Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

done Jamia Millia Islamia Solved Paper-2007 Total Questions - 170

• question_answer1) Which one of the following represents the correct dimensions of the coefficient of viscosity?
  A)
   \[[M{{L}^{-1}}{{T}^{-2}}]\]                         
  done clear
  B)
   \[[ML{{T}^{-1}}]\]
  done clear
  C)
   \[[M{{L}^{-1}}{{T}^{-1}}]\]                         
  done clear
  D)
   \[[M{{L}^{-2}}{{T}^{-2}}]\]
  done clear
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• question_answer2)     A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement \[x\]is proportional to:
  A)
   \[{{x}^{2}}\]                                     
  done clear
  B)
   \[{{e}^{x}}\]
  done clear
  C)
   \[x\]                                    
  done clear
  D)
   \[lo{{g}_{e}}x\]
  done clear
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• question_answer3)     A ball is released from the top of a tower of height h m. It takes T s to reach the ground. What is the position of the ball in 773 s?
  A)
  \[h/9\]m from the ground
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  B)
  \[7h/9\]m from the ground
  done clear
  C)
  \[8h/9\]m from the ground
  done clear
  D)
   \[17h/9\]m from the ground
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• question_answer4)     A projectile can have the same range R for two angles of projection. If\[{{T}_{1}}\]and\[{{T}_{2}}\]be the times of flights in the two cases, then the product of the two times of flights is directly proportional to
  A)
   \[\frac{1}{{{R}_{2}}}\]                                  
  done clear
  B)
   \[\frac{1}{R}\]
  done clear
  C)
   \[R\]                                    
  done clear
  D)
   \[{{R}^{2}}\]
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• question_answer5)     An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, ie., 120 km/h, the stopping distance will be:
  A)
   20m                                     
  done clear
  B)
   40m
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  C)
   60 m                                    
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  D)
   80 m
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• question_answer6)     A machine gun fires a bullet of mass 40 g with velocity\[1200\text{ }m{{s}^{-1}}\]. The man holding it, can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
  A)
   One                                     
  done clear
  B)
   Four
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  C)
   Two                                     
  done clear
  D)
   Three
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• question_answer7)     Two masses\[{{m}_{1}}=5\,kg\]and\[{{m}_{2}}=4.8\text{ }kg\] tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift is free to move? \[(g=9.8m/{{s}^{2}})\]
  A)
   \[0.2\text{ }m/{{s}^{2}}\]                           
  done clear
  B)
   \[9.8\text{ }m/{{s}^{2}}\]                  
  done clear
  C)
   \[5\text{ }m/{{s}^{2}}\]                               
  done clear
  D)
   \[4.8\text{ }m/{{s}^{2}}\]                  
  done clear
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• question_answer8)     A block rests on a rough inclined plane making an angle of\[30{}^\circ \]with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block Jin kg) is (take\[g=10\text{ }m/{{s}^{2}})\]
  A)
   2.0                                        
  done clear
  B)
   4.0
  done clear
  C)
   1.6                                        
  done clear
  D)
   2.5
  done clear
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• question_answer9)     A force\[\overrightarrow{F}=(5\hat{i}+3\text{ }\hat{j}+2\hat{k})N\]is applied over a particle which displaces it from its origin to the point\[\overrightarrow{r}=(2\hat{i}-\hat{j})m\]. The work done on the particle in joules is 
  A)
   \[-7\]                                   
  done clear
  B)
   \[+7\]
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  C)
   \[+10\]                               
  done clear
  D)
   \[+13\]
  done clear
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• question_answer10)     A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane, it follows that
  A)
   its velocity is constant
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  B)
   its acceleration is constant
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  C)
   its kinetic energy is constant
  done clear
  D)
   it moves in a straight line
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• question_answer11)     A ball is thrown from a point with a speed\[{{v}_{0}}\]at an angle of projection\[\theta \]. From the same point and at the same instant, a person starts running with a constant speed\[\frac{{{v}_{0}}}{2}\]to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?
  A)
   Yes,\[60{}^\circ \]          
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  B)
   Yes,\[30{}^\circ \]
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  C)
   No                                        
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  D)
   Yes,\[45{}^\circ \]
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• question_answer12)     One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively\[{{I}_{A}}\]and\[{{I}_{B}}\]such that
  A)
   \[{{I}_{A}}={{I}_{B}}\]                  
  done clear
  B)
   \[{{I}_{A}}>{{I}_{B}}\]
  done clear
  C)
   \[{{I}_{A}}<{{I}_{B}}\]                  
  done clear
  D)
   \[\frac{{{I}_{A}}}{{{I}_{B}}}=\frac{{{d}_{A}}}{{{d}_{B}}}\]
  done clear
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• question_answer13)     A satellite of mass m revolves around the earth of radius R at a height\[x\]from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
  A)
   \[gx\]                                  
  done clear
  B)
   \[\frac{gR}{R-x}\]
  done clear
  C)
   \[\frac{g{{R}^{2}}}{R+x}\]                           
  done clear
  D)
   \[{{\left( \frac{g{{R}^{2}}}{R+x} \right)}^{1/2}}\]
  done clear
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• question_answer14)     The time period of an earth satellite in circular orbit is independent of
  A)
   the mass of the satellite
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  B)
   radius of its orbit
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  C)
   both the mass and radius of the orbit
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  D)
   neither the mass of the satellite nor the radius of its orbit
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• question_answer15)     If g is the acceleration due to gravity on the earths surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is
  A)
   \[2mgR\]                           
  done clear
  B)
   \[\frac{1}{2}mgR\]
  done clear
  C)
   \[\frac{1}{4}mgR\]                         
  done clear
  D)
   \[mgR\]
  done clear
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• question_answer16)     Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to
  A)
   \[{{R}^{\left( \frac{n+1}{2} \right)}}\]                   
  done clear
  B)
   \[{{R}^{\left( \frac{n-1}{2} \right)}}\]
  done clear
  C)
   \[{{R}^{n}}\]                                     
  done clear
  D)
   \[{{R}^{\left( \frac{n-2}{2} \right)}}\]
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• question_answer17)     A wire fixed at the upper end 3tretches by length\[l\]by applying a force F. The work done, in stretching is
  A)
   \[\frac{F}{2l}\]                                 
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  B)
   \[Fl\]
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  C)
   \[2Fl\]                                 
  done clear
  D)
   \[\frac{Fl}{2}\]
  done clear
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• question_answer18)     If two soap bubbles of different radii are connected by a tube
  A)
   air flows from the bigger bubble to the smaller bubble till the sizes become equal
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  B)
   air flows from bigger bubble to the smaller bubble till the sizes are interchanged
  done clear
  C)
   air flows from the smaller bubble to the bigger
  done clear
  D)
   there is no flow of air
  done clear
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• question_answer19)     The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is\[{{t}_{0}}\]in air. Neglecting frictional force of water and given that the density of the bob is \[(4/3)\times 1000kg/{{m}^{3}}\].   What   relationship between\[t\]and\[{{t}_{0}}\]is true?
  A)
   \[t={{t}_{0}}\]                                  
  done clear
  B)
   \[t={{t}_{0}}/2\]
  done clear
  C)
   \[t=2{{t}_{0}}\]                
  done clear
  D)
   \[t=4{{t}_{0}}\]
  done clear
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• question_answer20)     The total energy of a particle, executing simple harmonic motion is
  A)
   \[\propto x\]                                   
  done clear
  B)
   \[\propto {{x}^{2}}\]
  done clear
  C)
   independent of\[x\]    
  done clear
  D)
  \[\propto {{x}^{1/2}}\]
  done clear
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• question_answer21)     The displacement y of a particle in a medium can be expressed as \[y={{10}^{-6}}\sin \left( 100t+20x+\frac{\pi }{4} \right)m,\]where t is in second and x in metre. The speed of the wave is
  A)
   2000 m/s            
  done clear
  B)
   5 m/s
  done clear
  C)
   20 m/s                                
  done clear
  D)
   57cm/s
  done clear
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• question_answer22)     A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency\[{{\omega }_{0}}\]. An external force F(t) proportional to\[\cos \omega t(\omega \ne {{\omega }_{0}})\]is applied to the oscillator. The time displacement of the oscillator will be proportional to
  A)
   \[\frac{m}{\omega _{0}^{2}-{{\omega }^{2}}}\]                               
  done clear
  B)
   \[\frac{1}{m(\omega _{0}^{2}-{{\omega }^{2}})}\]
  done clear
  C)
   \[\frac{1}{m(\omega _{0}^{2}+{{\omega }^{2}})}\]        
  done clear
  D)
   \[\frac{m}{\omega _{0}^{2}+{{\omega }^{2}}}\]
  done clear
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• question_answer23)     One mole of ideal monoatomic gas\[(\gamma =5/3)\].is mixed with one mole of diatomic gas\[(\gamma =7/5)\]. What is\[\gamma \]for the mixture? \[\gamma \] denotes the ratio of specific heat at constant pressure, to that at constant volume:
  A)
   3/2                                       
  done clear
  B)
   23/15
  done clear
  C)
   35/23                                   
  done clear
  D)
   4/3
  done clear
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• question_answer24)     If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously, will be
  A)
   4                                            
  done clear
  B)
   16
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  C)
   32                                         
  done clear
  D)
   64
  done clear
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• question_answer25)     Which of the following statements is correct for any thermodynamic system?
  A)
   The internal energy changes in all processes
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  B)
   Internal energy and entropy are state functions
  done clear
  C)
   The change in entropy can never be zero
  done clear
  D)
   The work done in an adiabatic process, is always zero
  done clear
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• question_answer26)     A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is:
  A)
  \[E/c\]                 
  done clear
  B)
  \[2E/c\]
  done clear
  C)
  \[Ec\]                                   
  done clear
  D)
  \[E/{{c}^{2}}\]
  done clear
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• question_answer27)     The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness\[x\]and\[4x,\]respectively are\[{{T}_{2}}\]and\[{{T}_{1}}({{T}_{2}}>{{T}_{1}})\]. The rate of heat transfer through the slab, in a steady state is \[\left( \frac{A({{T}_{2}}-{{T}_{1}})K}{x} \right)f,\]with\[f\]equals to
  A)
   1                                            
  done clear
  B)
   ½
  done clear
  C)
   2/3                                       
  done clear
  D)
   1/3
  done clear
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• question_answer28)     A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now, this lens has been .used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object?
  A)
   20 cm                                  
  done clear
  B)
   30 cm
  done clear
  C)
   60 cm                                  
  done clear
  D)
   80 cm
  done clear
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• question_answer29)     The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index n), is
  A)
   \[{{\sin }^{-1}}(n)\]                       
  done clear
  B)
   \[{{\sin }^{-1}}(1/n)\]
  done clear
  C)
   \[{{\tan }^{-1}}(1/n)\]                  
  done clear
  D)
   \[{{\tan }^{-1}}(n)\]
  done clear
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• question_answer30)     An electromagnetic wave of frequency \[v=3.0\text{ }MHz\]passes from vacuum into a dielectric medium with permittivity\[\varepsilon =4.0\]. Then
  A)
   wavelength is doubled and the frequency remains unchanged
  done clear
  B)
   wavelength is doubled and frequency becomes half
  done clear
  C)
   wavelength is halved, and frequency remains unchanged
  done clear
  D)
   wavelength and frequency both remain unchanged
  done clear
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• question_answer31)     Two spherical conductors B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged, is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is
  A)
   \[\frac{F}{4}\]                                  
  done clear
  B)
   \[\frac{3F}{4}\]
  done clear
  C)
   \[\frac{F}{8}\]                                  
  done clear
  D)
   \[\frac{3F}{8}\]
  done clear
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• question_answer32)     A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q was given a speed 2v, the closest distance of approach would be
  A)
   \[r\]                                     
  done clear
  B)
   \[2r\]
  done clear
  C)
   \[r/2\]                                 
  done clear
  D)
   \[r/4\]
  done clear
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• question_answer33)     Alternating current cannot be measured by DC ammeter because
  A)
   AC cannot pass through DC ammeter
  done clear
  B)
   AC changes direction
  done clear
  C)
   average value of current for complete cycle is zero
  done clear
  D)
   DC ammeter will get damaged
  done clear
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• question_answer34)     The resistance of the series combination of two resistances is S. When they are joined in parallel, the total resistance is P. If\[S=nP,\]then the minimum possible value of n is
  A)
   4                                            
  done clear
  B)
   3
  done clear
  C)
   2                                            
  done clear
  D)
   1
  done clear
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• question_answer35)     An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 4/3 and 2/3, then the ratio of the currents passing through the wire will be
  A)
   3                                            
  done clear
  B)
   1/3
  done clear
  C)
   8/9                                       
  done clear
  D)
   2
  done clear
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• question_answer36)     In a metre bridge experiment, null point is obtained at 20 cm from one end of the wire when resistance\[X\]is balanced against another resistance Y. If\[X<Y,\]then where will be the new position of the null point from the same end, if one decides to balance a resistance of\[4X\]against\[Y\]?
  A)
   50 cm                                  
  done clear
  B)
   80 cm
  done clear
  C)
   40cm                                   
  done clear
  D)
   70cm
  done clear
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• question_answer37)     The thermistors are usually made of
  A)
   metals with low temperature coefficient of resistivity
  done clear
  B)
   metals with high temperature coefficient of resistivity
  done clear
  C)
   metal oxides with high temperature coefficient of resistivity
  done clear
  D)
   semiconducting materials having low temperature coefficient of resistivity
  done clear
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• question_answer38)     Time taken by a 836 W heater to heat one litre of water from\[10{}^\circ C\]to\[40{}^\circ C\]is
  A)
   50s                                       
  done clear
  B)
   100s
  done clear
  C)
   150s    
  done clear
  D)
   200s
  done clear
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• question_answer39)     The thermo-emf of a thermocouple varies with the temperature\[\theta \]of the hot junction as\[E=a\theta +b{{\theta }^{2}}\]in volts where the ratio a/b is\[700{}^\circ C\]. If the cold junction is kept at\[0{}^\circ C,\] then the neutral temperature is
  A)
   \[700{}^\circ C\]
  done clear
  B)
   \[350{}^\circ C\]
  done clear
  C)
   \[1400{}^\circ C\]
  done clear
  D)
   no neutral temperature is possible for this thermocouple
  done clear
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• question_answer40)     The electrochemical equivalent of metal is \[3.3\times {{10}^{-7}}\]kg per coulomb. The mass of the metal liberated at the cathode when a 3 A current is passed for 2 s, will be
  A)
   \[19.8\times {{10}^{-7}}kg\]      
  done clear
  B)
   \[9.9\times {{10}^{-7}}kg\]
  done clear
  C)
   \[6.6\times {{10}^{-7}}kg\]        
  done clear
  D)
   \[1.1\times {{10}^{-7}}kg\]
  done clear
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• question_answer41)     A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be
  A)
   \[nB\]                                 
  done clear
  B)
   \[{{n}^{2}}B\]
  done clear
  C)
   \[2nB\]               
  done clear
  D)
   \[2{{n}^{2}}B\]
  done clear
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• question_answer42)     The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is\[5\mu T\]. What will be its value at the centre of the loop?
  A)
   \[250\mu T\]                    
  done clear
  B)
   \[150\mu T\]
  done clear
  C)
   \[125\mu T\]                    
  done clear
  D)
   \[75\mu T\]
  done clear
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• question_answer43)     Two long conductors, separated by a distance d carry currents\[{{I}_{1}}\]and\[{{I}_{2}}\]in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3 d. The new value of the force between them is
  A)
   \[-2F\]                                
  done clear
  B)
   \[F/3\]
  done clear
  C)
   \[-2F/3\]            
  done clear
  D)
  \[-F/3\]
  done clear
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• question_answer44)     The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be:
  A)
   \[2s\]                                  
  done clear
  B)
   \[2/3\text{ }s\]
  done clear
  C)
   \[2\sqrt{3}s\]                                   
  done clear
  D)
   \[2/\sqrt{3}\text{ }s\]
  done clear
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• question_answer45)     The   materials   suitable   for   making electromagnets should have
  A)
   high retentivity and high coercivity
  done clear
  B)
   low retentivity and low coercivity
  done clear
  C)
   high retentivity and low coercivity
  done clear
  D)
   low retentivity and high coercivity
  done clear
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• question_answer46)     In an LCR series ac circuit, the voltage across each of the components. L, C and R is 50 V. The voltage across the LC combination will be
  A)
   50V                                      
  done clear
  B)
   \[50\sqrt{2}V\]
  done clear
  C)
   100 V                                   
  done clear
  D)
   0 (zero)
  done clear
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• question_answer47)     In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to
  A)
   4L                                          
  done clear
  B)
   2L
  done clear
  C)
   L/2                                        
  done clear
  D)
   L/4
  done clear
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• question_answer48)     A metal conductor of length 1m rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earths magnetic field is\[0.2\times {{10}^{-4}}T,\]then the emf developed between the two ends of the conductor is
  A)
   \[5\mu V\]                                        
  done clear
  B)
   \[5\mu V\]
  done clear
  C)
   \[5mV\]                             
  done clear
  D)
   \[50\,mV\]
  done clear
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• question_answer49)     The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately
  A)
   540 nm                               
  done clear
  B)
   400 nm
  done clear
  C)
   310 nm                               
  done clear
  D)
   220 nm
  done clear
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• question_answer50)     A charged oil drop is suspended in uniform field of \[3\times {{10}^{4}}V/m\]so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge\[=9.9\times {{10}^{-15}}kg\]and\[=10m/{{s}^{2}}\])
  A)
   \[3.3\times {{10}^{-18}}C\]        
  done clear
  B)
  \[3.2\times {{10}^{-18}}C\]
  done clear
  C)
   \[1.6\times {{10}^{-18}}C\]        
  done clear
  D)
   \[4.8\times {{10}^{-18}}C\]
  done clear
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• question_answer51)     A nucleus disintegrates into two nuclear parts which have their velocities in the ratio\[2:1\]. The ratio of their nuclear sizes will be
  A)
   \[{{2}^{1/3}}:1\]                             
  done clear
  B)
   \[1:{{3}^{1/2}}\]
  done clear
  C)
   \[{{3}^{1/2}}:1\]                             
  done clear
  D)
   \[1:{{2}^{1/3}}\]
  done clear
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• question_answer52)     The binding energy per nucleon of deuteron \[(_{1}^{2}H)\]and helium nucleus\[(_{2}^{4}He)\]is 1.1 MeV and 7 MeV respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is
  A)
   13.9 MeV           
  done clear
  B)
   26.9 MeV
  done clear
  C)
   23.6 MeV           
  done clear
  D)
   19.2 MeV
  done clear
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• question_answer53)     An\[\alpha -\]particle of energy 5 MeV is scattered through\[180{}^\circ \]by a fixed uranium nucleus. The distance of the closest approach is of the order of
  A)
   \[1\overset{o}{\mathop{\text{A}}}\,\]                                
  done clear
  B)
   \[{{10}^{-10}}cm\]
  done clear
  C)
   \[{{10}^{-12}}cm\]                         
  done clear
  D)
   \[{{10}^{-15}}cm\]
  done clear
  View Answer play_arrow

• question_answer54)     When\[npn\]transistor is used as an amplifier
  A)
   electrons move from base to collector
  done clear
  B)
   holes move from emitter to base
  done clear
  C)
   electrons move from collector to base
  done clear
  D)
   holes move from base to emitter
  done clear
  View Answer play_arrow

• question_answer55)     The manifestation of band structure in solids is due to
  A)
   Heisenbergs uncertainty principle
  done clear
  B)
   Faults exclusion principle
  done clear
  C)
   Bohrs correspondence, principle
  done clear
  D)
   Boltzmanns law
  done clear
  View Answer play_arrow

• question_answer56) Which of the following sets of quantum numbers is correct for an electron in 4f orbital?
  A)
   \[n=4,l=3,m=+4,s=+1/2\]
  done clear
  B)
   \[n=4,l=4,m=-4,s=-1/2\]
  done clear
  C)
   \[n=4,\text{ l}=3,m=+1,s=+1/2\]
  done clear
  D)
   \[n=3,l=2,\text{ }m=-2,\text{ s}=+1/2\]
  done clear
  View Answer play_arrow

• question_answer57)     Which one of the following ions has the highest value of ionic radius?
  A)
   \[L{{i}^{+}}\]                                    
  done clear
  B)
   \[{{B}^{3+}}\]
  done clear
  C)
   \[{{O}^{2-}}\]                                   
  done clear
  D)
   \[{{F}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer58)     Which one of the following sets of ions represents the collection of isoelectronic species?
  A)
   \[{{K}^{+}},C{{a}^{2+}},S{{c}^{3+}},C{{l}^{-}}\]
  done clear
  B)
   \[N{{a}^{+}},C{{a}^{2+}},S{{c}^{3+}},{{F}^{-}}\]
  done clear
  C)
   \[{{K}^{+}},C{{l}^{-}},M{{g}^{2+}},S{{c}^{3+}}\]
  done clear
  D)
   \[N{{a}^{+}},M{{g}^{2+}},A{{l}^{3+}},C{{l}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer59)     The bond order in NO is 2.5 while that in\[N{{O}^{+}}\] is 3. Which of the following statements is true for these two species?
  A)
   Bond length in\[N{{O}^{+}}\]is greater than in\[NO\]
  done clear
  B)
   Bond length in\[NO\]is greater than in\[N{{O}^{+}}\]
  done clear
  C)
   Bond length in\[N{{O}^{+}}\]is equal to that in\[NO\]
  done clear
  D)
   Bond length is unpredictable
  done clear
  View Answer play_arrow

• question_answer60)     As the temperature is raised from\[20{}^\circ C\]to\[40{}^\circ C\],the average kinetic energy of neon atoms changes by a factor of which of the following?
  A)
   1/2                                       
  done clear
  B)
   \[\sqrt{313/293}\]
  done clear
  C)
   313/293                              
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer61)     The maximum number of\[90{}^\circ \]angles between bond pair-bond pair of electrons is observed in
  A)
   \[ds{{p}^{3}}\]hybridization
  done clear
  B)
  \[s{{p}^{3}}d\]hybridization
  done clear
  C)
  \[ds{{p}^{2}}\]hybridization
  done clear
  D)
   \[s{{p}^{2}}{{d}^{2}}\]hybridization
  done clear
  View Answer play_arrow

• question_answer62)     Which among the following factors is the most important in making fluorine the strongest oxidizing agent?
  A)
   Electron affinity
  done clear
  B)
   lonization enthalpy
  done clear
  C)
   Hydration enthalpy
  done clear
  D)
   Bond dissociation energy
  done clear
  View Answer play_arrow

• question_answer63)     In van der Waals equation of state of the gas law, the constant V is a measure of
  A)
   intermolecular repulsions
  done clear
  B)
   intermolecular attraction
  done clear
  C)
   volume occupied by the molecules
  done clear
  D)
   intermolecular collisions per unit volume
  done clear
  View Answer play_arrow

• question_answer64)     The conjugate base of\[{{H}_{2}}PO_{4}^{-}\]is
  A)
   \[PO_{4}^{3-}\]                              
  done clear
  B)
   PRs
  done clear
  C)
   \[{{H}_{3}}P{{O}_{4}}\]                                
  done clear
  D)
   \[HPO_{4}^{2-}\]
  done clear
  View Answer play_arrow

• question_answer65)     To neutralise completely 20 mL of 0.1M aqueous solution of phosphorous acid \[({{H}_{3}}P{{O}_{3}}),\]the volume of 0.1M aqueous KOH solution required is
  A)
   10 mL                                  
  done clear
  B)
   20 mL
  done clear
  C)
   40 mL                                  
  done clear
  D)
   60 mL
  done clear
  View Answer play_arrow

• question_answer66)     For which of the following parameters the structural isomers\[{{C}_{2}}{{H}_{5}}OH\]and\[C{{H}_{3}}OC{{H}_{3}}\] would be expected to have the same values? (Assume ideal behaviour)
  A)
   Heat of vaporization
  done clear
  B)
   Vapour pressure at the same temperature
  done clear
  C)
   Boiling points
  done clear
  D)
   Gaseous densities at the same temperature and pressure
  done clear
  View Answer play_arrow

• question_answer67)     Which one of the following statements is false?
  A)
   Raoulfs law states that the vapour pressure of a component over a solution is proportional to its mole fraction
  done clear
  B)
   The osmotic pressure\[(\pi )\]of a solution is given by the equation\[\pi =MRT,\]where M is the molarity of the solution
  done clear
  C)
   The correct order of osmotic pressure for 0.01 M aqueous solution of each compound is \[BaC{{l}_{2}}>KC1>C{{H}_{3}}COOH>sucrose\]
  done clear
  D)
   Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression
  done clear
  View Answer play_arrow

• question_answer68)     An ideal gas expands in volume from \[1\times {{10}^{-3}}{{m}^{3}}\]to\[1\times {{10}^{-2}}{{m}^{3}}\]at 300K against a constant pressure of\[1\times {{10}^{5}}N{{m}^{-2}}\]. The work done is              
  A)
   \[-900J\]                            
  done clear
  B)
   \[-900\text{ }kJ\]
  done clear
  C)
   \[270kJ\]                            
  done clear
  D)
   \[900kJ\]
  done clear
  View Answer play_arrow

• question_answer69)     In a first order reaction, the concentration of the reactant, decreases from 0.8 M to 0.4 M in 15 min. The time taken for the concentration to change from 0.1 M to 0.025 M is
  A)
   30 min                                 
  done clear
  B)
   15 min
  done clear
  C)
   7.5 min                               
  done clear
  D)
   60 min
  done clear
  View Answer play_arrow

• question_answer70)     What is the equilibrium expression for the reaction \[{{P}_{4}}(s)+5{{O}_{2}}(g){{P}_{4}}{{O}_{10}}(s)?\]
  A)
   \[{{K}_{c}}=\frac{[{{P}_{4}}{{O}_{10}}]}{[{{P}_{4}}]{{[{{O}_{2}}]}^{5}}}\]               
  done clear
  B)
   \[{{K}_{c}}=\frac{[{{P}_{4}}{{O}_{10}}]}{5[{{P}_{4}}][{{O}_{2}}]}\]
  done clear
  C)
   \[{{K}_{c}}={{[{{O}_{2}}]}^{5}}\]                              
  done clear
  D)
   \[{{K}_{c}}=\frac{1}{{{[{{O}_{2}}]}^{5}}}\]
  done clear
  View Answer play_arrow

• question_answer71)     The rate equation for the reaction\[2A+B\to C\] is found to be rate\[=k[A]\,[B]\] The correct statement in relation to this reaction is that the
  A)
   unit of k must be \[{{s}^{-1}}\]
  done clear
  B)
   \[{{t}_{1/2}}\]is a constant
  done clear
  C)
   rate of formation of C is twice the rate of, disappearance of A
  done clear
  D)
   value of k is independent of the initial concentrations of A and B
  done clear
  View Answer play_arrow

• question_answer72)     Consider the following\[E{}^\circ \]values \[E_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=+0.77\,V\] \[E_{S{{n}^{2+}}/Sn}^{o}=-0.14\,V\] Under standard conditions the potential for the reaction \[Sn(s)+2F{{e}^{3+}}(aq)\to 2F{{e}^{2+}}(aq)+S{{n}^{2+}}(aq)\]is
  A)
   1.68V                                   
  done clear
  B)
   1.40V
  done clear
  C)
   0.91V                                   
  done clear
  D)
   0.63V
  done clear
  View Answer play_arrow

• question_answer73)     The molar solubility (in\[mol\text{ }{{L}^{-1}}\]) of a sparingly soluble salt\[M\,{{X}_{4}}\]is s. The corresponding solubility product is\[{{K}_{sp}}\]. s is given in terms of. \[{{K}_{sp}}\]by the relation
  A)
   \[s={{({{K}_{sp}}/128)}^{1/4}}\]              
  done clear
  B)
   \[s={{(128{{K}_{sp}})}^{1/4}}\]
  done clear
  C)
   \[s={{(256{{K}_{sp}})}^{1/5}}\]
  done clear
  D)
   \[s={{({{K}_{sp}}/256)}^{1/5}}\]
  done clear
  View Answer play_arrow

• question_answer74)     The standard emf of a cell, involving one electron change is found to be 0.591 V at\[25{}^\circ C\]. The equilibrium constant of the reaction is \[(F=96,500\text{ }C\text{ }mo{{l}^{-1}})\]
  A)
   \[1.0\times {{10}^{1}}\]               
  done clear
  B)
   \[1.0\times {{10}^{5}}\]
  done clear
  C)
   \[1.0\times {{10}^{10}}\]            
  done clear
  D)
  \[1.0\times {{10}^{30}}\]
  done clear
  View Answer play_arrow

• question_answer75)     The enthalpies of combustion of carbon and carbon monoxide are\[-393.5\]and\[-283k\text{ }J\] \[mo{{l}^{-1}}\]respectively. The enthalpy of formation of carbon monoxide per mole is
  A)
   110.5kJ                               
  done clear
  B)
   676.5 kJ
  done clear
  C)
   \[-676.5\text{ }kJ\]        
  done clear
  D)
  \[-110.5kJ\]
  done clear
  View Answer play_arrow

• question_answer76)     The limiting molar conductivities\[a{}^\circ \]for \[NaCl,KBr\]and\[KCl\]are 126, 152 and 150 S \[c{{m}^{2}}mo{{l}^{-1}}\] respectively. The\[a{}^\circ \]for\[NaBr\]is
  A)
  \[128\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\]    
  done clear
  B)
  \[176\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\]
  done clear
  C)
   \[278\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\]   
  done clear
  D)
  \[302\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer77)     Which one of the following statements regarding helium is incorrect?
  A)
   It is used to fill gas balloons instead of hydrogen because   it is lighter and non-inflammable
  done clear
  B)
   It is used as a cryogenic agent for carrying out experiments at low temperatures
  done clear
  C)
   It is used to produce and sustain powerful superconducting magnets
  done clear
  D)
   It is used in gas-cooled nuclear reactors
  done clear
  View Answer play_arrow

• question_answer78)     Identify the correct statement regarding enzymes
  A)
   Enzymes are specific biological catalysts that can normally function at very high temperatures\[(T\sim 1000\text{ }K)\]
  done clear
  B)
   Enzymes are normally heterogeneous catalysts that are very specific in their action
  done clear
  C)
   Enzymes are specific biological catalysts that cannot be poisoned
  done clear
  D)
   Enzymes are specific biological catalysts that possess well defined active sites.
  done clear
  View Answer play_arrow

• question_answer79)     One mole of magnesium nitride on the reaction with an excess of water gives
  A)
   one mole of ammonia
  done clear
  B)
   one mole of nitric acid
  done clear
  C)
   two moles of ammonia
  done clear
  D)
   two moles of nitric acid
  done clear
  View Answer play_arrow

• question_answer80)     Which one of the following ores is best concentrated by froth-floatation method?
  A)
   Magnetite         
  done clear
  B)
   Cassiterite
  done clear
  C)
   Galena                                
  done clear
  D)
   Malachite
  done clear
  View Answer play_arrow

• question_answer81)     Beryllium and aluminium exhibit many properties which are similar. But, the two elements differ in
  A)
   exhibiting maximum covalency in compounds
  done clear
  B)
   forming polymeric hydrides
  done clear
  C)
   forming covalent halides
  done clear
  D)
   exhibiting amphoteric nature in their oxides
  done clear
  View Answer play_arrow

• question_answer82)     Aluminium chloride exists as dimer,\[A{{l}_{2}}C{{l}_{6}}\]in solid state as well as in solution of non-polar solvents such as benzene. When dissolved in water, it gives
  A)
   \[A{{l}^{3+}}+3C{{l}^{-}}\]
  done clear
  B)
   \[{{[Al{{({{H}_{2}}O)}_{6}}]}^{3+}}+3C{{l}^{-}}\]
  done clear
  C)
   \[{{[Al{{(OH)}_{6}}]}^{3-}}+3HCl\]
  done clear
  D)
   \[A{{l}_{2}}{{O}_{3}}+6HCl\]
  done clear
  View Answer play_arrow

• question_answer83)     The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. White metallic tin buttons got converted to grey powder. This transformation is related to
  A)
   a change in the crystalline structure of tin
  done clear
  B)
   an interaction with nitrogen of the air at very low temperatures
  done clear
  C)
   a change in the partial pressure of oxygen in the air
  done clear
  D)
   an interaction  with  water vapour contained in the humid air
  done clear
  View Answer play_arrow

• question_answer84)     Excess of\[KI\]reacts with\[CuS{{O}_{4}}\]solution and then\[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]solution is added to it. Which of the statements is incorrect for this reaction?
  A)
  \[C{{u}_{2}}{{I}_{2}}\]is formed
  done clear
  B)
  \[Cu{{I}_{2}}\]is formed
  done clear
  C)
   \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]is oxidized
  done clear
  D)
   Evolved\[{{I}_{2}}\]is reduced
  done clear
  View Answer play_arrow

• question_answer85)     The co-ordination number of a central metal atom in a complex is determined by
  A)
   the number of ligands around a metal ion bonded by sigma bonds
  done clear
  B)
   the number of ligands around a metal ion bonded by pi-bonds
  done clear
  C)
   the number of ligands around a metal ion bonded by sigma and pi-bonds both
  done clear
  D)
   the number of only anionic ligands bonded to the metal ion
  done clear
  View Answer play_arrow

• question_answer86)     Which one of the following complexes is an outer orbital complex?
  A)
   \[{{[Fe{{(CN)}_{6}}]}^{4-}}\]     
  done clear
  B)
   \[{{[Mn{{(CN)}_{6}}]}^{4-}}\]
  done clear
  C)
   \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]     
  done clear
  D)
   \[{{[Ni{{(N{{H}_{3}})}_{6}}]}^{2+}}\] (Atomic numbers\[Mn=25,\text{ }Fe=26,\text{ }Co=27,\] \[Ni=28\])
  done clear
  View Answer play_arrow

• question_answer87)     Co-ordination   compounds   have   great importance in biological systems. In this context which of the following statements is incorrect?
  A)
   Chlorophylls are green pigments in plants and contain calcium
  done clear
  B)
   Haemoglobin is the red pigment of blood and contains iron
  done clear
  C)
   Cyanocobalamin is vitamin\[{{B}_{12}}\]and contains cobalt
  done clear
  D)
   Carboxypeptidase-A is an enzyme and contains zinc
  done clear
  View Answer play_arrow

• question_answer88)     Cerium\[(Z=58)\]is an important member of the lanthanides. Which of the following statements about cerium is incorrect?
  A)
   The common oxidation states of cerium are +3 and +4
  done clear
  B)
   The +3 oxidation state of cerium is more stable than the +4 oxidation state
  done clear
  C)
   The +4 oxidation state of cerium is not known in solutions
  done clear
  D)
   Cerium (IV) acts as an oxidising agent
  done clear
  View Answer play_arrow

• question_answer89)     The correct order of magnetic moments (spin only values in BM) among the following is
  A)
   \[{{[MnC{{l}_{4}}]}^{2-}}>{{[CoC{{l}_{4}}]}^{2-}}>{{[Fe{{(CN)}_{6}}]}^{4-}}\]
  done clear
  B)
   \[{{[MnC{{l}_{4}}]}^{2-}}>{{[Fe{{(CN)}_{6}}]}^{4-}}>{{[CoC{{l}_{4}}]}^{2-}}\]
  done clear
  C)
   \[{{[Fe{{(CN)}_{6}}]}^{4-}}>{{[MnC{{l}_{4}}]}^{2-}}>{{[CoC{{l}_{4}}]}^{2-}}\]
  done clear
  D)
   \[{{[Fe{{(CN)}_{6}}]}^{4-}}>{{[CoC{{l}_{4}}]}^{2-}}>{{[MnC{{l}_{4}}]}^{2-}}\]
  done clear
  View Answer play_arrow

• question_answer90)     Consider the following nuclear reactions: \[_{92}^{238}M\to _{y}^{x}N+2_{2}^{4}He;_{y}^{x}N\to _{B}^{A}L+2{{\beta }^{+}}\] The number of neutrons in the element L is
  A)
   142                                       
  done clear
  B)
   144
  done clear
  C)
   140                                       
  done clear
  D)
   146
  done clear
  View Answer play_arrow

• question_answer91)     The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound is
  A)
   \[F{{e}_{4}}{{[Fe{{(CN)}_{6}}]}_{3}}\]
  done clear
  B)
   \[N{{a}_{3}}[Fe{{(CN)}_{6}}]\]
  done clear
  C)
   \[Fe{{(CN)}_{3}}\]
  done clear
  D)
   \[N{{a}_{4}}[Fe{{(CN)}_{5}}NOS]\]
  done clear
  View Answer play_arrow

• question_answer92)     The ammonia evolved from the treatment of 0.30g of an organic compound for the estimation of nitrogen was passed in 10s) ml, of M sulphuric acid. The excess of acid required 20 mL of 0.5 M sodium hydroxide solution for complete neutralization. The organic compound is
  A)
   acetamide         
  done clear
  B)
   benzAmide
  done clear
  C)
   urea                                     
  done clear
  D)
   thiourea
  done clear
  View Answer play_arrow

• question_answer93)     Which one of the following has the minimum boiling point?
  A)
   n-butane           
  done clear
  B)
   1-butyne
  done clear
  C)
   1-butene           
  done clear
  D)
   Isobutene
  done clear
  View Answer play_arrow

• question_answer94)     The IUPAC name of the compound is
  A)
   3,3-dimethyl-1-hydroxy cyclohexane
  done clear
  B)
   1,1-dimethyl-3-hydroxy cyclohexane
  done clear
  C)
   3,3-dimethyl-1-cyclohexanol
  done clear
  D)
   1,1-dimethyl-3-cyclohexanol
  done clear
  View Answer play_arrow

• question_answer95)     Which one of the following does not have\[s{{p}^{2}}\]hybridised carbon?
  A)
   Acetone             
  done clear
  B)
   Acetic acid
  done clear
  C)
   Acetonitrile     
  done clear
  D)
   Acetamide
  done clear
  View Answer play_arrow

• question_answer96)     Which of the following will have a meso-isomer also?
  A)
   2-chlorobutane
  done clear
  B)
   2,3-dichlorobufane
  done clear
  C)
   2,3-dichloropentane
  done clear
  D)
   2-hydroxypropanoic acid
  done clear
  View Answer play_arrow

• question_answer97)     Rate of the reaction is fastest when Z is
  A)
   \[Cl\]                                   
  done clear
  B)
   \[N{{H}_{2}}\]
  done clear
  C)
   \[O{{C}_{2}}{{H}_{5}}\]                                
  done clear
  D)
   \[OCOC{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer98)     Amongst the following compounds, the optically active alkane having lowest molecular mass is
  A)
   \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{3}}\]
  done clear
  B)
   \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix}  C{{H}_{3}} \\  | \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{3}}\]
  done clear
  C)
   
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}-C\equiv CH\]
  done clear
  View Answer play_arrow

• question_answer99)     Consider the acidity of the carboxylic acids  \[PhCOOH\]  \[o-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\]  \[p-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\]  \[m-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] Which of the following order is correct?
  A)
   \[I>II>III>IV\]  
  done clear
  B)
   \[II>IV>III>I\]
  done clear
  C)
   \[II>IV>I>III\]  
  done clear
  D)
   \[II>III>IV>I\]
  done clear
  View Answer play_arrow

• question_answer100)     Which of the following is the strongest base?
  A)
                         
  done clear
  B)
   
  done clear
  C)
                         
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer101)     Which base is present in RNA but not in DNA?
  A)
   Uracil                                   
  done clear
  B)
   Cytosine
  done clear
  C)
   Guanine                             
  done clear
  D)
   Thymine
  done clear
  View Answer play_arrow

• question_answer102)     The   compound   formed   on   heating chlorobenzene with chloral in the presence of concentrated sulphuric acid is
  A)
   gammexane     
  done clear
  B)
   DDT
  done clear
  C)
   freon                                   
  done clear
  D)
   hexachloroethane
  done clear
  View Answer play_arrow

• question_answer103)     On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant solution is
  A)
   \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}+NaCl\]
  done clear
  B)
   \[C{{H}_{3}}COONa+{{C}_{2}}{{H}_{5}}OH\]
  done clear
  C)
   \[C{{H}_{3}}COCl+{{C}_{2}}{{H}_{5}}OH+NaOH\]
  done clear
  D)
   \[C{{H}_{3}}Cl+{{C}_{2}}{{H}_{5}}COONa\]
  done clear
  View Answer play_arrow

• question_answer104)     Acetyl bromide reacts with excess of\[C{{H}_{3}}MgI\] followed by treatment with a saturated solution of\[N{{H}_{4}}Cl\]gives
  A)
   acetone
  done clear
  B)
   acetamide
  done clear
  C)
   2-methyl-2-propanol
  done clear
  D)
   acetyl iodide
  done clear
  View Answer play_arrow

• question_answer105)     Which one of the following is reduced with zinc and   hydrochloric   acid   to   give   the corresponding hydrocarbon?
  A)
   Ethyl acetate   
  done clear
  B)
   Acetic acid
  done clear
  C)
   Acetamide        
  done clear
  D)
   Butan-2-one
  done clear
  View Answer play_arrow

• question_answer106)     Which one of the following undergoes reaction with 50% sodium hydroxide solution to give the corresponding alcohol and acid?
  A)
   Phenol                                
  done clear
  B)
   Benzaldehyde
  done clear
  C)
   Butanal                               
  done clear
  D)
   Benzoic acid
  done clear
  View Answer play_arrow

• question_answer107)     Among the following compounds which can be dehydrated very easily?
  A)
   \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}OH\]
  done clear
  B)
   \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix}  OH \\  | \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,CHC{{H}_{3}}\]
  done clear
  C)
   \[C{{H}_{3}}C{{H}_{2}}\overset{\begin{smallmatrix}  OH \\  | \end{smallmatrix}}{\mathop{\underset{\begin{smallmatrix}  | \\  OH \end{smallmatrix}}{\mathop{C}}\,}}\,C{{H}_{2}}C{{H}_{3}}\]
  done clear
  D)
   \[C{{H}_{3}}C{{H}_{2}}\underset{\begin{smallmatrix}  | \\  C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,C{{H}_{2}}C{{H}_{2}}OH\]
  done clear
  View Answer play_arrow

• question_answer108)     Which of the following compounds is not chiral?
  A)
   1-chloropentane
  done clear
  B)
   2-chloropentane
  done clear
  C)
   1-chloro-2-methyl pentane
  done clear
  D)
   3-chloro-2-methyl pentane
  done clear
  View Answer play_arrow

• question_answer109)     Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories?
  A)
   A co-enzyme   
  done clear
  B)
   A hormone
  done clear
  C)
   An enzyme       
  done clear
  D)
   An antibiotic
  done clear
  View Answer play_arrow

• question_answer110)     The smog is essentially caused by the presence of
  A)
   \[{{O}_{2}}\]and \[{{O}_{3}}\]
  done clear
  B)
   \[{{O}_{2}}\]and \[{{N}_{2}}\]
  done clear
  C)
   oxides of sulphur and nitrogen
  done clear
  D)
   \[{{O}_{3}}\]and\[{{N}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer111) Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set\[A=\{1,2,3,4\}\]. The 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_answer112)     The range of the function\[f(x){{=}^{7-x}}{{P}_{x-3}}\]is
  A)
   \[\{1,\text{ }2,\text{ }3\}\]                        
  done clear
  B)
  \[\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6\}\]
  done clear
  C)
   \[\{1,2,3,4\}\]                                  
  done clear
  D)
  \[\{1,\,\,2,\,\,3,\,\,4,\,\,5\}\]
  done clear
  View Answer play_arrow

• question_answer113)     Let\[z,w\]be complex numbers such that \[\overline{z}+i\overline{w}=0\]and arg\[zw=\pi \]Then arg z equals:
  A)
   \[\frac{\pi }{4}\]                             
  done clear
  B)
   \[\frac{\pi }{2}\]
  done clear
  C)
   \[\frac{3\pi }{4}\]                                           
  done clear
  D)
   \[\frac{5\pi }{4}\]
  done clear
  View Answer play_arrow

• question_answer114)     If\[z=x-iy\]and\[{{z}^{1/3}}=p-iq,\]then\[{\left( \frac{x}{p}+\frac{y}{p} \right)}/{({{p}^{2}}+{{q}^{2}})}\;\]is equal to
  A)
   1                                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   2                                            
  done clear
  D)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer115)     If\[|{{z}^{2}}-1|=|z{{|}^{2}}+1,\]then z lies on
  A)
   the real axis      
  done clear
  B)
   the imaginary axis
  done clear
  C)
   a circle                                
  done clear
  D)
   an ellipse
  done clear
  View Answer play_arrow

• question_answer116)     Let\[A=\left[ \begin{matrix}    0 & 0 & -1  \\    0 & -1 & 0  \\    -1 & 0 & 0  \\ \end{matrix} \right]\].The only correct statement about the matrix A is
  A)
   A is a zero matrix
  done clear
  B)
  \[A=(-1),I\]where I is a unit matrix
  done clear
  C)
  \[{{A}^{-1}}\]does not exist
  done clear
  D)
   \[{{A}^{2}}=I\]
  done clear
  View Answer play_arrow

• question_answer117)     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 a is
  A)
   \[-2\]                                   
  done clear
  B)
   1
  done clear
  C)
   2                                            
  done clear
  D)
   5
  done clear
  View Answer play_arrow

• question_answer118)     If\[a,{{a}_{2}},{{a}_{3}},........{{a}_{n}},....\]are in GP, then the value of the determinant\[\left| \begin{matrix}    \log {{a}_{n}} & \log {{a}_{n+1}} & \log {{a}_{n+2}}  \\    \log {{a}_{n+3}} & \log {{a}_{n+4}} & \log {{a}_{n+5}}  \\    \log {{a}_{n+6}} & \log {{a}_{n+7}} & \log {{a}_{n+8}}  \\ \end{matrix} \right|,\]is
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   2                                            
  done clear
  D)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer119)     Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic 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_answer120)     If\[(1-p)\]is a root of quadratic equation \[{{x}^{2}}+px+(1-p)=0,\]then its roots are
  A)
   0, 1                                       
  done clear
  B)
   \[-1,1\]
  done clear
  C)
   0,-1                                      
  done clear
  D)
   \[-1,2\]
  done clear
  View Answer play_arrow

• question_answer121)     How many ways are there to arrange the letters in the Word GARDEN with the vowels in alphabetical order?
  A)
   120                                       
  done clear
  B)
   240
  done clear
  C)
   360                                       
  done clear
  D)
   480
  done clear
  View Answer play_arrow

• question_answer122)     The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty, is
  A)
   5                                            
  done clear
  B)
  \[-21\]
  done clear
  C)
   \[{{3}^{8}}\]                                     
  done clear
  D)
  \[^{8}{{C}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer123)     If one root of the equation\[{{x}^{2}}+px+12=0\]is 4, while the equation\[{{x}^{2}}+px+q=0\]has equal roots, then the value of q is
  A)
   \[\frac{49}{4}\]                               
  done clear
  B)
   12
  done clear
  C)
   3                                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer124)     The coefficient of the middle term in the binomial expansion in powers of\[x\]of\[{{(1+ax)}^{4}}\] and of\[{{(1-ax)}^{6}}\]is the same, if a equals:
  A)
   \[-\frac{5}{3}\]                                
  done clear
  B)
   \[\frac{10}{3}\]
  done clear
  C)
   \[-\frac{3}{10}\]                              
  done clear
  D)
   \[\frac{3}{5}\]                 The coefficient of\[x\]in the middle term of expansion of\[{{(1+\alpha x)}^{4}}{{=}^{4}}{{C}_{2}}.{{\alpha }^{2}}\] The coefficient of x in the middle term of the expansion of\[{{(1-\alpha x)}^{6}}{{=}^{6}}{{C}_{3}}{{(-\alpha )}^{3}}\] According to question, \[^{4}{{C}_{2}}{{\alpha }^{2}}{{=}^{6}}{{C}_{3}}{{(-\alpha )}^{3}}\] \[\Rightarrow \]               \[\frac{4!}{2!2!}{{\alpha }^{2}}=-\frac{6!}{3!3!}{{\alpha }^{3}}\] \[\Rightarrow \]               \[6{{\alpha }^{2}}=-20{{\alpha }^{3}}\] \[\Rightarrow \]               \[\alpha =-\frac{6}{20}\] \[\Rightarrow \]               \[\alpha =-\frac{3}{10}\]
  done clear
  View Answer play_arrow

• question_answer125)     The coefficient of\[{{x}^{n}}\]in expansion of \[(1+x){{(1-x)}^{n}}\]is
  A)
   \[(n-1)\]                             
  done clear
  B)
   \[{{(-1)}^{n}}(1-n)\]
  done clear
  C)
   \[{{(-1)}^{n-1}}{{(n-1)}^{2}}\]   
  done clear
  D)
   \[{{(-1)}^{n-1}}n\]
  done clear
  View Answer play_arrow

• question_answer126)     If\[{{s}_{n}}=\sum\limits_{r=0}^{n}{\frac{1}{^{n}{{C}_{r}}}}\]and\[{{t}_{n}}=\sum\limits_{r=0}^{n}{\frac{r}{^{n}{{C}_{r}}}},\]then\[\frac{{{t}_{n}}}{{{s}_{n}}}\]is equal to
  A)
   \[\frac{n}{2}\]                                 
  done clear
  B)
   \[\frac{n}{2}-1\]
  done clear
  C)
   \[n-1\]                                
  done clear
  D)
   \[\frac{2n-1}{2}\]
  done clear
  View Answer play_arrow

• question_answer127)     Let\[{{T}_{r}}\]be the rth term of an A P whose first term is a and common difference is d. If for some positive  integers\[m,n,m\ne n,{{T}_{m}}=\frac{1}{n}\]and \[{{T}_{n}}=\frac{1}{m},\]then\[a-d\]equals
  A)
   \[0\]                                    
  done clear
  B)
   \[1\]
  done clear
  C)
   \[\frac{1}{mn}\]                             
  done clear
  D)
   \[\frac{1}{m}+\frac{1}{n}\]
  done clear
  View Answer play_arrow

• question_answer128)     The sum of the first n terms of the series\[{{1}^{2}}+{{2.2}^{2}}+{{3}^{2}}+{{2.4}^{2}}+{{5}^{2}}+{{2.6}^{2}}+...\]is \[\frac{n{{(n+1)}^{2}}}{2}\]when n is even. When n is odd the sum is
  A)
   \[\frac{3n(n+1)}{2}\]                    
  done clear
  B)
   \[\frac{{{n}^{2}}(n+1)}{2}\]
  done clear
  C)
   \[\frac{n{{(n+1)}^{2}}}{4}\]                       
  done clear
  D)
   \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer129)     The sum of series\[\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+...\]is
  A)
   \[\frac{({{e}^{2}}-1)}{2}\]
  done clear
  B)
   \[\frac{{{(e-1)}^{2}}}{2e}\]
  done clear
  C)
   \[\frac{({{e}^{2}}-1)}{2e}\]                        
  done clear
  D)
   \[\frac{({{e}^{2}}-2)}{e}\]
  done clear
  View Answer play_arrow

• question_answer130)     Let\[\alpha ,\beta \]be such that\[\pi <\alpha -\beta <3\pi \]. If \[\sin \alpha +\sin \beta =-\frac{21}{65}\]and \[\cos \alpha +\cos \beta =-\frac{27}{65},\]then the value of\[\cos \frac{\alpha -\beta }{2}\]is
  A)
   \[-\frac{3}{\sqrt{130}}\]                              
  done clear
  B)
   \[\frac{3}{\sqrt{130}}\]
  done clear
  C)
   \[\frac{6}{65}\]                               
  done clear
  D)
   \[-\frac{6}{65}\]
  done clear
  View Answer play_arrow

• question_answer131)     If\[u=\sqrt{{{a}^{2}}{{\cos }^{2}}\theta +{{b}^{2}}{{\sin }^{2}}\theta }\]\[+\sqrt{{{a}^{2}}{{\sin }^{2}}\theta +{{b}^{2}}{{\cos }^{2}}\theta },\]then the difference between the maximum and minimum values of\[{{u}^{2}}\]is given by
  A)
   \[2({{a}^{2}}+{{b}^{2}})\]                           
  done clear
  B)
   \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\]
  done clear
  C)
   \[{{(a+b)}^{2}}\]                             
  done clear
  D)
   \[{{(a-b)}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer132)     The sides of a triangle are\[\sin \alpha ,\cos \alpha \]and\[\sqrt{1+\sin \alpha \cos \alpha }\]for some\[0<\alpha <\frac{\pi }{2}\]. Then the greatest angle of the triangle is
  A)
   \[60{}^\circ \]                                  
  done clear
  B)
   \[90{}^\circ \]
  done clear
  C)
   \[120{}^\circ \]                
  done clear
  D)
   \[150{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer133)     If\[f:R\to S,\]defined by \[f(x)=\sin x-\sqrt{3}\cos x+1,\]is onto , then the interval of S is
  A)
   [0, 3]                                    
  done clear
  B)
   \[[-1,\text{ }1]\]
  done clear
  C)
   [0, 1]                                    
  done clear
  D)
   \[[-1,\text{ }3]\]
  done clear
  View Answer play_arrow

• question_answer134)     The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\]
  A)
   [2, 3]                                    
  done clear
  B)
   [2, 3)
  done clear
  C)
   [1, 2]                                    
  done clear
  D)
   [1, 2)
  done clear
  View Answer play_arrow

• question_answer135)     if\[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{a}{x}+\frac{b}{{{x}^{2}}} \right)}^{2x}}={{e}^{2}},\]then the values of a and b are
  A)
   \[a\in R,b\in R\]
  done clear
  B)
   \[a=1,b\in R\]
  done clear
  C)
   \[a\in R,b=2\]
  done clear
  D)
   \[a=1,b=2\]
  done clear
  View Answer play_arrow

• question_answer136)     Let \[f(x)=\frac{1-\tan x}{4x-n},x\ne \frac{\pi }{4},x\in \left[ 0,\frac{\pi }{2} \right]\]. If  \[f(x)\]is continuous in\[\left[ 0,\frac{\pi }{2} \right],\]then\[f\left( \frac{\pi }{4} \right)\]is
  A)
   1                                            
  done clear
  B)
   \[1/2\]
  done clear
  C)
   \[-1/2\]                              
  done clear
  D)
   \[-1\]
  done clear
  View Answer play_arrow

• question_answer137)     If\[x={{e}^{y+{{e}^{y+......to\,\infty }}}},x>0,\]the\[\frac{dy}{dx}\]is
  A)
   \[\frac{x}{1+x}\]                             
  done clear
  B)
   \[\frac{1}{x}\]
  done clear
  C)
   \[\frac{1-x}{x}\]
  done clear
  D)
   \[\frac{1+x}{x}\]
  done clear
  View Answer play_arrow

• question_answer138)     A point on the parabola\[{{y}^{2}}=18x\]at which the ordinate increases at twice the rate of the abscissa, is
  A)
   \[(2,\,4)\]                          
  done clear
  B)
   \[(2,\,-4)\]
  done clear
  C)
   \[\left( -\frac{9}{8},\frac{9}{2} \right)\]                
  done clear
  D)
   \[\left( \frac{9}{8},\frac{9}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer139)     A function\[y=f(x)\]as a second order derivative\[f=6(x-1)\]. If its graph passes through the point (2, 1) and at that point the tangent to the graph is\[y=3x-5,\]then the function is
  A)
   \[{{(x-1)}^{2}}\]                              
  done clear
  B)
   \[{{(x-1)}^{3}}\]
  done clear
  C)
   \[{{(x+1)}^{3}}\]                             
  done clear
  D)
   \[{{(x+1)}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer140)     The normal to the curve\[x=a(1+cos\theta \text{)},\] \[y=a\sin \theta \]at\[\theta \]always passes through the fixed point
  A)
   \[(a,\text{ }0)\]               
  done clear
  B)
  \[(0,\text{ }a)\]
  done clear
  C)
   (0, 0)                                    
  done clear
  D)
  \[(a,\text{ }a)\]
  done clear
  View Answer play_arrow

• question_answer141)     If\[2a+3b+6c=0,\] then at least one root of the equation\[a{{x}^{2}}+bx+c=0\]lies in the interval
  A)
   (0, 1)
  done clear
  B)
   (1, 2)
  done clear
  C)
   (2, 3)                                    
  done clear
  D)
   (1, 3)
  done clear
  View Answer play_arrow

• question_answer142)     \[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{\frac{1}{n}{{e}^{r/n}}}\]is
  A)
   \[e\]                                    
  done clear
  B)
   \[e-1\]
  done clear
  C)
   \[1-e\]                                
  done clear
  D)
   \[e+1\]
  done clear
  View Answer play_arrow

• question_answer143)     If \[\int{\frac{\sin x}{\sin (x-\alpha )}}dx=Ax+B\log \sin (x-\alpha )+c,\] then value of (A, B) is
  A)
   \[(\sin \alpha ,\cos \alpha )\]    
  done clear
  B)
   \[(\cos \alpha ,\sin \alpha )\]
  done clear
  C)
   \[(-\sin \alpha ,\cos \alpha )\]  
  done clear
  D)
   \[(-\cos \alpha ,\sin \alpha )\]
  done clear
  View Answer play_arrow

• question_answer144)     \[\int{\frac{dx}{\cos x-\sin x}}\]is equal to
  A)
   \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{\pi }{8} \right) \right|+c\]
  done clear
  B)
   \[\frac{1}{\sqrt{2}}\log \left| cot\left( \frac{x}{2} \right) \right|+c\]
  done clear
  C)
   \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}-\frac{3\pi }{8} \right) \right|+c\]
  done clear
  D)
   \[\frac{1}{\sqrt{2}}\log \left| \tan \left( \frac{x}{2}+\frac{3\pi }{8} \right) \right|+c\]
  done clear
  View Answer play_arrow

• question_answer145)     The value of\[\int_{-2}^{3}{|1-{{x}^{2}}|dx}\]is
  A)
   \[\frac{28}{3}\]                               
  done clear
  B)
   \[\frac{14}{3}\]
  done clear
  C)
   \[\frac{7}{3}\]                                  
  done clear
  D)
   \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer146)     The value of\[\int_{0}^{\pi /2}{\frac{{{(\sin x+\cos x)}^{2}}}{\sqrt{1+\sin 2x}}}dx\]is
  A)
   0                                            
  done clear
  B)
   1
  done clear
  C)
   2                                            
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer147)     If\[\int_{0}^{\pi }{xf(\sin x)}dx=A\int_{0}^{\pi /2}{f(\sin x)dx,}\]then A is equal to
  A)
   0                                            
  done clear
  B)
   \[\pi \]
  done clear
  C)
   \[\frac{\pi }{4}\]                                             
  done clear
  D)
   \[2\pi \]
  done clear
  View Answer play_arrow

• question_answer148)     The area of the region bounded by the curves \[y=|x-2|,x=1,x=3\]the\[x-\]axis is
  A)
   1           
  done clear
  B)
   2
  done clear
  C)
   3                                            
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer149)     The differential equation for the family of curves\[{{x}^{2}}+{{y}^{2}}-2ay=0,\]where a is an arbitrary constant, is
  A)
   \[2({{x}^{2}}-{{y}^{2}})y=xy\]
  done clear
  B)
   \[2({{x}^{2}}+{{y}^{2}})y=xy\]
  done clear
  C)
   \[({{x}^{2}}-{{y}^{2}})y=2xy\]
  done clear
  D)
   \[({{x}^{2}}+{{y}^{2}})y=2xy\]
  done clear
  View Answer play_arrow

• question_answer150)     The solution of the differential equation\[y\,dx+(x+{{x}^{2}}y)dy=0\]is
  A)
   \[-\frac{1}{xy}=c\]                         
  done clear
  B)
   \[-\frac{1}{xy}+\log y=c\]
  done clear
  C)
   \[\frac{1}{xy}+\log y=c\]             
  done clear
  D)
   \[\log y=cx\]
  done clear
  View Answer play_arrow

• question_answer151)     Let\[A(2,-3)\]and\[B(-2,1)\]be vertices of a triangle ABC. If the centroid of this triangle moves on the line\[2x+3y=1,\]then the locus of the vertex C is the line:
  A)
   \[2x+3y=9\]      
  done clear
  B)
   \[2x-3y=7\]
  done clear
  C)
   \[3x+2y=5\]      
  done clear
  D)
   \[3x-2y=3\]
  done clear
  View Answer play_arrow

• question_answer152)     The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is\[-1,\]is
  A)
   \[\frac{x}{2}+\frac{y}{3}=-1\]and\[\frac{x}{-2}+\frac{y}{1}=-1\]
  done clear
  B)
   \[\frac{x}{2}-\frac{y}{3}=-1\]and\[\frac{x}{-2}+\frac{y}{1}=-1\]
  done clear
  C)
   \[\frac{x}{2}+\frac{y}{3}=1\]and\[\frac{x}{-2}+\frac{y}{1}=1\]
  done clear
  D)
   \[\frac{x}{2}-\frac{y}{3}=1\]and\[\frac{x}{-2}+\frac{y}{1}=1\]
  done clear
  View Answer play_arrow

• question_answer153)     If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\]is four times their product, then c has the value
  A)
   1                                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   2                                            
  done clear
  D)
   \[-2\]
  done clear
  View Answer play_arrow

• question_answer154)     If one of the lines given by\[6{{x}^{2}}-xy+4c{{y}^{2}}=0\] is\[3x+4y=0,\]then c equals:
  A)
   1                                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   3                                            
  done clear
  D)
   \[-3\]
  done clear
  View Answer play_arrow

• question_answer155)     If a circle passes through the point (a, b) and cuts the circle\[{{x}^{2}}+{{y}^{2}}=4\]orthogonally, then, the locus of its centre is
  A)
   \[2ax+2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
  done clear
  B)
   \[2ax+2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
  done clear
  C)
   \[2ax-2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
  done clear
  D)
   \[2ax-2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
  done clear
  View Answer play_arrow

• question_answer156)     If the lines\[2x+3y+1=0\]and\[3x-y-4=0\] lie along diameters of a circle of circumference\[10\pi ,\]then the equation of the circle is
  A)
   \[{{x}^{2}}+{{y}^{2}}-2x+2y-23=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}-2x-2y-23=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+2x+2y-23=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}+2x-2y-23=0\]
  done clear
  View Answer play_arrow

• question_answer157)     The intercept on the line\[y=x\]by the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\]is AB, Equation of the circle on AB as a diameter is
  A)
   \[{{x}^{2}}+{{y}^{2}}-x-y=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}-x+y=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}+x+y=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}+x-y=0\]
  done clear
  View Answer play_arrow

• question_answer158)     If\[a\ne 0\]and the line\[2bx+3cy+4d=0\]passes through the points of intersection of the parabolas\[{{y}^{2}}=4ax\]and\[{{x}^{2}}=4ay,\]then
  A)
   \[{{d}^{2}}+{{(2b+3c)}^{2}}=0\]
  done clear
  B)
   \[{{d}^{2}}+{{(3b+2c)}^{2}}=0\]
  done clear
  C)
   \[{{d}^{2}}+{{(2b-3c)}^{2}}=0\]
  done clear
  D)
   \[{{d}^{2}}+{{(3b-2c)}^{2}}=0\]
  done clear
  View Answer play_arrow

• question_answer159)     The eccentricity of an ellipse with its centre at the origin, is\[\frac{1}{2}\]. If one of the directrices is \[x=4,\]then the equation of the elapse is:
  A)
   \[3{{x}^{2}}+4{{y}^{2}}=1\]        
  done clear
  B)
   \[3{{x}^{2}}+4{{y}^{2}}=12\]
  done clear
  C)
   \[4{{x}^{2}}+3{{y}^{2}}=12\]     
  done clear
  D)
   \[4{{x}^{2}}+3{{y}^{2}}=1\]
  done clear
  View Answer play_arrow

• question_answer160)     A line makes the same angle. 9 with each of the\[x\]and z axis. If the angle P, which it makes with y-axis, is such that\[si{{n}^{2}}\beta =3\text{ }si{{n}^{2}}\theta ,\]then\[{{\cos }^{2}}\theta \]equals
  A)
   \[\frac{2}{3}\]                                  
  done clear
  B)
   \[\frac{1}{5}\]
  done clear
  C)
   \[\frac{3}{5}\]                                  
  done clear
  D)
   \[\frac{2}{5}\]
  done clear
  View Answer play_arrow

• question_answer161)     Distance between two parallel planes \[2x+y+2z=8\]and\[4x+2y+4z+5=0\]is
  A)
   \[\frac{3}{2}\]              
  done clear
  B)
   \[\frac{5}{2}\]
  done clear
  C)
   \[\frac{7}{2}\]                                  
  done clear
  D)
   \[\frac{9}{2}\]
  done clear
  View Answer play_arrow

• question_answer162)     A line with direction cosines proportional to 2,1, 2 meets each of the lines\[x=y+a=z\]and \[x+a=2y=2z\]. The co-ordinates of each of the points of intersection are given by
  A)
   \[(3a,3a,3a)(a,a,a)\]
  done clear
  B)
   \[(3a,2a,3a)(a,a,a)\]
  done clear
  C)
   \[(3a,2a,3a)(a,a,2a)\]
  done clear
  D)
   \[(2a,3a,3a)(2a,a,a)\]
  done clear
  View Answer play_arrow

• question_answer163)     If the straight lines\[x=1+s,y=-3-\lambda s,\]\[z=1+\lambda s\]and\[x=\frac{t}{2},y=1+t,z=2-t,\]with parameters s and t respectively, are co-planar, then\[\lambda \]equals
  A)
   \[-2\]                                   
  done clear
  B)
   \[-1\]
  done clear
  C)
   \[-\frac{1}{2}\]                                
  done clear
  D)
   \[0\]
  done clear
  View Answer play_arrow

• question_answer164)     Let\[\overrightarrow{a},\overrightarrow{d}\]and\[\overrightarrow{c}\]be three non-zero vectors such that no two of these are collinear. If the vector\[\overrightarrow{a}+2\overrightarrow{b}\]is collinear with\[\overrightarrow{c}\]and\[\overrightarrow{b}+3\overrightarrow{c}\]is collinear with\[\overrightarrow{a}\] (\[\lambda \]being some non-zero scalar), then\[\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}\]equals
  A)
   \[\lambda \overrightarrow{a}\]                              
  done clear
  B)
   \[\lambda \overrightarrow{b}\]
  done clear
  C)
   \[\lambda \overrightarrow{c}\]                               
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer165)     A particle is acted upon by constant forces\[4\hat{i}+\hat{j}-3\hat{k}\] and\[3\hat{i}+\hat{j}-\hat{k}\] which displace it from a point\[\hat{i}+2\hat{j}+3\hat{k}\]to the point\[5\hat{i}+4\hat{j}+\hat{k}\]. The work done in standard units by the forces is given by
  A)
   40                                         
  done clear
  B)
   30
  done clear
  C)
   25                                         
  done clear
  D)
   15
  done clear
  View Answer play_arrow

• question_answer166)     If\[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\]are non-coplanar vectors and\[\lambda \]is a real number, then the vectors\[\overrightarrow{a}+2\overrightarrow{b}+3\overrightarrow{c},\]and\[\lambda \overrightarrow{b}+4\overrightarrow{c}\]and\[(2\lambda -1)\overrightarrow{c}\]are non-coplanar for
  A)
   all values of k
  done clear
  B)
   all except one value of k
  done clear
  C)
   all except two values of X
  done clear
  D)
   no value of k
  done clear
  View Answer play_arrow

• question_answer167)     Let\[\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}\]be such that\[|\overrightarrow{u}|=1,|\overrightarrow{v}|=2,\]\[|\overrightarrow{w}|=3.\] If the projection\[\overrightarrow{v}\]long\[\overrightarrow{u}\]is equal to that of\[\overrightarrow{w}\] along\[\overrightarrow{u}\]and\[\overrightarrow{v},\overrightarrow{w}\]are perpendicular to each other, then\[|\overrightarrow{u}-\overrightarrow{v}+\overrightarrow{w}|\]equals:
  A)
   2                                            
  done clear
  B)
   \[\sqrt{7}\]
  done clear
  C)
   \[\sqrt{14}\]                                     
  done clear
  D)
   14
  done clear
  View Answer play_arrow

• question_answer168)     The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
  A)
   \[\frac{37}{256}\]                           
  done clear
  B)
   \[\frac{219}{256}\]
  done clear
  C)
   \[\frac{128}{256}\]                                        
  done clear
  D)
   \[\frac{28}{256}\]
  done clear
  View Answer play_arrow

• question_answer169)     With two forces acting at a point, the maximum effect is obtained when their resultant is 4N. If they act at right angles, then their resultant is 3N. Then the forces are
  A)
   \[(2+\sqrt{2})N\]and\[(2-\sqrt{2})N\]
  done clear
  B)
   \[(2+\sqrt{3})N\]and\[(2-\sqrt{3})N\]
  done clear
  C)
   \[\left( 2+\frac{1}{2}\sqrt{2} \right)N\]and\[\left( 2-\frac{1}{2}\sqrt{2} \right)N\]
  done clear
  D)
   \[\left( 2+\frac{1}{2}\sqrt{3} \right)N\]and\[\left( 2-\frac{1}{2}\sqrt{3} \right)N\]
  done clear
  View Answer play_arrow

• question_answer170)     In a right angle\[\Delta ABC,\text{ }\angle A=90{}^\circ \]and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force F has moments 0, 9 and 16 in N cm unit respectively about vertices A, B and C, the magnitude of F is
  A)
   3                                            
  done clear
  B)
   4
  done clear
  C)
   5                                            
  done clear
  D)
   9
  done clear
  View Answer play_arrow