Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2006

done CEE Kerala Engineering Solved Paper-2006 Total Questions - 240

• question_answer1) In Youngs experiment, using red light \[(\lambda =6600\overset{\text{o}}{\mathop{\text{A}}}\,),\] 60 fringes are seen in the field of view. How many fringes will be seen by using violet light \[(\lambda =4400\overset{\text{o}}{\mathop{\text{A}}}\,)\] ?
  A)
   10                                         
  done clear
  B)
   20
  done clear
  C)
   45                         
  done clear
  D)
          90
  done clear
  E)
   35
  done clear
  View Answer play_arrow

• question_answer2) At a temperature of\[30{}^\circ C,\]the susceptibility of a ferromagnetic material is found to be\[\chi \]. Its susceptibility at\[333{}^\circ C\]is:
  A)
   \[\chi \]                              
  done clear
  B)
          \[0.5\chi \]
  done clear
  C)
   \[2\chi \]                            
  done clear
  D)
          \[11.1\chi \]
  done clear
  E)
   \[0.09\chi \]
  done clear
  View Answer play_arrow

• question_answer3) To cover a population of 20 lakh, a transmission tower should have a height ..... (Radius of earth = 6400 km, population per square km = 1000):
  A)
   25 m                    
  done clear
  B)
          50 m
  done clear
  C)
   75 m                    
  done clear
  D)
          100 m
  done clear
  E)
   39 m
  done clear
  View Answer play_arrow

• question_answer4) Two identical air core capacitors are connected in series to a voltage source of 15 V. If one of the capacitors is filled with a medium of dielectric constant 4, the new potential across this capacitor is:
  A)
   5V                         
  done clear
  B)
          8V
  done clear
  C)
   10 V                     
  done clear
  D)
          12V
  done clear
  E)
   3V
  done clear
  View Answer play_arrow

• question_answer5) The range of frequencies allotted for FM radio is:
  A)
   88 to 108 kHz    
  done clear
  B)
   88 to 108 MHz
  done clear
  C)
   47 to 230 kHz  
  done clear
  D)
          47 to 230 MHz
  done clear
  E)
   470 to 960 MHz
  done clear
  View Answer play_arrow

• question_answer6) A string of density\[7.5\text{ }g\text{ }c{{m}^{-3}}\]and area of cross-section\[0.2\,m{{m}^{2}}\]is stretched under a tension of 20 N. When it is plucked at the mid-point, the speed of the transverse wave on the wire is:
  A)
   \[116\,m{{s}^{-1}}\]                      
  done clear
  B)
          \[40\,\,m{{s}^{-1}}\]
  done clear
  C)
   \[200\,m{{s}^{-1}}\]      
  done clear
  D)
          \[80\,\,m{{s}^{-1}}\]
  done clear
  E)
   \[5900\,\,m{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer7) In co-axial cable the material used as spacer is:
  A)
   teflon (or) polyethylene
  done clear
  B)
   glass or mica
  done clear
  C)
   a gaseous medium
  done clear
  D)
   glass
  done clear
  E)
   mica
  done clear
  View Answer play_arrow

• question_answer8) A work of\[2\times {{10}^{-2}}J\]is done on a wire of length 50 cm and area of cross-section\[0.5\text{ }m{{m}^{2}}\]. If the Youngs modulus of the material of the wire is\[2\times {{10}^{10}}N{{m}^{-2}},\] then the wire must be:
  A)
   elongated to 50.1414 cm
  done clear
  B)
   contracted by 2.0 mm
  done clear
  C)
   stretched by 0.707 mm
  done clear
  D)
   of length changed to 49.293 cm
  done clear
  E)
   of length changed to 50.2 cm
  done clear
  View Answer play_arrow

• question_answer9) Three blocks of masses\[{{m}_{1}},{{m}_{2}}\]and\[{{m}_{3}}\]are connected by massless string as shown kept on a frictionless table. They are pulled with a force\[{{T}_{3}}=40N.\]If \[{{m}_{1}}=10\,kg,{{m}_{2}}=6\,kg\]and\[{{m}_{3}}=4\text{ }kg,\]the tension\[{{T}_{2}}\]will be:
  A)
   20 N                     
  done clear
  B)
          40 N
  done clear
  C)
   10 N                     
  done clear
  D)
          32 N
  done clear
  E)
   16 N
  done clear
  View Answer play_arrow

• question_answer10) Two identical cells whether connected in parallel or in series gives the same current when connected to an external resistance\[1.5\,\Omega \]. Find the value of internal resistance of each cell.
  A)
   \[1\,\Omega \]               
  done clear
  B)
          \[0.5\,\Omega \]
  done clear
  C)
   zero                     
  done clear
  D)
          \[2\,\Omega \]
  done clear
  E)
   \[1.5\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer11) The binding energy per nucleon for deuteron and helium are 1.1 MeV and 7.0 MeV. The energy released when two deuterons ruse to form a helium nucleus is:
  A)
   23.6 MeV     
  done clear
  B)
          2.2 MeV
  done clear
  C)
   30.2 MeV           
  done clear
  D)
          3.6 MeV
  done clear
  E)
   28.0 MeV
  done clear
  View Answer play_arrow

• question_answer12) If the two vectors\[\overrightarrow{A}=2\hat{i}+3\hat{j}+4\hat{k}\]and\[\overrightarrow{B}=\hat{i}+2\hat{j}-n\hat{k}\]are perpendicular then the value of n is:
  A)
   1                            
  done clear
  B)
          2
  done clear
  C)
   3                            
  done clear
  D)
          4
  done clear
  E)
   5
  done clear
  View Answer play_arrow

• question_answer13) Force between two identical charges placed at a distance of r in vacuum is F. Now a slab of dielectric of dielectric constant 4 is inserted between these two charges. If the thickness of the slab is r/2, then the force between the charges will become:
  A)
   \[F\]                    
  done clear
  B)
   \[\frac{3}{5}F\]
  done clear
  C)
   \[\frac{4}{9}F\]               
  done clear
  D)
          \[\frac{F}{4}\]
  done clear
  E)
   \[\frac{F}{2}\]
  done clear
  View Answer play_arrow

• question_answer14) A stone of mass m tied to a string of length\[l\]is rotating along a circular path with constant speed v. The torque on the stone is:
  A)
   \[mlv\]               
  done clear
  B)
          \[\frac{mv}{l}\]
  done clear
  C)
   \[\frac{m{{v}^{2}}}{l}\]
  done clear
  D)
          \[m{{v}^{2}}l\]
  done clear
  E)
   zero
  done clear
  View Answer play_arrow

• question_answer15) A copper disc of radius 0.1 m is rotated about its centre with 20 rev/s in a uniform magnetic field of 0.1 T with its plane perpendicular to the field. The emf induced across the radius of the disc is:
  A)
   \[\frac{\pi }{20}V\]        
  done clear
  B)
          \[\frac{\pi }{10}V\]
  done clear
  C)
   \[20\pi \,mV\]       
  done clear
  D)
          \[10\pi \,mV\]
  done clear
  E)
   \[2\pi \,mV\]
  done clear
  View Answer play_arrow

• question_answer16) Water rises in a capillary tube to a height h. Choose false statement regarding capillary rise from the following:
  A)
   On the surface of Jupiter, height will be less than h
  done clear
  B)
   In a lift moving up with constant acceleration height is less than h
  done clear
  C)
   On the surface of moon the height is more than h
  done clear
  D)
   In a lift moving down with constant acceleration height is less than h
  done clear
  E)
   At the poles, height is less than that at equator
  done clear
  View Answer play_arrow

• question_answer17) A magnetized wire of magnetic moment M and length L is bent in the form of a semicircle of radius r. The new magnetic moment is:
  A)
   M                          
  done clear
  B)
          \[\frac{M}{2\pi }\]
  done clear
  C)
   \[\frac{M}{\pi }\]                           
  done clear
  D)
          \[\frac{2M}{\pi }\]
  done clear
  E)
   zero
  done clear
  View Answer play_arrow

• question_answer18) A proton, a deuteron and an alpha particle with the same kinetic energy enter a region of uniform magnetic field B at right angles to the field. The ratio of the radii of their circular paths is:
  A)
   \[1:1:1\]             
  done clear
  B)
          \[1:\sqrt{2}:\sqrt{2}\]
  done clear
  C)
   \[\sqrt{2}:1:1\]                
  done clear
  D)
          \[\sqrt{2}:\sqrt{2}:1\]
  done clear
  E)
   \[1:\sqrt{2}:1\]
  done clear
  View Answer play_arrow

• question_answer19) LANDSAT series of satellites move in near polar orbits at an altitude of:
  A)
   3600km              
  done clear
  B)
          3000 km
  done clear
  C)
   918 km                
  done clear
  D)
          512 km
  done clear
  E)
   9200km
  done clear
  View Answer play_arrow

• question_answer20) A boat travels 50 km east, then 120 km North and finally it comes back to the starting point through the shortest distance. The total time of journey is 3 h. What is the average velocity, in\[km\text{ }{{h}^{-1}},\]over the entire trip?
  A)
   zero                     
  done clear
  B)
          100
  done clear
  C)
   17                         
  done clear
  D)
          33.33
  done clear
  E)
   86.7
  done clear
  View Answer play_arrow

• question_answer21) The instantaneous displacement of a simple harmonic oscillator is given by \[y=A\cos \left( \omega t+\frac{\pi }{4} \right)\]Its speed will be maximum at the time:
  A)
   \[\frac{2\pi }{\omega }\]                            
  done clear
  B)
          \[\frac{\omega }{2\pi }\]
  done clear
  C)
   \[\frac{\omega }{\pi }\]                               
  done clear
  D)
          \[\frac{\pi }{4\omega }\]
  done clear
  E)
   \[\frac{\pi }{\omega }\]
  done clear
  View Answer play_arrow

• question_answer22) The surface area of a black body is\[5\times {{10}^{-4}}{{m}^{2}}\]and its temperature is\[727{}^\circ C\]. The energy radiated by it per minute is: \[(\sigma =5.67\times {{10}^{-8}}J/{{m}^{2}}-s-{{k}^{4}})\]
  A)
   \[1.7\times {{10}^{3}}J\]             
  done clear
  B)
          \[2.5\times {{10}^{2}}J\]
  done clear
  C)
   \[8\times {{10}^{3}}J\] 
  done clear
  D)
          \[3\times {{10}^{4}}J\]
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer23) Potential energy in a spring when stretched by 2 cm is U. Its potential energy, when stretched by 10 cm is:
  A)
   \[\frac{U}{25}\]                              
  done clear
  B)
          \[\frac{U}{5}\]
  done clear
  C)
   \[25U\]               
  done clear
  D)
          \[5U\]
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer24) A toy cyclist completes one round of a square track of side 2 m in 40s. What will be the displacement at the end of 3 min?
  A)
   52 m                    
  done clear
  B)
          Zero
  done clear
  C)
   16m                     
  done clear
  D)
          \[2\sqrt{2}m\]
  done clear
  E)
   \[4\sqrt{2}m\]
  done clear
  View Answer play_arrow

• question_answer25) The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is:
  A)
   \[\sqrt{3}v\]                     
  done clear
  B)
          \[\sqrt{2}v\]
  done clear
  C)
   \[v\]                    
  done clear
  D)
          \[\sqrt{5}v\]
  done clear
  E)
   \[\sqrt{12}v\]
  done clear
  View Answer play_arrow

• question_answer26) A particle of mass 5 g is executing simple harmonic motion with amplitude of 0.3 m and time period\[(\pi /5)\]s. The maximum value of the force acting on the particle is:
  A)
   5N                        
  done clear
  B)
          4N
  done clear
  C)
   0.5 N                    
  done clear
  D)
          0.3 N
  done clear
  E)
   0.15 N
  done clear
  View Answer play_arrow

• question_answer27) The inputs and outputs for different time intervals are given below the NAND gate

  Time	Input A	Input B	Output Y
  \[{{t}_{1}}\,to\,{{t}_{2}}\]	0	1	P
  \[{{t}_{2}}\,to\,{{t}_{3}}\]	0	0	Q
  \[{{t}_{3}}\,to\,{{t}_{4}}\]	1	0	R
  \[{{t}_{4}}\,to\,{{t}_{5}}\]	1	1	S

  The values taken by P, Q, R, S are respectively:
  A)
   1, 1, 1, 0        
  done clear
  B)
          0, 1, 0, 1
  done clear
  C)
   0, 1, 0, 0        
  done clear
  D)
          1, 0, 1, 1
  done clear
  E)
   1, 0, 1, 0
  done clear
  View Answer play_arrow

• question_answer28) A solenoid 600 mm long has 50 turns on it and is wound on an iron rod of 7.5 mm radius. Find the flux through the solenoid when the current in it is 3 A. The relative permeability of iron is 600:
  A)
   1.66 Wb                              
  done clear
  B)
   1.66 nWb
  done clear
  C)
   1.66 mWb    
  done clear
  D)
          \[1.66\mu Wb\]
  done clear
  E)
   1.66 pWb
  done clear
  View Answer play_arrow

• question_answer29) Two trains, each of length 200 m are running on parallel tracks. One overtakes the other in 20 s and one crosses the other in 10 s. The velocities of the two trains are:
  A)
   5 m/s, 10 m/s  
  done clear
  B)
          10 m/s, 30 m/s
  done clear
  C)
   15 m/s, 5 m/s  
  done clear
  D)
   20 m/s, 21 m/s
  done clear
  E)
   10 m/s, 5 m/s
  done clear
  View Answer play_arrow

• question_answer30) An electric dipole is placed at an angle of\[30{}^\circ \]with an electric field of intensity\[2\times {{10}^{5}}N{{C}^{-1}}\]. It experiences a torque equal to 4 Nm. Calculate the charge on the dipole if the dipole length is 2 cm.
  A)
   \[8\text{ }mC\]               
  done clear
  B)
          \[4\text{ }mC\]
  done clear
  C)
   \[8\mu C\]                        
  done clear
  D)
          \[4\mu C\]
  done clear
  E)
   \[2mC\]
  done clear
  View Answer play_arrow

• question_answer31) Two identical cells send the same current in\[3\,\Omega \]. resistance, whether connected in series or in parallel. The internal resistance of the cell should be:
  A)
   \[1\,\Omega \]               
  done clear
  B)
          \[3\,\Omega \]
  done clear
  C)
   \[\frac{1}{2}\,\Omega \]            
  done clear
  D)
          \[3.5\,\Omega \]
  done clear
  E)
   \[\frac{3}{2}\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer32) Which of the following statement is incorrect?
  A)
   In LCR series AC circuit, as the frequency of the source increases, the impedance of the circuit first decreases and then increases
  done clear
  B)
   If the net reactance of an LCR series AC circuit is same as its resistance, then the current lags behind the voltage by\[45{}^\circ \]
  done clear
  C)
   At resonance, the impedance of an AC circuit becomes purely resistive
  done clear
  D)
   At resonance in LCR series AC circuit, the potential drops across inductor and capacitor are equal in magnitude but opposite in sign
  done clear
  E)
   Below resonance, voltage leads the current while above it, current leads the voltage
  done clear
  View Answer play_arrow

• question_answer33) A ray of light passes from vacuum into a medium of refractive index p, the angle of incidence is found to be twice the angle of refraction. Then the angle of incidence is:
  A)
   \[{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]      
  done clear
  B)
          \[2{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
  done clear
  C)
   \[2{{\sin }^{-1}}(\mu )\]              
  done clear
  D)
          \[2{{\sin }^{-1}}\left( \frac{\mu }{2} \right)\]
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer34) The plot represents the flow of current through a wire at three different times. The ratio of charges flowing through the wire at different times is:
  A)
   \[2:1:2\]             
  done clear
  B)
          \[1:3:3\]
  done clear
  C)
   \[1:1:1\]             
  done clear
  D)
          \[2:3:4\]
  done clear
  E)
   \[2:3:3\]
  done clear
  View Answer play_arrow

• question_answer35) In a gas, two waves of wavelengths 1 m and 1.01 m are superposed and produce 10 beats in s. The velocity of sound in the medium is:
  A)
   300 m/s              
  done clear
  B)
          336.7 m/s
  done clear
  C)
   360.2 m/s     
  done clear
  D)
          270 m/s
  done clear
  E)
   390 m/s
  done clear
  View Answer play_arrow

• question_answer36) The distance between the centres of carbon and oxygen atoms in the carbon monoxide molecule is \[1.130\overset{\text{o}}{\mathop{\text{A}}}\,\] . Locate the centre of mass of Ac molecule relative to the carbon atom:
  A)
   \[5.428\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  B)
   \[1.130\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  C)
   \[0.6457\,\overset{\text{o}}{\mathop{\text{A}}}\,\]      
  done clear
  D)
                          \[0.3260\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer37) The pressure inside two soap bubbles is 1.01 and 1.02 atmosphere respectively. The ratio of their respective volumes is:
  A)
   2                            
  done clear
  B)
          4
  done clear
  C)
   6                            
  done clear
  D)
          8
  done clear
  E)
   16
  done clear
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• question_answer38) If\[\alpha \]and\[\beta \]are the current gain in the CB and CE configurations respectively of the transistor circuit, then\[\frac{\beta -\alpha }{\alpha \beta }=\]
  A)
   infinite                
  done clear
  B)
          1
  done clear
  C)
   2                            
  done clear
  D)
   0.5
  done clear
  E)
   zero
  done clear
  View Answer play_arrow

• question_answer39) Which of the following sets of quantities have same dimensional formula?
  A)
   Frequency, angular frequency and angular momentum
  done clear
  B)
   Surface tension, stress and spring constant
  done clear
  C)
   Acceleration, momentum and retardation
  done clear
  D)
   Thermal capacity, specific heat and entropy
  done clear
  E)
   Work, energy and torque
  done clear
  View Answer play_arrow

• question_answer40) A varying magnetic flux linking a coil is given by\[\phi -X{{t}^{2}}\]. If at time\[t=3\text{ }s,\]the emf induced is 9 V, then the value of\[X\]is:
  A)
   \[0.66\text{ }Wb\text{ }{{s}^{-2}}\]    
  done clear
  B)
          \[1.5\text{ }Wb\text{ }{{s}^{-2}}\]
  done clear
  C)
   \[-\text{ }0.66\text{ }Wb\text{ }{{s}^{-2}}\]  
  done clear
  D)
          \[-1.5\text{ }Wb\text{ }{{s}^{-2}}\]
  done clear
  E)
   \[-\,0.33\,Wb{{s}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer41) The apparent frequency of the whistle of an engine changes in the ratio\[9:8\]as the engine passes a stationary observer. If the velocity of the sound is\[340\text{ }m{{s}^{-1}},\]then the velocity of the engine is:
  A)
   \[40\text{ }m{{s}^{-1}}\]             
  done clear
  B)
          \[20\text{ }m{{s}^{-1}}\]
  done clear
  C)
   \[340\text{ }m{{s}^{-1}}\]      
  done clear
  D)
          \[\text{180 }m{{s}^{-1}}\]
  done clear
  E)
   \[50\text{ }m{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer42) The width of a single slit if the first minimum is observed at an angle\[2{}^\circ \]with a light of wavelength \[6980\overset{\text{o}}{\mathop{\text{A}}}\,\]:
  A)
   0.2mm                
  done clear
  B)
          \[2\times {{10}^{-5}}mm\]
  done clear
  C)
   \[2\times {{10}^{5}}mm\]    
  done clear
  D)
          2 mm
  done clear
  E)
   0.02mm
  done clear
  View Answer play_arrow

• question_answer43) A silicon specimen is made into a p-type semiconductor by doping, on an average, one indium atom per\[5\times {{10}^{7}}\]silicon atoms. If the number density of atoms in the silicon specimen is\[5\times {{10}^{28}}atom/{{m}^{3}},\]then the number of acceptor atoms in silicon per cubic centi metre will be:
  A)
   \[2.5\times {{10}^{30}}atom/c{{m}^{3}}\]
  done clear
  B)
   \[2.5\times {{10}^{35}}atom/c{{m}^{3}}\]
  done clear
  C)
   \[1\times {{10}^{13}}atom/c{{m}^{3}}\]
  done clear
  D)
   \[1\times {{10}^{15}}atom/c{{m}^{3}}\]
  done clear
  E)
   none of the above
  done clear
  View Answer play_arrow

• question_answer44) In a photoelectric effect measurement, the stopping potential for a given metal is found to be\[{{V}_{0}}\]volt when radiation of wavelength\[{{\lambda }_{0}}\]is used. If radiation of wavelength\[2{{\lambda }_{0}}\]is used with the same metal then the stopping potential (in volt) will be:
  A)
   \[\frac{{{V}_{0}}}{2}\]                  
  done clear
  B)
   \[2{{V}_{0}}\]
  done clear
  C)
   \[{{V}_{0}}+\frac{hc}{2e{{\lambda }_{0}}}\]       
  done clear
  D)
          \[{{V}_{0}}-\frac{hc}{2e{{\lambda }_{0}}}\]
  done clear
  E)
   \[{{V}_{0}}\]
  done clear
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• question_answer45) A 20 kg ball moving with a velocity 6 m/s collides with a 30 kg ball initially at rest. If both of them coalesce, then the final velocity of the combined mass is:
  A)
   6 m/s                   
  done clear
  B)
          5 m/s
  done clear
  C)
   3.6 m/s               
  done clear
  D)
          2.4 m/s
  done clear
  E)
   1.2 m/s
  done clear
  View Answer play_arrow

• question_answer46) A monkey climbs up and another monkey climbs down a rope hanging from a tree with same uniform acceleration separately. If the respective masses of monkeys are in the ratio \[2:3,\]the common acceleration must be:
  A)
   g/5                       
  done clear
  B)
          6g
  done clear
  C)
   g/2                       
  done clear
  D)
          g
  done clear
  E)
   g/3
  done clear
  View Answer play_arrow

• question_answer47) A running man has the same kinetic energy as that of a boy of half his mass. The man speeds up by\[2\text{ }m{{s}^{-1}}\]and the boy changes his speed by \[x\text{ }m{{s}^{-1}},\]so that the kinetic energies of the boy and the man are again equal. Then\[x\]in\[m{{s}^{-1}}\]is:
  A)
   \[-2\sqrt{2}\]                   
  done clear
  B)
          \[+2\sqrt{2}\]
  done clear
  C)
   \[\sqrt{2}\]                       
  done clear
  D)
          2
  done clear
  E)
   \[1/\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer48) In artificial radioactivity,\[1.414\times {{10}^{6}}\]nuclei are disintegrated into\[{{10}^{6}}\]nuclei in 10 min. The half-life in minutes must be:
  A)
   5       
  done clear
  B)
                                          20
  done clear
  C)
   15                         
  done clear
  D)
          30
  done clear
  E)
   25
  done clear
  View Answer play_arrow

• question_answer49) In a certain region of space there are only molecules per cm3 on an average. The temperature there is 3 K. The pressure of this dilute gas is: \[(k=1.38\times {{10}^{-~23}}J/K)\]
  A)
   \[20.7\times {{10}^{-17}}N/{{m}^{2}}\]
  done clear
  B)
   \[15.3\times {{10}^{-15}}N/{{m}^{2}}\]
  done clear
  C)
   \[2.3\times {{10}^{-10}}N/{{m}^{2}}\]
  done clear
  D)
   \[5.3\times {{10}^{-5}}N/{{m}^{2}}\]
  done clear
  E)
   \[3.5\times {{10}^{-8}}N/{{m}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer50) A network of six identical capacitors, each of value C, is made as shown in the figure. The equivalent capacitance between the points A and B is:
  A)
   \[\frac{4C}{11}\]                             
  done clear
  B)
          \[3C/4\]
  done clear
  C)
   \[3C/2\]             
  done clear
  D)
          \[3C\]
  done clear
  E)
   \[4C/3\]
  done clear
  View Answer play_arrow

• question_answer51) Two cars A and B are travelling in the same direction with velocities\[{{v}_{1}}\]and\[{{v}_{2}}({{v}_{1}}>{{v}_{2}})\]. When the car A is at a distance d behind the car B, the driver of the car A applies the brake producing uniform retardation, a. There will be no collision when:
  A)
   \[d<\left( \frac{{{v}_{1}}-{{v}_{2}}}{2a} \right)\]
  done clear
  B)
          \[d>\frac{v_{1}^{2}-v_{2}^{2}}{2a}\]
  done clear
  C)
   \[d>\frac{{{({{v}_{1}}-{{v}_{2}})}^{2}}}{2a}\]
  done clear
  D)
          \[d<\frac{v_{1}^{2}-v_{2}^{2}}{2a}\]
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer52) A simple pendulum has a time period\[{{T}_{1}}\]when on the earths surface and\[{{T}_{2}}\]when taken to a height 2R above the earths surface where R is the radius of the earth. The value of\[({{T}_{1}}/{{T}_{2}})\]is:
  A)
   \[\frac{1}{9}\]                  
  done clear
  B)
   \[\frac{1}{3}\]
  done clear
  C)
   \[\sqrt{3}\]                       
  done clear
  D)
          \[9\]
  done clear
  E)
   3
  done clear
  View Answer play_arrow

• question_answer53) A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being\[1\text{ }kg{{m}^{2}}\]and its rate of rotation 2 rev/s. The angular momentum is:
  A)
   \[1.257\,kg\,{{m}^{2}}/s\]  
  done clear
  B)
          \[12.57\,kg\,{{m}^{2}}/s\]
  done clear
  C)
   \[13.57\,kg\,{{m}^{2}}/s\]  
  done clear
  D)
          \[20\,kg\,{{m}^{2}}/s\]
  done clear
  E)
   \[1.357\,kg\,{{m}^{2}}/s\]
  done clear
  View Answer play_arrow

• question_answer54) The readings of a constant volume gas thermometer at\[0{}^\circ C\]and\[100{}^\circ C\]are 40 cm of mercury and 60 cm of mercury. If its reading at an unknown temperature is 100 cm of mercury column, then the temperature is:
  A)
  \[100{}^\circ C\]              
  done clear
  B)
          \[50{}^\circ C\]
  done clear
  C)
   \[25{}^\circ C\]                
  done clear
  D)
          \[300{}^\circ C\]
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer55) The amplitude of the sinusoidially oscillating electric field of a plane wave is 60 V/m. Then the amplitude of magnetic field is:
  A)
   \[2\times {{10}^{2}}T\]                
  done clear
  B)
          \[6\times {{10}^{7}}T\]
  done clear
  C)
   \[6\times {{10}^{2}}T\]                
  done clear
  D)
          \[2\times {{10}^{-7}}T\]
  done clear
  E)
   \[3\times {{10}^{8}}T\]
  done clear
  View Answer play_arrow

• question_answer56) A car of mass 1000 kg moves on a circular track of radius 20 m. If the coefficient of friction is 0.64, then the maximum velocity with which the car can move is:
  A)
   15 m/s                                
  done clear
  B)
   11.2 m/s
  done clear
  C)
   20 m/s                
  done clear
  D)
          18 m/s
  done clear
  E)
   22.4 m/s
  done clear
  View Answer play_arrow

• question_answer57) If\[{{\varepsilon }_{0}}\]and\[{{\mu }_{0}}\]are the electric permittivity and magnetic permeability of free space and\[\varepsilon \] and\[\mu \]are the corresponding quantities in the medium, the index of refraction of the medium in terms of above parameter is:
  A)
   \[\frac{\varepsilon \mu }{{{\varepsilon }_{0}}{{\mu }_{0}}}\]     
  done clear
  B)
          \[{{\left( \frac{\varepsilon \mu }{{{\varepsilon }_{0}}{{\mu }_{0}}} \right)}^{1/2}}\]
  done clear
  C)
   \[\left( \frac{{{\varepsilon }_{0}}{{\mu }_{0}}}{\varepsilon \mu } \right)\]           
  done clear
  D)
          \[{{\left( \frac{{{\varepsilon }_{0}}{{\mu }_{0}}}{\varepsilon \mu } \right)}^{1/2}}\]
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer58) Two planets have radii\[{{r}_{1}}\]and\[{{r}_{2}}\]and densities \[{{d}_{1}}\]and\[{{d}_{2}}\]respectively. Then the ratio of acceleration due to gravity on them will be:
  A)
   \[{{r}_{1}}{{d}_{1}}:{{r}_{2}}{{d}_{2}}\] 
  done clear
  B)
          \[{{r}_{1}}{{d}_{2}}:{{r}_{2}}{{d}_{1}}\]
  done clear
  C)
   \[r_{1}^{2}{{d}_{1}}:r_{2}^{2}{{d}_{2}}\]             
  done clear
  D)
          \[{{r}_{1}}:{{r}_{2}}\]
  done clear
  E)
   \[{{r}_{1}}/\sqrt{{{d}_{1}}}:{{r}_{2}}\sqrt{{{d}_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer59) A physical quantity P is related to four measurable quantities a, b, c and d as follows \[P=\frac{{{a}^{3}}{{b}^{2}}}{\sqrt{c}d}\] The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%. The percentage error in the quantity P is:
  A)
   10%                      
  done clear
  B)
          13%
  done clear
  C)
   5%                        
  done clear
  D)
          15%
  done clear
  E)
   17%
  done clear
  View Answer play_arrow

• question_answer60) The ratio of the resistance of conductor at temperature\[15{}^\circ C\]to its resistance at temperature\[37.5{}^\circ C\]is\[4:5\]. The temperature coefficient of resistance the conductor is:
  A)
   \[\frac{1}{25}{}^\circ {{C}^{-1}}\]            
  done clear
  B)
          \[\frac{1}{50}{}^\circ {{C}^{-1}}\]
  done clear
  C)
   \[\frac{1}{80}{}^\circ {{C}^{-1}}\]            
  done clear
  D)
          \[\frac{1}{75}{}^\circ {{C}^{-1}}\]
  done clear
  E)
   \[\frac{1}{40}{{\,}^{\text{o}}}{{C}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer61) A light ray of \[5895\overset{\text{o}}{\mathop{\text{A}}}\,\] wavelength travelling in vacuum enters a medium of refractive index 1.5. The speed of light in the medium is:
  A)
   \[3\times {{10}^{8}}m/s\]    
  done clear
  B)
          \[2\times {{10}^{8}}m/s\]
  done clear
  C)
   \[1.5\times {{10}^{8}}\text{ }m/s\] 
  done clear
  D)
          \[6\times {{10}^{8}}m/s\]
  done clear
  E)
   \[5\times {{10}^{7}}m/s\]
  done clear
  View Answer play_arrow

• question_answer62) The momentum of a body is increased by 25%. The kinetic energy is increased by about:
  A)
   25%                      
  done clear
  B)
          5%
  done clear
  C)
   56%                      
  done clear
  D)
          38%
  done clear
  E)
   65%
  done clear
  View Answer play_arrow

• question_answer63) Find the potential at the centre of a square of side\[\sqrt{2}m\]. Which carries at its four comers charges\[{{q}_{1}}=3\times {{10}^{-6}}C,{{q}_{2}}=-3\times {{10}^{-6}}C,\] \[{{q}_{3}}=-4\times {{10}^{-6}}C,{{q}_{4}}=7\times {{10}^{-6}}C\]
  A)
   \[2.7\times {{10}^{4}}V\]            
  done clear
  B)
          \[1.5\times {{10}^{3}}V\]
  done clear
  C)
   \[3\times {{10}^{2}}V\]               
  done clear
  D)
          \[5\times {{10}^{3}}V\]
  done clear
  E)
   \[3\times {{10}^{3}}V\]
  done clear
  View Answer play_arrow

• question_answer64) The half-life of radon is 3.8 days. How many radon will be left out of 1024 mg after 38 days:
  A)
   1 mg                    
  done clear
  B)
          2 mg
  done clear
  C)
   3 mg                    
  done clear
  D)
          4 mg
  done clear
  E)
   7mg
  done clear
  View Answer play_arrow

• question_answer65) In a cubic unit cell of bcc structure, the lattic points (i.e., number of atoms) are:
  A)
   2                            
  done clear
  B)
          6a
  done clear
  C)
   8                            
  done clear
  D)
          12
  done clear
  E)
   5
  done clear
  View Answer play_arrow

• question_answer66) A 2 kg copper block is heated to\[500{}^\circ C\]and then it is placed on a large block of ice at\[0{}^\circ C\]. If the specific   heat  capacity  of  copper  is \[400J\,k{{g}^{-1}}{}^\circ {{C}^{-1}}\]and latent heat of fusion of water is\[3.5\times {{10}^{5}}J\text{ }k{{g}^{-1}},\]the amount of ice that can melt is:
  A)
   7/8 kg                                  
  done clear
  B)
   7/5 kg
  done clear
  C)
   8/7 kg                  
  done clear
  D)
          5/7 kg
  done clear
  E)
   7/3 kg.
  done clear
  View Answer play_arrow

• question_answer67) In a common-emitter amplifier, the load resistance of the output circuit is 1000 times the resistance of the input circuit. If\[\alpha =0.98,\] then voltage gain is:
  A)
   \[49\times {{10}^{3}}\]                
  done clear
  B)
          \[2.5\times {{10}^{2}}\]
  done clear
  C)
   \[1.5\times {{10}^{2}}\]       
  done clear
  D)
          4.9
  done clear
  E)
   \[3.5\times {{10}^{3}}\]
  done clear
  View Answer play_arrow

• question_answer68) Two identical springs, each of spring constant K, are connected first series and then in parallel. A mass M is suspended from them. The ratio of the frequencies of vertical oscillations will be:
  A)
   \[2:1\]                 
  done clear
  B)
          \[1:1\]
  done clear
  C)
   \[1:4\]                 
  done clear
  D)
          \[4:1\]
  done clear
  E)
   \[1:2\]
  done clear
  View Answer play_arrow

• question_answer69) A particle of mass\[m=5\]units is moving with a uniform speed \[v=3\sqrt{2}\]m in the\[XOY\]plane along the line\[Y=X+4\]. The magnitude of the angular momentum about origin is:
  A)
   zero                     
  done clear
  B)
          60 unit
  done clear
  C)
   7.5 unit               
  done clear
  D)
         \[40\sqrt{2}\]unit
  done clear
  E)
   3.0 unit
  done clear
  View Answer play_arrow

• question_answer70) The plane faces of two identical plano-convex lenses each having a focal length of 50 cm are placed against each other to form a usual biconvex lens. The distance from this lens combination at which an object must be placed to obtain a real, inverted image which has the same size as the object is:
  A)
   50 cm                  
  done clear
  B)
          25 cm
  done clear
  C)
   100 cm                
  done clear
  D)
          40 cm
  done clear
  E)
   125cm
  done clear
  View Answer play_arrow

• question_answer71) A solid sphere of volume V and density\[\rho \]floats at the interface of two immiscible liquids of densities\[{{\rho }_{1}}\]and\[{{\rho }_{2}}\]respectively. If\[{{\rho }_{1}}<\rho <{{\rho }_{2}},\]then the ratio of volume of the parts of the sphere in upper and lower liquids is:
  A)
   \[\frac{\rho -{{\rho }_{2}}}{{{\rho }_{2}}-\rho }\]             
  done clear
  B)
          \[\frac{{{\rho }_{2}}-\rho }{\rho -{{\rho }_{1}}}\]
  done clear
  C)
   \[\frac{\rho +{{\rho }_{1}}}{\rho +{{\rho }_{2}}}\]           
  done clear
  D)
          \[\frac{\rho +{{\rho }_{2}}}{\rho +{{\rho }_{1}}}\]
  done clear
  E)
   \[\frac{\sqrt{{{\rho }_{1}}\,{{\rho }_{2}}}}{\rho }\]
  done clear
  View Answer play_arrow

• question_answer72) A short solenoid of length 4 cm, radius 2 cm and 100 turns is placed inside and on the axis of a long solenoid of length 80 cm and 1500 turns. A current of 3 A flows through the short solenoid. The mutual inductance of two solenoids is:
  A)
   \[2.96\times {{10}^{-4}}H\]  
  done clear
  B)
          \[5.3\times {{10}^{-5}}H\]
  done clear
  C)
   \[3.52\times {{10}^{-3}}H\]  
  done clear
  D)
          \[8.3\times {{10}^{-5}}H\]
  done clear
  E)
   \[2.96\times {{10}^{-3}}H\]
  done clear
  View Answer play_arrow

• question_answer73) Which one of the following has the highest molar conductivity?
  A)
  Diaminedichloroplatinum (II)
  done clear
  B)
  Tetraaminedichlorocobalt (III) chloride
  done clear
  C)
  Potassium hexacyanoferrate (II)
  done clear
  D)
  Hexaaquochromium (III) bromide
  done clear
  E)
  Pentacarbonyl iron (0)
  done clear
  View Answer play_arrow

• question_answer74) One mole of magnesium in the vapour state absorbed\[1200\text{ }kJ\text{ }mo{{l}^{-1}}\]of energy. If the first and second ionization energies of Mg are 750 and\[1450\text{ }kJ\text{ }mo{{l}^{-1}}\]respectively, the final composition of the mixture is:
  A)
  \[31%\text{ }M{{g}^{+}}+69%\text{ }M{{g}^{2+}}\]
  done clear
  B)
  \[69%\text{ }M{{g}^{+}}+31%\text{ }M{{g}^{2+}}\]
  done clear
  C)
  \[86%\text{ }M{{g}^{+}}+14%\text{ }M{{g}^{2+}}\]
  done clear
  D)
  \[14%\text{ }M{{g}^{+}}+86%\text{ }M{{g}^{2+}}\]
  done clear
  E)
  \[13%\text{ }M{{g}^{+}}+87%\text{ }M{{g}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer75) The first law of thermodynamic is expressed as:
  A)
  \[q-w=\Delta E\]             
  done clear
  B)
  \[\Delta E=q-w\]
  done clear
  C)
  \[q=\Delta E-w\]     
  done clear
  D)
         \[w=q+\Delta E\]
  done clear
  E)
  none of the these
  done clear
  View Answer play_arrow

• question_answer76) Which of the following complexes are not correctly matched with hybridization of their central metal ion? 1. \[[Ni{{(CO)}_{4}}]\]                    \[s{{p}^{3}}\] 2. \[{{[Ni{{(CN)}_{4}}]}^{2-}}\]                   \[s{{p}^{3}}\] 3. \[{{[Co{{F}_{6}}]}^{3-}}\]                         \[{{d}^{2}}s{{p}^{3}}\] 4. \[{{[Fe{{(CN)}_{6}}]}^{3-}}\]                   \[s{{p}^{3}}{{d}^{2}}\] Select the correct answer using the codes given below:
  A)
  1 and 2
  done clear
  B)
                                         1 and 3
  done clear
  C)
  2 and 4                 
  done clear
  D)
         1, 3 and 4
  done clear
  E)
  2, 3 and 4
  done clear
  View Answer play_arrow

• question_answer77) During the transformation of\[^{b}{{X}_{a}}{{\xrightarrow{{}}}^{d}}{{Y}_{c}}\] the number of \[\beta \]-particles emitted is:
  A)
  \[(b-d)/4\]
  done clear
  B)
  \[(c-a)+1/2(b-d)\]
  done clear
  C)
  \[(a-c)-1/2(b-d)\]
  done clear
  D)
  \[(b-d)+2(c-a)\]
  done clear
  E)
  \[(b-d)+1/2(c-a)\]
  done clear
  View Answer play_arrow

• question_answer78) The Markownikoffs rule is the best applicable to the reaction between:
  A)
  \[{{C}_{2}}{{H}_{4}}+HCl\]   
  done clear
  B)
         \[{{C}_{3}}{{H}_{6}}+B{{r}_{2}}\]
  done clear
  C)
  \[{{C}_{3}}{{H}_{6}}+HBr\]   
  done clear
  D)
         \[{{C}_{3}}{{H}_{8}}+C{{l}_{2}}\]
  done clear
  E)
  \[{{C}_{2}}{{H}_{4}}+{{I}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer79) Phenol can be distinguished from ethanol by the following reagents except:
  A)
  sodium
  done clear
  B)
  \[NaOH/{{I}_{2}}\]
  done clear
  C)
  neutral \[FeC{{l}_{3}}\]
  done clear
  D)
  \[B{{r}_{2}}/{{H}_{2}}O\]
  done clear
  E)
  phthalic anhydride/cone.\[{{H}_{2}}S{{O}_{4}}\]and\[NaOH\]
  done clear
  View Answer play_arrow

• question_answer80) The enol form of acetone after treatment with\[{{D}_{2}}O,\]gives:
  A)
  \[{{H}_{3}}C-\underset{\begin{smallmatrix}  | \\  OD \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}\]
  done clear
  B)
  \[{{H}_{3}}C-\underset{\begin{smallmatrix}  || \\  O \end{smallmatrix}}{\mathop{C}}\,=C{{D}_{3}}\]
  done clear
  C)
  \[{{H}_{2}}C=\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}D\]
  done clear
  D)
  \[{{H}_{2}}C=\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C}}\,=CH{{D}_{2}}\]
  done clear
  E)
  \[{{D}_{2}}C=\underset{\begin{smallmatrix}  | \\  OD \end{smallmatrix}}{\mathop{C}}\,-C{{D}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer81) Consider the following compounds:

  (i) chloroethene

  (ii) benzene

  (iii) 1, 3-butadiene

  (iv) 1, 3, 5-hexatriene

  All the carbon atoms are\[s{{p}^{2}}\]hybridized in:
  A)
  (i), (iii), (iv) only
  done clear
  B)
  (i), (ii) only
  done clear
  C)
  (ii), (iii), (iv) only
  done clear
  D)
  (iii), (iv) only
  done clear
  E)
  (i), (ii), (iii) and (iv)
  done clear
  View Answer play_arrow

• question_answer82) An alkene on reductive ozonolysis gives 2-molecules of\[C{{H}_{2}}{{(CHO)}_{2}}\]. The alkene is:
  A)
  2, 4-hexadiene
  done clear
  B)
  1, 3-cyclohexadiene
  done clear
  C)
  1, 4-cyclohexadiene
  done clear
  D)
  1-methyl-1, 3-cyclopentadiene
  done clear
  E)
  1, 2-dimethyl cyclopropene
  done clear
  View Answer play_arrow

• question_answer83) Which of the following statements are correct concerning redox properties?

  1. A metal M for which\[E{}^\circ \]for the half reaction \[{{M}^{n+}}+n{{e}^{-}}=M,\]is very negative will be a good reducing agent

  2. The oxidizing power of the halogens decreases from chlorine to iodine

  3. The reducing power of hydrogen halides increases from hydrogen chloride to hydrogen iodide.

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

• question_answer84) Identify the compound Z, In this reaction sequence \[C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[{}]{N{{H}_{3}}}X\xrightarrow[{}]{B{{r}_{2}}+KOH}\] \[Y\xrightarrow[{}]{HN{{O}_{2}}}Z:\]
  A)
  \[C{{H}_{3}}OH\]             
  done clear
  B)
         \[C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\]
  done clear
  C)
  \[C{{H}_{3}}C{{H}_{2}}OH\]   
  done clear
  D)
         \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\]
  done clear
  E)
  \[C{{H}_{3}}N{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer85) The following homogeneous gaseous reactions were experimentally found to be second order overall.

  1. \[2NO\xrightarrow[{}]{{}}{{N}_{2}}+{{O}_{2}}\]

  2. \[3{{O}_{2}}\xrightarrow[{}]{{}}2{{O}_{3}}\]

  3. \[{{N}_{2}}{{O}_{3}}\xrightarrow[{}]{{}}NO+N{{O}_{2}}\]

  4. \[{{H}_{2}}+{{I}_{2}}\xrightarrow[{}]{{}}2HI\]

  Which of these are most likely to be elementary reactions that occur in one step?
  A)
  3 only  
  done clear
  B)
                                         1 and 3
  done clear
  C)
  1 and 4                 
  done clear
  D)
         3 and 4
  done clear
  E)
  1, 2 and 3
  done clear
  View Answer play_arrow

• question_answer86) The successive ionization energy values for an element X are given below:

  (i) 1st ionization energy \[=410\text{ }kJ\text{ }mo{{l}^{-1}}\]

  (ii) 2nd ionization energy\[=820\text{ }kJ\text{ }mo{{l}^{-1}}\]

  (iii) 3rd ionization energy\[=1100\text{ }kJ\text{ }mo{{l}^{-1}}\]

  (iv) 4th ionization energy\[=1500\text{ }kJ\text{ }mo{{l}^{-1}}\]

  (v) 5th ionization energy\[=3200\text{ }kJ\text{ }mo{{l}^{-1}}\]

  Find out the number of valence electron for the atom
  A)
  4                                             
  done clear
  B)
  3
  done clear
  C)
  5                             
  done clear
  D)
         2
  done clear
  E)
  1
  done clear
  View Answer play_arrow

• question_answer87) On a humid day in summer, the mole fraction of gaseous\[{{H}_{2}}O\](water vapour) in the air at \[25{}^\circ C\]can be as high as 0.0287. Assuming a total pressure of 0.977 atm. What is the partial pressure of dry air?
  A)
  94.9 atm              
  done clear
  B)
  0.949 atm
  done clear
  C)
  949 atm               
  done clear
  D)
         0.648 atm
  done clear
  E)
  1.248 atm
  done clear
  View Answer play_arrow

• question_answer88) Match list I with list II and select the correct answer using the codes given below the lists.

  	List I: Metal ions		List II: Magnetic moment (BM)
  1	\[C{{r}^{3+}}\]	A	\[\sqrt{35}\]
  2	\[F{{e}^{2+}}\]	B	\[\sqrt{30}\]
  3	\[N{{i}^{2+}}\]	C	\[\sqrt{24}\]
  4	\[M{{n}^{2+}}\]	D	\[\sqrt{15}\]
  		E	\[\sqrt{8}\]

  Codes:
  A)
  1-A, 2-C, 3-E, 4-D
  done clear
  B)
  1-B, 2-C, 3-E, 4-A
  done clear
  C)
  1-D, 2-C, 3-E, 4-A
  done clear
  D)
  1-D, 2-E, 3-C, 4-A
  done clear
  E)
  1-E, 2-A, 3-B, 4-C
  done clear
  View Answer play_arrow

• question_answer89) The number of optical isomers of \[C{{H}_{3}}CH(OH)CH(OH)CHO\]is:
  A)
  zero         
  done clear
  B)
                         2
  done clear
  C)
  3                             
  done clear
  D)
         4
  done clear
  E)
  6
  done clear
  View Answer play_arrow

• question_answer90) For which of the following sparingly soluble salt, the solubility (s) and solubility product \[({{K}_{sp}})\]are related  by  the  expression \[s={{({{K}_{sp}}/4)}^{1/3}}\]?
  A)
  \[BaS{{O}_{4}}\]              
  done clear
  B)
         \[C{{a}_{3}}{{(P{{O}_{4}})}_{2}}\]
  done clear
  C)
  \[H{{g}_{2}}C{{l}_{2}}\] 
  done clear
  D)
         \[A{{g}_{3}}P{{O}_{4}}\]
  done clear
  E)
  \[CuS\]
  done clear
  View Answer play_arrow

• question_answer91) For the reaction\[CO(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow[{}]{{}}\]\[C{{O}_{2}}(g),\Delta H\]and \[\Delta S\] are\[-283kJ\]and\[-87J{{K}^{-1}},\]respectively. It was intended to carry out this reaction at 1000, 1500, 3000 and 3500 K. At which of these temperatures would this reaction be thermodynamically spontaneous?
  A)
  1500 and 3500 K
  done clear
  B)
  3000 and 3500 K
  done clear
  C)
  1000, 1500 and 3000 K
  done clear
  D)
  1500, 3000 and 3500 K
  done clear
  E)
  At all these temperatures
  done clear
  View Answer play_arrow

• question_answer92) At certain temperature a 5.12% solution of cane sugar is isotonic with a 0.9% solution of an unknown solute. The molar mass of solute is:
  A)
  60                          
  done clear
  B)
         46.17
  done clear
  C)
  120                        
  done clear
  D)
         90
  done clear
  E)
  92.34
  done clear
  View Answer play_arrow

• question_answer93) Which of the following is true in respect of adsorption?
  A)
  \[\Delta G<0;\text{ }\Delta S>0;\text{ }\Delta H<0\]
  done clear
  B)
   \[\Delta G<0;\text{ }\Delta S<0;\text{ }\Delta H<0\]
  done clear
  C)
  \[\Delta G>0;\text{ }\Delta S>0;\text{ }\Delta H<0\]
  done clear
  D)
  \[\Delta G<0;\text{ }\Delta S<0;\text{ }\Delta H>0\]
  done clear
  E)
  \[\Delta G>0;\text{ }\Delta S>0;\text{ }\Delta H>0\]
  done clear
  View Answer play_arrow

• question_answer94) Find the two third life\[({{t}_{2/3}})\]of a first order reaction in which\[k=5.48\times {{10}^{-14}}\]per second:
  A)
  \[201\times {{10}^{13}}s\]
  done clear
  B)
         \[2.01\times {{10}^{13}}s\]
  done clear
  C)
  \[201\times {{10}^{20}}s\]   
  done clear
  D)
         \[0.201\times {{10}^{10}}s\]
  done clear
  E)
  none of these
  done clear
  View Answer play_arrow

• question_answer95) If\[(x/m)\]is the mass of adsorbate adsorbed per unit mass of adsorbent. P is the pressure of the abdsorbate gas and a and b are constants, which of the following represents Langmuir adsorption isotherm?
  A)
  \[\log \left( \frac{x}{m} \right)=\log \left( \frac{a}{b} \right)+\frac{1}{a}\log p\]
  done clear
  B)
  \[\frac{x}{m}=\frac{b}{a}+\frac{1}{ap}\]
  done clear
  C)
  \[\frac{x}{m}=\frac{1+bp}{ap}\]
  done clear
  D)
  \[\frac{1}{(x/m)}=\frac{a}{b}+\frac{p}{a}\]
  done clear
  E)
  \[\frac{1}{(x/m)}=\frac{b}{a}+\frac{1}{ap}\]
  done clear
  View Answer play_arrow

• question_answer96) The amine which will not liberate nitrogen on reaction with nitrous acid is:
  A)
  Trimethyl amine
  done clear
  B)
         ethyl amine
  done clear
  C)
  sec-butyl amine
  done clear
  D)
         c-butyl amine
  done clear
  E)
  iso-propyl amine
  done clear
  View Answer play_arrow

• question_answer97) 5.6 g of an organic compound on burning with excess of oxygen gave 17.6 g of\[C{{O}_{2}}\]and 7.2 g of\[{{H}_{2}}O\]. The organic compound is:
  A)
  \[{{C}_{6}}{{H}_{6}}\]                    
  done clear
  B)
         \[{{C}_{4}}{{H}_{8}}\]
  done clear
  C)
  \[{{C}_{3}}{{H}_{8}}\]                    
  done clear
  D)
         \[C{{H}_{3}}COOH\]
  done clear
  E)
  \[C{{H}_{3}}CHO\]
  done clear
  View Answer play_arrow

• question_answer98) One mole of acidified\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]on reaction with excess KI will liberate ....... mole(s) of \[{{I}_{2}}\]:
  A)
  6                                             
  done clear
  B)
  1
  done clear
  C)
  7                             
  done clear
  D)
         2
  done clear
  E)
  3
  done clear
  View Answer play_arrow

• question_answer99) Which of the following exists as Zwitter ion?
  A)
  p-aminophenol                
  done clear
  B)
  Salicylic acid
  done clear
  C)
  Sulphanilic acid
  done clear
  D)
         Ethanolamine
  done clear
  E)
  p-amino acetophenone
  done clear
  View Answer play_arrow

• question_answer100) Match the lists I and II and pick the correct matching from the codes given below:

  List I	List II
  A Thymine	1. Pyrimidine base
  B Thiamine	2. Enzyme
  C Insulin	3. Cell-wall component
  D Pepsin	4. Hormone
  E Phospholipids	5. \[Vit\,{{B}_{1}}\]

  Codes:
  A)
  A-4; B-3; C-1; D-5; E-2
  done clear
  B)
  A-5; B-3; C-4; D-1; E-2
  done clear
  C)
  A-3; B-2; C-1; D-5; E-4
  done clear
  D)
  A-2; B-4; C-1; D-3; E-5
  done clear
  E)
  A-1; B-5; C-4; D-2; E-3
  done clear
  View Answer play_arrow

• question_answer101) The halogen compound which most readily undergoes nucleophilic substitution is:
  A)
  \[C{{H}_{2}}=CHCl\]
  done clear
  B)
  \[C{{H}_{3}}CH=CHCl\]
  done clear
  C)
  \[C{{H}_{2}}=CHC(Cl)=C{{H}_{2}}\]
  done clear
  D)
  \[C{{H}_{2}}=CHC{{H}_{2}}Cl\]
  done clear
  E)
  \[{{C}_{6}}{{H}_{5}}Cl\]
  done clear
  View Answer play_arrow

• question_answer102) Given the standard reduction potentials \[Z{{n}^{2+}}/Zn=-0.74\,V,\]       \[C{{l}_{2}}/C{{l}^{-}}=1.36\,V,\] \[{{H}^{+}}/1/2{{H}_{2}}=0\,V\]and \[F{{e}^{2+}}/F{{e}^{3+}}=0.77\,V\] The order of increasing strength as reducing agent is:
  A)
  \[C{{l}^{-}},Zn,{{H}_{2}},F{{e}^{2+}}\]
  done clear
  B)
         \[{{H}_{2}},Zn,F{{e}^{2+}},Cl\]
  done clear
  C)
  \[C{{l}^{-}}F{{e}^{2+}},Zn,{{H}_{2}}\]     
  done clear
  D)
  \[{{H}_{2}}F{{e}^{2+}},C{{l}^{-}},Zn\]
  done clear
  E)
  \[C{{l}^{-}},F{{e}^{2+}},{{H}_{2}},Zn\]
  done clear
  View Answer play_arrow

• question_answer103) The reaction\[2A+B+C\xrightarrow{{}}D+E\]is found to be first order in A, second in B and zero order in C. What is the effect on the rate of increasing concentration of A, B and C two times?
  A)
  72 times       
  done clear
  B)
         8 times
  done clear
  C)
  24 times       
  done clear
  D)
         36 times
  done clear
  E)
  none of the these
  done clear
  View Answer play_arrow

• question_answer104) Match list I with list II and select the correct answer using the codes given below the lists

  List-I Type of ore	List-II Example
  1. Oxide ore	A. Feldspar
  2. Sulphide ore	B. barytes
  3. Sulphate ore	C. Fluorspar
  4. Halide ore	D. Galena
  E. Corundum

  Codes:
  A)
  1-A, 2-E, 3-B, 4-C
  done clear
  B)
  1-B, 2-D, 3-C, 4-A
  done clear
  C)
  1-B, 2-D, 3-E, 4-A
  done clear
  D)
  1-E, 2-B, 3-D, 4-C
  done clear
  E)
  1-E, 2-D, 3-B, 4-C
  done clear
  View Answer play_arrow

• question_answer105) Consider the following halogen containing compounds:

  (A) \[CHC{{l}_{3}}\]

  (B) \[CC{{l}_{4}}\]

  (C) \[C{{H}_{2}}C{{l}_{2}}\]

  (D) \[C{{H}_{3}}Cl\]

  (E)

  The compounds with a net zero dipole moment are:
  A)
  B and E only
  done clear
  B)
          C only
  done clear
  C)
  C and D only   
  done clear
  D)
         A and D only
  done clear
  E)
  B only
  done clear
  View Answer play_arrow

• question_answer106) For the reaction\[{{N}_{2}}(g)+3{{H}_{2}}(g)\] \[2N{{H}_{3}}(g);\] \[\Delta H=-93.6\,kJ\,mo{{l}^{-1}},\]the concentration of \[N{{H}_{3}}\] at equilibrium can be increased by:

  (1) lowering the temperature

  (2) low pressure

  (3) excess of \[{{N}_{2}}\]

  (4) excess of \[{{H}_{2}}\]

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

• question_answer107) Which of the following is bacteriostatic?
  A)
  Penicillin             
  done clear
  B)
  Erythromycin
  done clear
  C)
  Amino glycodine             
  done clear
  D)
  Ofloxacin
  done clear
  E)
  Bithional
  done clear
  View Answer play_arrow

• question_answer108) Which one of the following set of quantum numbers is not possible for electron in the ground state of an atom with atomic number 19?
  A)
  \[n=2,l=0,\text{ }m=0\]
  done clear
  B)
  \[n=2,l=1,m=0\]
  done clear
  C)
  \[n=3,l=1,m=-1\]
  done clear
  D)
  \[n=3,l=2,\text{ }m=+2\]
  done clear
  E)
  \[n=4,\text{ }l=0,\text{ }m=0\]
  done clear
  View Answer play_arrow

• question_answer109) Match list I and list II and pick out correct matching codes from the given choices:

  List-I Compound	List-II Structure
  A.\[Cl{{F}_{3}}\]	1. Square planar
  B.\[PC{{l}_{5}}\]	2. Tetrahedral.
  C. \[I{{F}_{5}}\]	3. Trigonal bipyramidal
  D. \[CC{{l}_{4}}\]	4. Square pyramidal
  E. \[Xe{{F}_{4}}\]	5. T-shaped

  Codes:
  A)
  A-5, B-4, C-3, D-2, E-1
  done clear
  B)
  A-5, B-3, C-4, D-2, E-1
  done clear
  C)
  A-5, B-3, C-4, D-1, E-2
  done clear
  D)
  A-4, B-3, C-5, D-2, E-1
  done clear
  E)
  A-3, B-4, C-1, D-5, E-2
  done clear
  View Answer play_arrow

• question_answer110) The sequence that correctly describes the relative bond strength pertaining to oxygen molecule and its cation or anions is:
  A)
  \[O_{2}^{2-}>O_{2}^{-}>{{O}_{2}}>O_{2}^{+}\]
  done clear
  B)
  \[{{O}_{2}}>O_{2}^{+}>O_{2}^{-}>O_{2}^{2-}\]
  done clear
  C)
  \[O_{2}^{+}>{{O}_{2}}>O_{2}^{2-}>O_{2}^{-}\]
  done clear
  D)
  \[O_{2}^{+}>{{O}_{2}}>O_{2}^{-}>O_{2}^{2-}\]
  done clear
  E)
  \[{{O}_{2}}>O_{2}^{-}>O_{2}^{2-}>O_{2}^{+}\]
  done clear
  View Answer play_arrow

• question_answer111) The hybrid rocket propellant consists of:
  A)
  acrylic rubber and liquid nitrogen tetraoxide
  done clear
  B)
  polyurethane and ammonium perchlorate
  done clear
  C)
  nitroglycerine and nitrocellulose
  done clear
  D)
  liquid hydrogen and liquid oxygen
  done clear
  E)
  hydrogen peroxide
  done clear
  View Answer play_arrow

• question_answer112) The orbital angular momentum of an electron revolving in a p-orbital is:
  A)
  zero                      
  done clear
  B)
         \[\frac{h}{\sqrt{2\pi }}\]
  done clear
  C)
  \[\frac{h}{2\pi }\]                            
  done clear
  D)
         \[\frac{1}{2}\frac{h}{2\pi }\]
  done clear
  E)
  \[\frac{h}{2\sqrt{2\pi }}\]
  done clear
  View Answer play_arrow

• question_answer113) Boric acid is used in carom boards for smooth gliding of pawns because:
  A)
  \[{{H}_{3}}B{{O}_{3}}\]molecules are loosely chemically bonded and hence soft
  done clear
  B)
  its low density makes it fluffy
  done clear
  C)
  it can be powdered to a very small grain size
  done clear
  D)
  it is chemically inert with the plywood
  done clear
  E)
  H-bonding in \[{{H}_{3}}B{{O}_{3}}\] gives it a layered structure
  done clear
  View Answer play_arrow

• question_answer114) Consider the following molecules or ions:

  (i) \[{{H}_{2}}O\]

  (ii) \[NH_{4}^{+}\]

  (iii) \[SO_{4}^{2-}\]

  (vi) \[ClO_{4}^{-}\]

  (v) \[N{{H}_{3}}\]

  \[s{{p}^{3}}\]hybridization is involved in the formation of:
  A)
  (i), (ii), (v) only
  done clear
  B)
  (i), (ii) only
  done clear
  C)
  (ii) only
  done clear
  D)
  (i), (ii), (iii), (iv) only
  done clear
  E)
  (i), (ii), (iii), (iv) and (v)
  done clear
  View Answer play_arrow

• question_answer115) Gases X, Y, Z, P and Q have the van der Waals constants a and b (in CGS units) as shown below:

  	X	Y	Z	P	Q
  a	6	6	20	0.05	30
  b	0.025	0.15	0.1	0.02	0.2

  The gas with the highest critical temperature is:
  A)
  P                            
  done clear
  B)
         Q
  done clear
  C)
  Y                             
  done clear
  D)
         Z
  done clear
  E)
  X
  done clear
  View Answer play_arrow

• question_answer116) How many optically active stereoisomers are possible for butane-2, 3-diol?
  A)
  0                             
  done clear
  B)
         1
  done clear
  C)
  2                             
  done clear
  D)
         3
  done clear
  E)
  4
  done clear
  View Answer play_arrow

• question_answer117) Calculate the equilibrium constant for the reaction, at\[25{}^\circ C\] \[Cu(s)+2A{{g}^{+}}(aq)\xrightarrow[{}]{{}}C{{u}^{2+}}(aq)+2Ag(s)\] at\[25{}^\circ C,E_{cell}^{o}=0.47V,R=8.314\,J{{K}^{-1}}\] \[F=96500\,C\]:
  A)
  \[1.8\times {{10}^{15}}\]             
  done clear
  B)
         \[8.5\times {{10}^{15}}\]
  done clear
  C)
  \[1.8\times {{10}^{10}}\]             
  done clear
  D)
         \[85\times {{10}^{15}}\]
  done clear
  View Answer play_arrow

• question_answer118) Which of the following statements regarding the\[{{S}_{N}}1\]reaction shown by alkyl halide is not correct?
  A)
  The added nucleophile plays no kinetic role in\[{{S}_{N}}1\]reaction
  done clear
  B)
  The\[{{S}_{N}}1\]reaction involves the inversion of configuration of the optically active substrate
  done clear
  C)
  The\[{{S}_{N}}1\]reaction on the chiral starting material ends up with racemization of the product
  done clear
  D)
  The more stable the carbocation intermediate the faster the\[{{S}_{N}}1\]reaction
  done clear
  E)
  Polar protic solvent increases the rate of \[{{S}_{N}}1\]reaction
  done clear
  View Answer play_arrow

• question_answer119) Pick out the statement (s) which is (are) not true about the diagonal relationship of\[Li\]and Mg:

  (i) polarising powers of\[L{{i}^{+}}\]and\[M{{g}^{2+}}\]are almost same

  (ii) like\[Li,\]\[Mg\]decomposes water very fast

  (iii)\[LiCl\]and\[MgC{{l}^{2}}\]are deliquescent

  (iv) like\[Li,Mg\]do not form solid bicarbonates

  A)
  (i) and (ii)     
  done clear
  B)
         (ii) and (iii)
  done clear
  C)
  only (ii)                
  done clear
  D)
         only (i)
  done clear
  E)
  (ii) and (iv)
  done clear
  View Answer play_arrow

• question_answer120) Which of the following concentration terms is/are independent of temperature?
  A)
  Molarity
  done clear
  B)
  Molarity and mole fraction
  done clear
  C)
  Mole fraction and molality
  done clear
  D)
  Molality and normality
  done clear
  E)
  Only molality
  done clear
  View Answer play_arrow

• question_answer121) For an equilateral triangle the centre is the origin and the length of altitude is a. Then, the equation of the circumcircle is:
  A)
   \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]
  done clear
  B)
   \[3{{x}^{2}}+3{{y}^{2}}=2{{a}^{2}}\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}=4{{a}^{2}}\]
  done clear
  D)
   \[3{{x}^{2}}+3{{y}^{2}}={{a}^{2}}\]
  done clear
  E)
   \[9{{x}^{2}}+9{{y}^{2}}=4{{a}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer122) If the two pair of lines\[{{x}^{2}}-2mxy-{{y}^{2}}=0\]and \[{{x}^{2}}-2nxy-{{y}^{2}}=0\]are such that one of them represents the bisector of the angles between the other, then:
  A)
   \[mn+1=0\]
  done clear
  B)
          \[mn-1=0\]
  done clear
  C)
   \[\frac{1}{m}+\frac{1}{n}=0\]     
  done clear
  D)
          \[\frac{1}{m}-\frac{1}{n}=0\]
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer123) Let\[f\]be a function such that\[f(1)=10\]and \[f(x)\ge 2\]for\[1\le x<4\]. How small can\[f(4)\]possibly be?
  A)
   8              
  done clear
  B)
                          12
  done clear
  C)
   16                         
  done clear
  D)
          2
  done clear
  E)
   10
  done clear
  View Answer play_arrow

• question_answer124) The solution of the differential equation \[x\frac{dy}{dx}+2y={{x}^{2}}\]is:
  A)
   \[y=\frac{{{x}^{2}}+c}{4{{x}^{2}}}\]                        
  done clear
  B)
   \[y=\frac{{{x}^{2}}}{4}+c\]
  done clear
  C)
   \[y=\frac{{{x}^{4}}+c}{{{x}^{2}}}\]          
  done clear
  D)
   \[y=\frac{{{x}^{4}}+c}{4{{x}^{2}}}\]
  done clear
  E)
   \[y=\frac{{{x}^{3}}}{4}+\frac{c}{{{x}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer125) \[\frac{1}{\cos 80{}^\circ }-\frac{\sqrt{3}}{\sin 80{}^\circ }\]is equal to:
  A)
   \[\sqrt{2}\]                                       
  done clear
  B)
   \[\sqrt{3}\]
  done clear
  C)
   2                            
  done clear
  D)
          4
  done clear
  E)
   \[\sqrt{5}\]
  done clear
  View Answer play_arrow

• question_answer126) \[y=-A\text{ }cos\text{ }5x+B\text{ }sin\text{ }5x\]satisfies the differential equation:
  A)
   \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+10\frac{dy}{dx}+25y=0\]
  done clear
  B)
   \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-10\frac{dy}{dx}+25y=0\]
  done clear
  C)
   \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-25y=0\]
  done clear
  D)
   \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+25y=0\]
  done clear
  E)
   none of the above
  done clear
  View Answer play_arrow

• question_answer127) If \[\int{\frac{\sqrt{x}}{x+1}}dx=A\sqrt{x}+B{{\tan }^{-1}}\sqrt{x}+c,\]then:
  A)
  \[A=1,\text{ }B=1\]        
  done clear
  B)
  \[A=1,\text{ }B=2\]
  done clear
  C)
  \[A=2,B=2\]    
  done clear
  D)
          \[A=2,B=-2\]
  done clear
  E)
  \[A=-2,B=-2\]
  done clear
  View Answer play_arrow

• question_answer128) The equation of the tangent to the curve \[y={{(1+x)}^{y}}+{{\sin }^{-1}}({{\sin }^{2}}x)\]at\[x=0\]is:
  A)
   \[x-y+1=0\]      
  done clear
  B)
   \[x+y+1=0\]
  done clear
  C)
   \[2x-y+1=0\] 
  done clear
  D)
          \[x+2y+2=0\]
  done clear
  E)
   \[2x+y-1=0\]
  done clear
  View Answer play_arrow

• question_answer129) \[\int{\frac{{{x}^{3}}\sin [{{\tan }^{-1}}{{(x)}^{4}}]}{1+{{x}^{8}}}}dx\]is equal to:
  A)
   \[\frac{1}{4}\cos [{{\tan }^{-1}}({{x}^{4}})]+c\]
  done clear
  B)
   \[\frac{1}{4}\sin [{{\tan }^{-1}}({{x}^{4}})]+c\]
  done clear
  C)
   \[-\frac{1}{4}\cos [{{\tan }^{-1}}({{x}^{4}})]+c\]
  done clear
  D)
   \[\frac{1}{4}{{\sec }^{-1}}[{{\tan }^{-1}}({{x}^{4}})]+c\]
  done clear
  E)
   \[-\frac{1}{4}{{\cos }^{-1}}[{{\tan }^{-1}}({{x}^{4}})]+c\]
  done clear
  View Answer play_arrow

• question_answer130) An anti-aircraft gun can take a maximum of four shots at any plane moving away from it. The probabilities of hitting the plane at the 1 st, 2 nd, 3 rd and 4 th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that at least one shot hits the plane?
  A)
   0.6976                                 
  done clear
  B)
   0.3024
  done clear
  C)
   0.72                      
  done clear
  D)
          0.6431
  done clear
  E)
   0.7391
  done clear
  View Answer play_arrow

• question_answer131) The statement\[\tilde{\ }(p\to q)\]is equivalent to:
  A)
   \[p\wedge (\tilde{\ }p)\]                            
  done clear
  B)
   \[\tilde{\ }p\wedge q\]
  done clear
  C)
   \[p\wedge q\]
  done clear
  D)
          \[\tilde{\ }p\wedge \tilde{\ }q\]
  done clear
  E)
   \[p\vee q\]
  done clear
  View Answer play_arrow

• question_answer132) \[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}x}dx,\]then \[\underset{n\to \infty }{\mathop{\lim }}\,n[{{I}_{n}}+{{I}_{n+2}}]\]equal is:
  A)
   \[\frac{1}{2}\]                  
  done clear
  B)
          1
  done clear
  C)
   \[\infty \]                          
  done clear
  D)
          zero
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer133) A bag contains 3 black, 3 white and 2 red balls. One by one, three balls are drawn without replacement. The probability that the third ball is red is equal to:
  A)
   \[\frac{2}{56}\]
  done clear
  B)
                          \[\frac{3}{56}\]
  done clear
  C)
   \[\frac{1}{56}\]               
  done clear
  D)
          \[\frac{12}{56}\]
  done clear
  E)
   \[\frac{14}{56}\]
  done clear
  View Answer play_arrow

• question_answer134) The angle between the line \[\frac{x-3}{2}=\frac{y-1}{1}=\frac{z+4}{-2}\]and   the   plane, \[x+y+z+5=0\]is:
  A)
   \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]                 
  done clear
  B)
   \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]
  done clear
  C)
   \[\frac{\pi }{4}\]                             
  done clear
  D)
          \[{{\sin }^{-1}}\left( \frac{1}{3\sqrt{3}} \right)\]
  done clear
  E)
   \[{{\sin }^{-1}}(2)\]
  done clear
  View Answer play_arrow

• question_answer135) A vector perpendicular to\[2\hat{i}+\hat{j}+\hat{k}\]and coplanar with\[\hat{i}+2\hat{j}+\hat{k}\] and\[\hat{i}+\hat{j}+2\hat{k}\]is:
  A)
   \[5(\hat{j}-\hat{k})\]                    
  done clear
  B)
          \[\hat{i}+7\hat{j}-\hat{k}\]
  done clear
  C)
   \[5(\hat{j}+\hat{k})\]                   
  done clear
  D)
          \[2\hat{i}-7\hat{j}-\hat{k}\]
  done clear
  E)
   \[5(\hat{i}+\hat{k})\]
  done clear
  View Answer play_arrow

• question_answer136) If\[\left[ \begin{matrix}    2 & 1  \\    3 & 2  \\ \end{matrix} \right]A\left[ \begin{matrix}    -3 & 2  \\    5 & -3  \\ \end{matrix} \right]=\left[ \begin{matrix}    1 & 0  \\    0 & 1  \\ \end{matrix} \right],\]then A is equal to:
  A)
   \[-\left[ \begin{matrix}    1 & 1  \\    1 & 0  \\ \end{matrix} \right]\]   
  done clear
  B)
          \[\left[ \begin{matrix}    1 & 1  \\    0 & 1  \\ \end{matrix} \right]\]
  done clear
  C)
   \[\left[ \begin{matrix}    1 & 0  \\    1 & 1  \\ \end{matrix} \right]\]   
  done clear
  D)
          \[\left[ \begin{matrix}    0 & 1  \\    1 & 1  \\ \end{matrix} \right]\]
  done clear
  E)
   \[\left[ \begin{matrix}    2 & 1  \\    0 & 1  \\ \end{matrix} \right]\]
  done clear
  View Answer play_arrow

• question_answer137) The point on the curve\[y=2{{x}^{2}}-6x-4\]at which the tangent is parallel to the\[x-\]axis, is:
  A)
   \[\left( \frac{3}{2},\frac{13}{2} \right)\]               
  done clear
  B)
   \[\left( -\frac{5}{2},-\frac{17}{2} \right)\]
  done clear
  C)
   \[\left( \frac{3}{2},\frac{17}{2} \right)\]
  done clear
  D)
          \[(0,-4)\]
  done clear
  E)
   \[\left( \frac{3}{2},-\frac{17}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer138) If \[\overrightarrow{a}=2\hat{i}-3\hat{j}+p\hat{k}\]and\[\overrightarrow{a}\times \overrightarrow{b}=4\hat{i}+2\hat{j}-2\hat{k},\]then p is:
  A)
   0            
  done clear
  B)
                          \[-1\]
  done clear
  C)
   1                            
  done clear
  D)
          2
  done clear
  E)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer139) Let\[\overrightarrow{a}=\hat{i}-\hat{j},\overrightarrow{b}=\hat{j}-\hat{k},\overrightarrow{c}=\hat{k}-\hat{i}\]. If\[\overrightarrow{d}\]is a unit vector such that\[\overrightarrow{a}.\overrightarrow{d}=0=[\overrightarrow{b}\overrightarrow{c}\overrightarrow{d}],\]then d is (are):
  A)
   \[\pm \frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}}\]
  done clear
  B)
                          \[\pm \frac{\hat{i}+\hat{j}-2\hat{k}}{\sqrt{6}}\]
  done clear
  C)
   \[\pm \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\]               
  done clear
  D)
          \[\pm \hat{k}\]
  done clear
  E)
   \[\hat{i}+\hat{j}\]
  done clear
  View Answer play_arrow

• question_answer140) A tower subtends an angle\[\alpha \] at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b ft just above A is \[\beta \]. Then, the height of the tower is:
  A)
   \[b\text{ }tan\text{ }\alpha \text{ }cot\text{ }\beta \]
  done clear
  B)
          \[b\text{ }\cot \,\alpha \text{ tan}\,\beta \]
  done clear
  C)
   \[b\text{ cot}\,\alpha \text{ }cot\,\beta \]   
  done clear
  D)
          \[b\text{ }\tan \,\alpha \text{ tan}\,\beta \]
  done clear
  E)
   \[b\text{ ta}{{\text{n}}^{2}}\,\alpha \text{ }cot\,\beta \]
  done clear
  View Answer play_arrow

• question_answer141) If\[\alpha \]and\[\beta \]are the roots of the equation \[{{x}^{2}}-7x+1=0,\]then the value of\[\frac{1}{{{(\alpha -7)}^{2}}}+\frac{1}{{{(\beta -7)}^{2}}}\]is:
  A)
   45
  done clear
  B)
                                          47
  done clear
  C)
   49                         
  done clear
  D)
          50
  done clear
  E)
   51
  done clear
  View Answer play_arrow

• question_answer142) The equation of the sphere whose centre is \[(6,-1,\text{ }2)\]and which touches the plane \[2x-y+2z-2=0,\]is:
  A)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-12x+2y-4z-16=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-12x+2y-4z=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-12x+2y-4z+16=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-12x+2y-4z+6=0\]
  done clear
  E)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-12x+2y-4z-5=0\]
  done clear
  View Answer play_arrow

• question_answer143) Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then\[n(X\cap Y)\]is equal to:
  A)
   4                                            
  done clear
  B)
   6
  done clear
  C)
   8                            
  done clear
  D)
          10
  done clear
  E)
   12
  done clear
  View Answer play_arrow

• question_answer144) The value of\[lo{{g}_{2}}lo{{g}_{2}}lo{{g}_{4}}256+2lo{{g}_{\sqrt{2}}}2\]is:
  A)
   1                                            
  done clear
  B)
   2
  done clear
  C)
   3                            
  done clear
  D)
          4
  done clear
  E)
   5
  done clear
  View Answer play_arrow

• question_answer145) The radius of a sphere is measured as 5 cm with an error possibly as large as 0.02 cm. The error and percentage error in computing the surface area of the sphere are:
  A)
   \[0.87\pi \,and\,0.2%\]                
  done clear
  B)
   \[0.8\pi \,and\,0.8%\]
  done clear
  C)
   \[0.4\pi \,and\,0.4%\]
  done clear
  D)
          \[\pi \,and\,1%\]
  done clear
  E)
   \[0.6\pi \,and\,0.6%\]
  done clear
  View Answer play_arrow

• question_answer146) If\[\int{x}\,f(x)dx=\frac{f(x)}{2},\]then\[f(x)\]is equal to:
  A)
   \[{{e}^{x}}\]                                     
  done clear
  B)
   \[{{e}^{-x}}\]
  done clear
  C)
   \[\log x\]           
  done clear
  D)
          \[\frac{{{e}^{{{x}^{2}}}}}{2}\]
  done clear
  E)
   \[{{e}^{{{x}^{2}}}}\]
  done clear
  View Answer play_arrow

• question_answer147) The value of \[\left| \begin{matrix}    \cos (x-a) & \cos (x+a) & \cos x  \\    \sin (x+a) & \sin (x-a) & \sin x  \\    \cos a\tan x & \cos a\cot x & \cos ec2x  \\ \end{matrix} \right|\]is equal to:
  A)
   1                                            
  done clear
  B)
  \[sin\text{ }a\text{ }cos\text{ }a\]           
  done clear
  C)
          0                            
  done clear
  D)
         \[sin\text{ }x\text{ }cos\text{ }x\]
  done clear
  E)
   \[cosec\text{ }2x\]
  done clear
  View Answer play_arrow

• question_answer148) The eccentricity of the hyperbola in the standard form\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]passing through (3,0) and\[(3\sqrt{2},2)\]is:
  A)
   \[\frac{13}{3}\]                               
  done clear
  B)
   \[\sqrt{13}\]
  done clear
  C)
   \[\sqrt{3}\]                       
  done clear
  D)
          \[\frac{\sqrt{13}}{3}\]
  done clear
  E)
   \[\frac{5}{3}\]
  done clear
  View Answer play_arrow

• question_answer149) If a, b and c are in geometric progression and the roots of the equations\[a{{x}^{2}}+2bx+c=0\]are \[\alpha \] and \[\beta \] and those of\[e{{x}^{2}}+2\text{ }bx+a=0\]are \[\gamma \] and \[\delta ,\] then:
  A)
   \[\alpha \ne \beta \ne \gamma \ne \delta \]    
  done clear
  B)
   \[\alpha \ne \beta and\,\gamma \ne \delta \]
  done clear
  C)
   \[a\alpha =a\beta =c\gamma =c\delta \]            
  done clear
  D)
   \[\alpha =\beta \,and\,\gamma \ne \delta \]
  done clear
  E)
   \[\alpha \ne \beta \,and\,\gamma =\delta \]
  done clear
  View Answer play_arrow

• question_answer150) If in the triangle\[ABC,B=45{}^\circ ,\]then \[{{a}^{4}}+{{b}^{4}}+{{c}^{4}}\]is equal to:
  A)
  \[2\text{ }{{a}^{2}}({{b}^{2}}+{{c}^{2}})\]
  done clear
  B)
   \[2{{c}^{2}}({{a}^{2}}+{{b}^{2}})\]
  done clear
  C)
   \[2{{b}^{2}}({{a}^{2}}+{{c}^{2}})\]
  done clear
  D)
   \[2({{a}^{2}}{{b}^{2}}+{{b}^{2}}{{c}^{2}}+{{c}^{2}}{{a}^{2}})\]
  done clear
  E)
   \[2{{a}^{2}}{{b}^{2}}+2{{b}^{2}}{{c}^{2}}+3{{a}^{2}}{{c}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer151) Let\[f\]be twice differentiable function such that\[f(x)=-f(x)\]and\[f(x)=g(x),\]\[h(x)=\{f{{(x)}^{2}}\}+{{\{g(x)\}}^{2}}.\]then\[h(5)=11,\]is equal to:
  A)
   22                                         
  done clear
  B)
   11
  done clear
  C)
   0                            
  done clear
  D)
          20
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer152) Suppose A is a matrix of order 3 and\[B=|A|{{A}^{-1}}.\]If \[|A|=-5,\]then\[|B|\]is equal to:
  A)
   1                                            
  done clear
  B)
   \[-5\]
  done clear
  C)
   \[-1\]                   
  done clear
  D)
          \[25\]
  done clear
  E)
   \[-125\]
  done clear
  View Answer play_arrow

• question_answer153) A differentiable function\[f(x)\]is defined for all \[x>0\]and satisfies\[f({{x}^{3}})=4{{x}^{4}}\]for all\[x>0\]. The value of\[f(8)\]is:
  A)
   \[\frac{16}{3}\]                               
  done clear
  B)
   \[\frac{32}{3}\]
  done clear
  C)
   \[\frac{16\sqrt{2}}{3}\]
  done clear
  D)
          \[\frac{32\sqrt{2}}{3}\]
  done clear
  E)
   \[\frac{32{{(2)}^{1/3}}}{3}\]
  done clear
  View Answer play_arrow

• question_answer154) The equation of the hyperbola whose vertices are at (5, 0) and\[(-\text{ }5,0)\]and one of the  directrices is\[x=\frac{25}{7},\]is:
  A)
   \[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{24}=1\]                   
  done clear
  B)
   \[\frac{{{x}^{2}}}{24}-\frac{{{y}^{2}}}{25}=1\]
  done clear
  C)
   \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{25}=1\]   
  done clear
  D)
          \[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{16}=1\]
  done clear
  E)
   \[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{24}=-1\]
  done clear
  View Answer play_arrow

• question_answer155) If a and P are different complex numbers with \[|\beta |=1,\]then\[\left| \frac{\beta -\alpha }{1-\alpha \beta } \right|\]is:
  A)
   0                                            
  done clear
  B)
   \[\frac{3}{2}\]
  done clear
  C)
   \[\frac{1}{2}\]                  
  done clear
  D)
          1
  done clear
  E)
   2
  done clear
  View Answer play_arrow

• question_answer156) \[\int_{0}^{2}{[{{x}^{2}}]}dx\]is:
  A)
   \[2-\sqrt{2}\]                                   
  done clear
  B)
   \[2+\sqrt{2}\]
  done clear
  C)
   \[\sqrt{2}-1\]                   
  done clear
  D)
          \[-\sqrt{2}-\sqrt{3}+5\]
  done clear
  E)
   none of these
  done clear
  View Answer play_arrow

• question_answer157) The point (4, 1) undergoes the following three transformations successively: (i) reflection about the line\[y=x\] (ii) translation through a distance of 2 unit along the positive direction of\[x-\]axis (iii) rotation through an angle of\[\frac{\pi }{4}\]about the origin in the anticlockwise direction The final position of the point is:
  A)
   \[\left( \frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)\]                       
  done clear
  B)
   \[\left( -\frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)\]
  done clear
  C)
   \[(-\sqrt{2},7\sqrt{2})\]               
  done clear
  D)
          \[(\sqrt{2},7\sqrt{2})\]
  done clear
  E)
   \[(\sqrt{2},-7\sqrt{2})\]
  done clear
  View Answer play_arrow

• question_answer158) Suppose a circle passes through (2, 2) and (9, 9) and touches the\[x-\]axis at P. If O is the origin, then OP is equal to:
  A)
   4                                            
  done clear
  B)
   5
  done clear
  C)
   6                            
  done clear
  D)
          9
  done clear
  E)
   11
  done clear
  View Answer play_arrow

• question_answer159) If \[{{e}^{{{e}^{x}}}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+......,\]then:
  A)
   \[{{a}_{0}}=1\]                                
  done clear
  B)
  \[{{a}_{0}}=e\]
  done clear
  C)
   \[{{a}_{0}}={{e}^{e}}\]                 
  done clear
  D)
         \[{{a}_{0}}={{e}^{2}}\]
  done clear
  E)
   \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer160) The    period     of    the     function \[f(x)=|\sin x|+|\cos x|\]is:
  A)
   \[2\pi \]                                              
  done clear
  B)
   \[3\pi \]
  done clear
  C)
   \[\frac{3\pi }{2}\]                           
  done clear
  D)
          \[\pi \]
  done clear
  E)
   \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer161) The equation of the line passing through the origin and the point of intersection of the lines\[\frac{x}{a}+\frac{y}{b}=1\]and\[\frac{x}{b}+\frac{y}{a}=1\]is:
  A)
   \[bx-ay=0\]     
  done clear
  B)
         \[x+y=0\]
  done clear
  C)
   \[ax-by=0\]     
  done clear
  D)
         \[x-y=0\]
  done clear
  E)
   \[ax+by=0\]
  done clear
  View Answer play_arrow

• question_answer162) If\[\overrightarrow{a}\]and\[\overrightarrow{b}\]are unit vectors such that \[[\overrightarrow{a}\,\overrightarrow{b}\,\overrightarrow{a}\times \overrightarrow{b}]=\frac{1}{4},\]then angle between\[\overrightarrow{a}\]and\[\overrightarrow{b}\]is:
  A)
   \[\frac{\pi }{3}\]                             
  done clear
  B)
          \[\frac{\pi }{4}\]
  done clear
  C)
   \[\frac{\pi }{6}\]                             
  done clear
  D)
          \[\frac{\pi }{2}\]
  done clear
  E)
   \[\frac{\pi }{12}\]
  done clear
  View Answer play_arrow

• question_answer163) If the eccentricities of the ellipse \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{3}=1\] and the hyperbola\[\frac{{{x}^{2}}}{64}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]are reciprocals of each other, then\[{{b}^{2}}\]is equal to:
  A)
   192                       
  done clear
  B)
          64
  done clear
  C)
   16                         
  done clear
  D)
          32
  done clear
  E)
   128
  done clear
  View Answer play_arrow

• question_answer164) The order and degree of the differential equation\[\sqrt{\sin x}(dx+dy)=\sqrt{\cos x}(dx-dy)\]is:
  A)
   (1, 2)                    
  done clear
  B)
          (2, 2)
  done clear
  C)
   (1, 1)                    
  done clear
  D)
          (2, 1)
  done clear
  E)
   (0, 1)
  done clear
  View Answer play_arrow

• question_answer165) The domain of the real valued function\[f(x)=\sqrt{5-4x-{{x}^{2}}}+{{x}^{2}}\log (x+4)\]is:
  A)
  \[-5\le x\le 1\]      
  done clear
  B)
         \[-5\le x\] and\[x>1\]
  done clear
  C)
   \[-4<x\le 1\]     
  done clear
  D)
         \[\phi \]
  done clear
  E)
  \[0\le x\le 1\]
  done clear
  View Answer play_arrow

• question_answer166) If\[{{a}_{1}},{{a}_{2}},.....,{{a}_{50}}\]are in GP, then \[\frac{{{a}_{1}}-{{a}_{3}}+{{a}_{5}}-....+{{a}_{49}}}{{{a}_{2}}-{{a}_{4}}+{{a}_{6}}-....+{{a}_{50}}}\]is equal to:
  A)
   0                            
  done clear
  B)
          \[1\]
  done clear
  C)
   \[\frac{{{a}_{1}}}{{{a}_{2}}}\]                    
  done clear
  D)
          \[\frac{{{a}_{25}}}{{{a}_{24}}}\]
  done clear
  E)
   \[\frac{2{{a}_{1}}}{3{{a}_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer167) Suppose the number of elements in set A is p, the number of elements in set B is q and the number of elements in\[A\times B\]is 7. Then \[{{p}^{2}}+{{q}^{2}}\]is equal to:
  A)
   42                         
  done clear
  B)
          49
  done clear
  C)
   50                         
  done clear
  D)
          51
  done clear
  E)
   55
  done clear
  View Answer play_arrow

• question_answer168) The value of\[\cos [2{{\tan }^{-1}}(-7)]\]is:
  A)
   \[\frac{49}{50}\]                             
  done clear
  B)
          \[-\frac{49}{50}\]
  done clear
  C)
   \[\frac{24}{25}\]                             
  done clear
  D)
          \[-\frac{24}{25}\]
  done clear
  E)
   \[\frac{48}{49}\]
  done clear
  View Answer play_arrow

• question_answer169) \[\int\limits_{0}^{\pi }{|\cos x|}dx\]is equal to:
  A)
   \[\frac{1}{2}\]                  
  done clear
  B)
          \[-2\]
  done clear
  C)
   \[1\]                    
  done clear
  D)
          \[-1\]
  done clear
  E)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer170) \[\int{\left( \frac{\sin 2x}{\sin 3x\sin 5x} \right)}dx\]is equal to:
  A)
   \[\frac{1}{5}{{\log }_{e}}|\sin 5x|-\frac{1}{3}{{\log }_{e}}|\sin 3x|+c\]
  done clear
  B)
   \[\frac{1}{3}{{\log }_{e}}|\sin 3x|-\frac{1}{5}{{\log }_{e}}|\sin 5x|+c\]
  done clear
  C)
   \[\frac{1}{3}{{\log }_{e}}|\sin 3x|+\frac{1}{5}{{\log }_{e}}|\sin 5x|+c\]
  done clear
  D)
   \[-\frac{1}{2}\cos 2x+\frac{1}{3}{{\log }_{e}}|\sin 3x|\] \[+\frac{1}{5}{{\log }_{e}}|sin5x|+c\]
  done clear
  E)
   \[-\frac{1}{2}\cos 2x-\frac{1}{3}{{\log }_{e}}|\sin 3x|\]\[-\frac{1}{5}{{\log }_{e}}|\sin 5x|+c\]
  done clear
  View Answer play_arrow

• question_answer171) If\[\left| \begin{matrix}    2i & -3i & 1  \\    3 & 3i & -1  \\    4 & 3 & i  \\ \end{matrix} \right|=x+iy,\]then:
  A)
  \[x=3,\text{ }y=1\]     
  done clear
  B)
          \[x=2,\text{ }y=5\]
  done clear
  C)
  \[x=0,y=0\]     
  done clear
  D)
          \[x=1,\text{ }y=1\]
  done clear
  E)
  \[x=0,\text{ }y=5\]
  done clear
  View Answer play_arrow

• question_answer172) If \[y={{\log }_{a}}x,x>0,\]then,\[\frac{dy}{dx}\]is equal to:
  A)
   \[\frac{1}{x}\]                  
  done clear
  B)
          \[\frac{1}{ax}\]
  done clear
  C)
   \[\frac{1}{x}{{\log }_{x}}a\]       
  done clear
  D)
          \[\frac{1}{a}{{\log }_{e}}x\]
  done clear
  E)
   \[\frac{1}{x}{{\log }_{a}}e\]
  done clear
  View Answer play_arrow

• question_answer173) The value of\[\left| \begin{matrix}    ^{10}{{C}_{4}} & ^{10}{{C}_{5}} & ^{11}{{C}_{m}}  \\    ^{11}{{C}_{6}} & ^{11}{{C}_{7}} & ^{12}{{C}_{m+2}}  \\    ^{12}{{C}_{8}} & ^{12}{{C}_{9}} & ^{13}{{C}_{m+4}}  \\ \end{matrix} \right|=0\]when m is equal to:
  A)
   6                            
  done clear
  B)
          5
  done clear
  C)
   4                            
  done clear
  D)
          1
  done clear
  E)
   2     
  done clear
  View Answer play_arrow

• question_answer174)                              The minimum value of\[2\cos \theta +\frac{1}{\sin \theta }\] \[+\sqrt{2}\tan \theta \]the interval\[\left( 0,\frac{\pi }{2} \right)\]is:
  A)
   \[2+\sqrt{2}\]                  
  done clear
  B)
          \[3\sqrt{2}\]
  done clear
  C)
   \[2\sqrt{3}\]            
  done clear
  D)
          \[3+\sqrt{2}\]
  done clear
  E)
   7
  done clear
  View Answer play_arrow

• question_answer175) If\[\frac{1}{^{4}{{C}_{n}}}=\frac{1}{^{5}{{C}_{n}}}+\frac{1}{^{6}{{C}_{n}}},\]then n is equal to:
  A)
   3                            
  done clear
  B)
          2
  done clear
  C)
   1                            
  done clear
  D)
          0
  done clear
  E)
   4
  done clear
  View Answer play_arrow

• question_answer176) Let\[{{x}_{1}}\]and\[{{x}_{2}}\]be solutions of the equation\[{{\sin }^{-1}}\left( {{x}^{2}}-3x+\frac{5}{2} \right)=\frac{\pi }{6}\].Then, the value of \[x_{1}^{2}+x_{2}^{2}\]is:
  A)
   4                            
  done clear
  B)
          5
  done clear
  C)
   \[\frac{5}{2}\]                  
  done clear
  D)
          6
  done clear
  E)
   \[\frac{15}{2}\]
  done clear
  View Answer play_arrow

• question_answer177) If the points (- 1, 2, - 3), (4, a, 1) and (b, 8, 5) are collinear, then a and b are respectively equal to:
  A)
   5 and 5                
  done clear
  B)
          9 and 5
  done clear
  C)
   5 and 9                
  done clear
  D)
         \[-5\]and 9
  done clear
  E)
   5 and\[-9\]
  done clear
  View Answer play_arrow

• question_answer178) The locus of the point\[(l,m)\]so that\[lx+my=1\] touches the circle\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]is:
  A)
   \[{{x}^{2}}+{{y}^{2}}-ax=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}=\frac{1}{{{a}^{2}}}\]
  done clear
  C)
   \[{{y}^{2}}=4ax\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}-ax-ay+{{a}^{2}}=0\]
  done clear
  E)
   \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer179) If the derivative of the function\[f(x)\]is every where continuous and is given by \[f(x)=\left\{ \begin{matrix}    b{{x}^{2}}+ax+4; & x\ge -1  \\    a{{x}^{2}}+b; & x<-1  \\ \end{matrix}, \right.\]then:
  A)
  \[a=2,b=-3\]      
  done clear
  B)
   \[a=3,b=2\]
  done clear
  C)
   \[a=-2,b=-3\]
  done clear
  D)
          \[a=-3,b=-2\]
  done clear
  E)
   \[a=-1,b=-2\]
  done clear
  View Answer play_arrow

• question_answer180) Let\[a={{e}^{i\frac{2\pi }{3}}}\]. Then the equation whose roots are\[a+{{a}^{-2}}\]and\[{{a}^{2}}+{{a}^{-4}}\]is:
  A)
   \[{{x}^{2}}-2x+4=0\]     
  done clear
  B)
  \[{{x}^{2}}-x+1=0\]
  done clear
  C)
   \[{{x}^{2}}+x+4=0\] 
  done clear
  D)
         \[{{x}^{2}}+2x-4=0\]
  done clear
  E)
   \[{{x}^{2}}+2x+4=0\]
  done clear
  View Answer play_arrow

• question_answer181) Let\[n=2006!.\]Then \[\frac{1}{{{\log }_{2}}n}+\frac{1}{{{\log }_{3}}n}+...+\frac{1}{{{\log }_{2006}}n}\]is equal to:
  A)
   2006                                     
  done clear
  B)
   2005
  done clear
  C)
   2005!                   
  done clear
  D)
          1
  done clear
  E)
   0
  done clear
  View Answer play_arrow

• question_answer182) \[\int{{{e}^{x}}}\{log\text{ }sin\text{ }x+cot\text{ }x\}dx\] is equal to:
  A)
   \[{{\text{e}}^{x}}cot\text{ }x+c\]
  done clear
  B)
   \[{{e}^{x}}\,log\text{ }sin\text{ }x+c\]
  done clear
  C)
   \[{{e}^{x}}log\text{ }sin\text{ }x+tan\text{ }x+c\]
  done clear
  D)
   \[{{e}^{x}}+sin\text{ }x+c\]
  done clear
  E)
   \[log(sin\,x+cos\,x)+{{e}^{x}}+c\]
  done clear
  View Answer play_arrow

• question_answer183) \[\int\limits_{-10}^{10}{\log \left( \frac{a+x}{a-x} \right)}dx\]is equal to:
  A)
   0                            
  done clear
  B)
          \[-2\log (a+10)\]
  done clear
  C)
   \[2\log \left( \frac{a+10}{a-10} \right)\]
  done clear
  D)
          \[2\log (a+10)\]
  done clear
  E)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer184) If\[f(x+y)=f(x)f(y)\]for all real\[x\]and\[y,\] \[f(6)=3\]and\[f(0)=10,\]then\[f(6)\]is:
  A)
   30                         
  done clear
  B)
          13
  done clear
  C)
   10                         
  done clear
  D)
          0
  done clear
  E)
   6
  done clear
  View Answer play_arrow

• question_answer185) The value of the determinant, \[\left| \begin{matrix}    \sqrt{13}+\sqrt{3} & 2\sqrt{5} & \sqrt{5}  \\    15+\sqrt{26} & 5 & \sqrt{10}  \\    3+\sqrt{65} & \sqrt{15} & 5  \\ \end{matrix} \right|\]is:
  A)
   \[5(\sqrt{6}-5)\]             
  done clear
  B)
          \[5\sqrt{3}(\sqrt{6}-5)\]
  done clear
  C)
   \[\sqrt{5}(\sqrt{6}-\sqrt{3})\]
  done clear
  D)
          \[\sqrt{2}(\sqrt{7}-\sqrt{5})\]
  done clear
  E)
   \[3(\sqrt{5}-\sqrt{2})\]
  done clear
  View Answer play_arrow

• question_answer186) If\[{{\alpha }_{1}},{{\alpha }_{2}},{{\alpha }_{3}},{{\alpha }_{4}}\]are the roots of the equation\[{{x}^{4}}+(2-\sqrt{3}){{x}^{2}}+2+\sqrt{3}=0,\]then the value of\[(1-{{\alpha }_{1}})(1-{{\alpha }_{2}})(1-{{\alpha }_{3}})(1-{{\alpha }_{4}})\]is:
  A)
   1                            
  done clear
  B)
          4
  done clear
  C)
   \[2+\sqrt{3}\]                  
  done clear
  D)
          5
  done clear
  E)
   0
  done clear
  View Answer play_arrow

• question_answer187) The values of\[\lambda \] so that the line\[3x-4y=\lambda \] touches\[{{x}^{2}}+{{y}^{2}}-4x-8y-5=0\]are:
  A)
   \[-35,15\]          
  done clear
  B)
          \[3,-5\]
  done clear
  C)
   \[35,-15\]          
  done clear
  D)
          \[-3,5\]
  done clear
  E)
   20, 15
  done clear
  View Answer play_arrow

• question_answer188) Suppose\[0<t<\frac{\pi }{2}\]and\[\sin t+\cos t=\frac{1}{5}\] then \[\tan \frac{t}{2}\] is equal to:
  A)
   2                            
  done clear
  B)
          3
  done clear
  C)
   \[\frac{1}{3}\]                  
  done clear
  D)
          5
  done clear
  E)
   \[\frac{1}{5}\]
  done clear
  View Answer play_arrow

• question_answer189) The point of intersection of the line\[\overrightarrow{r}=7\hat{i}+10\hat{j}+13\hat{k}+s(2\hat{i}+3\hat{j}+4\hat{k})\]and\[\overrightarrow{r}=3\hat{i}+5\hat{j}+7\hat{k}+t(\hat{i}+2\hat{j}+3\hat{k})\]is:
  A)
   \[\hat{i}+\hat{j}-\hat{k}\]          
  done clear
  B)
          \[2\hat{i}-\hat{j}+4\hat{k}\]
  done clear
  C)
   \[\hat{i}-\hat{j}+\hat{k}\]          
  done clear
  D)
          \[\hat{i}-\hat{j}-\hat{k}\]
  done clear
  E)
   \[\hat{i}+\hat{j}+\hat{k}\]
  done clear
  View Answer play_arrow

• question_answer190) The value of \[cos\text{ }480{}^\circ -sin\text{ }150{}^\circ +sin\text{ }600{}^\circ .cos\text{ }390{}^\circ \]is equal to:
  A)
   0  
  done clear
  B)
                                          1
  done clear
  C)
   \[\frac{1}{2}\]                  
  done clear
  D)
         \[-1\]
  done clear
  E)
   \[-\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer191) Define\[f(x)=\int\limits_{0}^{x}{\sin t}\,dt,\,x\ge 0\]Then:
  A)
  \[f\]is increasing only in the interval \[\left[ 0,\frac{\pi }{2} \right]\]
  done clear
  B)
  \[f\]is decreasing in the interval \[[0,\pi ]\]
  done clear
  C)
  \[f\]attains maximum at \[x=\frac{\pi }{2}\]
  done clear
  D)
  \[f\]attains minimum at\[x=\pi \]
  done clear
  E)
  \[f\]attains maximum at\[x=\pi \]
  done clear
  View Answer play_arrow

• question_answer192) Let \[f(x)=\frac{{{\sin }^{2}}\pi x}{1+{{\pi }^{x}}}\] Then, \[\int{(f(x)+f(-x))}dx\]is equal to:
  A)
   \[0\]                                    
  done clear
  B)
   \[x+c\]
  done clear
  C)
   \[\frac{x}{2}-\frac{\cos \pi x}{2\pi }+c\]
  done clear
  D)
          \[\frac{1}{1+{{\pi }^{x}}}\frac{{{\cos }^{2}}\pi x}{2\pi }+c\]
  done clear
  E)
   \[\frac{x}{2}-\frac{\sin 2\pi x}{4\pi }+c\]
  done clear
  View Answer play_arrow

• question_answer193) For the arithmetic progression \[a,(a+d),(a+2d),(a+3d),....,(a+2nd),\] the mean deviation from mean is:
  A)
   \[\frac{n(n+1)d}{2n-1}\]                             
  done clear
  B)
   \[\frac{n(n+1)d}{2n+1}\]
  done clear
  C)
   \[\frac{n(n-1)d}{2n+1}\]             
  done clear
  D)
          \[\frac{(n+1)d}{2}\]
  done clear
  E)
   \[\frac{n(n-1)d}{2n-1}\]
  done clear
  View Answer play_arrow

• question_answer194) If the angles of a triangle are in the ratio\[3:4:5,\]then the ratio of the largest side to the smallest side of the triangle is:
  A)
   \[\frac{\sqrt{3}}{2}\]                                    
  done clear
  B)
   \[\frac{\sqrt{3}+1}{2\sqrt{2}}\]
  done clear
  C)
   \[\frac{\sqrt{3}+1}{2}\]
  done clear
  D)
          \[\frac{\sqrt{3}+1}{\sqrt{2}}\]
  done clear
  E)
   \[\frac{\sqrt{3}}{2\sqrt{2}}\]
  done clear
  View Answer play_arrow

• question_answer195) If\[\frac{\sin (x+y)}{\sin (x-y)}=\frac{a+b}{a-b},\]then\[\frac{\tan x}{\tan y}\]is equal to:
  A)
   \[\frac{{{a}^{2}}}{{{b}^{2}}}\]                                   
  done clear
  B)
   \[\frac{a}{b}\]
  done clear
  C)
   \[\frac{b}{a}\]                 
  done clear
  D)
          \[\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}}\]
  done clear
  E)
   \[\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer196) Let R be a relation on the set of integers given by\[aRb\Leftrightarrow a={{2}^{k}}.b\]for some integer k. Then R is:
  A)
   an equivalence relation
  done clear
  B)
   reflexive but not symmetric
  done clear
  C)
   reflexive and transitive but not symmetric
  done clear
  D)
   reflexive and symmetric but not transitive
  done clear
  E)
   symmetric and transitive but not reflexive
  done clear
  View Answer play_arrow

• question_answer197) . The position of reflection of the point (4, 1) about the line\[y=x-1\]is:
  A)
   (1, 2)                                    
  done clear
  B)
   (3, 4)
  done clear
  C)
   \[(-\text{ }1,0)\]          
  done clear
  D)
         \[(-2,-1)\]
  done clear
  E)
   (2, 3)
  done clear
  View Answer play_arrow

• question_answer198) Derivative of\[{{\sec }^{-1}}\left( \frac{1}{1-2{{x}^{2}}} \right)\]w.r.t. \[{{\sin }^{-1}}(3x-4{{x}^{3}})\]is:
  A)
   \[\frac{1}{4}\]                  
  done clear
  B)
          \[\frac{3}{2}\]
  done clear
  C)
   1                            
  done clear
  D)
          \[\frac{2}{3}\]
  done clear
  E)
   \[-\frac{2}{3}\]
  done clear
  View Answer play_arrow

• question_answer199) Let ABCD be a parallelogram and let E be the midpoint of side AB. If EC is perpendicular to ED, then:
  A)
   \[ED=EC\]       
  done clear
  B)
          \[EB=EC\]
  done clear
  C)
   \[EA=ED\]       
  done clear
  D)
         \[EC+ED=2BC\]
  done clear
  E)
   \[EC+ED=2DC\]
  done clear
  View Answer play_arrow

• question_answer200) The radius of a circle is increasing at the rate of 0.1 cm/s. When the radius of the circle is 5 cm, the rate of change of its area, is:
  A)
   \[-\pi \,c{{m}^{2}}/s\]  
  done clear
  B)
          \[10\pi \,c{{m}^{2}}/s\]
  done clear
  C)
   \[0.1\pi \,c{{m}^{2}}/s\]              
  done clear
  D)
          \[5\pi \,c{{m}^{2}}/s\]
  done clear
  E)
   \[\pi \,c{{m}^{2}}/s\]
  done clear
  View Answer play_arrow

• question_answer201) Let\[D=\{1,2,3,5,6,10,15,30\}\]. Define the operations +, .and on D as follows \[a+b=LCM(a,b),\]\[a.b=GCD(a,b)\]and \[a=\frac{30}{a}.\]Then\[(15+6).10\]is equal to:
  A)
   1                            
  done clear
  B)
          2
  done clear
  C)
   3                            
  done clear
  D)
          5
  done clear
  E)
   10
  done clear
  View Answer play_arrow

• question_answer202) If\[A+B=\frac{\pi }{4},\]then\[(tan\text{ }A+1)\text{ }(tan\text{ }B+1)\]equals:
  A)
   1                            
  done clear
  B)
          \[\sqrt{3}\]
  done clear
  C)
   2                            
  done clear
  D)
          \[\frac{1}{\sqrt{3}}\]
  done clear
  E)
  \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer203) \[{{\log }_{e}}3-\frac{{{\log }_{e}}9}{{{2}^{2}}}+\frac{{{\log }_{e}}27}{{{3}^{2}}}-\frac{{{\log }_{e}}81}{{{4}^{2}}}+...\]is:
  A)
   \[({{\log }_{e}}3)({{\log }_{e}}2)\]
  done clear
  B)
          \[{{\log }_{e}}3\]
  done clear
  C)
   \[{{\log }_{e}}2\]            
  done clear
  D)
          \[\frac{{{\log }_{e}}5}{{{\log }_{e}}3}\]
  done clear
  E)
   \[\frac{{{\log }_{e}}3}{{{\log }_{e}}2}\]
  done clear
  View Answer play_arrow

• question_answer204) The roots of the equation \[(q-r){{x}^{2}}+(r-p)x+(p-q)=0\]are:
  A)
   \[\frac{r-p}{q-r},1\]       
  done clear
  B)
          \[\frac{p-q}{q-r},1\]
  done clear
  C)
   \[\frac{p-r}{q-r},2\]       
  done clear
  D)
   \[\frac{q-r}{p-q},2\]
  done clear
  E)
   \[\frac{r-p}{p-q},1\]
  done clear
  View Answer play_arrow

• question_answer205) The interior angles of a polygon are in AP. The smallest angle is\[120{}^\circ \]and the common difference is\[5{}^\circ \]. The number of sides of the polygon is:
  A)
   9                            
  done clear
  B)
          10
  done clear
  C)
   16                         
  done clear
  D)
          5
  done clear
  E)
   8
  done clear
  View Answer play_arrow

• question_answer206) The   direction   cosines   of   the   line\[4x-4=1-3y=2z-1\]are:
  A)
   \[\frac{3}{\sqrt{56}},\frac{-4}{\sqrt{56}},\frac{6}{\sqrt{56}}\]
  done clear
  B)
   \[\frac{3}{\sqrt{29}},\frac{-4}{\sqrt{29}},\frac{6}{\sqrt{29}}\]
  done clear
  C)
   \[\frac{3}{\sqrt{61}},\frac{-4}{\sqrt{61}},\frac{6}{\sqrt{61}}\]
  done clear
  D)
   \[4,-3,2\]
  done clear
  E)
   \[\frac{4}{\sqrt{29}},\frac{-3}{\sqrt{29}},\frac{2}{\sqrt{29}}\]
  done clear
  View Answer play_arrow

• question_answer207) The digit at the unit place in the number\[{{19}^{2005}}+{{11}^{2005}}-{{9}^{2005}}\]is:
  A)
   2                            
  done clear
  B)
          1
  done clear
  C)
   0                            
  done clear
  D)
          8
  done clear
  E)
   9                 
  done clear
  View Answer play_arrow

• question_answer208)   If\[x{{e}^{xy}}=y+si{{n}^{2}}x,\]then\[\frac{dy}{dx}\]at\[x=0\]is:
  A)
   \[-1\]                   
  done clear
  B)
          0
  done clear
  C)
   1                            
  done clear
  D)
          2
  done clear
  E)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer209) The number of triangles which can be formed by using the vertices of a regular polygon of \[(n+3)\]sides is 220. Then n is equal to:
  A)
   8                                            
  done clear
  B)
   9
  done clear
  C)
   10                         
  done clear
  D)
          11
  done clear
  E)
   12
  done clear
  View Answer play_arrow

• question_answer210) lf\[[x]\]denotes the greatest integer\[\le x,\]then\[\left[ \frac{2}{3} \right]+\left[ \frac{2}{3}+\frac{1}{99} \right]+\left[ \frac{2}{3}+\frac{2}{99} \right]+....+\left[ \frac{2}{3}+\frac{98}{99} \right]\]is equal to:
  A)
   99                                         
  done clear
  B)
   98
  done clear
  C)
   66                         
  done clear
  D)
          65
  done clear
  E)
   33
  done clear
  View Answer play_arrow

• question_answer211) The centre of the sphere passing through the origin and through the intersection points of the plane\[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\]with axes is:
  A)
   \[\left( \frac{a}{2},0,0 \right)\]                 
  done clear
  B)
   \[\left( 0,\frac{a}{2},0 \right)\]
  done clear
  C)
   \[\left( 0,0,\frac{a}{2} \right)\] 
  done clear
  D)
          \[\left( \frac{a}{2},\,\frac{b}{2},\,0 \right)\]
  done clear
  E)
   \[\left( \frac{a}{2},\frac{a}{2},\frac{c}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer212) In an arithmetic progression, the 24 th term is 100. Then the sum of the first 47 terms of the arithmetic progression is:
  A)
   2300                     
  done clear
  B)
          2350
  done clear
  C)
   2400                     
  done clear
  D)
          4600
  done clear
  E)
   4700
  done clear
  View Answer play_arrow

• question_answer213) If the vertex of the parabola\[y={{x}^{2}}-16x+k\]lies on\[x-\]axis, then the value of k is:
  A)
   16                                         
  done clear
  B)
   8
  done clear
  C)
   64                         
  done clear
  D)
         \[-64\]
  done clear
  E)
   \[-8\]
  done clear
  View Answer play_arrow

• question_answer214) Let co be an imaginary root of\[{{x}^{n}}=1\]. Then \[(5-\omega ){{(5-\omega )}^{2}}....(5-{{\omega }^{n-1}})\]is:
  A)
   1                            
  done clear
  B)
          \[\frac{{{5}^{n}}+1}{4}\]
  done clear
  C)
   \[{{4}^{n-1}}\]                 
  done clear
  D)
          \[\frac{{{5}^{n}}-1}{4}\]
  done clear
  E)
   \[{{5}^{n-1}}\]
  done clear
  View Answer play_arrow

• question_answer215) An integrating factor of the differential equation, \[(1+y+{{x}^{2}}y)dx+(x+{{x}^{3}})dy=0\]is:
  A)
   \[\log x\]           
  done clear
  B)
          \[x\]
  done clear
  C)
   \[{{e}^{x}}\]                     
  done clear
  D)
          \[\frac{1}{x}\]
  done clear
  E)
   \[\frac{-1}{x}\]
  done clear
  View Answer play_arrow

• question_answer216) The line\[2x-y=1\]bisects angle between two lines. If equation of one line is\[y=x,\]then the equation of the other line is:
  A)
   \[7x-y-6=0\]     
  done clear
  B)
  \[x-2y+1=0\]
  done clear
  C)
   \[3x-2y-1=0\]
  done clear
  D)
         \[x-7y+6=0\]
  done clear
  E)
          \[2x-3y+1=0\]
  done clear
  View Answer play_arrow

• question_answer217) If\[f(x)=\tan x-{{\tan }^{3}}x+{{\tan }^{5}}x-.....\]to\[\infty \]with \[0<x<\frac{\pi }{4},\] then\[\int_{0}^{\frac{\pi }{4}}{f(x)}dx\]is equal to:
  A)
   1            
  done clear
  B)
                          0
  done clear
  C)
   \[\frac{1}{4}\]                  
  done clear
  D)
          \[\frac{1}{2}\]
  done clear
  E)
   \[-\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer218) The standard deviation of n observations \[{{x}_{1}},{{x}_{2}},.....,{{x}_{n}}\]is 2. If\[\sum\limits_{i=1}^{n}{{{x}_{i}}}=20\]and\[\sum\limits_{i=1}^{n}{x_{i}^{2}}=100,\]then n is:
  A)
   10 or 20              
  done clear
  B)
          5 or 10
  done clear
  C)
   5 or 20                 
  done clear
  D)
          5 or 15
  done clear
  E)
   25
  done clear
  View Answer play_arrow

• question_answer219) Area (in sq unit) enclosed by \[y=1,\,2x+y=2\] and\[x+y=2\]is:
  A)
   \[\frac{1}{2}sq\,unit\]  
  done clear
  B)
          \[\frac{1}{4}sq\,unit\]
  done clear
  C)
   \[1sq\,unit\]    
  done clear
  D)
          \[2\,sq\,unit\]
  done clear
  E)
   4 sq unit
  done clear
  View Answer play_arrow

• question_answer220) The ratio in which the line\[x+y=4\]divides the line joining the points\[(1,-1)\]and (5, 7) is:
  A)
   \[1:2\]                 
  done clear
  B)
          \[2:1\]
  done clear
  C)
   \[1:3\]                 
  done clear
  D)
          \[3:1\]
  done clear
  E)
   \[3:2\]
  done clear
  View Answer play_arrow

• question_answer221) The set of all\[x\]satisfying the inequality\[\frac{4x-1}{3x+1}\ge 1\]is:
  A)
   \[\left( -\infty ,-\frac{1}{3} \right)\cup \left[ \frac{1}{4},\infty  \right)\]
  done clear
  B)
   \[\left( -\infty ,-\frac{2}{3} \right)\cup \left[ \frac{1}{5},\infty  \right)\]
  done clear
  C)
   \[\left( -\infty ,-\frac{1}{3} \right)\cup \left[ 2,\infty  \right)\]
  done clear
  D)
   \[\left( -\infty ,-\frac{2}{3} \right)\cup \left[ 4,\infty  \right)\]
  done clear
  E)
   \[\left( -\infty ,-\frac{1}{3} \right)\cup \left[ \frac{1}{2},\infty  \right)\]
  done clear
  View Answer play_arrow

• question_answer222) \[\left| \begin{matrix}    a+x & b & c  \\    a & b+y & c  \\    a & b & c+z  \\ \end{matrix} \right|\]is equal to:
  A)
   \[abc\left( 1+\frac{x}{a}+\frac{y}{b}+\frac{z}{c} \right)\]
  done clear
  B)
   \[abc\left( 1+\frac{a}{x}+\frac{b}{y}+\frac{c}{z} \right)\]
  done clear
  C)
   \[xyz\left( 1+\frac{a}{x}+\frac{b}{y}+\frac{c}{z} \right)\]
  done clear
  D)
   \[xyz\left( 1+\frac{x}{a}+\frac{y}{b}+\frac{z}{c} \right)\]
  done clear
  E)
   \[xyz(a+b+c+1)\]
  done clear
  View Answer play_arrow

• question_answer223) If\[^{18}{{C}_{15}}+c{{(}^{18}}{{C}_{16}}){{+}^{17}}{{C}_{16}}+1{{=}^{n}}{{C}_{3}},\]then n is equal to:
  A)
   19                         
  done clear
  B)
          20
  done clear
  C)
   18                         
  done clear
  D)
          24
  done clear
  E)
   21                       
  done clear
  View Answer play_arrow

• question_answer224) \[\underset{n\to \infty }{\mathop{\lim }}\,\left( \frac{{{1}^{2}}}{1-{{n}^{3}}}+\frac{{{2}^{2}}}{1-{{n}^{3}}}+....+\frac{{{n}^{2}}}{1-{{n}^{3}}} \right)\]is equal to:
  A)
   \[\frac{1}{3}\]                  
  done clear
  B)
          \[-\frac{1}{3}\]
  done clear
  C)
   \[\frac{1}{6}\]                  
  done clear
  D)
          \[-\frac{1}{6}\]
  done clear
  E)
   0
  done clear
  View Answer play_arrow

• question_answer225) If \[\overrightarrow{A}=\hat{i}+2\hat{j}+3\hat{k},\overrightarrow{B}=-\hat{i}+2\hat{j}+\hat{k}\]and \[\overrightarrow{C}=3\hat{i}+\hat{j},\]then\[\overrightarrow{A}+t\overrightarrow{B}\] is perpendicular to \[\overrightarrow{C},\] if t is equal to:
  A)
   \[-5\]                   
  done clear
  B)
          4
  done clear
  C)
   5                            
  done clear
  D)
          \[-4\]
  done clear
  E)
   \[-7\]
  done clear
  View Answer play_arrow

• question_answer226) The number of ways in which one can select three distinct integers between 1 and 30, both inclusive, whose sum is even, is:
  A)
   455                       
  done clear
  B)
          1575
  done clear
  C)
   1120                     
  done clear
  D)
          2030
  done clear
  E)
   1930
  done clear
  View Answer play_arrow

• question_answer227) The set of values of\[x\]satisfying\[2\le \,|x-3|<4\] is:
  A)
   \[(-1,1]\cup [5,7)\]
  done clear
  B)
   \[-4\le x\le 2\]
  done clear
  C)
   \[-1<x<7or\,x\ge 5\]
  done clear
  D)
   \[x<7or\,x\ge 5\]
  done clear
  E)
   \[-\infty \,<x\le 1\,or\,\,5\le x<8\]
  done clear
  View Answer play_arrow

• question_answer228) If\[i=\sqrt{-1},\]then \[4+5{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{334}}+3{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{365}}\]is equal to:
  A)
   \[1-i\sqrt{3}\]  
  done clear
  B)
          \[-1+i\sqrt{3}\]
  done clear
  C)
   \[i\sqrt{3}\]                      
  done clear
  D)
          \[-i\sqrt{3}\]
  done clear
  E)
   \[1+i\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer229) The angle between the lines\[\sqrt{3}x-y-2=0\] and\[x-\sqrt{3}y+1=0\]is:
  A)
   \[90{}^\circ \]
  done clear
  B)
                                          \[{{60}^{\text{o}}}\]
  done clear
  C)
   \[45{}^\circ \]                  
  done clear
  D)
          \[15{}^\circ \]
  done clear
  E)
   \[30{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer230)                 Let\[f(x)=x-[x],\]for every real\[x,\]where\[[x]\]is the greatest integer less than or equal to\[x\]. Then,\[\int\limits_{-1}^{1}{f(x)}dx\]is:
  A)
   1                            
  done clear
  B)
          2
  done clear
  C)
   3                            
  done clear
  D)
          0
  done clear
  E)
   \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer231) If\[\int\limits_{0}^{{{x}^{2}}}{f(t)}dt=x\cos \pi x,\]then the value of\[f(4)\]is:
  A)
   \[1\]                    
  done clear
  B)
          \[\frac{1}{4}\]
  done clear
  C)
   \[-1\]                   
  done clear
  D)
          \[\frac{-1}{4}\]
  done clear
  E)
   \[-4\]
  done clear
  View Answer play_arrow

• question_answer232) If\[y=\left( 1+\frac{1}{x} \right)\left( 1+\frac{2}{x} \right)\left( 1+\frac{3}{x} \right)......\left( 1+\frac{n}{x} \right)\] and\[x\ne 0\]then\[\frac{dy}{dx}\]when\[x=-1\]is:
  A)
   \[n!\]                  
  done clear
  B)
          \[(n-1)!\]
  done clear
  C)
   \[{{(-1)}^{n}}(n-1)!\]    
  done clear
  D)
          \[{{(-1)}^{n}}n!\]
  done clear
  E)
   \[(n+1)!\]
  done clear
  View Answer play_arrow

• question_answer233) If in a triangle ABC,\[a=15,\text{ }b=36,\text{ }c=39,\]then sin c is equal to:
  A)
   \[\frac{\sqrt{3}}{2}\]                    
  done clear
  B)
          \[\frac{1}{2}\]
  done clear
  C)
   \[\frac{1}{\sqrt{2}}\]                    
  done clear
  D)
          \[-\frac{1}{\sqrt{2}}\]
  done clear
  E)
   \[-\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer234) Let A = {1, 2, 3, 4}, B = {2, 4, 6}. Then the number of sets C such that\[A\cap B\subseteq C\subseteq A\cup B\]is:
  A)
   \[6\]                    
  done clear
  B)
          \[9\]
  done clear
  C)
   \[8\]                    
  done clear
  D)
          \[10\]
  done clear
  E)
   \[12\]
  done clear
  View Answer play_arrow

• question_answer235) A force of magnitude \[\sqrt{6}\] acting along line joining the points\[A(2,-1,1)\]and B (3, 1, 2) displaces a particle from A to B. The work done by ±e force is:
  A)
   6                            
  done clear
  B)
          \[6\sqrt{6}\]
  done clear
  C)
  \[\sqrt{6}\]                        
  done clear
  D)
          12
  done clear
  E)
   \[2\sqrt{6}\]
  done clear
  View Answer play_arrow

• question_answer236) If z is a complex number such that \[\operatorname{Re}(z)=\operatorname{Im}(z),\]then:
  A)
  \[\operatorname{Re}({{z}^{2}})=0\]      
  done clear
  B)
         \[\operatorname{Im}({{z}^{2}})=0\]
  done clear
  C)
   \[\operatorname{Re}({{z}^{2}})=\operatorname{Im}({{z}^{2}})\]
  done clear
  D)
          \[\operatorname{Re}({{x}^{2}})=-\operatorname{Im}({{z}^{2}})\]
  done clear
  E)
  \[{{z}^{2}}=0\]
  done clear
  View Answer play_arrow

• question_answer237) Equation of the plane parallel to the planes \[c+2y+3z-5=0,\text{ }x+2y+3z-7=0\]and equidistant from them is:
  A)
   \[x+2y+3z-6=0\]
  done clear
  B)
   \[x+2y+3z-1=0\]
  done clear
  C)
  \[x+2y+3z-8=0\]
  done clear
  D)
   \[x+2y+\text{ }3z-3=0\]
  done clear
  E)
   \[x+2y+3z-10=0\]
  done clear
  View Answer play_arrow

• question_answer238) The number of binary operations that can be defined on the set\[A=\{a,\text{ }b,\text{ }c\}\] is:
  A)
   \[{{3}^{3}}\]                     
  done clear
  B)
          \[{{3}^{4}}\]
  done clear
  C)
   \[{{3}^{9}}\]                     
  done clear
  D)
          \[{{9}^{3}}\]
  done clear
  E)
   3
  done clear
  View Answer play_arrow

• question_answer239) If\[{{(2{{x}^{2}}-x-1)}^{5}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...\] \[+{{a}_{10}}{{x}^{10}},\] then\[{{a}_{2}}+{{a}_{4}}+{{a}_{6}}+{{a}_{8}}+{{a}_{10}}\]is equal to:
  A)
   15                         
  done clear
  B)
          30
  done clear
  C)
   16                         
  done clear
  D)
          32
  done clear
  E)
   17
  done clear
  View Answer play_arrow

• question_answer240) If the plane\[2x-y+z=0\]is parallel to the line \[\frac{2x-1}{2}=\frac{2-y}{2}=\frac{z+1}{a},\]then the value of a is:
  A)
   4                            
  done clear
  B)
          \[-4\]
  done clear
  C)
   2                            
  done clear
  D)
          \[-2\]
  done clear
  E)
   0
  done clear
  View Answer play_arrow