+}}\]                              
  done clear
  B)
   \[HOCl\]
  done clear
  C)
   \[PbS\]               
  done clear
  D)
          \[F{{e}^{2+}}\]
  done clear
  E)
   \[{{I}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer99) According to Ellingham diagram, the oxidation reaction of carbon to carbon monoxide may be used to reduce which one of the following oxides at the lowest temperature?
  A)
   \[A{{l}_{2}}{{O}_{3}}\]                                 
  done clear
  B)
   \[C{{u}_{2}}O\]
  done clear
  C)
   \[MgO\]             
  done clear
  D)
          \[ZnO\]
  done clear
  E)
   \[FeO\]
  done clear
  View Answer play_arrow

• question_answer100) The metal that produces red-violet colour in the non-luminous flame is
  A)
   Ba                                         
  done clear
  B)
   Ag
  done clear
  C)
   Rb                         
  done clear
  D)
          Pb
  done clear
  E)
   Zn
  done clear
  View Answer play_arrow

• question_answer101) Halogens exist in\[-1,+\text{ }1,+3,+5\]and +7 oxidation states. The halogen that exists only in\[-1\]state is
  A)
   \[F\]                                    
  done clear
  B)
   \[Cl\]
  done clear
  C)
   \[Br\]                  
  done clear
  D)
          \[I\]
  done clear
  E)
   \[At\]
  done clear
  View Answer play_arrow

• question_answer102) Among the oxyacids of phosphorus, the dibasic acid is
  A)
   \[{{H}_{4}}{{P}_{2}}{{O}_{7}}\]                 
  done clear
  B)
   \[{{H}_{3}}P{{O}_{2}}\]
  done clear
  C)
   \[HP{{O}_{3}}\]               
  done clear
  D)
          \[{{H}_{3}}P{{O}_{4}}\]
  done clear
  E)
   \[{{H}_{3}}P{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer103) Pick out the correct statement(s).

  1. Manganese exhibits + 7 oxidation state

  2. Zinc forms coloured ions

  3.\[{{[Co{{F}_{6}}]}^{3-}}\]is diamagnetic

  4. Sc forms +4 oxidation state

  5. Zn exhibits only +2 oxidation state

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

• question_answer104) The maximum oxidation state exhibited by actinide ions is
  A)
   +5
  done clear
  B)
   +4
  done clear
  C)
   +7                         
  done clear
  D)
          +8
  done clear
  E)
   +6
  done clear
  View Answer play_arrow

• question_answer105) Calculate the standard enthalpy change (in kJ \[mo{{l}^{-1}}\]) for the reaction \[{{H}_{2}}(g)+{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}{{O}_{2}}(g)\] Given that bond enthalpies of\[HH,\text{ O}=O,\]\[OH\]and\[OO\](in kJ\[mo{{l}^{-1}}\]) are respectively 438, 498, 464 and 138.
  A)
   \[-130\]                              
  done clear
  B)
   \[-\,65\]
  done clear
  C)
   + 130                   
  done clear
  D)
          \[-\,334\]
  done clear
  E)
   + 334
  done clear
  View Answer play_arrow

• question_answer106) According to the first law of thermodynamics which of the following quantities represents the change in a state function?
  A)
   \[{{q}_{rev}}\]                                 
  done clear
  B)
   \[{{q}_{rev}}-{{W}_{rev}}\]
  done clear
  C)
   \[{{q}_{rev}}/{{W}_{rev}}\]          
  done clear
  D)
          \[{{W}_{rev}}\]
  done clear
  E)
   \[{{q}_{rev}}+{{W}_{rev}}\]
  done clear
  View Answer play_arrow

• question_answer107) The aqueous solution of which of the salt has pH close to 7?
  A)
   \[FeC{{l}_{3}}\]                               
  done clear
  B)
  \[C{{H}_{3}}COONa\]
  done clear
  C)
   \[N{{a}_{2}}C{{O}_{3}}\]       
  done clear
  D)
         \[C{{H}_{3}}COON{{H}_{4}}\]
  done clear
  E)
   \[KCN\]
  done clear
  View Answer play_arrow

• question_answer108) Consider the following reactions in which all the reactants and the products are in gaseous state. \[2PQ{{P}_{2}}+{{Q}_{2}};\]        \[{{K}_{1}}=2.5\times {{10}^{5}}\] \[PQ+\frac{1}{2}{{R}_{2}}PQR;\]               \[{{K}_{2}}=5\times {{10}^{-3}}\] The value of\[{{K}_{3}}\]for the equilibrium \[\frac{1}{2}{{P}_{2}}+\frac{1}{2}{{Q}_{2}}+\frac{1}{2}{{R}_{2}}PQR,\]is
  A)
   \[2.5\times {{10}^{-3}}\]             
  done clear
  B)
  \[2.5\times {{10}^{3}}\]
  done clear
  C)
   \[1.0\times {{10}^{-5}}\]       
  done clear
  D)
         \[5\times {{10}^{3}}\]
  done clear
  E)
  \[5\times {{10}^{-3}}\]
  done clear
  View Answer play_arrow

• question_answer109) The amount of solute (molar mass\[60\text{ }g\text{ }mo{{l}^{-1}}\]) that must be added to 180 g of water so that the vapour pressure of water is lowered by 10%, is
  A)
   30 g                                      
  done clear
  B)
   60 g
  done clear
  C)
   120 g                    
  done clear
  D)
          12 g
  done clear
  E)
   24 g
  done clear
  View Answer play_arrow

• question_answer110) 200 mL of water is added to a 500 mL of 0.2 M solution. What is the molarity of this diluted solution?
  A)
   0.5010 M            
  done clear
  B)
   0.2897 M
  done clear
  C)
   0.7093 M       
  done clear
  D)
          0.1428 M
  done clear
  E)
   0.4005 M
  done clear
  View Answer play_arrow

• question_answer111) Which of the following species can function both as oxidising as well as reducing agent?
  A)
   \[C{{l}^{-}}\]                                     
  done clear
  B)
   \[ClO_{4}^{-}\]
  done clear
  C)
   \[Cl{{O}^{-}}\]                 
  done clear
  D)
          \[MnO_{4}^{-}\]
  done clear
  E)
   \[NO_{3}^{-}\]
  done clear
  View Answer play_arrow

• question_answer112) One Faraday of electricity is passed through molten\[A{{l}_{2}}{{O}_{3}},\]aqueous solution of\[CuS{{O}_{4}}\]and molten\[NaCl\]taken in three different electrolytic cells connected in series. The mole ratio of\[Al,Cu\]and Na deposited at the respective cathode is
  A)
   2 : 3 : 6                                
  done clear
  B)
   \[6:2:3\]
  done clear
  C)
   6 : 3 : 2                                
  done clear
  D)
   \[1:2:3\]
  done clear
  E)
   3 : 6 : 2
  done clear
  View Answer play_arrow

• question_answer113) Half-lives of a first order and a zero order reactions are same. Then, the ratio of the initial rates of first order reaction to that of the zero order reaction is
  A)
   \[\frac{1}{0.93}\]            
  done clear
  B)
          \[2\times 0.693\]
  done clear
  C)
   0.693   
  done clear
  D)
          \[\frac{2}{0.693}\]
  done clear
  E)
   6.93
  done clear
  View Answer play_arrow

• question_answer114) If the activation energy for the forward reaction is\[150\text{ }kJ\text{ }mo{{l}^{-1}}\]and that of the reverse reaction is\[260\text{ }kJ\text{ }mo{{l}^{-1}},\] what is the enthalpy change for the reaction?
  A)
  \[410\text{ }kJ\text{ }mo{{l}^{-1}}\]       
  done clear
  B)
   \[110\,kJ\,mo{{l}^{-1}}\]
  done clear
  C)
   \[-110\,kJ\,mo{{l}^{-1}}\]   
  done clear
  D)
          \[-\,410\,kJ\,mo{{l}^{-1}}\]
  done clear
  E)
   \[90\,kJ\,mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer115) The dispersed phase and dispersion medium in soap lather are respectively
  A)
   gas and liquid                   
  done clear
  B)
   liquid and gas
  done clear
  C)
   solid and gas    
  done clear
  D)
          solid and liquid
  done clear
  E)
   gas and solid
  done clear
  View Answer play_arrow

• question_answer116) In petrochemical industry, alcohols are directly converted to gasoline by passing over heated
  A)
   platinum        
  done clear
  B)
          ZSM-5
  done clear
  C)
   iron                      
  done clear
  D)
          nickel
  done clear
  E)
   palladium
  done clear
  View Answer play_arrow

• question_answer117) Which among the following statements are true for the complex\[[Co{{(N{{H}_{3}})}_{6}}][Cr{{(CN)}_{6}}]\]?

  1. It is a non-electrolyte

  2. The magnitude of the charge on each complex ion is 3

  3. The complex will not conduct current

  4. The complex will exhibit coordination isomerism

  5. The magnitude of the charge on each complex ion is 1

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

• question_answer118) An example of ambidentate ligand is
  A)
   ammine             
  done clear
  B)
   aquo
  done clear
  C)
   chloro                 
  done clear
  D)
          oxalato
  done clear
  E)
   thiocyanato
  done clear
  View Answer play_arrow

• question_answer119) In Lassaignes test for the detection of halogens, the sodium fusion extract is first boiled with concentrated nitric acid. This is
  A)
   to remove silver halides
  done clear
  B)
   to decompose\[N{{a}_{2}}S\]and\[NaCN,\]if present
  done clear
  C)
   to dissolve \[A{{g}_{2}}S\]
  done clear
  D)
   to dissolve\[AgCN,\]if formed
  done clear
  E)
   because\[A{{g}_{2}}S\]and\[AgCN\]are insoluble in nitric acid
  done clear
  View Answer play_arrow

• question_answer120) All carbon atoms are\[s{{p}^{2}}-\]hybridised in
  A)
   1, 3-butadiene                
  done clear
  B)
   \[C{{H}_{2}}=C=C{{H}_{2}}\]
  done clear
  C)
   cyclohexane    
  done clear
  D)
          2-butene
  done clear
  E)
   \[CH\equiv CC\equiv CH\]
  done clear
  View Answer play_arrow

• question_answer121) One of the points on the parabola\[{{y}^{2}}=12x\]with focal distance 12, is
  A)
   (3, 6)                                    
  done clear
  B)
   \[(9,6\sqrt{3})\]
  done clear
  C)
   \[(7,2\sqrt{21})\]       
  done clear
  D)
          \[(8,4\sqrt{6})\]
  done clear
  E)
   \[(1,\sqrt{12})\]
  done clear
  View Answer play_arrow

• question_answer122) If the length of the major axis of an ellipse is\[\frac{17}{8}\]times the length of the minor axis, then the eccentricity of the ellipse is
  A)
   \[\frac{8}{17}\]
  done clear
  B)
                                          \[\frac{15}{17}\]
  done clear
  C)
   \[\frac{9}{17}\]               
  done clear
  D)
          \[\frac{2\sqrt{2}}{17}\]
  done clear
  E)
   \[\frac{13}{17}\]
  done clear
  View Answer play_arrow

• question_answer123) If a point\[P(x,\text{ }y)\]moves along the ellipse \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\]and if C is the centre of the ellipse, then the sum of maximum and minimum values of CP is
  A)
   25         
  done clear
  B)
                          9
  done clear
  C)
   4                            
  done clear
  D)
          5
  done clear
  E)
   16
  done clear
  View Answer play_arrow

• question_answer124) The distance between the foci of the conic \[7{{x}^{2}}-9{{y}^{2}}=63\]is equal to
  A)
   8         
  done clear
  B)
   4
  done clear
  C)
   3                            
  done clear
  D)
          7
  done clear
  E)
   12
  done clear
  View Answer play_arrow

• question_answer125) If\[|\overrightarrow{a}|=5,|\overrightarrow{b}|=6\]and\[\overrightarrow{a}.\overrightarrow{b}=-25,\]then\[|\overrightarrow{a}\times \overrightarrow{b}|\]is equal to
  A)
   25                                         
  done clear
  B)
   \[6\sqrt{11}\]
  done clear
  C)
   \[11\sqrt{5}\]                  
  done clear
  D)
          \[11\sqrt{6}\]
  done clear
  E)
   \[5\sqrt{11}\]
  done clear
  View Answer play_arrow

• question_answer126) If\[\overrightarrow{p},\overrightarrow{q}\]and\[\overrightarrow{r}\]are perpendicular to\[\overrightarrow{q}+\overrightarrow{r},\overrightarrow{r}+\overrightarrow{p}\]and\[\overrightarrow{p}+\overrightarrow{q}\]respectively and if\[|\overrightarrow{p}+\overrightarrow{q}|=6,\]\[|\overrightarrow{q}+\overrightarrow{r}|=4\sqrt{3}\]and\[|\overrightarrow{r}+\overrightarrow{p}|=4,\]then\[|\overrightarrow{p}+\overrightarrow{q}+\overrightarrow{r}|\]is
  A)
   \[5\sqrt{2}\]                                     
  done clear
  B)
   10
  done clear
  C)
   15                         
  done clear
  D)
          5
  done clear
  E)
   25
  done clear
  View Answer play_arrow

• question_answer127) The vectors of magnitude a, 2a, 3a meet at a point and their directions are along the diagonals of three adjacent faces of a cube. Then, the magnitude of their resultant is
  A)
   \[5a\]                                  
  done clear
  B)
   \[6a\]
  done clear
  C)
   \[10a\]                
  done clear
  D)
          \[9a\]
  done clear
  E)
   \[7a\]
  done clear
  View Answer play_arrow

• question_answer128) Which one of the following vectors is of magnitude 6 and perpendicular to both \[\overrightarrow{a}=2\hat{i}+2\hat{j}+\hat{k}\]and\[\overrightarrow{b}=\hat{i}-2\hat{j}+2\hat{k}?\]
  A)
   \[2\hat{i}+\hat{j}-2\hat{k}\]                     
  done clear
  B)
   \[2(2\hat{i}-\hat{j}+2\hat{k})\]
  done clear
  C)
   \[3(2\hat{i}-\hat{j}-2\hat{k})\]
  done clear
  D)
          \[2(2\hat{i}+\hat{j}-2\hat{k})\]
  done clear
  E)
   \[2(2\hat{i}-\hat{j}-2\hat{k})\]
  done clear
  View Answer play_arrow

• question_answer129) If the vectors\[\overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k}\]and\[\overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k}\]are coplanar, then the value of k is equal to
  A)
   2                                            
  done clear
  B)
   1
  done clear
  C)
   3                            
  done clear
  D)
          \[-1\]
  done clear
  E)
   0
  done clear
  View Answer play_arrow

• question_answer130) Let\[A(1,-1,2)\]and\[B(2,3,-1)\]be two points. If a point P divides AB internally in the ratio\[2:3,\]then the position vector of P is
  A)
   \[\frac{1}{\sqrt{5}}(\hat{i}+\hat{j}+\hat{k})\]
  done clear
  B)
   \[\frac{1}{\sqrt{3}}(\hat{i}+6\hat{j}+\hat{k})\]
  done clear
  C)
   \[\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})\]
  done clear
  D)
   \[\frac{1}{5}(7\hat{i}+3\hat{j}+4\hat{k})\]
  done clear
  E)
   \[\frac{1}{\sqrt{5}}(\hat{i}+\hat{j}+9\hat{k})\]
  done clear
  View Answer play_arrow

• question_answer131) If the scalar product of the vector \[\hat{i}+\hat{j}+2\hat{k}\]with the unit vector along\[m\hat{i}+2\hat{j}+3\hat{k}\]is equal to 2, then one of the values of m is
  A)
   3                                            
  done clear
  B)
   4
  done clear
  C)
   5                            
  done clear
  D)
          6
  done clear
  E)
   7
  done clear
  View Answer play_arrow

• question_answer132) A plane makes intercepts a, b, c at A, B, C on the coordinate axes respectively. If the centroid of the\[\Delta ABC\]is at (3, 2, 1), then the equation of the plane is
  A)
   \[x+2y+3z=9\]
  done clear
  B)
   \[2x-3y-6z=18\]
  done clear
  C)
   \[2x+3y+6z=18\]
  done clear
  D)
   \[2x+y+6z=18\]
  done clear
  E)
   \[2x+3y+6z=9\]
  done clear
  View Answer play_arrow

• question_answer133) If the plane\[3x+y+2z+6=0\]is parallel to the line\[\frac{3x-1}{2b}=3-y=\frac{z-1}{a},\]then the value of \[3a+3b\]is
  A)
   \[\frac{1}{2}\]                                  
  done clear
  B)
   \[\frac{3}{2}\]
  done clear
  C)
   \[3\]                    
  done clear
  D)
          \[4\]
  done clear
  E)
   \[\frac{5}{2}\]
  done clear
  View Answer play_arrow

• question_answer134) The equation of the line passing through the point\[(3,0,-4)\]and perpendicular to the plane \[2x-3y+5z-7=0\]is
  A)
   \[\frac{x-2}{3}=\frac{y}{-3}=\frac{z+4}{5}\]
  done clear
  B)
   \[\frac{x-3}{2}=\frac{y}{-3}=\frac{z-4}{5}\]
  done clear
  C)
   \[\frac{x-3}{2}=\frac{-y}{3}=\frac{z+4}{5}\]
  done clear
  D)
   \[\frac{x+3}{2}=\frac{y}{3}=\frac{z-4}{5}\]
  done clear
  E)
   \[\frac{x-2}{3}=\frac{y}{3}=\frac{z+4}{5}\]
  done clear
  View Answer play_arrow

• question_answer135) The plane \[\overrightarrow{r}=s(\hat{i}+2\hat{j}-4\hat{k})+t(3\hat{i}+4\hat{j}-4\hat{k})\] \[+(1-t)(2\hat{i}-7\hat{j}-3\hat{k})\] is parallel to the line
  A)
   \[\overrightarrow{r}=(-\hat{i}+\hat{j}-\hat{k})+t(-\hat{i}-2\hat{j}+4\hat{k})\]
  done clear
  B)
   \[\overrightarrow{r}=(-\hat{i}+\hat{j}-\hat{k})+t(\hat{i}-2\hat{j}+4\hat{k})\]
  done clear
  C)
   \[\overrightarrow{r}=(\hat{i}+\hat{j}-\hat{k})+t(-\hat{i}-4\hat{j}+7\hat{k})\]
  done clear
  D)
   \[\overrightarrow{r}=(-\hat{i}+\hat{j}-\hat{k})+t(-2\hat{i}+2\hat{j}+4\hat{k})\]
  done clear
  E)
   \[\overrightarrow{r}=(-\hat{i}+\hat{j}-3\hat{k})+t(2\hat{i}+6\hat{j}-8\hat{k})\]
  done clear
  View Answer play_arrow

• question_answer136) The   distance   between   the   line\[\overrightarrow{r}=(2\hat{i}+2\hat{j}-\hat{k})+\lambda (2\hat{i}+\hat{j}-2\hat{k})\]and the plane\[\overrightarrow{r}.(\hat{i}+2\hat{j}+2\hat{k})=10\]is equal to
  A)
   5                                            
  done clear
  B)
   4
  done clear
  C)
   3                            
  done clear
  D)
          2
  done clear
  E)
   1
  done clear
  View Answer play_arrow

• question_answer137) Equation of the plane passing through the intersection of the planes\[x+y+z=6\]and \[2x+3y+4z+5=0\]and the point (1, 1, 1) is
  A)
   \[20x+23y+26z-69=0\]
  done clear
  B)
   \[31x+45y+49z+52=0\]
  done clear
  C)
   \[8x+5y+2z-69=0\]
  done clear
  D)
  \[4x+5y+6z-7=0\]
  done clear
  E)
   \[x+y+2z+17=0\]
  done clear
  View Answer play_arrow

• question_answer138) The equation of the plane containing the lines \[\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{3}\]and\[\frac{x}{2}=\frac{y-2}{-1}=\frac{z+1}{3}\]is
  A)
   \[8x-y+5z-8=0\]
  done clear
  B)
   \[8x+y-5z-7=0\]
  done clear
  C)
   \[x-8y+3z+6=0\]
  done clear
  D)
   \[8x+y-5z+7=0\]
  done clear
  E)
   \[x+y+z-6=0\]
  done clear
  View Answer play_arrow

• question_answer139) The vector equation of the straight line \[\frac{1-x}{3}=\frac{y+1}{-2}\,=\frac{3-z}{-1}\]
  A)
   \[\overrightarrow{r}=(\hat{i}-\hat{j}+3\hat{k})+\lambda (3\hat{i}+2\hat{j}-\hat{k})\]
  done clear
  B)
   \[\overrightarrow{r}=(\hat{i}-\hat{j}+3\hat{k})+\lambda (3\hat{i}-2\hat{j}-\hat{k})\]
  done clear
  C)
   \[\overrightarrow{r}=(3\hat{i}-2\hat{j}-\hat{k})+\lambda (\hat{i}-\hat{j}+3\hat{k})\]
  done clear
  D)
   \[\overrightarrow{r}=(3\hat{i}+2\hat{j}-\hat{k})+\lambda (\hat{i}-\hat{j}+3\hat{k})\]
  done clear
  E)
   \[\overrightarrow{r}=(\hat{i}-\hat{j}+3\hat{k})+\lambda (3\hat{i}+2\hat{j}+\hat{k})\]
  done clear
  View Answer play_arrow

• question_answer140) The arithmetic mean of 7 consecutive integers starting with a is m. Then, the arithmetic mean of 11 consecutive integers starting with \[a+2\]is
  A)
   \[2a\]                                  
  done clear
  B)
   \[2m\]
  done clear
  C)
   \[a+4\]                               
  done clear
  D)
   \[m+4\]
  done clear
  E)
  \[a+m+2\]
  done clear
  View Answer play_arrow

• question_answer141) The probability distribution of a random variable\[X\]is given as

  \[x\]	-5	-4	-3	-2	-1	0	1	2	3	4	5
  \[P(X=x)\]	P	2p	3p	4p	5p	7p	8p	9p	10p	11p	12p

  Then, the value of p is
  A)
   \[\frac{1}{72}\]               
  done clear
  B)
          \[\frac{3}{73}\]
  done clear
  C)
   \[\frac{5}{72}\]               
  done clear
  D)
          \[\frac{1}{74}\]
  done clear
  E)
   \[\frac{1}{73}\]
  done clear
  View Answer play_arrow

• question_answer142) The mean and variance of n observations\[{{x}_{1}},{{x}_{2}},{{x}_{3}},......,{{x}_{n}}\]and 0 respectively. If\[\sum\limits_{i=1}^{n}{x_{i}^{2}}=400,\]then the value of n is equal to
  A)
   80                                         
  done clear
  B)
   25
  done clear
  C)
   20                         
  done clear
  D)
          16
  done clear
  E)
   4
  done clear
  View Answer play_arrow

• question_answer143) If A and B are mutually exclusive events and if\[p(B)=\frac{1}{3},p(A\cup B)=\frac{13}{21},\]then P is equal to
  A)
   \[\frac{1}{7}\]                                  
  done clear
  B)
   \[\frac{4}{7}\]
  done clear
  C)
   \[\frac{2}{7}\]                  
  done clear
  D)
          \[\frac{5}{7}\]
  done clear
  E)
   \[\frac{6}{7}\]
  done clear
  View Answer play_arrow

• question_answer144) If\[f\]is a real valued function such that\[f(x+y)=f(x)+f(y)\]and\[f(1)=5,\]then the value of f(100) is
  A)
   200                                       
  done clear
  B)
   300
  done clear
  C)
   350                       
  done clear
  D)
          400
  done clear
  E)
   500
  done clear
  View Answer play_arrow

• question_answer145) Let\[f(x)=\frac{{{({{e}^{x}}-1)}^{2}}}{\sin \left( \frac{x}{a} \right)\log \left( 1+\frac{x}{4} \right)}\]for\[x\ne 0\]and \[f(0)=12,\]If\[f\]is continuous at\[x=0,\]then the value of a is equal to
  A)
   1                                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   2                            
  done clear
  D)
          \[-2\]
  done clear
  E)
   3
  done clear
  View Answer play_arrow

• question_answer146) \[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{x}{\sqrt{1+x}-\sqrt{1-x}} \right)\]is equal to
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   2                            
  done clear
  D)
          \[-1\]
  done clear
  E)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer147) \[\underset{x\to \infty }{\mathop{\lim }}\,\left( \frac{{{x}^{3}}}{3{{x}^{2}}-4}-\frac{{{x}^{2}}}{3x+2} \right)\]is equal to
  A)
   \[-\frac{1}{4}\]                                
  done clear
  B)
   \[-\frac{1}{2}\]
  done clear
  C)
   \[0\]                    
  done clear
  D)
          \[\frac{2}{9}\]
  done clear
  E)
   \[-\frac{6}{5}\]
  done clear
  View Answer play_arrow

• question_answer148) If\[{{x}^{y}}={{e}^{2(x-y)}},\]then\[\frac{dy}{dx}\]is equal to
  A)
   \[\frac{2(1+\log x)}{{{(2+\log x)}^{2}}}\]                              
  done clear
  B)
   \[\frac{1+\log x}{{{(2+\log x)}^{2}}}\]
  done clear
  C)
   \[\frac{2}{2+\log x}\]    
  done clear
  D)
          \[\frac{2(1-\log x)}{{{(2+\log x)}^{2}}}\]
  done clear
  E)
   \[\frac{2+\log x}{{{(2+\log x)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer149) If\[y={{\sin }^{-1}}\sqrt{1-x},\]then\[\frac{dy}{dx}\]is equal to
  A)
   \[\frac{1}{\sqrt{1-x}}\]                
  done clear
  B)
   \[\frac{-1}{2\sqrt{1-x}}\]
  done clear
  C)
   \[\frac{1}{\sqrt{x}}\]                    
  done clear
  D)
          \[\frac{-1}{2\sqrt{x}\sqrt{1-x}}\]
  done clear
  E)
   \[\frac{1}{\sqrt{x}\sqrt{1-x}}\]
  done clear
  View Answer play_arrow

• question_answer150) The derivative of\[{{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}})\]with respect to\[{{\sin }^{-1}}(3x-4{{x}^{3}})\]is
  A)
   \[\frac{2}{3}\]                                  
  done clear
  B)
   \[\frac{3}{2}\]
  done clear
  C)
   \[\frac{1}{2}\]                  
  done clear
  D)
          \[1\]
  done clear
  E)
   \[0\]
  done clear
  View Answer play_arrow

• question_answer151) If\[y={{\tan }^{-1}}x+{{\sec }^{-1}}x+{{\cot }^{-1}}x+\cos e{{c}^{-1}}x,\]then \[\frac{dy}{dx}\]is equal to
  A)
   \[\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\]                           
  done clear
  B)
   \[\pi \]
  done clear
  C)
   \[0\]                    
  done clear
  D)
          \[1\]
  done clear
  E)
   \[\frac{1}{x\sqrt{{{x}^{2}}-1}}\]
  done clear
  View Answer play_arrow

• question_answer152) If\[f(x)=|x-2|+|x+1|-x,\]then\[f(-10)\]is equal to
  A)
   \[-3\]                                   
  done clear
  B)
   \[-2\]
  done clear
  C)
   \[-1\]                   
  done clear
  D)
          \[0\]
  done clear
  E)
   \[1\]
  done clear
  View Answer play_arrow

• question_answer153) If\[x=a(1+\cos \theta ),y=a(\theta +\sin \theta ),\]then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\]at \[\theta =\frac{\pi }{2}\]is
  A)
   \[-\frac{1}{a}\]                                
  done clear
  B)
   \[\frac{1}{a}\]
  done clear
  C)
   \[-1\]                   
  done clear
  D)
          \[-2\]
  done clear
  E)
   \[-\frac{2}{a}\]
  done clear
  View Answer play_arrow

• question_answer154) If\[y={{\tan }^{-1}}\left( \frac{\cos x}{1+\sin x} \right),\]then\[\frac{dy}{dx}\]is equal to
  A)
   \[\frac{1}{2}\]                                  
  done clear
  B)
   \[2\]
  done clear
  C)
   \[-2\]                   
  done clear
  D)
          \[-\frac{1}{2}\]
  done clear
  E)
   \[-1\]
  done clear
  View Answer play_arrow

• question_answer155) The distance between the origin and the normal to the curve\[y={{e}^{2x}}+{{x}^{2}}\]at\[x=0\]is
  A)
   \[2\]                                    
  done clear
  B)
   \[\frac{2}{\sqrt{3}}\]
  done clear
  C)
   \[\frac{2}{\sqrt{5}}\]                    
  done clear
  D)
          \[\frac{1}{2}\]
  done clear
  E)
   \[\frac{1}{\sqrt{5}}\]
  done clear
  View Answer play_arrow

• question_answer156) The value of c in (0, 2) satisfying the mean value theorem for the function\[f(x)=x{{(x-1)}^{2}},x\in [0,2]\]is equal to
  A)
   \[\frac{3}{4}\]  
  done clear
  B)
                          \[\frac{4}{3}\]
  done clear
  C)
   \[\frac{1}{3}\]                  
  done clear
  D)
          \[\frac{2}{3}\]
  done clear
  E)
   \[\frac{5}{3}\]
  done clear
  View Answer play_arrow

• question_answer157) The point on the curve\[{{x}^{2}}+{{y}^{2}}={{a}^{2}},\text{ }y\ge 0\]at which the tangent is parallel to\[x-\]axis is
  A)
   \[(a,0)\]                             
  done clear
  B)
   \[(-a,0)\]
  done clear
  C)
   \[\left( \frac{a}{2},\frac{\sqrt{3}}{2}a \right)\]  
  done clear
  D)
          \[(0,a)\]
  done clear
  E)
   \[(0,{{a}^{2}})\]
  done clear
  View Answer play_arrow

• question_answer158) The angle between the curves,\[y={{x}^{2}}\]and \[{{y}^{2}}-x=0\]at the point (1, 1), is
  A)
   \[\frac{\pi }{2}\]                                             
  done clear
  B)
   \[{{\tan }^{-1}}\frac{4}{3}\]
  done clear
  C)
   \[\frac{\pi }{3}\]                             
  done clear
  D)
          \[\frac{\pi }{4}\]
  done clear
  E)
   \[{{\tan }^{-1}}\frac{3}{4}\]
  done clear
  View Answer play_arrow

• question_answer159) An edge of a variable cube is increasing at the rate of 10 cm/s. How fast the volume of the cube will increase when the edge is 5 cm long?
  A)
   \[750\text{ }c{{m}^{3}}/s\]        
  done clear
  B)
   \[75\,c{{m}^{3}}/s\]
  done clear
  C)
   \[300\text{ }c{{m}^{3}}/s\]     
  done clear
  D)
          \[150\,\,c{{m}^{3}}/s\]
  done clear
  E)
   \[25c{{m}^{3}}/s\]
  done clear
  View Answer play_arrow

• question_answer160) The minimum value of\[f(x)=|3-x|+7\]is
  A)
   0                                            
  done clear
  B)
   6
  done clear
  C)
   7                            
  done clear
  D)
          8
  done clear
  E)
   10
  done clear
  View Answer play_arrow

• question_answer161) If the error committed in measuring the radius of the circle is 0.05%, then the corresponding error in calculating the area is
  A)
   0.05%                                  
  done clear
  B)
   0.0025%
  done clear
  C)
   0.25%                  
  done clear
  D)
          0.1%
  done clear
  E)
   0.2%
  done clear
  View Answer play_arrow

• question_answer162) If\[\int{\frac{x+2}{2{{x}^{2}}+6x+5}}dx\] \[=P\int{\frac{4x+6}{2{{x}^{2}}+6x+5}}dx+\frac{1}{2}\int{\frac{dx}{2{{x}^{2}}+6x+5}},\] then the values of\[P\]is
  A)
   \[\frac{1}{3}\]                                  
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[\frac{1}{4}\]                  
  done clear
  D)
          \[2\]
  done clear
  E)
   \[1\]
  done clear
  View Answer play_arrow

• question_answer163) \[\int{(x+1){{(x+2)}^{7}}}(x+3)dx\]is equal to
  A)
   \[\frac{{{(x+2)}^{10}}}{10}-\frac{{{(x+2)}^{8}}}{8}+C\]
  done clear
  B)
   \[\frac{{{(x+1)}^{2}}}{2}-\frac{{{(x+2)}^{8}}}{8}-\frac{{{(x+3)}^{2}}}{2}+C\]
  done clear
  C)
   \[\frac{{{(x+2)}^{10}}}{10}+C\]
  done clear
  D)
   \[\frac{{{(x+1)}^{2}}}{2}+\frac{{{(x+2)}^{8}}}{8}+\frac{{{(x+3)}^{2}}}{2}+C\]
  done clear
  E)
   \[\frac{{{(x+2)}^{9}}}{9}-\frac{{{(x+2)}^{7}}}{7}+C\]
  done clear
  View Answer play_arrow

• question_answer164) \[\int{({{x}^{2}}+1)}\sqrt{x+1}dx\]is equal to
  A)
   \[\frac{{{(x+1)}^{7/2}}}{7}-2\frac{{{(x+1)}^{5/2}}}{5}\]\[+2\frac{{{(x+1)}^{3/2}}}{3}+C\]
  done clear
  B)
  \[2\left[ \frac{{{(x+1)}^{7/2}}}{7}-2\frac{{{(x+1)}^{5/2}}}{5} \right.\]\[\left. +2\frac{{{(x+1)}^{3/2}}}{3} \right]+c\]
  done clear
  C)
   \[\frac{{{(x+1)}^{7/2}}}{7}-2\frac{{{(x+1)}^{5/2}}}{5}+c\]
  done clear
  D)
   \[\frac{{{(x+1)}^{7/2}}}{7}-3\frac{{{(x+1)}^{5/2}}}{5}\]\[+11{{(x+1)}^{1/2}}+c\]
  done clear
  E)
   \[{{(x+1)}^{7/2}}+{{(x+1)}^{5/2}}+{{(x+1)}^{3/2}}+c\]
  done clear
  View Answer play_arrow

• question_answer165) \[\int{\frac{1+x}{x+{{e}^{-x}}}}\]is equal to
  A)
   \[\log |(x-{{e}^{-x}})|+c\]
  done clear
  B)
   \[\log |(x+{{e}^{-x}})|+c\]
  done clear
  C)
   \[\log |(1+x{{e}^{x}})|+c\]
  done clear
  D)
   \[{{(1+x{{e}^{x}})}^{2}}+c\]
  done clear
  E)
   \[\log |(1-x{{e}^{x}})|+c\]
  done clear
  View Answer play_arrow

• question_answer166) \[\int{\frac{\log (x+\sqrt{1+{{x}^{2}}})}{\sqrt{1+{{x}^{2}}}}}dx\]is equal to
  A)
   \[{{[\log (x+\sqrt{1+{{x}^{2}}})]}^{2}}+c\]
  done clear
  B)
   \[x\log (x+\sqrt{1+{{x}^{2}}})+c\]
  done clear
  C)
   \[\frac{1}{2}\log (x+\sqrt{1+{{x}^{2}}})+c\]
  done clear
  D)
   \[\frac{1}{2}{{[\log (x+\sqrt{1+{{x}^{2}}})]}^{2}}+c\]
  done clear
  E)
   \[\frac{x}{2}\log (x+\sqrt{1+{{x}^{2}}})+c\]
  done clear
  View Answer play_arrow

• question_answer167) \[\int{\frac{dx}{\sqrt{1-{{e}^{2x}}}}}\]is equal to
  A)
   \[\log |{{e}^{-x}}+\sqrt{{{e}^{-2x}}-1}|+c\]
  done clear
  B)
   \[\log |{{e}^{x}}+\sqrt{{{e}^{2x}}-1}|+c\]
  done clear
  C)
   \[-\log |{{e}^{-x}}+\sqrt{{{e}^{-2x}}-1}|+c\]
  done clear
  D)
   \[-\log |{{e}^{-2x}}+\sqrt{{{e}^{-2x}}-1}|+c\]
  done clear
  E)
   \[\log |{{e}^{-2x}}+\sqrt{{{e}^{-2x}}-1}|+c\]
  done clear
  View Answer play_arrow

• question_answer168) \[\int{\frac{\cos x+x\sin x}{{{x}^{2}}+x\cos x}}\]is equal to
  A)
   \[\log \left| \frac{\sin x}{1+\cos x} \right|+c\]
  done clear
  B)
   \[\log \left| \frac{\sin x}{x+\cos x} \right|+c\]
  done clear
  C)
   \[\log \left| \frac{2\sin x}{x+\cos x} \right|+c\]
  done clear
  D)
   \[\log \left| \frac{x\sin x}{x+\cos x} \right|+c\]
  done clear
  E)
   \[\log \left| \frac{x}{x+\cos x} \right|+c\]
  done clear
  View Answer play_arrow

• question_answer169) The integral\[\int_{0}^{1}{\frac{2{{\sin }^{-1}}\frac{x}{2}}{x}}dx\] equals
  A)
   \[\int_{0}^{\pi /6}{\frac{xdx}{\tan x}}\]                               
  done clear
  B)
   \[\int_{0}^{\pi /6}{\frac{2x}{\tan x}}dx\]
  done clear
  C)
   \[\int_{0}^{\pi /2}{\frac{2xdx}{\tan x}}\]             
  done clear
  D)
          \[\int_{0}^{\pi /6}{\frac{xdx}{\sin x}}\]
  done clear
  E)
   \[\int_{0}^{\pi /6}{\frac{2x}{\sin x}}dx\]
  done clear
  View Answer play_arrow

• question_answer170) The area of the plane region bounded by the curve\[x={{y}^{2}}-2\]and the line\[y=-x\]is (in square units)
  A)
   \[\frac{13}{3}\]                               
  done clear
  B)
   \[\frac{2}{5}\]
  done clear
  C)
   \[\frac{9}{5}\]                  
  done clear
  D)
          \[\frac{5}{2}\]
  done clear
  E)
   \[\frac{13}{2}\]
  done clear
  View Answer play_arrow

• question_answer171) If\[\int_{0}^{a}{f(2a-x)dx}=m\]and\[\int_{0}^{a}{f(x)dx}=n,\]then\[\int_{0}^{2a}{f(x)dx}\]is equal to
  A)
   \[2m+n\]           
  done clear
  B)
   \[m+2n\]
  done clear
  C)
   \[m-n\]           
  done clear
  D)
                          \[n-m\]
  done clear
  E)
   \[m+n\]
  done clear
  View Answer play_arrow

• question_answer172) \[\int_{-100}^{100}{f(x)}dx\]is equal to
  A)
   \[\int_{-100}^{100}{f({{x}^{2}})}\,dx\]
  done clear
  B)
   \[\int_{-100}^{100}{f(-{{x}^{2}})}\,dx\]
  done clear
  C)
   \[\int_{-100}^{100}{f\left( \frac{1}{x} \right)}\,dx\]
  done clear
  D)
   \[\int_{-100}^{100}{f(-x)}\,dx\]
  done clear
  E)
   \[\int_{-100}^{100}{[f(x)+f(-x)}]\,dx\]
  done clear
  View Answer play_arrow

• question_answer173) \[\int_{-1}^{1}{({{e}^{{{x}^{3}}}}+{{e}^{-{{x}^{3}}}})({{e}^{x}}-{{e}^{-x}})}dx\]is equal to
  A)
   \[\frac{{{e}^{2}}}{2}-2e\]                            
  done clear
  B)
   \[{{e}^{2}}-2e\]
  done clear
  C)
   \[2({{e}^{2}}-e)\]        
  done clear
  D)
          \[2{{e}^{2}}-2e\]
  done clear
  E)
   \[0\]
  done clear
  View Answer play_arrow

• question_answer174) The family of curves\[y={{e}^{a\sin x}},\]where a is an arbitrary constant, is represented by the differential equation
  A)
   \[\log y=\tan x\frac{dy}{dx}\]
  done clear
  B)
   \[y\log y=\tan x\frac{dy}{dx}\]
  done clear
  C)
   \[y\log y=\sin x\frac{dy}{dx}\]
  done clear
  D)
   \[\log y=\cos x\frac{dy}{dx}\]
  done clear
  E)
   \[y\log y=\cos x\frac{dy}{dx}\]
  done clear
  View Answer play_arrow

• question_answer175) The integrating factor of \[x\frac{dy}{dx}+(1+x)y=x\] is
  A)
   \[x\]                    
  done clear
  B)
   \[2x\]
  done clear
  C)
   \[{{e}^{x\log x}}\]          
  done clear
  D)
          \[{{e}^{x}}\]
  done clear
  E)
    \[x{{e}^{x}}\]
  done clear
  View Answer play_arrow

• question_answer176) The degree and order of the differential equation\[y=px+\sqrt[3]{{{a}^{2}}{{p}^{2}}+{{b}^{2}}},\]where\[p=\frac{dy}{dx},\]are respectively
  A)
   3, 1                                       
  done clear
  B)
   1, 3
  done clear
  C)
   1, 1                       
  done clear
  D)
          3, 3
  done clear
  E)
   3, 2
  done clear
  View Answer play_arrow

• question_answer177) The solution of the differential equation\[\frac{dy}{dx}+1={{e}^{x+y}}\]is
  A)
   \[x+{{e}^{x+y}}=c\]                      
  done clear
  B)
   \[x-{{e}^{x+y}}=c\]
  done clear
  C)
   \[x+{{e}^{-(x+y)}}=c\]
  done clear
  D)
          \[x-{{e}^{-(x+y)}}=c\]
  done clear
  E)
   \[x{{e}^{x+y}}+y=c\]
  done clear
  View Answer play_arrow

• question_answer178) Let\[f(x)=\frac{a{{x}^{2}}}{x+1},x\ne -1,\]The value of a for which\[f(a)=a,(a\ne 0)\]is
  A)
   \[1-\frac{1}{a}\]                              
  done clear
  B)
   \[\frac{1}{a}\]
  done clear
  C)
   \[1+\frac{1}{a}\]             
  done clear
  D)
          \[\frac{1}{a}-1\]
  done clear
  E)
   \[-\frac{1}{a}\]
  done clear
  View Answer play_arrow

• question_answer179) For\[a,b\in R,\]define\[a*b=\frac{a}{a+b},\]where. \[a+b\ne 0.\]If\[a*b=5,\]then the value of\[b*a\]is
  A)
   5   
  done clear
  B)
                                          \[-5\]
  done clear
  C)
   4                            
  done clear
  D)
          \[-7\]
  done clear
  E)
   \[-4\]
  done clear
  View Answer play_arrow

• question_answer180) Let\[A=\{x,\text{ }y,\text{ }z\}\]and\[B=\{a,\text{ }b,\text{ }c,\text{ }d\}\]. Which one of the following is not a relation from A to B?
  A)
   \[\{(x,a),(x,c)\}\]
  done clear
  B)
   \[\{(y,c),(y,d)\}\]
  done clear
  C)
   \[\{(z,a),(z,d)\}\]
  done clear
  D)
   \[\{(z,b),(y,b),(a,b)\}\]
  done clear
  E)
   \[\{(x,c)\}\]
  done clear
  View Answer play_arrow

• question_answer181) The domain of\[{{\sin }^{-1}}\left[ {{\log }_{2}}\left( \frac{x}{12} \right) \right]\]is
  A)
   \[[2,12]\]           
  done clear
  B)
          \[[-1,1]\]
  done clear
  C)
   \[\left[ \frac{1}{3},24 \right]\]  
  done clear
  D)
          \[\left[ \frac{2}{3},24 \right]\]
  done clear
  E)
   \[[6,24]\]
  done clear
  View Answer play_arrow

• question_answer182) If\[f(x)={{x}^{2}}-1\]and\[g(x)={{(x+1)}^{2}},\]then\[(gof)(x)\]is
  A)
   \[{{(x+1)}^{4}}-1\]
  done clear
  B)
          \[{{x}^{4}}-1\]
  done clear
  C)
   \[{{x}^{4}}\]                     
  done clear
  D)
          \[{{(x+1)}^{4}}\]
  done clear
  E)
   \[{{(x-1)}^{4}}-1\]
  done clear
  View Answer play_arrow

• question_answer183) The shaded region in the figure represents
  A)
   \[A\cap B\]                       
  done clear
  B)
   \[A\cup B\]
  done clear
  C)
   \[B-A\]
  done clear
  D)
          \[A-B\]
  done clear
  E)
   \[(A-B)\cup (B-A)\]
  done clear
  View Answer play_arrow

• question_answer184) If\[{{(x+iy)}^{1/3}}=2+3i,\]then\[3x+2y\]is equal to
  A)
   \[-20\]                                
  done clear
  B)
   \[-60\]
  done clear
  C)
   \[-120\]              
  done clear
  D)
          60
  done clear
  E)
   \[156\]
  done clear
  View Answer play_arrow

• question_answer185) The modulus of the complex number\[z\]such that\[|z+3-i|=1\]and \[arg\,(z)=\pi \] is equal to
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   9                            
  done clear
  D)
          4
  done clear
  E)
   3
  done clear
  View Answer play_arrow

• question_answer186) If\[{{z}_{1}},{{z}_{2}},......,{{z}_{n}}\]are complex numbers such that \[|{{z}_{1}}|=|{{z}_{2}}=.....=|{{z}_{n}}|=1,\]then \[|{{z}_{1}}+{{z}_{2}}+...+{{z}_{n}}|\]is equal to
  A)
   \[|{{z}_{1}}{{z}_{2}}{{z}_{3}}.....{{z}_{n}}|\]
  done clear
  B)
   \[|{{z}_{1}}|+|{{z}_{2}}|+....+|{{z}_{n}}|\]
  done clear
  C)
   \[\left| \frac{1}{{{z}_{1}}}+\frac{1}{{{z}_{2}}}+....+\frac{1}{{{z}_{n}}} \right|\]
  done clear
  D)
   \[n\]    
  done clear
  E)
   \[\sqrt{n}\]
  done clear
  View Answer play_arrow

• question_answer187) The value of\[\frac{\cos 30{}^\circ +i\sin 30{}^\circ }{\cos 60{}^\circ -i\sin 60{}^\circ }\]is equal to
  A)
   \[i\]                                      
  done clear
  B)
   \[-i\]
  done clear
  C)
   \[\frac{1+\sqrt{3}i}{2}\]              
  done clear
  D)
          \[\frac{1-\sqrt{3}i}{2}\]
  done clear
  E)
   \[1+i\]
  done clear
  View Answer play_arrow

• question_answer188) If\[z=r(\cos \theta +i\sin \theta ),\]then the value of\[\frac{z}{z}=\frac{\overline{z}}{z}\]
  A)
   \[\cos 2\theta \]                             
  done clear
  B)
   \[2\cos 2\theta \]
  done clear
  C)
   \[2\cos \theta \]             
  done clear
  D)
          \[2\sin \theta \]
  done clear
  E)
   \[2\sin 2\theta \]
  done clear
  View Answer play_arrow

• question_answer189) If\[{{z}_{1}}=\sqrt{2}\left( \cos \frac{\pi }{4}+i\sin \frac{\pi }{4} \right)\]and\[{{z}_{2}}=\sqrt{3}\left( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} \right),\]then\[|{{z}_{1}}{{z}_{2}}|\]is
  A)
   \[6\]                                    
  done clear
  B)
   \[\sqrt{2}\]
  done clear
  C)
   \[\sqrt{6}\]                       
  done clear
  D)
          \[\sqrt{3}\]
  done clear
  E)
   \[\sqrt{2}+\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer190) The value of a for which the equation\[2{{x}^{2}}+2\sqrt{6}x+a=0\]has equal roots, is
  A)
   3                                            
  done clear
  B)
   \[4\]
  done clear
  C)
   2                            
  done clear
  D)
          \[\sqrt{3}\]
  done clear
  E)
   \[\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer191) If\[\frac{3}{2}+\frac{7}{2}i\]is a solution of the equation\[a{{x}^{2}}-6x+b=0,\]where a and b are real numbers, then the value of\[a+b\]is equal to
  A)
   10                                         
  done clear
  B)
   22
  done clear
  C)
   30                         
  done clear
  D)
          29
  done clear
  E)
   31
  done clear
  View Answer play_arrow

• question_answer192) If the roots of the equation\[{{x}^{2}}-bx+c=0\]are two consecutive integers, then\[{{b}^{2}}-4c\]is
  A)
   \[-1\]                   
  done clear
  B)
          0
  done clear
  C)
   1                            
  done clear
  D)
          2
  done clear
  E)
   3
  done clear
  View Answer play_arrow

• question_answer193) If\[\alpha \]and\[\beta \]are the roots of the equation\[a{{x}^{2}}+bx+c=0,\]\[(c\ne 0),\]then the equation whose roots are\[\frac{1}{a\alpha +b}\]and\[\frac{1}{a\beta +b}\]is
  A)
   \[ac{{x}^{2}}-bx+1=0\]
  done clear
  B)
   \[{{x}^{2}}-acx+bc+1=0\]
  done clear
  C)
   \[ac{{x}^{2}}+bx-1=0\]
  done clear
  D)
   \[{{x}^{2}}+acx-bc+11=0\]
  done clear
  E)
   \[ac{{x}^{2}}-bx-11=0\]
  done clear
  View Answer play_arrow

• question_answer194) If a and b are the roots of the equation \[{{x}^{2}}+ax+b=0,\]\[a\ne 0,b\ne 0,\]then the values of a and b are respectively
  A)
   2 and\[-2\]       
  done clear
  B)
   2 and \[-1\]
  done clear
  C)
   1 and\[-2\]       
  done clear
  D)
          1 and 2
  done clear
  E)
   \[-1\]and 2
  done clear
  View Answer play_arrow

• question_answer195) If\[{{x}^{2}}+px+q=0\]has the roots\[\alpha \]and\[\beta \]then the value of\[{{(\alpha -\beta )}^{2}}\]is equal to
  A)
   \[{{p}^{2}}-4q\]              
  done clear
  B)
   \[{{({{p}^{2}}-4q)}^{2}}\]
  done clear
  C)
   \[{{p}^{2}}+4q\]         
  done clear
  D)
          \[{{({{p}^{2}}+4q)}^{2}}\]
  done clear
  E)
   \[{{q}^{2}}-4q\]
  done clear
  View Answer play_arrow

• question_answer196) If the sum to first n terms of the AP 2, 4,6,... is 240, then the value of n is
  A)
   14                                         
  done clear
  B)
   15
  done clear
  C)
   16                         
  done clear
  D)
          17
  done clear
  E)
   18
  done clear
  View Answer play_arrow

• question_answer197) The value of \[\frac{1}{\sqrt{10}-\sqrt{9}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{12}-\sqrt{11}}\]\[-....-\frac{1}{\sqrt{121}-\sqrt{120}}\] is equal to
  A)
   \[-10\]                
  done clear
  B)
          11
  done clear
  C)
   14                         
  done clear
  D)
          13
  done clear
  E)
   \[-8\]
  done clear
  View Answer play_arrow

• question_answer198) An AP consists of 23 terms. If the sum of the three terms in the middle is 141 and the sum of the last three terms is 261, then the first term is
  A)
   6                                            
  done clear
  B)
   5
  done clear
  C)
   4                            
  done clear
  D)
          3
  done clear
  E)
   2
  done clear
  View Answer play_arrow

• question_answer199) If\[{{a}_{1}},{{a}_{2}},{{a}_{3}},.....{{a}_{n}}\]On are in AP with common difference 5 and if\[{{a}_{i}}{{a}_{j}}\ne -1\]for, \[j=1,2,...,n,\]then \[{{\tan }^{-1}}\left( \frac{5}{1+{{a}_{1}}{{a}_{2}}} \right)+{{\tan }^{-1}}\left( \frac{5}{1+{{a}_{2}}{{a}_{3}}} \right)\]\[+....+{{\tan }^{-1}}\left( \frac{5}{1+{{a}_{n-1}}{{a}_{n}}} \right)\] Is equal to
  A)
   \[{{\tan }^{-1}}\left( \frac{5}{1+{{a}_{n}}{{a}_{n-1}}} \right)\]
  done clear
  B)
   \[{{\tan }^{-1}}\left( \frac{5{{a}_{1}}}{1+{{a}_{n}}{{a}_{1}}} \right)\]
  done clear
  C)
   \[{{\tan }^{-1}}\left( \frac{5n-5}{1+{{a}_{n}}{{a}_{1}}} \right)\]
  done clear
  D)
   \[{{\tan }^{-1}}\left( \frac{5n-5}{1+{{a}_{n}}{{a}_{n+1}}} \right)\]
  done clear
  E)
   \[{{\tan }^{-1}}\left( \frac{5n}{1+{{a}_{1}}{{a}_{n}}} \right)\]
  done clear
  View Answer play_arrow

• question_answer200) The sum of all two digit natural numbers which leave a remainder 5 when they are divided by 7 is equal to
  A)
   715                       
  done clear
  B)
          702
  done clear
  C)
   615                       
  done clear
  D)
          602
  done clear
  E)
   589
  done clear
  View Answer play_arrow

• question_answer201) Let a be a positive number such that the arithmetic mean of a and 2 exceeds their geometric mean by 1. Then, the value of a is
  A)
   3                                            
  done clear
  B)
   5
  done clear
  C)
   9                                            
  done clear
  D)
   8
  done clear
  E)
   10
  done clear
  View Answer play_arrow

• question_answer202) The coefficient of the middle term in the expansion of\[{{(x+2y)}^{6}}\]is
  A)
   \[^{6}{{C}_{3}}\]                             
  done clear
  B)
          \[8{{(}^{6}}{{C}_{3}})\]
  done clear
  C)
   \[8{{(}^{6}}{{C}_{4}})\]
  done clear
  D)
          \[^{6}{{C}_{4}}\]
  done clear
  E)
   \[8{{(}^{6}}{{C}_{5}})\]
  done clear
  View Answer play_arrow

• question_answer203) Let\[{{(1+x)}^{n}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}}\].If\[{{a}_{1}},{{a}_{2}}\]and\[{{a}_{3}}\]are in AP, then the value of n is
  A)
   4                                            
  done clear
  B)
   5
  done clear
  C)
   6                            
  done clear
  D)
          7
  done clear
  E)
   8
  done clear
  View Answer play_arrow

• question_answer204) The number of positive integers less than 40000 that can be formed by using all the digits 1, 2, 3, 4 and 5 is equal to
  A)
   24                                         
  done clear
  B)
   78
  done clear
  C)
   32                         
  done clear
  D)
          216
  done clear
  E)
   72
  done clear
  View Answer play_arrow

• question_answer205) If the sum of the coefficients in the expansion of\[{{({{a}^{2}}{{x}^{2}}-6ax+11)}^{10}},\]where a is constant, is 1024, then the value of a is
  A)
   5                                            
  done clear
  B)
   1
  done clear
  C)
   2                            
  done clear
  D)
          3
  done clear
  E)
   4
  done clear
  View Answer play_arrow

• question_answer206) If\[^{56}{{P}_{r+6}}{{:}^{54}}{{p}_{r+3}}=30800:1,\]then the value of r is
  A)
   40                                         
  done clear
  B)
   51
  done clear
  C)
   101                       
  done clear
  D)
          410
  done clear
  E)
   41
  done clear
  View Answer play_arrow

• question_answer207) From 12 books, the difference between number of ways a selection of 5 books when one specified book is always excluded and one specified book is always included is
  A)
   64                                         
  done clear
  B)
   118
  done clear
  C)
   132                       
  done clear
  D)
          330
  done clear
  E)
   462
  done clear
  View Answer play_arrow

• question_answer208) If\[A=\left[ \begin{matrix}    x & -2  \\    3 & 7  \\ \end{matrix} \right]\]and\[{{A}^{-1}}=\left[ \begin{matrix}    \frac{7}{34} & \frac{1}{17}  \\    \frac{-3}{34} & \frac{2}{17}  \\ \end{matrix} \right]\],then the value of x is
  A)
   2                                            
  done clear
  B)
   3
  done clear
  C)
   \[-4\]                   
  done clear
  D)
          4
  done clear
  E)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer209) 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)
          22
  done clear
  E)
   21
  done clear
  View Answer play_arrow

• question_answer210) The value of the determinant\[\left| \begin{matrix}    15! & 16! & 17!  \\    16! & 17! & 18!  \\    17! & 18! & 19!  \\ \end{matrix} \right|\]is equal to
  A)
   \[15!+16!\]                       
  done clear
  B)
   \[2(15!)(16!)(17!)\]
  done clear
  C)
   \[15!+16!+17!\]              
  done clear
  D)
          \[16!+17!\]
  done clear
  E)
   \[2(15!+16!)\]
  done clear
  View Answer play_arrow

• question_answer211) If A is a non-singular matrix of order 3, then adj (adj A) is equal to
  A)
   \[A\]                                    
  done clear
  B)
   \[{{A}^{-1}}\]
  done clear
  C)
   \[\frac{1}{|A|}A\]         
  done clear
  D)
          \[|A|A\]
  done clear
  E)
   \[\frac{1}{|A|}{{A}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer212) If \[\left[ \begin{matrix}    x-y-x  \\    -y+z  \\    z  \\ \end{matrix} \right]=\left[ \begin{matrix}    0  \\    5  \\    3  \\ \end{matrix} \right],\]then the values of\[x,y\] and\[z\]are respectively
  A)
   \[5,2,2\]                             
  done clear
  B)
   \[1,-2,3\]
  done clear
  C)
   \[0,-3,3\]           
  done clear
  D)
          \[11,8,3\]
  done clear
  E)
   \[4,1,3\]
  done clear
  View Answer play_arrow

• question_answer213) Which one of the following is true always for any two non-singular matrices A and B of same order?
  A)
   \[AB=BA\]                         
  done clear
  B)
   \[{{(AB)}^{t}}={{A}^{t}}{{B}^{t}}\]
  done clear
  C)
   \[(A+B)(A-B)={{A}^{2}}-{{B}^{2}}\]
  done clear
  D)
   \[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}\]
  done clear
  E)
   \[AB=-BA\]
  done clear
  View Answer play_arrow

• question_answer214) The solution set of the in equation\[\frac{x+11}{x-3}>0\]is
  A)
   \[(-\infty ,-11)\cup (3,\infty )\]
  done clear
  B)
   \[(-\infty ,-10)\cup (2,\infty )\]
  done clear
  C)
   \[(-100,-11)\cup (1,\infty )\]
  done clear
  D)
   \[(0,5)\cup (-1,0)\]
  done clear
  E)
   \[(-5,0)\cup (3,7)\]
  done clear
  View Answer play_arrow

• question_answer215) If\[3\le 3t-18\le 18,\]then which one of the following is true?
  A)
   \[15\le 2t+1\le 20\]       
  done clear
  B)
   \[8\le t<12\]
  done clear
  C)
   \[8\le t+1\le 13\]            
  done clear
  D)
          \[21\le 3t\le 24\]
  done clear
  E)
   \[t\le 7\]or\[t\ge 12\]
  done clear
  View Answer play_arrow

• question_answer216) Let p: 7 is not greater than 4 and q: Paris is in France be two statements. Then,\[\tilde{\ }(p\vee q)\]is the statement
  A)
   7 is greater than 4 or Paris is not in France
  done clear
  B)
   7 is not greater than 4 and Paris is not in France
  done clear
  C)
   7 is greater than 4 and Paris is in France
  done clear
  D)
   7 is not greater than 4 or Paris is not in France
  done clear
  E)
   7 is greater than 4 and Paris is not in France
  done clear
  View Answer play_arrow

• question_answer217) If\[S(p,q,r)=(\tilde{\ }p)\vee [\tilde{\ }(q\vee r)]\]is a compound statement, then\[S(\tilde{\ }p,\tilde{\ }q,\tilde{\ }r)\]is
  A)
   \[-S(p,q,r)\]                      
  done clear
  B)
   \[S(p,q,r)\]
  done clear
  C)
   \[p\vee (q\wedge r)\] 
  done clear
  D)
          \[p\vee (q\vee r)\]
  done clear
  E)
   \[S(p,q,\tilde{\ }r)\]
  done clear
  View Answer play_arrow

• question_answer218) For   any   two   statements   p   and\[q,\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\]is logically equivalent to
  A)
   p                                           
  done clear
  B)
   \[\tilde{\ }p\]
  done clear
  C)
   q                           
  done clear
  D)
          \[\tilde{\ }q\]
  done clear
  E)
   \[p\vee q\]
  done clear
  View Answer play_arrow

• question_answer219) If\[\tan \alpha =\frac{b}{a},a>b>0\]and if\[0<\alpha <\frac{\pi }{4},\]then\[\sqrt{\frac{a+b}{a-b}}-\sqrt{\frac{a-b}{a+b}}\]is equal to
  A)
   \[\frac{2\sin \alpha }{\sqrt{\cos 2\alpha }}\]                      
  done clear
  B)
   \[\frac{2\cos \alpha }{\sqrt{\cos 2\alpha }}\]
  done clear
  C)
   \[\frac{2\sin \alpha }{\sqrt{\sin 2\alpha }}\]       
  done clear
  D)
          \[\frac{2\cos \alpha }{\sqrt{\sin 2\alpha }}\]
  done clear
  E)
   \[\frac{2\tan \alpha }{\sqrt{\cos 2\alpha }}\]
  done clear
  View Answer play_arrow

• question_answer220) If\[{{\tan }^{-1}}(x+2)+{{\tan }^{-1}}(x-2)-{{\tan }^{-1}}\left( \frac{1}{2} \right)=0,\]then one of the values of\[x\]is equal to
  A)
   \[-1\]                                   
  done clear
  B)
   \[5\]
  done clear
  C)
   \[\frac{1}{2}\]                  
  done clear
  D)
          \[1\]
  done clear
  E)
   \[-\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer221) If\[\alpha ,\beta \in \left( 0,\frac{\pi }{2} \right),\sin \alpha =\frac{4}{5}\]\[\cos (\alpha +\beta )=-\frac{12}{13},\]then\[\sin \beta \]is equal to
  A)
   \[\frac{63}{65}\]                                             
  done clear
  B)
   \[\frac{61}{65}\]
  done clear
  C)
   \[\frac{3}{5}\]                  
  done clear
  D)
          \[\frac{5}{13}\]
  done clear
  E)
   \[\frac{8}{65}\]
  done clear
  View Answer play_arrow

• question_answer222) The number of solutions of\[\cos 2\theta =\sin \theta \]in\[(0,2\pi )\]is
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   3                            
  done clear
  D)
          4
  done clear
  E)
   0
  done clear
  View Answer play_arrow

• question_answer223) The value of\[{{\sin }^{-1}}\left( \frac{4}{5} \right)+2{{\tan }^{-1}}\left( \frac{1}{3} \right)\]is equal to
  A)
   \[\frac{\pi }{3}\]                                             
  done clear
  B)
    \[\frac{\pi }{4}\]
  done clear
  C)
   \[\frac{\pi }{2}\]                             
  done clear
  D)
          \[\pi \]
  done clear
  E)
   \[2\pi \]
  done clear
  View Answer play_arrow

• question_answer224) The value of \[tan\text{ }40{}^\circ +tan\text{ }20{}^\circ +\sqrt{3}\text{ }tan\text{ }20{}^\circ tan\text{ }40{}^\circ \]is equal to
  A)
   \[\sqrt{12}\]                     
  done clear
  B)
   \[\frac{1}{\sqrt{3}}\]
  done clear
  C)
   1                            
  done clear
  D)
          \[\frac{\sqrt{3}}{2}\]
  done clear
  E)
   \[\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer225) The period of the function\[f(\theta )=4+4{{\sin }^{3}}\theta -3\sin \theta \]is
  A)
   \[\frac{2\pi }{3}\]                                           
  done clear
  B)
   \[\frac{\pi }{3}\]
  done clear
  C)
   \[\frac{\pi }{2}\]                             
  done clear
  D)
          \[\pi \]
  done clear
  E)
   \[2\pi \]
  done clear
  View Answer play_arrow

• question_answer226) The value of\[x\]in\[\left( 0,\frac{\pi }{2} \right)\]satisfying the equation \[\sin x\cos x=\frac{1}{4}\]is
  A)
   \[\frac{\pi }{6}\]                                             
  done clear
  B)
   \[\frac{\pi }{3}\]
  done clear
  C)
   \[\frac{\pi }{8}\]                             
  done clear
  D)
          \[\frac{\pi }{4}\]
  done clear
  E)
   \[\frac{\pi }{12}\]
  done clear
  View Answer play_arrow

• question_answer227) The value of\[{{\sin }^{-1}}\{\cos (4095{}^\circ )\}\]is equal to
  A)
   \[-\frac{\pi }{3}\]                                            
  done clear
  B)
   \[\frac{\pi }{6}\]
  done clear
  C)
   \[-\frac{\pi }{4}\]                            
  done clear
  D)
          \[\frac{\pi }{4}\]
  done clear
  E)
   \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer228) If the distance between (2, 3) and\[(-\text{ }5,\text{ }2)\] is equal to the distance between\[(x,\text{ }2)\]and (1,3), then the values of \[x\]are
  A)
   \[-6,8\]                               
  done clear
  B)
   \[6,8\]
  done clear
  C)
   \[-8,6\]               
  done clear
  D)
          \[-7,7\]
  done clear
  E)
   \[-8,-6\]
  done clear
  View Answer play_arrow

• question_answer229) The line segment joining the points (4, 7) and \[(-2,-1)\]is a diameter of a circle. If the circle intersects the x-axis at A and B, then AB is equal to
  A)
   4                                            
  done clear
  B)
   5
  done clear
  C)
   6                            
  done clear
  D)
          7
  done clear
  E)
   8
  done clear
  View Answer play_arrow

• question_answer230) If the three points (0, 1),\[(0,-1)\]and\[(x,0)\]are vertices of an equilateral triangle, then the values of\[x\]are
  A)
   \[\sqrt{3},\sqrt{2}\]
  done clear
  B)
                          \[\sqrt{3},-\sqrt{3}\]
  done clear
  C)
   \[-\sqrt{5},\sqrt{3}\]    
  done clear
  D)
          \[\sqrt{2},-\sqrt{2}\]
  done clear
  E)
   \[\sqrt{5},-\sqrt{5}\]
  done clear
  View Answer play_arrow

• question_answer231) The area of the triangle formed by the points (2, 2), (5, 5), (6, 7) is equal to (in square units)
  A)
   9                                            
  done clear
  B)
   5
  done clear
  C)
   10                         
  done clear
  D)
          3
  done clear
  E)
   14
  done clear
  View Answer play_arrow

• question_answer232) If the line\[px-qy=r\]intersects the coordinate axes at (a, 0) and (0, b), then the value of\[a+b\]is equal to
  A)
   \[r\left( \frac{q+p}{pq} \right)\]                              
  done clear
  B)
   \[r\left( \frac{q-p}{pq} \right)\]
  done clear
  C)
   \[r\frac{(p-q)}{pq}\]     
  done clear
  D)
          \[r\left( \frac{p+q}{p-q} \right)\]
  done clear
  E)
   \[r\left( \frac{p-q}{p+q} \right)\]
  done clear
  View Answer play_arrow

• question_answer233) The vertices of a triangle are A (3, 7), B (3, 4) and C (5, 4). The equation of the bisector of the angle ABC is
  A)
   \[y=x+1\]          
  done clear
  B)
   \[y=x-1\]
  done clear
  C)
   \[y=3x-5\]      
  done clear
  D)
          \[y=x\]
  done clear
  E)
   \[y=-x\]
  done clear
  View Answer play_arrow

• question_answer234) The equation of a straight line which passes through the point\[(a{{\cos }^{3}}\theta ,a{{\sin }^{3}}\theta )\]and perpendicular to\[x\sec \theta +y\cos ec\theta =a\]is
  A)
   \[\frac{x}{a}+\frac{y}{a}=a\cos \theta \]
  done clear
  B)
   \[x\text{ }cos\theta -y\text{ }sin\theta =a\text{ }cos2\theta \]
  done clear
  C)
   \[x\text{ }cos\theta +y\text{ }sin\theta =a\text{ }cos\text{ }2\theta \]
  done clear
  D)
   \[x\text{ }cos\theta +y\text{ }sin\theta -a\text{ }cos\text{ }2\theta =1\]
  done clear
  E)
   \[x\text{ }cos\theta -y\text{ }sin\theta +a\text{ }cos\text{ }2\theta =-1\]
  done clear
  View Answer play_arrow

• question_answer235) The slopes of the lines which make an angle \[45{}^\circ \]with the line\[3x-y=-5\]are
  A)
   \[1,-1\]     
  done clear
  B)
          \[\frac{1}{2},-1\]
  done clear
  C)
   \[1,\frac{1}{2}\]                              
  done clear
  D)
          \[2,-\frac{1}{2}\]
  done clear
  E)
   \[-2,\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer236) The equation of one of the lines parallel to \[4x-3y=5\]and at a unit distance from the point\[(-1,-4)\]is
  A)
   \[3x+4y-3=0\]  
  done clear
  B)
   \[3x+4y+3=0\]
  done clear
  C)
   \[4x-3y+3=0\]
  done clear
  D)
          \[4x-3y-3=0\]
  done clear
  E)
   \[4x-3y-4=0\]
  done clear
  View Answer play_arrow

• question_answer237) The equation of family of circles with centre at\[(h,\text{ }k)\]touching the\[x-\]axis is given by
  A)
   \[{{x}^{2}}+{{y}^{2}}-2hx+{{h}^{2}}=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}-2hx-2fy+{{h}^{2}}=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}-2hx-2ky-{{h}^{2}}=0\]
  done clear
  D)
   \[{{x}^{2}}-{{y}^{2}}-2hx-2ky=0\]
  done clear
  E)
   \[{{x}^{2}}+{{y}^{2}}+2hx+2ky=0\]
  done clear
  View Answer play_arrow

• question_answer238) If the two circles\[{{(x+7)}^{2}}+{{(y-3)}^{2}}=36\]and \[{{(x-5)}^{2}}+{{(y+2)}^{2}}=49\]touch each other externally, then the point of contact is
  A)
   \[\left( \frac{-19}{13},\frac{19}{13} \right)\]                       
  done clear
  B)
   \[\left( \frac{-19}{13},\frac{9}{13} \right)\]
  done clear
  C)
   \[\left( \frac{17}{13},\frac{9}{13} \right)\]           
  done clear
  D)
          \[\left( \frac{-17}{13},\frac{9}{13} \right)\]
  done clear
  E)
   \[\left( \frac{19}{13},\frac{19}{13} \right)\]
  done clear
  View Answer play_arrow

• question_answer239) The equation of the chord of the circle \[{{x}^{2}}+{{y}^{2}}=81\] which is bisected at the point \[(-2,3)\]is
  A)
   \[3x-y=13\]       
  done clear
  B)
   \[3x-4y=13\]
  done clear
  C)
   \[2x-3y=13\]    
  done clear
  D)
          \[3x-3y=13\]
  done clear
  E)
   \[2x-3y=-13\]
  done clear
  View Answer play_arrow

• question_answer240) The distance of the midpoint of line joining two points (4, 0) and (0, 4) from the centre of the circle\[{{x}^{2}}+{{y}^{2}}=16\]is
  A)
   \[\sqrt{2}\]                                       
  done clear
  B)
   \[2\sqrt{2}\]
  done clear
  C)
   \[3\sqrt{2}\]                     
  done clear
  D)
          \[2\sqrt{3}\]
  done clear
  E)
   \[\sqrt{3}\]
  done clear
  View Answer play_arrow