Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2007

done Rajasthan PET Solved Paper-2007 Total Questions - 150

• question_answer1) A Carnot's engine has an efficiency of 50% at sink temperature\[50{}^\circ C\]. Calculate the temperature of source.
  A)
  \[133{}^\circ C\]           
  done clear
  B)
  \[143{}^\circ C\]
  done clear
  C)
  \[100{}^\circ C\]           
  done clear
  D)
  \[373{}^\circ C\]
  done clear
  View Answer play_arrow

• question_answer2) Which of the following is not a state function?
  A)
   Work done at constant pressure
  done clear
  B)
   Enthalpy
  done clear
  C)
   Work done by conservative force
  done clear
  D)
   Work done by non-conservative force
  done clear
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• question_answer3) What is the Q-value of the reaction? \[P{{+}^{7}}Li{{\xrightarrow[{}]{{}}}^{4}}He{{+}^{4}}He\] The atomic masses of \[^{1}H,\,{{\,}^{4}}He\,\,and\,{{\,}^{7}}Li\]are 1.0078254U, 4.0026034U and 7.016004U respectively
  A)
   17.35 MeV      
  done clear
  B)
   18.06 MeV
  done clear
  C)
   177.35 MeV     
  done clear
  D)
   170.35 MeV
  done clear
  View Answer play_arrow

• question_answer4) If average velocity becomes 4 times then, what will be the effect on rms velocity at that temperature?
  A)
   1.4 times        
  done clear
  B)
   4 times
  done clear
  C)
   2 times          
  done clear
  D)
   \[\frac{1}{4}\]times
  done clear
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• question_answer5) An aluminium rod and a copper rod are taken such that their lengths are same and their resistances are also same. The specific resistance of copper is half that of aluminium, but its density is three times that of aluminium. The ratio of the mass of aluminium rod and that of copper rod will be
  A)
   1/6              
  done clear
  B)
   2/3
  done clear
  C)
   1/3              
  done clear
  D)
   6
  done clear
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• question_answer6) In a potentiometer, the null point is received at 7th wire. If now we have to change the null point at 9th wire, what should we do?
  A)
   Attach resistance in series with battery
  done clear
  B)
   Increase resistance in main circuit
  done clear
  C)
   Decrease resistance in main circuit
  done clear
  D)
   Decrease applied emf
  done clear
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• question_answer7) The earth moves in an elliptical orbit with the sun S at one of foci as shown in the figure. Its rotational kinetic energy is maximum at the point.                 
  A)
   A
  done clear
  B)
   B         
  done clear
  C)
   C          
  done clear
  D)
   D                                 
  done clear
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• question_answer8) If BH = \[\frac{1}{\sqrt{3}}{{B}_{V}},\]find the angle of dip. (where symbols have at their usual meanings)
  A)
   \[60{}^\circ \]             
  done clear
  B)
   \[30{}^\circ \]
  done clear
  C)
   \[45{}^\circ \]             
  done clear
  D)
   \[90{}^\circ \]
  done clear
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• question_answer9) Reverberation time does not depend upon
  A)
   temperature     
  done clear
  B)
   volume of room
  done clear
  C)
   size of window   
  done clear
  D)
   carpet and curtain
  done clear
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• question_answer10) The water of volume\[4\text{ }{{m}^{3}}\]at the height 20 m is pressed by\[2\times {{10}^{5}}N\]pressure. The work done by motor is
  A)
   \[8\times {{10}^{5}}J\]         
  done clear
  B)
   \[16\times {{10}^{5}}J\]
  done clear
  C)
   \[12\times {{10}^{5}}J\]        
  done clear
  D)
   \[32\times {{10}^{5}}J\]
  done clear
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• question_answer11) The wavelength of K \[\alpha \] line in copper is 1.5\[\overset{o}{\mathop{\text{A}}}\,\]. The ionization energy of K electron in copper is
  A)
   \[11.2\times {{10}^{-17}}J\]  
  done clear
  B)
   \[12.9\times {{10}^{-16}}J\]
  done clear
  C)
   \[1.7\times {{10}^{-15}}J\]     
  done clear
  D)
   \[10\times {{10}^{-16}}J\]
  done clear
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• question_answer12) If mass [M], length [L], time [T] and current [A] as fundamental units, the dimensional formula for permeability will be
  A)
   \[[{{M}^{-1}}L{{T}^{-2}}A]\]    
  done clear
  B)
   \[[M{{L}^{-2}}{{T}^{-2}}{{A}^{-1}}]\]
  done clear
  C)
   \[[ML{{T}^{-2}}{{A}^{-2}}]\]    
  done clear
  D)
   \[[ML{{T}^{-1}}{{A}^{-1}}]\]
  done clear
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• question_answer13) If in the following figure, height of object is\[{{H}_{1}}=+\]2.5 cm, then height of image\[{{H}_{2}}\]formed is
  A)
   \[-5\text{ }cm\]            
  done clear
  B)
   +5 cm            
  done clear
  C)
   +7.5cm          
  done clear
  D)
   \[-7.5\text{ }cm\]  
  done clear
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• question_answer14) Moment of inertia of ring about its diameter is\[I\]. Then. moment of inertia about an axis passing through centre and perpendicular to its plane is
  A)
   \[2I\]             
  done clear
  B)
   \[\frac{I}{2}\]
  done clear
  C)
   \[\frac{3}{2}I\]            
  done clear
  D)
   \[I\]
  done clear
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• question_answer15) Which of the following is true regarding beats?
  A)
   Frequency different, amplitude same
  done clear
  B)
   Frequency same, amplitude same
  done clear
  C)
   Frequency same, amplitude different
  done clear
  D)
   None of the above
  done clear
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• question_answer16) When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer?
  A)
   More frequency, less wavelength
  done clear
  B)
   More frequency, more wavelength
  done clear
  C)
   Less frequency, less wavelength
  done clear
  D)
   More frequency, constant wavelength
  done clear
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• question_answer17) In which of the following, force is constant?
  A)
   Uniform circular motion
  done clear
  B)
   Elliptical motion
  done clear
  C)
   Uniform linear motion
  done clear
  D)
   Projectile motion
  done clear
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• question_answer18) The coefficient of friction between the tyres and the road is 0.25. The maximum speed with which car can be driven round a curve of radius 40 m without skidding is (assume \[g=10m/{{s}^{2}}\])
  A)
   40 m/s           
  done clear
  B)
   20 m/s
  done clear
  C)
   15 m/s           
  done clear
  D)
   10 m/s
  done clear
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• question_answer19) A bomb of mass 3 kg explodes in air and splits in two parts of 2 kg and 1 kg. Small peace moves with a speed of 80 m/s, then the total energy of both the pieces will be
  A)
   1.07 kJ          
  done clear
  B)
   2.14 kJ
  done clear
  C)
   2.4 kJ            
  done clear
  D)
   4.8 kJ
  done clear
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• question_answer20) If\[{{k}_{s}}\]and\[{{k}_{p}}\]respectively are effective spring constant in series and parallel combination of springs as shown in figure, find \[\frac{{{k}_{s}}}{{{k}_{p}}}\]  
  A)
   \[\frac{9}{2}\]                 
  done clear
  B)
   \[\frac{3}{7}\]
  done clear
  C)
   \[\frac{2}{9}\]              
  done clear
  D)
   \[\frac{7}{3}\]
  done clear
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• question_answer21) A bob of pendulum was filled with Hg and entire Hg is drained out, then the time period of pendulum                   
  A)
   remains unchanged
  done clear
  B)
   decreases                         
  done clear
  C)
   increases                          
  done clear
  D)
   first increases then decreases
  done clear
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• question_answer22) The minimum force required to move a body of mass m vertically upward is
  A)
   \[mg\]            
  done clear
  B)
   \[mg/2\]
  done clear
  C)
   more than 2 mg  
  done clear
  D)
   more than mg
  done clear
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• question_answer23) The uncertainty in the momentum of a particle is\[{{10}^{-30}}kg-m/s\]. The minimum uncertainty in its position will be
  A)
   \[{{10}^{-8}}m\] 
  done clear
  B)
   \[{{10}^{-12}}m\]
  done clear
  C)
   \[{{10}^{-16}}m\]        
  done clear
  D)
   \[{{10}^{-4}}m\]
  done clear
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• question_answer24) If distance between earth and sun become four times than time period becomes
  A)
   4 times         
  done clear
  B)
   8 times
  done clear
  C)
   1/4 times        
  done clear
  D)
   1/8 times
  done clear
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• question_answer25) An air bubble is contained inside water. It behaves as
  A)
   concave lens
  done clear
  B)
   convex lens
  done clear
  C)
   neither convex nor concave
  done clear
  D)
   Cannot say
  done clear
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• question_answer26) The power dissipated across resistance R which is connected across a battery of potential V is P. If resistance is doubled, then the power becomes
  A)
   1/2              
  done clear
  B)
   2
  done clear
  C)
   1/4              
  done clear
  D)
   2
  done clear
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• question_answer27) BE/nucleon relation with mass number
  A)
   first decreases then increases
  done clear
  B)
   first increases then decreases
  done clear
  C)
   increases
  done clear
  D)
   decreases
  done clear
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• question_answer28) A 100 V, AC source of frequency 500 Hz is connected to an L-C-R circuit with L = 8.1 mH, C = 12.5 \[\mu \] F, R = 10 \[\Omega \] all connected. What is the quality factor of circuit?
  A)
   2.02           
  done clear
  B)
   2.5434                  
  done clear
  C)
   20.54                        
  done clear
  D)
   200.54          
  done clear
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• question_answer29) The inductance of a coil is L = 10 H and resistance R = 5\[\Omega \]. If applied voltage of battery is 10 V and it switches off in 1 millisecond, find induced emf of inductor.
  A)
   \[2\times {{10}^{4}}V\]        
  done clear
  B)
   \[1.2\times {{10}^{4}}V\]
  done clear
  C)
   \[2\times {{10}^{-4}}V\]        
  done clear
  D)
   None of these
  done clear
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• question_answer30) Two bodies A and B having masses in the ratio of 3 : 1 possess the same kinetic energy. The ratio of linear momenta of B to A is
  A)
   1 : 3            
  done clear
  B)
   3 : 1
  done clear
  C)
   1 : \[\sqrt{3}\]              
  done clear
  D)
   \[\sqrt{3}\]: 1
  done clear
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• question_answer31) Which of the following four fundamental forces has shortest range?
  A)
   Nuclear         
  done clear
  B)
   Gravitational
  done clear
  C)
   Electromagnetic
  done clear
  D)
   Weak force
  done clear
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• question_answer32) A proton is moving in a uniform magnetic field B in a circular path of radius a in a direction perpendicular to Z axis along which field B exists. Calculate the angular momentum, if the radius is a and charge on proton is e.
  A)
   \[\frac{Be}{{{a}^{2}}}\]
  done clear
  B)
   \[e{{B}^{2}}a\]
  done clear
  C)
   \[{{a}^{2}}eB\]
  done clear
  D)
   \[aeB\]
  done clear
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• question_answer33) If acceleration of a particle at any time is given by \[a=2t+5\] Calculate, the velocity after 5s, if it starts from rest.
  A)
   50 m/s            
  done clear
  B)
   25 m/s
  done clear
  C)
   100 m/s          
  done clear
  D)
   75 m/s
  done clear
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• question_answer34) To look inside an atom of diameter 100 pm we have to penetrate it upto a breadth of 10 pm. If we use an electron microscope, the minimum required energy will be
  A)
   1.5 keV          
  done clear
  B)
   15 keV
  done clear
  C)
   150 keV         
  done clear
  D)
   1.05 keV
  done clear
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• question_answer35) A body from height h is dropped. If the coefficient of restitution is e, then calculate the height achieved after one bounce.
  A)
   \[{{h}_{1}}={{e}^{2}}h\]
  done clear
  B)
   \[{{h}_{1}}={{e}^{4}}h\]
  done clear
  C)
   \[{{h}_{1}}=eh\]
  done clear
  D)
   \[{{h}_{1}}=h/e\]
  done clear
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• question_answer36) A body moves with uniform acceleration, then which of the following graph is correct?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
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• question_answer37)   Two vectors are perpendicular, if
  A)
   \[A\to .B\to =1\]
  done clear
  B)
   \[A\to \times B\to =0\]
  done clear
  C)
   \[A\to .B\to =0\]
  done clear
  D)
   \[A\to \times B\to =AB\]
  done clear
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• question_answer38) If coefficient of static friction is \[{{\mu }_{s}}\]and coefficient of kinetic friction is \[{{\mu }_{k}}\], which is correct?
  A)
   \[{{\mu }_{s}}={{\mu }_{k}}\]
  done clear
  B)
   \[{{\mu }_{s}}>{{\mu }_{k}}\]
  done clear
  C)
   \[{{\mu }_{s}}<{{\mu }_{k}}\]          
  done clear
  D)
   Cannot predicted
  done clear
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• question_answer39) Light year is used to measure
  A)
   distance between stars
  done clear
  B)
   distance between atoms
  done clear
  C)
   revolution time of earth around sun
  done clear
  D)
   None of the above
  done clear
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• question_answer40) Electromagnetic waves are produced by
  A)
   accelerated charged particle
  done clear
  B)
   decelerated charged particle
  done clear
  C)
   charge in uniform motion
  done clear
  D)
   None of the above
  done clear
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• question_answer41) A beam of proton with velocity\[4\times {{10}^{5}}m/s\]enters a uniform magnetic field of 0.3 T at an angle of \[60{}^\circ \]to the magnetic field. Find the radius of the helical path taken by the proton beam.
  A)
   0.2 cm          
  done clear
  B)
   1.2 cm
  done clear
  C)
   2.2 cm          
  done clear
  D)
   0.122 cm
  done clear
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• question_answer42) Three progressive waves A, B and C are shown in the figure with respect to A, the progressive wave
  A)
   B lags by \[\frac{\pi }{2}\] and C leads by \[\frac{\pi }{2}\]
  done clear
  B)
   B lags by \[\pi \] and C leads by \[\pi \]
  done clear
  C)
   B leads by \[\frac{\pi }{2}\] and C lags by \[\frac{\pi }{2}\]
  done clear
  D)
   B leads by \[\pi \] and C lags by \[\pi \]
  done clear
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• question_answer43) When light passes from one medium to other then which will not change?
  A)
   Frequency       
  done clear
  B)
   Wavelength
  done clear
  C)
   Amplitude       
  done clear
  D)
   Velocity
  done clear
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• question_answer44) Total internal reflection takes place
  A)
   When a ray moves from denser to rarer and incident angle is greater than critical angle.
  done clear
  B)
   When a ray moves from rarer to denser and incident angle is less than critical angle.
  done clear
  C)
   When a ray moves from rarer to denser and incident angle is equal to critical angle.
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer45) A beam of light travelling along z-axis is described by the electric field \[{{E}_{y}}=(600\,V/m)\sin \omega \left( t-\frac{x}{c} \right)\] then maximum magnetic force on a charge\[q=2e\] moving along y-axis with a speed of \[3.0\times {{10}^{7}}m/s\]is\[(e=1.6\times {{10}^{-19}}C)\]
  A)
   \[19.2\times {{10}^{-17}}N\]    
  done clear
  B)
   \[1.92\times {{10}^{-17}}N\]
  done clear
  C)
   0.992 N         
  done clear
  D)
   None of these
  done clear
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• question_answer46) In hydrogen atom, transition takes from state 2 to 1, an electromagnetic wave of frequency \[2.7\times {{10}^{15}}\]Hz is emitted. If this transition takes place from 3 to 1, emitted frequency will be
  A)
   \[3.2\times {{10}^{15}}z\]     
  done clear
  B)
   \[32\times {{10}^{15}}Hz\]
  done clear
  C)
   \[1.6\times 15\text{ }Hz\]     
  done clear
  D)
   \[16\times {{10}^{15}}Hz\]
  done clear
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• question_answer47) The equipotential surface related to an electric field, increases in magnitude along\[x-\]axis is
  A)
   plane parallel to y-z plane
  done clear
  B)
   plane parallel to x-y plane
  done clear
  C)
   plane parallel to x-z plane
  done clear
  D)
   equi axis cylinder of increasing radius about\[x-\]axis
  done clear
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• question_answer48) If 200 MeV energy is released in the fission of 92 U235. What will be the required number of fission per second to produce 1 kW of power?
  A)
   \[3.12\times {{10}^{13}}\]       
  done clear
  B)
   \[3.12\times {{10}^{3}}\]
  done clear
  C)
   \[3.1\times {{10}^{17}}\]        
  done clear
  D)
   \[3.12\times {{10}^{19}}\]
  done clear
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• question_answer49) During projectile motion, the horizontal velocity
  A)
   first increases then decreases
  done clear
  B)
   first decreases then increases
  done clear
  C)
   always increases
  done clear
  D)
   always constant
  done clear
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• question_answer50) Find the ratio of acceleration due to gravity g at depth d and at height A, where, d = 2h.
  A)
   1 : 1             
  done clear
  B)
   1 : 2
  done clear
  C)
   2 : 1             
  done clear
  D)
   1 : 4
  done clear
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• question_answer51) What is the stoichiometry coefficient of\[Ca\]in the following reaction? \[Ca+A{{l}^{3+}}\xrightarrow[{}]{{}}C{{a}^{2+}}+Al\]
  A)
   2              
  done clear
  B)
   1
  done clear
  C)
   3              
  done clear
  D)
   4
  done clear
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• question_answer52) What is the value of x in the potash alum \[{{K}_{2}}S{{O}_{4}}.A{{l}_{x}}{{(S{{O}_{4}})}_{3}}.24{{H}_{2}}O\]?
  A)
   4               
  done clear
  B)
   1
  done clear
  C)
   2               
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer53) Ozone is useful in the purification of water because
  A)
   it releases oxygen on dissociation
  done clear
  B)
   it does not give unpleasant smell like chlorine
  done clear
  C)
   it acts as bactericide and destroys the bacteria, fungi etc
  done clear
  D)
   All of the above
  done clear
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• question_answer54) Internal energy is the sum of
  A)
   kinetic energy and potential energy
  done clear
  B)
   all types of energy of system
  done clear
  C)
   energies of internal system
  done clear
  D)
   None of the above
  done clear
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• question_answer55) Which of the following is a combustion reaction?
  A)
   \[C+{{O}_{2}}\xrightarrow[{}]{{}}C{{O}_{2}}\]
  done clear
  B)
   \[C{{H}_{4}}+{{O}_{2}}\xrightarrow[{}]{{}}C{{O}_{2}}+{{H}_{2}}O\]
  done clear
  C)
   \[Mg+{{O}_{2}}\xrightarrow[{}]{{}}MgO\]
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer56) \[{{C}_{6}}{{H}_{5}}^{14}COOH\]is heated with\[N{{a}_{2}}C{{O}_{3}}\]to release
  A)
   \[C{{O}_{2}}\]
  done clear
  B)
   \[^{14}C{{O}_{2}}\]
  done clear
  C)
   CO            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer57) The mass of two molecules A and B are 100 kg and 64 kg respectively. If the diffusion rate of A is\[12\times {{10}^{-3}}\]then, the diffusion rate of B will be
  A)
   \[15\times {{10}^{-3}}\]         
  done clear
  B)
   \[64\times {{10}^{-3}}\]
  done clear
  C)
   \[5\times {{10}^{-3}}\]        
  done clear
  D)
   \[46\times {{10}^{-3}}\]
  done clear
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• question_answer58) Commercially ethyl bromide is manufactured by
  A)
   ethyl alcohol \[+HBr\]
  done clear
  B)
   ethanol\[+B{{r}_{2}}\]
  done clear
  C)
   alcohol \[+HBr\]
  done clear
  D)
   None of the above
  done clear
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• question_answer59) In the presence of\[Fe/HCl,\]aniline obtains from which of the following?
  A)
   Benzene         
  done clear
  B)
   Nitrobenzene
  done clear
  C)
   Dinitrobenzene   
  done clear
  D)
   None of these
  done clear
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• question_answer60) Which of the following is a strong base?
  A)
   Benzamide      
  done clear
  B)
   Butanamine
  done clear
  C)
   Nitrobenzene    
  done clear
  D)
   Benzene
  done clear
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• question_answer61) On comparison of S and\[S\]the\[{{S}^{2-}}\]has
  A)
   large radius and large size
  done clear
  B)
   small radius and large size
  done clear
  C)
   large radius and small size
  done clear
  D)
   small radius and small size
  done clear
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• question_answer62) Which of the following is not correct?
  A)
   \[{{t}_{1/2}}=\frac{0.693}{k}\]
  done clear
  B)
   \[N={{N}_{0}}{{e}^{-kt}}\]
  done clear
  C)
   \[\frac{1}{N}-\frac{1}{{{N}_{0}}}=In\,k{{t}_{1/2}}\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer63) Which of the following is the second most electronegative element?
  A)
   Oxygen         
  done clear
  B)
   Nitrogen
  done clear
  C)
   Fluorine         
  done clear
  D)
   Sulphur
  done clear
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• question_answer64) Which of the following is not correct according to Aufbau's rule?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer65) Which of the following has the lowest ionization potential?
  A)
   Oxygen          
  done clear
  B)
   Nitrogen
  done clear
  C)
   Fluorine         
  done clear
  D)
   Sulphur
  done clear
  View Answer play_arrow

• question_answer66) On homolytic fission,\[C{{H}_{3}}C{{H}_{2}}Cl\]gives
  A)
   \[C{{H}_{3}}\overset{\bullet }{\mathop{C}}\,{{H}_{2}}\]and\[C\overset{\bullet }{\mathop{l}}\,\]
  done clear
  B)
   \[C{{H}_{3}}\overset{\oplus }{\mathop{C}}\,{{H}_{2}}\]and\[C{{l}^{-}}\]
  done clear
  C)
   \[C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]and\[C\overset{\bullet }{\mathop{I}}\,\]
  done clear
  D)
   \[C{{H}_{3}}\overset{\bullet }{\mathop{C}}\,{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer67) If the diffusion rate of\[N{{H}_{3}}\]is double of X, then the molecular weight of X will be
  A)
   68              
  done clear
  B)
   48
  done clear
  C)
   12              
  done clear
  D)
   8
  done clear
  View Answer play_arrow

• question_answer68) The bond order of\[C-C\]bond of benzene.
  A)
   1               
  done clear
  B)
   2
  done clear
  C)
   between 1 and 2  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer69) The decreasing order of bond length of following , Ethane  Ethene  Ethyne
  A)
   \[A>B>C\]       
  done clear
  B)
   \[B>A>C\]
  done clear
  C)
   \[C>B>A\]       
  done clear
  D)
   \[C>A>B\]
  done clear
  View Answer play_arrow

• question_answer70) What is the range of the size of colloidal particle?
  A)
   1 to 100 nm     
  done clear
  B)
   1 to 1000 cm
  done clear
  C)
   1 to 1000 mm    
  done clear
  D)
   1 to 100 km
  done clear
  View Answer play_arrow

• question_answer71) \[Z{{n}^{2+}}\xrightarrow[{}]{{}}Zn(s)\] \[E{}^\circ =-0.76V\] \[C{{u}^{2+}}\xrightarrow[{}]{{}}Cu(s)\] \[E{}^\circ =-0.34V\] Which of the following is the spontaneous reaction?
  A)
   \[Z{{n}^{2+}}+Cu\xrightarrow[{}]{{}}Zn+C{{u}^{2+}}\]
  done clear
  B)
   \[C{{u}^{2+}}+Zn\xrightarrow[{}]{{}}Cu+Z{{n}^{2+}}\]
  done clear
  C)
   \[Z{{n}^{2+}}+C{{u}^{2+}}\xrightarrow[{}]{{}}Zn+Cu\]
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer72) Which of the following element has the maximum electron affinity?
  A)
   Fluorine        
  done clear
  B)
   Chlorine
  done clear
  C)
   Sulphur         
  done clear
  D)
   Xenon
  done clear
  View Answer play_arrow

• question_answer73) Which is the most reactive inert gas?
  A)
   \[He\]              
  done clear
  B)
   \[Ne\]
  done clear
  C)
   \[Ar\]               
  done clear
  D)
   \[Xe\]
  done clear
  View Answer play_arrow

• question_answer74) Which type of bond presents in\[Xe\]molecule?
  A)
   Covalent         
  done clear
  B)
   lon-dipole
  done clear
  C)
   van der Waals   
  done clear
  D)
   Dipole-dipole
  done clear
  View Answer play_arrow

• question_answer75) Which of the following is irreversible reaction?
  A)
   \[2N{{H}_{3}}\xrightarrow[{}]{{}}{{N}_{2}}+3{{H}_{2}}\]
  done clear
  B)
   \[PC{{l}_{5}}\xrightarrow[{}]{{}}PC{{l}_{3}}+C{{l}_{2}}\]
  done clear
  C)
   \[KCl{{O}_{3}}\xrightarrow[{}]{{}}KCl+{{O}_{2}}\]
  done clear
  D)
   \[2S{{O}_{3}}\xrightarrow[{}]{{}}2S{{O}_{2}}+{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer76) Heavy water is
  A)
   \[{{H}_{2}}O\]             
  done clear
  B)
   \[{{D}_{2}}O\]
  done clear
  C)
   \[{{H}_{2}}{{O}_{2}}\]           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer77) \[{{H}_{2}}S\]is not a
  A)
   reducing agent   
  done clear
  B)
   acidic
  done clear
  C)
   oxidising agent   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer78) At constant temperature, the curve between p and V is
  A)
   straight line
  done clear
  B)
   increasing curve
  done clear
  C)
   straight line with slope
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer79) At constant temperature, on doubling the p and V, the reversible constant will become
  A)
   constant         
  done clear
  B)
   double
  done clear
  C)
   quarter          
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer80) The electronic configuration of\[M{{n}^{2+}}\]is
  A)
   \[[Ne]3{{d}^{5}},4{{s}^{0}}\]
  done clear
  B)
   \[[Ar]3{{d}^{5}},4{{s}^{2}}\]
  done clear
  C)
   \[[Ar]3{{d}^{5}},4{{s}^{0}}\]
  done clear
  D)
   \[[Ne]3{{d}^{5}},4{{s}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer81) Generally the +3 oxidation state is
  A)
   Ni (28)           
  done clear
  B)
   Fe (26)
  done clear
  C)
   Zn (30)          
  done clear
  D)
   Cu (29)
  done clear
  View Answer play_arrow

• question_answer82) The structure of 1, 2-dihydroxy butane is
  A)
   \[C(OH)-C(OH)-C-C\]
  done clear
  B)
   \[C-C{{(OH)}_{2}}-C-C\]
  done clear
  C)
   \[(OH)C-C-C-C(OH)\]
  done clear
  D)
   \[C-C(OH)-C(OH)-C\]
  done clear
  View Answer play_arrow

• question_answer83) The atomic size increases on moving downward because
  A)
   the number of electrons increases
  done clear
  B)
   the number of protons and neutrons increases
  done clear
  C)
   the number of protons increases
  done clear
  D)
   the number of protons, neutrons and electrons increases
  done clear
  View Answer play_arrow

• question_answer84) The ionization energy decreases on moving downward because
  A)
   charge increases
  done clear
  B)
   atomic size increases
  done clear
  C)
   atomic size decreases
  done clear
  D)
   screening effect decreases
  done clear
  View Answer play_arrow

• question_answer85) Which of the following is tribasic acid?
  A)
   \[{{H}_{3}}P{{O}_{2}}\]          
  done clear
  B)
   \[{{H}_{3}}P{{O}_{4}}\]
  done clear
  C)
   \[{{H}_{4}}{{P}_{2}}{{O}_{7}}\]          
  done clear
  D)
   \[{{H}_{3}}P{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer86) Which has the maximum dipole moment?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer87) In electrolytic cell, the cathode acts as
  A)
   oxidising agent   
  done clear
  B)
   reducing agent
  done clear
  C)
   Either [a] or [b]   
  done clear
  D)
   Neither [a] nor [b]
  done clear
  View Answer play_arrow

• question_answer88) The order of reaction may be
  A)
   zero
  done clear
  B)
   fraction
  done clear
  C)
   whole number
  done clear
  D)
   zero, fraction, whole number
  done clear
  View Answer play_arrow

• question_answer89) Which has the maximum relative ionization power?
  A)
   \[\alpha -\]rays            
  done clear
  B)
   \[\beta -\]rays
  done clear
  C)
   \[\gamma -\]rays             
  done clear
  D)
   \[X-\]rays
  done clear
  View Answer play_arrow

• question_answer90) Which of the following is a vitamin?
  A)
   Benzoic acid
  done clear
  B)
   Ascorbic acid
  done clear
  C)
   Oxalic acid
  done clear
  D)
   Formic acid
  done clear
  View Answer play_arrow

• question_answer91) Which isomerism is shown by following compounds? \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\]and\[C{{H}_{3}}C{{H}_{2}}OC{{H}_{3}}\]
  A)
   Position isomerism
  done clear
  B)
   Functional isomerism
  done clear
  C)
   Structural isomerism
  done clear
  D)
   Chain isomerism
  done clear
  View Answer play_arrow

• question_answer92) White lead is
  A)
   \[P{{b}_{3}}{{O}_{4}}\]
  done clear
  B)
   \[PbO\]
  done clear
  C)
   \[2PbC{{O}_{3}}.Pb{{(OH)}_{2}}\]
  done clear
  D)
   \[Pb{{(C{{H}_{3}}COO)}_{2}}.Pb{{(OH)}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer93) The blister copper is
  A)
   impure copper
  done clear
  B)
   alloy of copper
  done clear
  C)
   pure copper
  done clear
  D)
   copper with 1% impurity
  done clear
  View Answer play_arrow

• question_answer94) Claisen condensation is not given by
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer95) \[AgN{{O}_{3}}\]does not give precipitate with\[CHC{{l}_{3}}\] because
  A)
  \[CHC{{l}_{3}}\]does not dissociate in water
  done clear
  B)
   Chemically\[AgN{{O}_{3}}\]is unreactive
  done clear
  C)
   Chemically\[CH{{l}_{3}}\]is unreactive
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer96) In\[_{90}T{{h}^{228}}{{\xrightarrow[{}]{{}}}_{83}}B{{i}^{212}},\]the emitted\[\alpha \]and\[\beta \] particles are
  A)
   \[4\alpha ,1\beta \]           
  done clear
  B)
   \[4\alpha ,2\beta \]
  done clear
  C)
   \[5\alpha ,1\beta \]          
  done clear
  D)
   \[5\alpha ,2\beta \]
  done clear
  View Answer play_arrow

• question_answer97) Which of the following is obtained on the hydrolysis of\[PC{{l}_{3}}\]?
  A)
   \[{{H}_{3}}P{{O}_{3}}\]          
  done clear
  B)
   \[P{{H}_{3}}\]
  done clear
  C)
   \[{{H}_{3}}P{{O}_{4}}\]          
  done clear
  D)
   \[POC{{l}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer98) Which bond is presents in protein and peptides?
  A)
   \[-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-NH-\]
  done clear
  B)
   \[-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-O-\]
  done clear
  C)
   \[-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-O-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-\]
  done clear
  D)
   \[-NH-\]
  done clear
  View Answer play_arrow

• question_answer99) Blood cells do not shrink in blood, because blood is
  A)
   hypotonic        
  done clear
  B)
   isotonic
  done clear
  C)
   isomolecular     
  done clear
  D)
   hypertonic
  done clear
  View Answer play_arrow

• question_answer100) On isothermal expansion of ideal gas, its
  A)
   internal energy increases
  done clear
  B)
   enthalpy increases
  done clear
  C)
   enthalpy becomes zero on decreasing
  done clear
  D)
   enthalpy remains unchanged
  done clear
  View Answer play_arrow

• question_answer101) Let the coordinates of P are (1,0) and point Q lies on the curve\[{{y}^{2}}=8x\]. The locus of the midpoint of PQ is
  A)
   \[{{y}^{2}}-4x+2=0\]
  done clear
  B)
  \[{{y}^{2}}+4x+2=0\]
  done clear
  C)
   \[{{x}^{2}}+4y+2=0\]    
  done clear
  D)
   \[{{x}^{2}}-4y+2=0\]
  done clear
  View Answer play_arrow

• question_answer102) If\[{{A}^{2}}-A+I=O,\]then inverse of A is
  A)
   \[A+I\]             
  done clear
  B)
   A
  done clear
  C)
   \[A-I\]             
  done clear
  D)
   \[I-A\]
  done clear
  View Answer play_arrow

• question_answer103) If\[1,\omega \]and\[{{\omega }^{2}}\]are the cube roots of unity, then the roots of the equation\[{{(x-1)}^{3}}+8=0\]are
  A)
   \[-1,-1+2\omega ,-1-2{{\omega }^{2}}\]
  done clear
  B)
   \[-1,-1,-1\]
  done clear
  C)
   \[-1,1-2\omega ,1-2{{\omega }^{2}}\]
  done clear
  D)
   \[-1,1+2\omega ,1+2{{\omega }^{2}}\]
  done clear
  View Answer play_arrow

• question_answer104) The value of \[\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{{{n}^{2}}}{{\sec }^{2}}\frac{1}{{{n}^{2}}}+\frac{2}{{{n}^{2}}}{{\sec }^{2}}\frac{4}{{{n}^{2}}}+...+\frac{1}{n}{{\sec }^{2}}1 \right]\]is
  A)
   \[\frac{1}{2}\sec 1\]
  done clear
  B)
   \[\frac{1}{2}co\sec 1\]
  done clear
  C)
   \[\tan 1\]
  done clear
  D)
   \[\frac{1}{2}\tan 1\]
  done clear
  View Answer play_arrow

• question_answer105) Area of the greatest rectangle that can be inscribed in the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]is
  A)
   \[2ab\]
  done clear
  B)
   \[ab\]
  done clear
  C)
   \[\sqrt{ab}\]
  done clear
  D)
   \[\frac{a}{b}\]
  done clear
  View Answer play_arrow

• question_answer106) The order and degree of the differential equation of the family of curve \[{{y}^{2}}=2c(x+\sqrt{c}),\]where c is a arbitrary constant, is
  A)
   order 1, degree 2  
  done clear
  B)
   order 1, degree 1
  done clear
  C)
   order 1, degree 3 
  done clear
  D)
   order 2, degree 2
  done clear
  View Answer play_arrow

• question_answer107) If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the rank of SACHIN is
  A)
   601             
  done clear
  B)
   600
  done clear
  C)
   603             
  done clear
  D)
   602
  done clear
  View Answer play_arrow

• question_answer108) The value of\[^{50}{{C}_{4}}+\sum\limits_{r=1}^{6}{^{56-r}{{C}_{3}}}\]is
  A)
   \[^{55}{{C}_{4}}\]                
  done clear
  B)
   \[^{55}{{C}_{3}}\]
  done clear
  C)
   \[^{56}{{C}_{3}}\]                
  done clear
  D)
   \[^{56}{{C}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer109) If the coefficient of\[{{x}^{4}}\]in the expansion of \[{{\left[ a{{x}^{2}}+\left( \frac{1}{bx} \right) \right]}^{11}},\]is equal to the coefficient of \[{{x}^{-7}}\]in the expansion of\[{{\left[ ax-\left( \frac{1}{b{{x}^{2}}} \right) \right]}^{11}},\]then the relation between a and b is
  A)
   \[a-b=1\]
  done clear
  B)
   \[a+b=1\]
  done clear
  C)
   \[\frac{a}{b}=1\]
  done clear
  D)
   \[ab=1\]
  done clear
  View Answer play_arrow

• question_answer110) Let\[f:(-1,1)\to B\]is defined as \[f(x)={{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}}.\]Function\[f\]is one-one and onto, then the interval B is
  A)
   \[\left( 0,\frac{\pi }{2} \right)\]
  done clear
  B)
   \[\left[ 0,\frac{\pi }{2} \right)\]
  done clear
  C)
   \[\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\]
  done clear
  D)
   \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer111) lf\[w=\frac{z}{z-\frac{i}{3}}\]and\[|w|=1,\] then z lies on
  A)
   a ellipse           
  done clear
  B)
   a circle
  done clear
  C)
   a straight line     
  done clear
  D)
   a parabola
  done clear
  View Answer play_arrow

• question_answer112) If\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=-2\]and \[f(x)=\left| \begin{matrix}    1+{{a}^{2}}x & (1+{{b}^{2}})x & (1+{{c}^{2}})x  \\    (1+{{a}^{2}})x & 1+{{b}^{2}}x & (1+{{c}^{2}})x  \\    (1+{{a}^{2}})x & (1+{{b}^{2}})x & 1+{{c}^{2}}x  \\ \end{matrix} \right|,\] then\[f(x)\]is a polynomial of power
  A)
   1               
  done clear
  B)
   0
  done clear
  C)
   3               
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer113) Let\[f(x)\]is differentiable at\[x=1\]and \[\underset{h\to 0}{\mathop{\lim }}\,\frac{1}{h}(1+h)=5,\]then the value of\[f'(1)\]is
  A)
   3                   
  done clear
  B)
   4
  done clear
  C)
   5                   
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer114) The value of\[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{\int_{0}^{{{x}^{2}}}{{{\sec }^{2}}t\,dt}}{x\sin x} \right)\]is
  A)
   3                   
  done clear
  B)
   2
  done clear
  C)
   1                   
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer115) In a triangle, let\[\angle C=\pi /2\]. If r is the radius of incircle and R is the radius of circumcircle, then value of\[2(r+R)\]is
  A)
   \[b+c\]             
  done clear
  B)
   \[a+b\]
  done clear
  C)
   \[a+b+c\]          
  done clear
  D)
   \[c+a\]
  done clear
  View Answer play_arrow

• question_answer116) If\[{{\cos }^{-1}}x-{{\cos }^{-1}}\frac{y}{2}=\alpha ,\]then the value of \[4{{x}^{2}}-4xy\,cos\alpha +{{y}^{2}}\]is
  A)
   \[2\text{ }si{{n}^{2}}\alpha \]           
  done clear
  B)
   4
  done clear
  C)
   \[\text{4 }si{{n}^{2}}\alpha \]           
  done clear
  D)
   \[\text{-4 }si{{n}^{2}}\alpha \]
  done clear
  View Answer play_arrow

• question_answer117) If\[\alpha \]and\[\beta \]are two unequal roots of the equation\[a{{x}^{2}}+bx+c=0,\]  then   the   value of\[\underset{x\to \alpha }{\mathop{\lim }}\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}}\]is
  A)
   \[\frac{{{a}^{2}}}{2}{{(\alpha -\beta )}^{2}}\]
  done clear
  B)
   \[0\]
  done clear
  C)
   \[\frac{-{{a}^{2}}}{2}{{(\alpha -\beta )}^{2}}\]
  done clear
  D)
   \[\frac{1}{2}{{(\alpha -\beta )}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer118) If\[x\frac{dy}{dx}y=y(log\text{ }y-log\text{ }x+1),\]then, the solution of the equation is
  A)
   \[y\log \left( \frac{x}{y} \right)=cx\]
  done clear
  B)
   \[x\log \left( \frac{y}{x} \right)=cy\]
  done clear
  C)
   \[\log \left( \frac{y}{x} \right)=cx\]
  done clear
  D)
   \[\log \left( \frac{x}{y} \right)=cy\]
  done clear
  View Answer play_arrow

• question_answer119) The value of\[{{\int{\left\{ \frac{(\log x-1)}{1+{{(\log x)}^{2}}} \right\}}}^{2}}dx\]is
  A)
   \[\frac{\log x}{{{(\log x)}^{2}}+1}+c\]
  done clear
  B)
   \[\frac{x}{{{x}^{2}}+1}+c\]
  done clear
  C)
   \[\frac{x{{e}^{x}}}{1+{{x}^{2}}}+c\]
  done clear
  D)
   \[\frac{x}{{{(\log x)}^{2}}+1}+c\]
  done clear
  View Answer play_arrow

• question_answer120) Let\[f:R\to R\]is a differentiable function\[f(2)=6,f'(x)=\frac{1}{48},\]then\[\underset{x\to 2}{\mathop{\lim }}\,\int_{6}^{f(x)}{\frac{4{{t}^{3}}}{x-2}}dt\]is equal to
  A)
   24               
  done clear
  B)
   36
  done clear
  C)
   12               
  done clear
  D)
   18
  done clear
  View Answer play_arrow

• question_answer121) Let a non-negative continuous function\[f(x)\]is such that the area of the region bounded by the curve\[y=f(x),\]\[x-\]axis and the lines\[x=\frac{\pi }{4}\]ands\[x=\beta >\frac{\pi }{4}\]is\[\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta  \right),\]then the value of \[f\left( \frac{\pi }{2} \right)\]is
  A)
   \[\left( \frac{\pi }{4}+\sqrt{2}-1 \right)\]
  done clear
  B)
   \[\left( \frac{\pi }{4}-\sqrt{2}+1 \right)\]
  done clear
  C)
   \[\left( 1-\frac{\pi }{4}-\sqrt{2} \right)\]
  done clear
  D)
   \[\left( 1-\frac{\pi }{4}+\sqrt{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer122) The area of the region bounded by the curve \[y=lo{{g}_{e}}(x+e)\]and axes is
  A)
   1               
  done clear
  B)
   2
  done clear
  C)
   3               
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer123) The parabolas\[{{y}^{2}}=4x\]and\[{{x}^{2}}=4y\]divide the square region bounded by the lines\[x=4,\text{ }y=4\]and the coordinates axes. If \[{{S}_{1}},{{S}_{2}},{{S}_{3}}\]are respectively the areas of these parts numbered from top to bottom, then \[{{S}_{1}}:{{S}_{2}}:{{S}_{3}}\]is
  A)
   1 : 2 : 1            
  done clear
  B)
   1 : 2 : 3
  done clear
  C)
   2 : 1 : 2            
  done clear
  D)
   1 : 1 : 1
  done clear
  View Answer play_arrow

• question_answer124) If the plane\[2ax-3at+4az+6=0\]passes through the midpoint of the line joining the centres of the spheres \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+6x-8y-2z=13\] and\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-10x+4y-2z=8,\]then a equals
  A)
   \[-1\]             
  done clear
  B)
   1
  done clear
  C)
   \[-2\]             
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer125) The distance between the line\[\overrightarrow{a}=2\hat{i}-2\hat{j}+3\hat{k}\] \[\lambda (\hat{i}+5\hat{j}+\hat{k})=5\]and the plane\[\overrightarrow{r}.(\hat{i}+5\hat{j}+\hat{k})=5\]is
  A)
   \[\frac{10}{9}\]
  done clear
  B)
   \[\frac{10}{3\sqrt{3}}\]
  done clear
  C)
   \[\frac{3}{10}\]
  done clear
  D)
   \[\frac{10}{3}\]
  done clear
  View Answer play_arrow

• question_answer126) For any vector\[\overrightarrow{a}\]the value of\[{{(\overrightarrow{a}\times i)}^{2}}+{{(\overrightarrow{a}\times \hat{j})}^{2}}+{{(\overrightarrow{a}\times \hat{k})}^{2}}\]is equal to
  A)
   \[3{{\overrightarrow{a}}^{2}}\]
  done clear
  B)
   \[{{\overrightarrow{a}}^{2}}\]
  done clear
  C)
   \[2{{\overrightarrow{a}}^{2}}\]
  done clear
  D)
   \[4{{\overrightarrow{a}}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer127) If non-zero numbers a, b, c are in HP, then line \[\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0\]always passes through a fixed point. That point is
  A)
   \[(-1,2)\]
  done clear
  B)
   \[(-1,-2)\]
  done clear
  C)
   \[(1,-2)\]
  done clear
  D)
   \[\left( 1,-\frac{1}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer128) If the circles \[{{x}^{2}}+{{y}^{2}}+2ax+cy+a=0\]and \[{{x}^{2}}+{{y}^{2}}-3ax+dy-1=0\]intersects at two different points P and Q, then the line \[5x+by-a=0\]passes through the points P and Q for
  A)
   only one value of a
  done clear
  B)
   no value of a
  done clear
  C)
   infinite values of a
  done clear
  D)
   only two values of a
  done clear
  View Answer play_arrow

• question_answer129) In an ellipse OB is a semi-minor axis, F and F' are its focus and angle FBF' is right angle. Then, eccentricity of the ellipse is
  A)
   \[\frac{1}{\sqrt{2}}\]
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[\frac{1}{4}\]
  done clear
  D)
   \[\frac{1}{\sqrt{3}}\]
  done clear
  View Answer play_arrow

• question_answer130) If\[y=ax+p\]is a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]then the locus of the point \[P(\alpha ,\beta )\]or is
  A)
   an ellipse         
  done clear
  B)
   a circle
  done clear
  C)
   a parabola        
  done clear
  D)
   a hyperbola
  done clear
  View Answer play_arrow

• question_answer131) If the angle between the line \[\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}\]and the plane\[2x-y+\sqrt{\lambda z}+4=0\]is\[\theta \]such that\[\sin \theta =\frac{1}{3},\]then the value of\[\lambda \]is,
  A)
   \[\frac{5}{3}\]
  done clear
  B)
   \[-\frac{3}{5}\]
  done clear
  C)
   \[\frac{3}{4}\]
  done clear
  D)
   \[-\frac{4}{3}\]
  done clear
  View Answer play_arrow

• question_answer132) Let A and B be two events such that\[P\overline{(A\cup B)}=\frac{1}{6},P(A\cap B)=\frac{1}{4}\]an\[P(\overline{A})=\frac{1}{4},\]where A stands for complement of event A. Then, events A and B are
  A)
   mutually exclusive and independent
  done clear
  B)
   independent but not equally likely
  done clear
  C)
   equally likely but not independent
  done clear
  D)
   equally likely and mutually exclusive
  done clear
  View Answer play_arrow

• question_answer133) Three houses are available in a locality. Three persons apply for the houses. Each applie for one house without consulting others. The probability that all three apply for the same house, is
  A)
   \[\frac{2}{9}\]
  done clear
  B)
   \[\frac{1}{9}\]
  done clear
  C)
   \[\frac{8}{9}\]
  done clear
  D)
   \[\frac{7}{9}\]
  done clear
  View Answer play_arrow

• question_answer134) If\[\overrightarrow{a}=\hat{i}-\hat{k},\overrightarrow{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}\]and\[\overrightarrow{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k},\]then\[[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]\]depends on
  A)
   only y            
  done clear
  B)
   only\[x\]
  done clear
  C)
   both\[x\]and y     
  done clear
  D)
   neither\[x\] nor y
  done clear
  View Answer play_arrow

• question_answer135) Let a, b and c are different non-negative numbers. If vectors\[a\hat{i}+a\hat{j}+c\hat{k},\text{ }\hat{i}+\hat{k}\] and \[c\hat{i}+c\hat{j}+b\hat{k}\]lies in the same plane, then the value of c is
  A)
   geometric mean of a and b
  done clear
  B)
   arithmetic mean of a and b
  done clear
  C)
   zero
  done clear
  D)
   harmonic mean of a and b
  done clear
  View Answer play_arrow

• question_answer136) If\[\vec{a},\text{ }\overrightarrow{b}\]and\[\overrightarrow{c}\]are non-coplanar vectors and\[\lambda \]is a real number, then \[[\lambda (\overrightarrow{a}+\overrightarrow{b}){{\lambda }^{2}}\overrightarrow{b}\,\lambda \,\overrightarrow{c}]=[\overrightarrow{a}\overrightarrow{b}+\overrightarrow{c}\overrightarrow{b}]\]for
  A)
   only one value of \[\lambda \]
  done clear
  B)
   no value of \[\lambda \]
  done clear
  C)
   only three values of\[\lambda \]
  done clear
  D)
   only two values of\[\lambda \]
  done clear
  View Answer play_arrow

• question_answer137) The value of\[\int_{-\pi }^{\pi }{\frac{{{\cos }^{2}}x}{1+{{a}^{x}}}}dx,a>0\]is
  A)
   \[a\pi \]
  done clear
  B)
   \[\frac{\pi }{2}\]
  done clear
  C)
   \[\frac{\pi }{a}\]
  done clear
  D)
   \[2\pi \]
  done clear
  View Answer play_arrow

• question_answer138) The radius of the circle in which the sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-x+z-2=0\]cuts by the plane \[x+2y-z=4,\]is
  A)
   3               
  done clear
  B)
   1
  done clear
  C)
   2               
  done clear
  D)
   \[\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer139) The value of\[\tan \left\{ {{\cos }^{-1}}\left( -\frac{2}{7} \right)-\frac{\pi }{2} \right\}\]is
  A)
   \[\frac{2}{3\sqrt{5}}\]
  done clear
  B)
   \[\frac{2}{3}\]
  done clear
  C)
   \[\frac{1}{\sqrt{5}}\]
  done clear
  D)
   \[\frac{4}{\sqrt{5}}\]
  done clear
  View Answer play_arrow

• question_answer140) If\[{{\tan }^{-1}}(x-1)+{{\tan }^{-1}}x+{{\tan }^{-1}}(x+1)\] \[={{\tan }^{-1}}3x,\]then the value of\[x\]is
  A)
   \[\pm \frac{1}{2}\]
  done clear
  B)
   \[0,\frac{1}{2}\]
  done clear
  C)
   \[0,-\frac{1}{2}\]
  done clear
  D)
   \[0,\pm \frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer141) The sum of the sequence\[1+\frac{1}{4.2!}+\frac{1}{16.4!}+\frac{1}{64.6!}+......\infty \]is
  A)
   \[\frac{e-1}{\sqrt{e}}\]
  done clear
  B)
   \[\frac{e+1}{\sqrt{e}}\]
  done clear
  C)
   \[\frac{e-1}{2\sqrt{e}}\]
  done clear
  D)
   \[\frac{e+1}{2\sqrt{e}}\]
  done clear
  View Answer play_arrow

• question_answer142) If\[{{x}_{0}}=1\]is to find the real roots of the equation \[{{x}^{2}}-x=2\]by Newton-Raphson's method then the value of\[{{x}_{2}}\]is
  A)
   9/15             
  done clear
  B)
   3
  done clear
  C)
   11/5            
  done clear
  D)
   19/5
  done clear
  View Answer play_arrow

• question_answer143) Let\[R=\{(1,\text{ }3),\text{(}4,\text{ }2),(2,\text{ }4),(2,\text{ }3),(3,\text{ }1)\}\]is a relation on the set\[A=\{1,2,3,4\}\]. Then, relation R is
  A)
   a function        
  done clear
  B)
   transitive
  done clear
  C)
   not symmetric    
  done clear
  D)
   reflexive
  done clear
  View Answer play_arrow

• question_answer144) Let z and w are two complex numbers such that\[\overline{z}+i\overline{w}=0\]and arg\[zw=\pi ,\]then arg z is equal to
  A)
   \[\pi /4\]                 
  done clear
  B)
   \[\pi /2\]
  done clear
  C)
   \[3\pi /4\]              
  done clear
  D)
   \[5\pi /4\]
  done clear
  View Answer play_arrow

• question_answer145) If\[z=x-iy\]and\[{{z}^{1/3}}=p+iq,\]then\[{\left( \frac{x}{p}+\frac{y}{q} \right)}/{({{p}^{2}}+{{q}^{2}})}\;\]equal to
  A)
   1                  
  done clear
  B)
   \[-1\]
  done clear
  C)
   2                  
  done clear
  D)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer146) If \[|{{z}^{2}}-1|=|{{z}^{2}}|+1,\].then z
  A)
   lies on real axis
  done clear
  B)
   lies on imaginary axis
  done clear
  C)
   lies on a circle
  done clear
  D)
   lies on an ellipse
  done clear
  View Answer play_arrow

• question_answer147) Let\[A=\left[ \begin{matrix}    1 & -1 & 1  \\    2 & 1 & -3  \\    1 & 1 & 1  \\ \end{matrix} \right]\]and\[(10)B=\left[ \begin{matrix}    4 & 2 & 2  \\    -5 & 0 & \alpha   \\    1 & -2 & 3  \\ \end{matrix} \right]\] If B is the inverse of matrix A, then the value of \[\alpha \]is
  A)
   \[-2\]              
  done clear
  B)
   \[-1\]
  done clear
  C)
   2                   
  done clear
  D)
   5
  done clear
  View Answer play_arrow

• question_answer148) If \[{{a}_{1}},{{a}_{2}},{{a}_{3}},.....,{{a}_{n}}\]are in GP, then the value of \[\left| \begin{matrix}    \log {{a}_{n}} & \log {{a}_{n+1}} & \log {{a}_{n+2}}  \\    \log {{a}_{n+3}} & \log {{a}_{n+4}} & \log {{a}_{n+5}}  \\    \log {{a}_{n+6}} & \log {{a}_{n+7}} & \log {{a}_{n+8}}  \\ \end{matrix} \right|\]is
  A)
   0              
  done clear
  B)
   1
  done clear
  C)
   2              
  done clear
  D)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer149) Let the arithmetic mean and geometric mean of two numbers are 9 and 4 respectively. Then, these numbers are the roots of following equation
  A)
   \[{{x}^{2}}+18x+16=0\]
  done clear
  B)
   \[{{x}^{2}}-18x+16=0\]
  done clear
  C)
   \[{{x}^{2}}+18x-16=0\]
  done clear
  D)
   \[{{x}^{2}}-18x-16=0\]
  done clear
  View Answer play_arrow

• question_answer150) If\[(1-p)\]is one root of the equation \[{{x}^{2}}+px+(1-p)=0,\]then its roots are
  A)
   \[0,\text{ }1\]              
  done clear
  B)
   \[-1,\text{ }1\]
  done clear
  C)
   \[0,-1\]            
  done clear
  D)
  \[-1,\text{ }2\]
  done clear
  View Answer play_arrow