Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2015

done J and K - CET Engineering Solved Paper-2015 Total Questions - 180

• question_answer1) Conductivity of semiconductors             
  A)
   is maximum at 0 K
  done clear
  B)
   Decreases with increase in temperature
  done clear
  C)
   Increases with increase in temperature
  done clear
  D)
   is maximum at 300 K
  done clear
  View Answer play_arrow

• question_answer2) Two copper spheres having same radii, one solid and other hollow, are charged to the same potential. Which of the following statements is correct?
  A)
   Hollow sphere will hold more charge
  done clear
  B)
   Solid sphere will hold more charge
  done clear
  C)
   Solid sphere will have uniform volume charge density
  done clear
  D)
   Both spheres will hold same charge-
  done clear
  View Answer play_arrow

• question_answer3) Two pendula oscillate with a constant phase difference of \[{{45}^{o}}\] and same amplitude. If the maximum velocity of one of them is v and that of other is \['v+x',\] then the value of Y will be
  A)
   \[0\]       
  done clear
  B)
  \[v/2\]
  done clear
  C)
  \[v/\sqrt{2}\]
  done clear
  D)
  \[(\sqrt{2})v\]
  done clear
  View Answer play_arrow

• question_answer4) An observer standing near the sea-coast counts 48 waves per min. If the wavelength of the wave is \[10\text{ }m,\] the velocity of the waves will be
  A)
  \[8\,\,m/s\]             
  done clear
  B)
  \[12\,\,m/s\]
  done clear
  C)
  \[16\,\,m/s\]            
  done clear
  D)
  \[20\,\,m/s\]
  done clear
  View Answer play_arrow

• question_answer5) The carbon resistor has the color band sequence of green, orange, blue and silver. The value of resistance will be
  A)
  \[64\times {{10}^{7}}\pm 20%\,\,\Omega \]
  done clear
  B)
  \[53\times {{10}^{6}}\pm 20%\,\,\Omega \]
  done clear
  C)
  \[64\times {{10}^{7}}\pm 10%\,\,\Omega \]
  done clear
  D)
  \[53\times {{10}^{6}}\pm 10%\,\,\Omega \]
  done clear
  View Answer play_arrow

• question_answer6) A parallel narrow-beam of light is falling normally on a glass sphere. It will come to a focus
  A)
   Inside the sphere (except at its centre)
  done clear
  B)
   On the surface of the sphere
  done clear
  C)
   Outside the sphere
  done clear
  D)
   Exactly at the centre of the sphere
  done clear
  View Answer play_arrow

• question_answer7) Which of the following is NOT an electromagnetic wave?
  A)
   Sound wave       
  done clear
  B)
   Thermal radiation
  done clear
  C)
   Microwave        
  done clear
  D)
   Gamma ray
  done clear
  View Answer play_arrow

• question_answer8) The ratio of mass defect of the nucleus to its mass number is maximum for
  A)
  \[{{U}^{238}}\]    
  done clear
  B)
  \[{{N}^{14}}\]   
  done clear
  C)
  \[S{{i}^{28}}\]    
  done clear
  D)
  \[F{{e}^{56}}\]
  done clear
  View Answer play_arrow

• question_answer9) Assuming density d of a planet to be uniform, we can say that the time period of its artificial satellite is proportional to
  A)
   \[d\]      
  done clear
  B)
  \[\sqrt{d}\]
  done clear
  C)
  \[1/\sqrt{d}\]   
  done clear
  D)
  \[1/d\]
  done clear
  View Answer play_arrow

• question_answer10) An ideal gas is heated at constant volume until its pressure doubles. Which one of the following statements is correct?
  A)
   The mean speed of the molecules doubles
  done clear
  B)
   Root mean square speed of the molecules doubles
  done clear
  C)
   Mean square speed of the molecules doubles
  done clear
  D)
   Mean square speed of the molecules remains unchanged
  done clear
  View Answer play_arrow

• question_answer11) In a cyclic process, the change in the internal energy of a system over one complete cycle
  A)
   Depends on the path
  done clear
  B)
   is always negative
  done clear
  C)
   Is always zero
  done clear
  D)
   is always positive
  done clear
  View Answer play_arrow

• question_answer12) In a transformer the number of primary turns is four times that of the secondary turns. Its primary is connected to an AC source of voltage V. Then,
  A)
   Current through its secondary is about four times that of the current through its primary
  done clear
  B)
   Voltage across its secondary is about four times that of the voltage across its primary            
  done clear
  C)
   Voltage across its secondary is about two times that of the voltage across its primary
  done clear
  D)
   Voltage across its secondary is about times that of the voltage across its primary
  done clear
  View Answer play_arrow

• question_answer13) The path of a charge particle after it enters a region of a uniform electrostatic field with velocity perpendicular to the field will be
  A)
   Straight line          
  done clear
  B)
   Circular
  done clear
  C)
   Helical               
  done clear
  D)
   Parabolic
  done clear
  View Answer play_arrow

• question_answer14) The dimension of magnetic flux is
  A)
   \[[ML{{T}^{-1}}{{A}^{-1}}]\]
  done clear
  B)
   \[[M{{L}^{-1}}T{{A}^{-2}}]\]
  done clear
  C)
   \[[M{{L}^{-2}}{{T}^{2}}{{A}^{-2}}]\]   
  done clear
  D)
   \[[M{{L}^{2}}{{T}^{-2}}{{A}^{-1}}]\]
  done clear
  View Answer play_arrow

• question_answer15) A ball is dropped from the top of \[80\text{ }m\]high tower. If after 2 s of fall the gravity \[(g=10\,m/{{s}^{2}})\] disappears, then time taken to reach the ground since the gravity disappeared is
  A)
  \[2\,s\]              
  done clear
  B)
  \[3\,s\]
  done clear
  C)
  \[4\,s\]              
  done clear
  D)
  \[5\,s\]
  done clear
  View Answer play_arrow

• question_answer16) Which of the following is correct statement about the magnitude of the acceleration 'a' of the particle executing simple harmonic motion?
  A)
   A will be maximum at the equilibrium position
  done clear
  B)
   A will be maximum at the extreme position
  done clear
  C)
   A will be always constant
  done clear
  D)
   A will always be zero
  done clear
  View Answer play_arrow

• question_answer17) A concave mirror has focal length f. A convergent beam of light is made incident on it. Then the image distance v is
  A)
   Zero             
  done clear
  B)
   less than T
  done clear
  C)
   Equal to T        
  done clear
  D)
   more than T
  done clear
  View Answer play_arrow

• question_answer18) In an n-p-n transistor, 'p' is
  A)
   Intrinsic semiconductor
  done clear
  B)
   Emitter
  done clear
  C)
   Collector
  done clear
  D)
   Base
  done clear
  View Answer play_arrow

• question_answer19) In the fringe pattern of a Young's double slit experiment the ratio of intensities of maxima and minima is\[25:9\]. Then, the ratio of the amplitudes of interfering waves is
  A)
  \[4:1\]             
  done clear
  B)
  \[5:3\]
  done clear
  C)
  \[4:3\]             
  done clear
  D)
  \[25:9\]
  done clear
  View Answer play_arrow

• question_answer20) Consider a ray of light travelling from a denser to a rarer medium. If it is incident at the critical angle then
  A)
   it will emerge out into the rarer medium
  done clear
  B)
   it will undergo total internal reflection
  done clear
  C)
   it will travel along the interface separating the two media
  done clear
  D)
   it will retrace its path
  done clear
  View Answer play_arrow

• question_answer21) Radius of Earth is \[6400\text{ }km\]and that of Mars is \[3200\text{ }km\]. Mass of Mars is \[0.1\] that of Earth's mass. Then, the acceleration due to gravity on Mars is nearly
  A)
  \[1m/{{s}^{2}}\]          
  done clear
  B)
  \[2.5\text{ }m/{{s}^{2}}\]
  done clear
  C)
  \[4m/{{s}^{2}}\]          
  done clear
  D)
  \[5\,m/{{s}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer22) Consider boiling water converting into steam. Under this condition, the specific heat of water is
  A)
   less than zero
  done clear
  B)
   zero                                             
  done clear
  C)
   slightly greater than zero                        
  done clear
  D)
   infinite
  done clear
  View Answer play_arrow

• question_answer23) Smallest division on the main scale of given vernier calipers is \[0.5\text{ }mm\]. Vernier scale has 25 divisions and these coincide with 24 main scale divisions. The least count of vernier calipers is
  A)
  \[0.001\text{ }cm\]           
  done clear
  B)
  \[0.002\,\,cm\]
  done clear
  C)
  \[~0.01\text{ }cm\]            
  done clear
  D)
  \[0.02\,\,cm\]
  done clear
  View Answer play_arrow

• question_answer24) If R is Rydberg's constant, the series limit of the wavelength of Balmer series for hydrogen atom is given by
  A)
   \[1/R\]    
  done clear
  B)
   \[4/R\]
  done clear
  C)
   \[9/R\]  
  done clear
  D)
   \[16/R\]
  done clear
  View Answer play_arrow

• question_answer25) In which of the following both transverse and longitudinal waves propagate?
  A)
   Heat transfer
  done clear
  B)
   Elastic wave motion in a solid
  done clear
  C)
   Microwave communication
  done clear
  D)
   X-ray motion
  done clear
  View Answer play_arrow

• question_answer26) The combination of gates as shown in the figure forms the
  A)
   AND gate         
  done clear
  B)
   OR gale
  done clear
  C)
   NOR gate         
  done clear
  D)
   NOT gate
  done clear
  View Answer play_arrow

• question_answer27) A magnet makes a single pass through a coil. Then, across the ends of the coil it produces
  A)
   DC voltage         
  done clear
  B)
   Sinusoidal voltage
  done clear
  C)
   Single voltage pulse
  done clear
  D)
   Two voltage pulses
  done clear
  View Answer play_arrow

• question_answer28) The energy per mole per degree of freedom of an ideal gas is
  A)
   \[(3/2){{k}_{B}}T\]          
  done clear
  B)
   \[(1/2){{k}_{B}}T\]
  done clear
  C)
   \[(3/2)RT\]          
  done clear
  D)
   \[(1/2)RT\]
  done clear
  View Answer play_arrow

• question_answer29) Metal alloys are used for making standard resistance coils because
  A)
   They have high thermal conductivity
  done clear
  B)
   Their resistance depends weakly on temperature
  done clear
  C)
   They have low thermal conductivity
  done clear
  D)
   Their resistance depends strongly on temperature
  done clear
  View Answer play_arrow

• question_answer30) The dielectric constant of a perfect conductor is
  A)
   \[+1\]                     
  done clear
  B)
   \[0\]
  done clear
  C)
   Infinite                
  done clear
  D)
   \[-1\]
  done clear
  View Answer play_arrow

• question_answer31) The \[220\text{ }V\]AC line voltage that we receive in our homes is
  A)
   Rms value          
  done clear
  B)
   peak value
  done clear
  C)
   Average value      
  done clear
  D)
   none of these
  done clear
  View Answer play_arrow

• question_answer32) A person is standing on a weighing-scale and observes that the reading is\[60\text{ }kg\]. He then suddenly jumps up and observes that reading goes to\[70\text{ }kg\]. Then his maximum upward acceleration is
  A)
   zero               
  done clear
  B)
  \[1.4\text{ }m/{{s}^{2}}\]
  done clear
  C)
  \[1.63\text{ }m/{{s}^{2}}\]           
  done clear
  D)
  \[9.8\text{ }m/{{s}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer33) A solid sphere is rolling down an inclined plane. Then, the ratio of its translational kinetic energy to its rotational kinetic energy is
  A)
  \[2.5\]                  
  done clear
  B)
  \[1.5\]
  done clear
  C)
  \[1\]                    
  done clear
  D)
  \[0.4\]
  done clear
  View Answer play_arrow

• question_answer34) A block of mass 3 kg starts from rest and slides down a curved path in the shape of a quarter-circle of radius \[2\text{ }m\]and reaches the bottom of path with a speed \[1\text{ }m/s\]. If ?g' is \[10\text{ }m/{{s}^{2}},\] the amount of work done against friction is
  A)
  \[60\,\,J\]            
  done clear
  B)
  \[36\,\,J\]
  done clear
  C)
  \[24\,\,J\]            
  done clear
  D)
  \[12\,\,J\]
  done clear
  View Answer play_arrow

• question_answer35) Values for Brewster's angle can be
  A)
   only less than \[{{45}^{o}}\]
  done clear
  B)
   only greater than \[{{45}^{o}}\]
  done clear
  C)
   any value in the range \[{{0}^{o}}\] to \[{{90}^{o}}\] except \[{{45}^{o}}\]
  done clear
  D)
   any value in the range \[{{0}^{o}}\] to \[{{90}^{o}}\] including \[{{45}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer36) Consider a bi-convex lens and a plano-convex lens, with radii of curvature of all the curved surfaces being same. If 'f is the focal length of bi-convex lens then, the focal length of the plano-convex lens is
  A)
  \[4\,f\]    
  done clear
  B)
  \[2\,f\]
  done clear
  C)
  \[f\]   
  done clear
  D)
  \[0.5\,\,f\,\]
  done clear
  View Answer play_arrow

• question_answer37) A body is travelling towards East with a speed of \[9\text{ }m/s\]and with an acceleration of \[2\text{ }m/{{s}^{2}}\]acting along West on it. The displacement of the body during the 5th second of its motion is
  A)
  \[0.25\text{ }m\]  
  done clear
  B)
  \[0.5\text{ }m\]
  done clear
  C)
  \[0.75\text{ }m\] 
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer38) Bulk modulus is defined by
  A)
   increase in length per unit length per unit applied stress
  done clear
  B)
   increase in volume per unit volume per unit applied stress
  done clear
  C)
   lateral displacement per unit length per unit applied stress
  done clear
  D)
   change in cross-sectional area per unit area per unit applied stress
  done clear
  View Answer play_arrow

• question_answer39) A bullet fired from a rifle loses \[20%\]of its speed while passing through a wooden plank. Then, minimum number of wooden planks required to completely stop the bullet is
  A)
  \[3\]      
  done clear
  B)
  \[5\]
  done clear
  C)
  \[15\]     
  done clear
  D)
  \[25\]
  done clear
  View Answer play_arrow

• question_answer40) If the forward bias voltage in a p-n junction diode is decreased, the length of depletion region will
  A)
   Increase
  done clear
  B)
   Decrease
  done clear
  C)
   Not change
  done clear
  D)
   Initially increase and then decrease
  done clear
  View Answer play_arrow

• question_answer41) A particle is undergoing uniform circular motion with angular momentum L. While moving on the same path if its kinetic energy becomes four times, then its angular momentum will be
  A)
  \[L/4\]     
  done clear
  B)
  \[L/2\]
  done clear
  C)
  \[L\]      
  done clear
  D)
  \[2L\]
  done clear
  View Answer play_arrow

• question_answer42) A \[1m\] long solenoid containing 1000 turns produces a flux density of \[3.14\times {{10}^{-3}}\text{ }T\]. The current in the solenoid will be
  A)
  \[2.0\text{ }A\]              
  done clear
  B)
  \[2.5\,\,A\]
  done clear
  C)
  \[3.0\,\,A\]              
  done clear
  D)
  \[3.5\,\,A\]
  done clear
  View Answer play_arrow

• question_answer43) Which of the following is incorrect about sky waves?
  A)
   Sky waves are not used in long distance communication
  done clear
  B)
   Their propagation takes place by total internal reflection
  done clear
  C)
   Sky waves support the so-called AM band
  done clear
  D)
   The frequency of sky waves ranges typically from \[3\text{ }MHz\]to \[30\text{ }MHz\]
  done clear
  View Answer play_arrow

• question_answer44) The wave nature of electrons is demonstrated by the
  A)
   Photoelectric effect
  done clear
  B)
   Rutherford's experiment
  done clear
  C)
   Doppler's effect
  done clear
  D)
   Davisson and Germer experiment
  done clear
  View Answer play_arrow

• question_answer45) A person carrying a whistle emitting continuously a note of \[272\text{ }Hz\]is running towards a reflecting surface with a speed of\[18\text{ }km/h\]. If the speed of sound is \[345\text{ }m/s,\]the number of beats heard by him are
  A)
  \[4\]              
  done clear
  B)
  \[6\]
  done clear
  C)
  \[8\]              
  done clear
  D)
  \[10\]
  done clear
  View Answer play_arrow

• question_answer46) Consider the two cells having emf \[{{E}_{1}}\] and \[{{E}_{2}}\] \[({{E}_{1}}>{{E}_{2}})\] connected as shown in the figure. A potentiometer is used to measure potential difference between P and Q and the balancing length of the potentiometer wire is\[0.8m\]. Same potentiometer is then used to measure potential difference between P and R and the balancing length is \[0.2\text{ }m\]. Then, the ratio \[{{E}_{1}}/{{E}_{2}}\] is
  A)
  \[4/3\]                  
  done clear
  B)
  \[5/4\]
  done clear
  C)
  \[5/3\]                  
  done clear
  D)
  \[4/1\]
  done clear
  View Answer play_arrow

• question_answer47) Which of the following is NOT an example of primary cell?
  A)
   Voltaic cell           
  done clear
  B)
   Lead-acid cell
  done clear
  C)
   Daniel ceil           
  done clear
  D)
   Leclanche cell
  done clear
  View Answer play_arrow

• question_answer48) Red, blue, green and violet colour lights are one by one made incident on a photocathode. It is observed that only one color light produces photo-electrons.
  A)
   Red                 
  done clear
  B)
   Blue
  done clear
  C)
   Green               
  done clear
  D)
   Violet
  done clear
  View Answer play_arrow

• question_answer49) What amount of original radioactive material is left?
  A)
  \[6.5%\]             
  done clear
  B)
  \[12.5%\]
  done clear
  C)
  \[25.5%\]             
  done clear
  D)
  \[33.3%\]
  done clear
  View Answer play_arrow

• question_answer50) Consider a region of uniform magnetic field directed along positive X-axis. Now a positive test charge Q, located at origin O \[(0,0)\] inside the field, is released from rest position. The particle will
  A)
   Remain stationary at origin O
  done clear
  B)
   Move along positive X-axis
  done clear
  C)
   Move along negative X-axis
  done clear
  D)
   Undergo a circular motion in the X-Y plane
  done clear
  View Answer play_arrow

• question_answer51) A charge particle having charge \[1\times {{10}^{-19}}\,C\] revolves in an orbit of radius 1 A such that the frequency of revolution is\[1016\text{ }Hz\]. The resulting magnetic moment in SI units will be
  A)
   \[1.57\times {{10}^{-21}}\]          
  done clear
  B)
   \[3.14\times {{10}^{-21}}\]
  done clear
  C)
   \[1.57\times {{10}^{-23}}\]         
  done clear
  D)
   \[3.14\times {{10}^{-23}}\]
  done clear
  View Answer play_arrow

• question_answer52) The length of antenna to transmit waves of \[1\text{ }MHz\]will be
  A)
  \[3\,\,m\]              
  done clear
  B)
  \[15\,\,m\]
  done clear
  C)
  \[30\,\,m\]             
  done clear
  D)
  \[300\,\,m\]
  done clear
  View Answer play_arrow

• question_answer53) A series LCR circuit is connected to an AC source and is showing resonance. Then
  A)
   \[{{V}_{R}}=0\]           
  done clear
  B)
   \[{{V}_{L}}={{V}_{R}}\]
  done clear
  C)
    \[{{V}_{C}}={{V}_{R}}\]
  done clear
  D)
   \[{{V}_{L}}={{V}_{C}}\]
  done clear
  View Answer play_arrow

• question_answer54) Dimensions of Planck's constant are
  A)
   \[[M{{L}^{2}}{{T}^{-1}}]\]          
  done clear
  B)
   \[[M{{L}^{2}}{{T}^{-3}}]\]
  done clear
  C)
   \[[ML{{T}^{-1}}]\]         
  done clear
  D)
   \[[M{{L}^{3}}{{T}^{-3}}]\]
  done clear
  View Answer play_arrow

• question_answer55) Consider an electric dipole placed in a region of non-uniform electric field. Choose the correct statement out of the following options:
  A)
   The dipole will experience only a force
  done clear
  B)
   The dipole will experience only a torque
  done clear
  C)
   The dipole will experience both the force and torque
  done clear
  D)
   The dipole will neither experience a force nor a torque
  done clear
  View Answer play_arrow

• question_answer56) A block of mass 'm' is placed on an inclined plane having coefficient of friction 'm?. The plane is making an angle \[\theta \] with the horizontal. The minimum value of upward force acting along the inclined plane that can just move the block up is
  A)
   \[mg\,\,\cos \,\theta \]        
  done clear
  B)
   \[mmg\,\,\cos \,\theta \]
  done clear
  C)
   \[mg\,\,sin\,\theta \]         
  done clear
  D)
   \[mmg\,\,sin\,\theta \]
  done clear
  View Answer play_arrow

• question_answer57) A ball is projected up at an angle 9 with horizontal from the top of a tower with speed V. It hits the ground at point A after time \[{{t}_{A}}\] with speed \[{{v}_{A}}\]. Now, this ball is projected at ' same angle and speed from the base of the tower (located at point P) and it hits ground at point B after time \[{{t}_{B}}\] with speed \[{{v}_{B}}\]. Then
  A)
   \[PA=PB\]
  done clear
  B)
   \[{{t}_{A}}<{{t}_{B}}\]
  done clear
  C)
   \[{{v}_{A}}<{{v}_{B}}\]
  done clear
  D)
   Ball A hits the ground at an angle \[(-\theta )\] with horizontal
  done clear
  View Answer play_arrow

• question_answer58) The electric field of an electric dipole at a point on its axis at a distance 'd? from the centre of the dipole varies as
  A)
   \[1/d\]
  done clear
  B)
   \[1/{{d}^{2}}\]
  done clear
  C)
   \[1/{{d}^{3}}\]  
  done clear
  D)
   \[1/{{d}^{3/2}}\]
  done clear
  View Answer play_arrow

• question_answer59) Un-polarised light is travelling from a medium of refractive index 2 to a medium of refractive index 3. The angle of incidence is\[{{60}^{o}}\]. Then
  A)
   Reflected light will be partially polarized
  done clear
  B)
   Reflected light will be plane polarised in a plane perpendicular to plane of incidence
  done clear
  C)
   Refracted light will be plane polarised in a plane perpendicular to plane of incidence
  done clear
  D)
   Refracted light will be plane polarised in a plane parallel to plane of incidence
  done clear
  View Answer play_arrow

• question_answer60) Newton's law of cooling applies when a body is losing heat to its surroundings by
  A)
   Conduction
  done clear
  B)
   Convection
  done clear
  C)
   Radiation
  done clear
  D)
   Conduction as well as radiation
  done clear
  View Answer play_arrow

• question_answer61) If a homogeneous colloid placed in dark is observed in the direction of light, it appears clear and if it is observed from a direction at right angles to the direction of light beam, it appears perfectly dark. This is known as
  A)
  Brownian effect
  done clear
  B)
  Hardy Schuize effect
  done clear
  C)
  Einstein effect
  done clear
  D)
  Tyndall effect                            
  done clear
  View Answer play_arrow

• question_answer62) When powdered plaster of Paris is mixed with correct amount of water, it sets into a solid mass of
  A)
  \[CaS{{O}_{4}}.5{{H}_{2}}O\]
  done clear
  B)
   \[CaS{{O}_{4}}.3{{H}_{2}}O\]
  done clear
  C)
   \[CaS{{O}_{4}}.2{{H}_{2}}O\]
  done clear
  D)
   \[CaS{{O}_{4}}.1/2{{H}_{2}}O\]
  done clear
  View Answer play_arrow

• question_answer63) pV value decreases with increases in p at constant temperature when
  A)
   there is no attractive or repulsive forces  between molecules
  done clear
  B)
   attractive and    repulsive forces between molecules are equal
  done clear
  C)
   attractive forces between molecules are  predominant
  done clear
  D)
   repulsive forces between molecules are  predominant
  done clear
  View Answer play_arrow

• question_answer64) For a reaction, \[C(s)+C{{O}_{2}}(g)\xrightarrow{{}}2CO(g);\]the partial pressure of \[C{{O}_{2}}\]and CO are 4 and 8 atm, respectively. \[{{K}_{p}}\]for the reaction is
  A)
   0.5     
  done clear
  B)
   2      
  done clear
  C)
   16     
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer65) HA is a weak acid. At\[\text{25}{{\,}^{\text{o}}}\text{C,}\]the molar conductivity   of   0.02   M   HA   is \[150\,{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}.\]If its\[\text{ }\!\!\Lambda\!\!\text{ }_{\text{m}}^{\text{o}}\] is \[300\,{{\Omega }^{-1}}\,c{{m}^{2}}mo{{l}^{-1}},\]then equilibrium constant of  HA dissociation is
  A)
   0.001  
  done clear
  B)
   0.005  
  done clear
  C)
   0.01   
  done clear
  D)
   0.02
  done clear
  View Answer play_arrow

• question_answer66) The product of the following reaction is
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer67) Identify the major product for the reaction given below:
  A)
  
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer68) 30 mL of 0.02 M ammonium hydroxide is mixed with 15 mL of 0.02 M HCl. What will be the pH of the solution \[(p{{K}_{b}}=4.0)\]?
  A)
   4      
  done clear
  B)
   8     
  done clear
  C)
   4     
  done clear
  D)
   10
  done clear
  View Answer play_arrow

• question_answer69) In an acidified aqueous solution of\[\text{M}{{\text{n}}^{\text{2+}}}\text{,N}{{\text{i}}^{\text{2+}}}\text{,C}{{\text{u}}^{\text{2+}}}\]and \[\text{H}{{\text{g}}^{\text{2+}}}\,\text{ions,}\,{{\text{H}}_{\text{2}}}\text{S}\]gas was passed. Precipitates are
  A)
  MnS and CuS     
  done clear
  B)
   NiS and HgS
  done clear
  C)
   MnS and NiS      
  done clear
  D)
   CuS and HgS
  done clear
  View Answer play_arrow

• question_answer70) Shape of \[\text{S}{{\text{F}}_{\text{4}}}\]is
  A)
   tetrahedral         
  done clear
  B)
   square planar
  done clear
  C)
   trigonal pyramid     
  done clear
  D)
   see-saw
  done clear
  View Answer play_arrow

• question_answer71) The following tripeptide can be synthesized from the following ammo acid
  A)
   Glycine, Leucine and Alanine                   
  done clear
  B)
   Alanine, Isoleucine and Glycine
  done clear
  C)
   Valine, Afanine and Glycine
  done clear
  D)
   Alanine, Serine and Glycine
  done clear
  View Answer play_arrow

• question_answer72) The species which cannot serve as an initiator for the free radical polymerisation, is
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer73) Nylon is a
  A)
   polyamide          
  done clear
  B)
   carbonate
  done clear
  C)
   ester               
  done clear
  D)
   polycarboxylic acid
  done clear
  View Answer play_arrow

• question_answer74) A gas at high temperature is cooled. The highest temperature at which liquefaction of   gas first occurs is called                     
  A)
   Boyle temperature                              
  done clear
  B)
   critical temperature
  done clear
  C)
   boiling temperature
  done clear
  D)
   freezing temperature
  done clear
  View Answer play_arrow

• question_answer75) Buna-N synthetic rubber is obtained by copolymerisation of
  A)
  \[C{{H}_{2}}=CH-CH=C{{H}_{2}}\]and \[{{H}_{5}}{{C}_{6}}-CH=C{{H}_{2}}\]
  done clear
  B)
  \[C{{H}_{2}}=CH-CN\]and \[{{H}_{2}}C=CH-CH=C{{H}_{2}}\]
  done clear
  C)
  \[{{H}_{2}}C=CH-CN\]and \[C{{H}_{2}}=CH-C(C{{H}_{3}})=C{{H}_{2}}\]
  done clear
  D)
  \[{{H}_{2}}C=CH-C(Cl)=C{{H}_{2}}\]and \[{{H}_{2}}C=CH-CH=C{{H}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer76) When the following amide is treated with \[B{{r}_{2}}/KOH,\]it gives
  A)
  
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer77) The IUPAC name of the coordination compound\[[Co{{({{H}_{2}}O)}_{2}}{{(N{{H}_{3}})}_{4}}]C{{l}_{3}}\] is
  A)
   tetraamminediaquacobalt (III) chloride
  done clear
  B)
   cobalt (III) tetraamminediaqua chloride
  done clear
  C)
   diaquatetraammine cobalt (III) chloride
  done clear
  D)
   tetraamminediaquacobalt (II) chloride
  done clear
  View Answer play_arrow

• question_answer78) Siderite is mainly ore of
  A)
   Zn
  done clear
  B)
   Fe
  done clear
  C)
   Cd
  done clear
  D)
   Ru
  done clear
  View Answer play_arrow

• question_answer79) Among P, S, Cl, F, the elements with most negative and least negative electron gain enthalpy respectively, are
  A)
   CI, S
  done clear
  B)
   F, S
  done clear
  C)
   CI, P
  done clear
  D)
   F, P
  done clear
  View Answer play_arrow

• question_answer80) For a reaction \[\text{2A}\xrightarrow{\text{3B}}\text{3B;}\]if the rate of formation of B is\[x\,\text{mol/L,}\]the rate of consumption of A is
  A)
  \[x\]
  done clear
  B)
   \[\frac{3x}{2}\]
  done clear
  C)
   \[\frac{2x}{3}\]
  done clear
  D)
   \[3x\]
  done clear
  View Answer play_arrow

• question_answer81) The following alcohol after treatment with acid gives compound A. Ozonolsis of A gives nonane-2, 8-dione. The compound A is
  A)
  
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer82) In \[\text{H}{{\text{e}}_{\text{2}}}\text{,}\]the electrons in bonding and anti-bonding orbitals are
  A)
   2, 2     
  done clear
  B)
   4, 2       
  done clear
  C)
   4, 0     
  done clear
  D)
   2, 4
  done clear
  View Answer play_arrow

• question_answer83) 0.5 molal solution of a solute in benzene shows a depression in freezing point equal to 2 K. Molal depression constant for benzene is \[\text{5}\,\text{K}\,\text{kg}\,\text{mo}{{\text{l}}^{-1}}.\]If the solute forms dimer in benzene, what is the % association?
  A)
   40    
  done clear
  B)
   50    
  done clear
  C)
   60    
  done clear
  D)
   80
  done clear
  View Answer play_arrow

• question_answer84) The major product of the following transformation is
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer85) A highly stable conformation for the following compound is
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer86) Molar enthalpy change for melting of ice is 6 kJ/mol. Then the internal energy change (in kJ/mol) when 1 mole of water is converted into ice at 1 atm at \[0{{\,}^{o}}C\]is
  A)
  \[RT/1000\]
  done clear
  B)
   6
  done clear
  C)
   \[6-(RT/1000)\]
  done clear
  D)
   \[6+(RT/1000)\]
  done clear
  View Answer play_arrow

• question_answer87) Identify the correct product of the following reaction
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer88) Among second period elements/the correct order for first ionisation enthalpy is         
  A)
   \[Li<Be<B<C<N<O<F<Ne\]
  done clear
  B)
   \[Li<B<Be<C<O<N<F<Ne\]
  done clear
  C)
   \[Li>Be>B>C>N>O>F>Ne\]
  done clear
  D)
  .\[Li>B>C>Be>O>N>F>Ne\]
  done clear
  View Answer play_arrow

• question_answer89) For the reaction \[A(s)+2{{B}^{+}}(aq)\to {{A}^{2+}}(aq)+2B(s);\]the \[{{E}^{o}}\]is 1.18 V. Then the equilibrium constant for the reaction is
  A)
   \[{{10}^{10}}\]
  done clear
  B)
   \[{{10}^{20}}\]
  done clear
  C)
   \[{{10}^{40}}\]
  done clear
  D)
   \[{{10}^{60}}\]
  done clear
  View Answer play_arrow

• question_answer90) Identify the correct statement about the following pairs of compounds.
  A)
   A and B diastereomer; C and D  diastereomer
  done clear
  B)
   A and B enantiomer; C and D diastereomer
  done clear
  C)
   A and B diastereomer; C and D enantiomer
  done clear
  D)
   A and B enantiomer; C and D enantiomer      
  done clear
  View Answer play_arrow

• question_answer91) One of the following complexes shows geometrical isomerism. The complex is     
  A)
  \[PtC{{l}_{4}}\]
  done clear
  B)
   \[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}\]
  done clear
  C)
   \[Pt{{(N{{H}_{3}})}_{3}}Cl\]
  done clear
  D)
   \[Ni{{(N{{H}_{3}})}_{3}}Cl\]
  done clear
  View Answer play_arrow

• question_answer92) The ionisation potential of hydrogen atom is 13.6 eV. The energy required to remove an electron from \[n=2\]state of hydrogen atom is
  A)
  \[27.2\,eV\]
  done clear
  B)
   \[13.6\,\,eV\]
  done clear
  C)
   \[6.8\,eV\]
  done clear
  D)
   \[3.4\,eV\]
  done clear
  View Answer play_arrow

• question_answer93) Among the following pair, which one has both variables as intensive variable?
  A)
  \[T,V\]
  done clear
  B)
  \[m,p\]
  done clear
  C)
   \[d,V\]
  done clear
  D)
  \[\rho ,T\]
  done clear
  View Answer play_arrow

• question_answer94) Which one of the following will quickly react with \[\text{AgN}{{\text{O}}_{\text{3}}}\]?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer95) The number of tetrahedral and octahedral void per unit cell of cubic closed packed structure is
  A)
   4, 8     
  done clear
  B)
   4.4    
  done clear
  C)
   8,4     
  done clear
  D)
   8,8
  done clear
  View Answer play_arrow

• question_answer96) In the following disaccharide,
  A)
   Ring [A] ispyranonewith\[\alpha -\]glycosidiclink
  done clear
  B)
   Ring [A] is furanone with \[\alpha -\]glycosidic link
  done clear
  C)
   Ring [S] is pyranone with \[\beta -\]glycosidic link
  done clear
  D)
   Ring [B] is furanone with \[\alpha -\]glycosidic link
  done clear
  View Answer play_arrow

• question_answer97) When a dilute solution of ammonia is  saturated with \[{{\text{H}}_{\text{2}}}\text{S}\]it gives
  A)
  \[{{(N{{H}_{4}})}_{2}}S\]
  done clear
  B)
  \[N{{H}_{4}}HS\]
  done clear
  C)
   \[{{(N{{H}_{3}})}_{2}}{{H}_{2}}S\]
  done clear
  D)
   \[N{{H}_{3}}.{{H}_{2}}S\]
  done clear
  View Answer play_arrow

• question_answer98) If \[{{E}^{o}}_{{{M}^{+}}/M}=-1.2V,{{E}^{o}}_{{{x}_{2}}/{{x}^{-}}}=-1.1\,V\]and \[{{E}^{o}}_{{{o}_{2}}/{{H}_{2}}O}=1.23\,V,\]then on electrolysis of aqueous solution of salt MX, the products obtained are
  A)
  \[M,{{X}_{2}}\]
  done clear
  B)
  \[{{H}_{2}},{{X}_{2}}\]
  done clear
  C)
   \[{{H}_{2}},{{O}_{2}}\]
  done clear
  D)
   \[M,{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer99) For the process to occur under adiabatic condition, the correct condition is
  A)
   \[\Delta T=0\]
  done clear
  B)
  \[\Delta U=0\]
  done clear
  C)
   \[\Delta p=0\]
  done clear
  D)
  \[\Delta q=0\]
  done clear
  View Answer play_arrow

• question_answer100) Which of the element is available in carbonic anhydrase?
  A)
   Pd    
  done clear
  B)
   Fe    
  done clear
  C)
   Zn    
  done clear
  D)
   Pt
  done clear
  View Answer play_arrow

• question_answer101) Identify reactant  for the following reaction
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer102) Identify the product of the following reaction.
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer103) The absolute configuration of the following compound is
  A)
  \[R,R,R\]
  done clear
  B)
   \[R,R,S\]
  done clear
  C)
   \[R,S,R\]
  done clear
  D)
   \[S,R,R\]
  done clear
  View Answer play_arrow

• question_answer104) The wrong statement among the following is
  A)
   acid rain is mostly because of oxides of nitrogen and sulphur
  done clear
  B)
   green house effect is responsible for global warming
  done clear
  C)
   ozone layer does not permit infrared infrared radiation from the sun to reach earth
  done clear
  D)
   chlorofluorocarbons are responsible for ozone layer depletion
  done clear
  View Answer play_arrow

• question_answer105) The vapour pressure of pure benzene at certain temperature is 1 bar. A non-volatile, non-electrolyte solid weighing 2 g when added to 39 g of benzene (molar mass\[78\,g\,mo{{l}^{-1}}\]) yields solution of vapour pressure of 0.8 bar. The molar mass of solid substance is
  A)
   32               
  done clear
  B)
   16
  done clear
  C)
   64               
  done clear
  D)
   48
  done clear
  View Answer play_arrow

• question_answer106) \[\text{HCl}{{\text{O}}_{\text{4}}}\text{.2}{{\text{H}}_{\text{2}}}\text{O}\]after reaction with fuming sulphuric acid generates.                 
  A)
  \[Cl{{O}_{2}}+{{H}_{2}}S{{O}_{4}}\]
  done clear
  B)
  \[C{{l}_{2}}{{O}_{7}}+{{H}_{2}}S{{O}_{4}}\]
  done clear
  C)
   \[HCl{{O}_{4}}+{{H}_{2}}S{{O}_{4}}\]
  done clear
  D)
   \[C{{l}_{2}}{{O}_{6}}+{{H}_{2}}S{{O}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer107) The compound formed upon combustion of potassium metal in excess air is
  A)
  \[{{K}_{2}}{{O}_{2}}\]
  done clear
  B)
  \[K{{O}_{2}}\]
  done clear
  C)
   \[{{K}_{2}}O\]
  done clear
  D)
  \[KOH\]
  done clear
  View Answer play_arrow

• question_answer108) Energy of activation of forward reaction for an endothermic process is 90 kJ. If enthalpy change for the reaction is 50 kJ then activation  energy for backward reaction will be
  A)
   40 kJ
  done clear
  B)
   140 kJ
  done clear
  C)
   90 kJ
  done clear
  D)
   50 kJ
  done clear
  View Answer play_arrow

• question_answer109) For ion \[{{O}_{2}}^{-},\]the bond order is
  A)
   2
  done clear
  B)
   1.5
  done clear
  C)
   2.5
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer110) Extraction of mercury from cinnabar is achieved by
  A)
   heating it in air
  done clear
  B)
   electrolytic reduction                              
  done clear
  C)
   roasting followed by reduction with carbon
  done clear
  D)
   roasting followed by reduction with another metal
  done clear
  View Answer play_arrow

• question_answer111) The   correct  order  of  the  ligands,\[O{{H}^{-}},NO_{3}^{-},PP{{h}_{3}},\] pyridine, according to their increasing field strength is
  A)
  \[NO_{3}^{-}<O{{H}^{-}}<pyridine<PP{{h}_{3}}\]
  done clear
  B)
   \[O{{H}^{-}}<NO_{3}^{-}<PP{{h}_{3}}<\text{pyridine}\]
  done clear
  C)
   \[O{{H}^{-}}<NO_{3}^{-}<\text{pyridine}<PP{{h}_{3}}\]
  done clear
  D)
   \[NO_{3}^{-}<O{{H}^{-}}<PP{{h}_{3}}<Pyridine\]
  done clear
  View Answer play_arrow

• question_answer112) When \[{{\text{(C}{{\text{H}}_{\text{3}}}\text{)}}_{\text{3}}}\text{CC}{{\text{H}}_{\text{2}}}\text{Cl}\]is heated at \[\text{300}{{\,}^{o}}\text{C,}\] it gives
  A)
  
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer113) If the density of methanol is \[0.8\,\text{kg}\,{{\text{L}}^{-1}},\] what is its volume needed for making 4 L of its 0.25 M solution?
  A)
   4mL  
  done clear
  B)
   8 mL  
  done clear
  C)
   40 mL 
  done clear
  D)
   80 mL
  done clear
  View Answer play_arrow

• question_answer114) The number of Na atom in 46 g Na (atomic weight of Na= 2 3) is
  A)
  \[6.023\times {{10}^{23}}\]
  done clear
  B)
   2
  done clear
  C)
   1
  done clear
  D)
   \[12.046\times {{10}^{23}}\]
  done clear
  View Answer play_arrow

• question_answer115) If the solubility of a sparingly soluble salt\[\text{A}{{\text{X}}_{\text{2}}}\] is s mol/L, the solubility product is
  A)
  \[4{{s}^{3}}\]
  done clear
  B)
   \[8{{s}^{3}}\]
  done clear
  C)
   \[4{{s}^{2}}\]
  done clear
  D)
  \[{{s}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer116) Which one of the following does not have \[\text{s}{{\text{p}}^{\text{3}}}\]hybridisation?
  A)
  \[C{{H}_{4}}\]
  done clear
  B)
  \[Xe{{F}_{4}}\]
  done clear
  C)
  \[{{H}_{2}}O\]
  done clear
  D)
  \[N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer117) Milk is an example of
  A)
   emulsion           
  done clear
  B)
   sol
  done clear
  C)
   gel                
  done clear
  D)
   foam
  done clear
  View Answer play_arrow

• question_answer118) \[\frac{{{K}_{p}}}{{{K}_{C}}}\]for the reaction \[A(g)+2{{B}_{2}}(g)\xrightarrow{{}}A{{B}_{2}}(g)\]is
  A)
  \[RT\]
  done clear
  B)
  \[{{(RT)}^{2}}\]
  done clear
  C)
   \[\frac{1}{RT}\]
  done clear
  D)
  \[\frac{1}{{{(RT)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer119) One mole of an ideal gas expands isothermally and reversibly from 2 L to 20 L at 300 K. If the final pressure of the gas is 1 bar, the work done by the gas is
  A)
  \[-300\,R\,\ln \,10\]
  done clear
  B)
  \[300\,R\,\ln \,10\]
  done clear
  C)
   \[18\]
  done clear
  D)
   \[-18\]
  done clear
  View Answer play_arrow

• question_answer120) A unit cell with edge length \[a\ne b\ne c\]and axial angles \[\alpha =\beta =\gamma ={{90}^{o}}\]is called
  A)
   cubic              
  done clear
  B)
   tetragonal
  done clear
  C)
   orthorhombic       
  done clear
  D)
   hexagonal
  done clear
  View Answer play_arrow

• question_answer121) The number of values of \[\alpha \in \,[-\pi ,\pi ]\] for which \[{{\sin }^{2}}\left( \frac{\pi }{8}+\alpha  \right)-{{\sin }^{2}}\left( \frac{\pi }{8}-\alpha  \right)=\frac{1}{2\sqrt{2}}\], is
  A)
   \[1\]                
  done clear
  B)
   \[2\]
  done clear
  C)
   \[3\]                
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer122) The area of the parallelogram with co-terminal   edges   \[a=3\hat{i}-3\hat{j}+k\] and \[b=4\hat{i}+9\hat{j}+2\hat{k}\]is
  A)
   \[5\sqrt{70}\]            
  done clear
  B)
   \[50\,\sqrt{7}\]
  done clear
  C)
   \[\,\sqrt{70}\]              
  done clear
  D)
   \[5\,\sqrt{7}\]
  done clear
  View Answer play_arrow

• question_answer123) The number of values of \[\theta \,\,\in \,(-\pi ,\pi ),\] satisfying \[\sin 5\theta \,\cos 3\theta =\sin \,6\theta \,\cos 2\theta ,\] is
  A)
   \[1\]                  
  done clear
  B)
   \[2\]
  done clear
  C)
   \[3\]                 
  done clear
  D)
   \[4\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer124) Let \[X=\{a,b,c,d,e\}\] and \[R=\{(a,a),\,(b,b),\]\[(c,c),\,\,(a,b),\,\,(b,a)\}.\] Then, the relation R on X is
  A)
   reflexive and symmetric
  done clear
  B)
   not reflexive, but symmetric
  done clear
  C)
   symmetric and transitive, but not reflexive
  done clear
  D)
   reflexive, but not transitive
  done clear
  View Answer play_arrow

• question_answer125) If \[\sin \theta +\cos \theta =\sqrt{2},\] is \[{{\cos }^{6}}\theta +{{\sin }^{6}}\theta \]equal to
  A)
   \[\frac{1}{4}\]               
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[\frac{3}{4}\]
  done clear
  D)
   \[2\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer126) The shortest distance between the lines \[\frac{x}{-1}=\frac{y}{1}=\frac{z}{1}\] and \[\frac{x-3}{0}=\frac{y+3}{1}=\frac{z-3}{-1}\] is
  A)
   \[\sqrt{6}\]
  done clear
  B)
   \[6\]
  done clear
  C)
   \[2\sqrt{3}\]
  done clear
  D)
   \[3\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer127) The last digit in the integer \[{{3}^{101}}+1\] is
  A)
   \[1\]        
  done clear
  B)
   \[2\]     
  done clear
  C)
   \[3\]      
  done clear
  D)
   \[4\]
  done clear
  View Answer play_arrow

• question_answer128) If \[^{32}{{P}_{6}}=k\,{{(}^{32}}{{C}_{6}}),\] then k is equal to
  A)
   \[6\]            
  done clear
  B)
   \[24\]
  done clear
  C)
   \[120\]              
  done clear
  D)
   \[720\]
  done clear
  View Answer play_arrow

• question_answer129) The integer \[\int_{0}^{\pi }{\frac{x}{2\,\text{cosec}\,\text{x-sin}\,\text{x}}\,\,dx}\] is equal to
  A)
   \[\frac{\pi }{4}\]
  done clear
  B)
   \[\frac{\pi }{2}\]
  done clear
  C)
   \[\frac{{{\pi }^{2}}}{2}\]
  done clear
  D)
   \[\frac{{{\pi }^{2}}}{4}\]
  done clear
  View Answer play_arrow

• question_answer130) Let P be the set of real numbers and let \[G\subseteq {{R}^{2}}\] be a relation defined by \[G=\{(a,b),\,(c,d)|\,b-a=d-c\}.\]. Then, G is
  A)
   reflexive only        
  done clear
  B)
   symmetric only
  done clear
  C)
   transitive only     
  done clear
  D)
   an equivalence relation
  done clear
  View Answer play_arrow

• question_answer131) \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{\sin {{x}^{2}}}{1-\cos x}\] is
  A)
   \[\frac{1}{2}\]     
  done clear
  B)
   \[0\]     
  done clear
  C)
   \[1\]      
  done clear
  D)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer132) The sum of lengths of major and minor axes- of an ellipse whose eccentricity is \[\frac{4}{5}\] and  length of latuserectum is \[14.4\], is
  A)
   \[24\]                
  done clear
  B)
   \[32\]
  done clear
  C)
   \[64\]                
  done clear
  D)
   \[48\]
  done clear
  View Answer play_arrow

• question_answer133) If \[|a|=7\] and \[|b|=11,\] then the angle between the vectors \[a+b\]and \[a-b\] is equal to
  A)
   \[\pi \]      
  done clear
  B)
   \[\frac{5\pi }{6}\]
  done clear
  C)
   \[\frac{2\pi }{3}\]    
  done clear
  D)
   \[\frac{3\pi }{4}\]
  done clear
  View Answer play_arrow

• question_answer134) The number of integer value(s) of A: for which the  expression  \[{{x}^{2}}-2(4k-1)x+15{{k}^{2}}\] \[-2k-7>0\] for every real number x, is/are
  A)
   None
  done clear
  B)
   one
  done clear
  C)
   finitely many, but greater than 1
  done clear
  D)
   infinitely many
  done clear
  View Answer play_arrow

• question_answer135) At present, a firm manufactures 1099 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by \[\frac{dP}{dx}=100-12\sqrt{x}.\]. If the firm empower  25 more workers, then the new level of production of items is
  A)
   \[2000\]   
  done clear
  B)
   \[2500\]  
  done clear
  C)
   \[3000\]   
  done clear
  D)
   \[3500\]
  done clear
  View Answer play_arrow

• question_answer136) The function  is \[f(x)=\frac{1}{2-\cos \,3x},\,x\,\in \left[ 0,\frac{\pi }{3} \right],\]is
  A)
   one-one, but not onto
  done clear
  B)
   onto, but not one-one
  done clear
  C)
   one-one as well as onto
  done clear
  D)
   neither one-one nor onto
  done clear
  View Answer play_arrow

• question_answer137) Let function \[f(x)={{(x-1)}^{2}}{{(x+1)}^{3}}.\]Then, which of the following is false?
  A)
   There exists a point where \[f(x)\] has a maximum value
  done clear
  B)
   There exists a point where \[f(x)\] has a minimum value
  done clear
  C)
   There exists a point where \[f(x)\] has neither maximum nor minimum value
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer138) Consider the curve given by \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=4({{x}^{2}}-{{y}^{2}})\].  Which     of the following is not true?
  A)
   The curve has two tangents parallel to X-axis
  done clear
  B)
   The curve has two tangents parallel to Y-axis
  done clear
  C)
   The area of the region bounded by this curve is less than 8
  done clear
  D)
   All of the above
  done clear
  View Answer play_arrow

• question_answer139) Let A and B be points \[(8,\,\,10)\] and \[(18,\,20),\] respectively. If the point Q divides AB externally in the ratio \[2:3\] and M is the S mid-point of AB, then the length MQ is equal to
  A)
   \[25\]                
  done clear
  B)
   \[5\sqrt{34}\]
  done clear
  C)
   \[25\sqrt{2}\]              
  done clear
  D)
    \[5\sqrt{26}\]
  done clear
  View Answer play_arrow

• question_answer140) The number of the solutions of the equation \[{{5}^{2x-1}}+{{5}^{x+1}}=250,\] is/are
  A)
   \[0\]                   
  done clear
  B)
   \[1\]
  done clear
  C)
   \[2\]                  
  done clear
  D)
   infinitely many
  done clear
  View Answer play_arrow

• question_answer141) A crime is committed by one of two suspects, A and B. Initially, there is equal evidence against both of them. In further investigation at the crime scene, it is found that the guilty party had a blood type found in 20% of the population. If the suspect A does match this blood type, whereas the blood type of suspect B is unknown, then the probability that A is the guilty party, is             
  A)
   \[\frac{3}{5}\]
  done clear
  B)
   \[\frac{5}{6}\]
  done clear
  C)
   \[\frac{1}{3}\]
  done clear
  D)
   \[\frac{2}{3}\]
  done clear
  View Answer play_arrow

• question_answer142) Let \[A=\left( \begin{matrix}    1 & 2  \\    2 & 1  \\ \end{matrix} \right)\] Then, determinant of \[\frac{1}{3}A[adj\,(adj\,A)]\] is
  A)
   \[1\]
  done clear
  B)
   \[-1\]
  done clear
  C)
    \[\frac{1}{3}\]
  done clear
  D)
   \[3\]
  done clear
  View Answer play_arrow

• question_answer143) Let X be a random variable with its expectation \[E(X)=3\]and its variance \[V(X)=2\]. If V is another random variable defined by \[Y=10X,\]then the ordered pair \[(E(Y),\,V(Y))\] is equal to
  A)
   \[(10,\,200)\]  
  done clear
  B)
   \[(30,\,20)\]
  done clear
  C)
   \[(10,\,20)\]            
  done clear
  D)
   \[(30,\,200)\]
  done clear
  View Answer play_arrow

• question_answer144) The number of values of k for which the following system of equations has at least three solutions \[8x+16y\,\,\,+8z=25,\] \[x+y+z=k\]and \[3x+y+3z={{k}^{2}},\] is
  A)
   \[0\]     
  done clear
  B)
   \[1\]     
  done clear
  C)
   \[2\]     
  done clear
  D)
   \[3\]
  done clear
  View Answer play_arrow

• question_answer145) If the plane \[2x-3y+6z-11=0\]makes an angle \[\theta \] with the X-axis, then the value of \[\tan \theta \]is equal to
  A)
   \[\frac{2}{3}\]
  done clear
  B)
   \[\frac{2}{15}\]
  done clear
  C)
   \[\frac{\sqrt{2}}{3}\]
  done clear
  D)
   \[\frac{2\sqrt{5}}{15}\]
  done clear
  View Answer play_arrow

• question_answer146) Let the general term of a series be \[(2k-1)\,\,(2k)\]\[(2k+1),\,\,k=1,2,3...,n.\]If the sum of first. N terms is. \[24090,\]then n is equal to
  A)
   \[8\]      
  done clear
  B)
   \[9\]     
  done clear
  C)
   \[10\]     
  done clear
  D)
   \[11\]
  done clear
  View Answer play_arrow

• question_answer147) In an isosceles right angled triangle ABC, a  value of \[\tan \left( \frac{A}{2} \right)+\tan \left( \frac{B}{2} \right)+\tan \left( \frac{C}{2} \right)\] is
  A)
   \[\sqrt{2}-1\]
  done clear
  B)
   \[2\sqrt{2}\]
  done clear
  C)
   \[2\sqrt{2}-1\]
  done clear
  D)
   \[2\sqrt{2}+1\]
  done clear
  View Answer play_arrow

• question_answer148) Suppose, 70% of all voters in a city support ,a candidate A. If 40 voters in the city are randomly selected, then the expected number of voters that will support candidate A in this group, is
  A)
   \[12\]     
  done clear
  B)
   \[20\]   
  done clear
  C)
  \[28\]     
  done clear
  D)
   \[32\]
  done clear
  View Answer play_arrow

• question_answer149) The radius of the largest circle, having centre \[(1,0),\] that can be inscribed in the ellipse \[{{x}^{2}}+4{{y}^{2}}=16,\]is
  A)
   \[\sqrt{11}\]        
  done clear
  B)
   \[\sqrt{\frac{11}{3}}\]
  done clear
  C)
   \[\sqrt{\frac{22}{3}}\]
  done clear
  D)
   \[\sqrt{22}\]
  done clear
  View Answer play_arrow

• question_answer150) The area bounded by the curves \[y=\sqrt{|x|}\] and \[y=\pm x,\] is
  A)
   \[0\]
  done clear
  B)
   \[\frac{1}{6}\]
  done clear
  C)
   \[\frac{1}{3}\]
  done clear
  D)
   \[\frac{2}{3}\]
  done clear
  View Answer play_arrow

• question_answer151) Let \[M=\left[ \begin{matrix}    0 & 0 & 1  \\    0 & 1 & 0  \\    1 & 0 & 0  \\ \end{matrix} \right],\]Then, \[\frac{1}{3}\,\det \,(3\,(M+{{M}^{T}}))\] is equal to
  A)
   \[-18\]              
  done clear
  B)
   \[54\]
  done clear
  C)
   \[-72\]              
  done clear
  D)
   \[72\]
  done clear
  View Answer play_arrow

• question_answer152) If there are 6 red and 30 white beads, then the probability of drawing red beads in 2 successive trials, with replacement, is
  A)
   \[\frac{1}{18}\]
  done clear
  B)
   \[\frac{1}{6}\]
  done clear
  C)
   \[\frac{5}{216}\]
  done clear
  D)
   \[\frac{1}{36}\]
  done clear
  View Answer play_arrow

• question_answer153) The sum of the common roots of the equations , \[{{x}^{3}}+2{{x}^{2}}-5x+2=0~\]  and\[{{x}^{3}}+\text{ }{{x}^{2}}-8x+4=0,\]is
  A)
   \[-3\]     
  done clear
  B)
   \[\frac{3}{2}\]
  done clear
  C)
   \[-\frac{\sqrt{17}}{2}\]
  done clear
  D)
   \[\frac{\sqrt{17}}{2}\]
  done clear
  View Answer play_arrow

• question_answer154) Which of the following is a tangent to the curve given by \[{{x}^{3}}+{{y}^{3}}=2xy?\]
  A)
   \[y=x\]         
  done clear
  B)
   \[y=x+2\]
  done clear
  C)
   \[y=-x+2\]      
  done clear
  D)
   \[y=-x+3\]
  done clear
  View Answer play_arrow

• question_answer155) If a tangent to the hyperbola \[4{{x}^{2}}-9{{y}^{2}}=1\] cuts the ellipse \[4\text{ }{{x}^{2}}+9{{y}^{2}}=1\] in points L and R, then the locus of the mid-point of segment LR is
  A)
   \[{{(4{{x}^{2}}+9{{y}^{2}})}^{2}}=4{{x}^{2}}-9{{y}^{2}}\]
  done clear
  B)
   \[{{(4{{x}^{2}}-9{{y}^{2}})}^{2}}=4{{x}^{2}}+9{{y}^{2}}\]
  done clear
  C)
   \[{{(2{{x}^{2}}+3{{y}^{2}})}^{2}}=2{{x}^{2}}-3{{y}^{2}}\]
  done clear
  D)
  \[{{(2{{x}^{2}}-3{{y}^{2}})}^{2}}=2{{x}^{2}}+3{{y}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer156) Let an odd number of terms n of an AP be such that the sum and product of its first and last terms are 10 and 0, respectively. If the common difference is \[\frac{1}{10}\], then the number of terms n is
  A)
   \[99\]                
  done clear
  B)
   \[101\]
  done clear
  C)
   \[103\]               
  done clear
  D)
   \[191\]
  done clear
  View Answer play_arrow

• question_answer157) If \[^{n}{{C}_{r}}\]denotes the binomial coefficient, then which of the following formula is correct?
  A)
   \[^{n+1}{{C}_{r}}{{-}^{n}}{{C}_{r-1}}{{=}^{n}}{{C}_{r}}\]
  done clear
  B)
   \[^{n+1}{{C}_{r}}{{-}^{n-1}}{{C}_{r}}{{=}^{n}}{{C}_{r}}\]
  done clear
  C)
   \[^{n}{{C}_{r+1}}{{-}^{n}}{{C}_{r-1}}{{=}^{n}}{{C}_{r}}\]
  done clear
  D)
   \[^{n=1}{{C}_{r}}{{+}^{n}}{{C}_{r}}{{=}^{n+1}}{{C}_{r}}\]
  done clear
  View Answer play_arrow

• question_answer158) Let \[G=\{(b,b),\,(b,c),\,(c,c),\,(c,d)\}\]    and \[H=\{(b,a),\,(c,b),\,(d,c)\}\] Then, the number of  elements in the set \[(G\cup H)\oplus {{(G\cup H)}^{-1}}\] where \[\oplus \] denotes the symmetric difference, is
  A)
   \[0\]   
  done clear
  B)
   \[2\]    
  done clear
  C)
   \[7\]     
  done clear
  D)
   \[14\]
  done clear
  View Answer play_arrow

• question_answer159) Let the nth term of a sequence be \[{{t}_{n}}=\frac{1}{2}\{{{(1+\sqrt{3})}^{n}}+{{(1-\sqrt{3})}^{n}}\},\]\[n=3,4,5,.....\]Then, form \[=100\] which of the following is true?
  A)
   \[\frac{1}{4}{{t}_{m}}\] is the arithmetic mean of \[{{t}_{m-1}}\] and \[{{t}_{m-2}}\]
  done clear
  B)
   \[\frac{1}{4}{{t}_{m-1}}\] is the arithmetic mean of \[{{t}_{m}}\] and \[{{t}_{m-2}}\]
  done clear
  C)
   \[\frac{1}{4}{{t}_{m}}\] is the geometric mean of \[{{t}_{m-1}}\] and \[{{t}_{m-2}}\]
  done clear
  D)
   \[\frac{1}{4}{{t}_{m-1}}\]  is the geometric mean of \[{{t}_{m}}\] and \[{{t}_{m-2}}\]
  done clear
  View Answer play_arrow

• question_answer160) The roots of the equation \[6\,{{\sin }^{-1}}\left( {{x}^{3}}-6{{x}^{2}}+8x+\frac{1}{2} \right)=\pi ,\]are
  A)
   in AP              
  done clear
  B)
   in GP
  done clear
  C)
   in AP and GP both  
  done clear
  D)
   neither in AP nor in
  done clear
  View Answer play_arrow

• question_answer161) Sum of the first 100 terms of the series \[1+3+7+15+31+....,\]  is
  A)
   \[{{2}^{100}}-102\]         
  done clear
  B)
   \[{{2}^{101}}-102\]
  done clear
  C)
   \[{{2}^{102}}-103\]         
  done clear
  D)
   \[{{2}^{102}}\text{ }-104\]
  done clear
  View Answer play_arrow

• question_answer162) The points \[(1,3,4),\,(-1,6,10),\,(-7,4,7)\] and \[(-5,1,1)\]
  A)
   form a rectangle which is not a square
  done clear
  B)
   form a rhombus which is not a square
  done clear
  C)
   form a parallelogram which is not a rhombus
  done clear
  D)
   are collinear
  done clear
  View Answer play_arrow

• question_answer163) A bag contains one marble which is either green or blue, with equal probability. A green marble is put in the bag (so there are 2 marbles now) and then a marble is picked at random from the bag. If the marble taken out is green, then the probability that the remaining marble is also green, is
  A)
   \[\frac{1}{2}\]     
  done clear
  B)
   \[1\]     
  done clear
  C)
   \[\frac{2}{3}\]     
  done clear
  D)
   \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer164) If the image of the point \[(1,\,-2,3)\] in the plane \[2x+3y-z=7\]is the point \[(\alpha ,\beta ,\gamma )\] then \[\alpha +\beta +\gamma \] is equal to
  A)
   \[-6\]    
  done clear
  B)
   \[10\]    
  done clear
  C)
   \[8\]     
  done clear
  D)
   \[-4\]
  done clear
  View Answer play_arrow

• question_answer165) Equation of the circle having the diameter as the line segment joining the complex numbers \[-1-i\]and \[1+i\]  is
  A)
   \[|z+1+i{{|}^{2}}+|z-1-i{{|}^{2}}=8\]
  done clear
  B)
   \[|z{{|}^{2}}=|1+i{{|}^{2}}+|-1-i{{|}^{2}}\]
  done clear
  C)
   \[|z-1+i{{|}^{2}}-|z+1-i{{|}^{2}}=4\]
  done clear
  D)
   \[|z+1+i{{|}^{2}}=|z-1-i{{|}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer166) The range of the function  \[y(x)=4\,\sin \,x-3\,\cos x\]is
  A)
   \[(-5,5)\]  
  done clear
  B)
   \[(-5,5]\]  
  done clear
  C)
   \[[-5,5)\]  
  done clear
  D)
   \[[-5,5]\]
  done clear
  View Answer play_arrow

• question_answer167) An equation of the plane, parallel to the plane passing through the points \[(1,1,1),\,\,(2,3,5)\] and \[(-1,0,2)\] and at a distance 3 from it, is
  A)
   \[2x-3y+z+3\sqrt{14}=0\]
  done clear
  B)
   \[2x-3y+z+2\sqrt{14}=0\]
  done clear
  C)
   \[2x-3y+z+\sqrt{14}=0\]
  done clear
  D)
   \[2x-3y+z-2\sqrt{14}=0\]
  done clear
  View Answer play_arrow

• question_answer168) In which of the following interval, the function \[y(x)={{x}^{3}}-3{{x}^{2}}-9x+5\] is always decreasing?
  A)
   \[(-1,3)\]              
  done clear
  B)
   \[(-3,3)\]
  done clear
  C)
   \[(-4,4)\]              
  done clear
  D)
   \[(-2,2)\]
  done clear
  View Answer play_arrow

• question_answer169) If getting a number greater than 4 is a success in a throw of a fair die, then the probability of at least 2 successes in six throws of a fair die is
  A)
   \[0.649\]   
  done clear
  B)
   \[0.351\]  
  done clear
  C)
   \[0.267\]   
  done clear
  D)
   \[0.667\]
  done clear
  View Answer play_arrow

• question_answer170) Let \[f(x)={{x}^{2}},\,g(x)={{\log }_{e}}x\]. The number of values of for which \[(fog)\,(x)=(gof)\,(x),\] is
  A)
   1
  done clear
  B)
   2
  done clear
  C)
   finite but greater than 2
  done clear
  D)
   infinitely many
  done clear
  View Answer play_arrow

• question_answer171) If \[{{z}_{1}}=\cos \alpha +i\,\sin \alpha \]since and \[{{z}_{2}}=\cos \beta +i\,\sin \beta ,\] then \[\frac{({{z}_{1}}-{{z}_{2}})\,({{z}_{1}}{{z}_{2}}+1)}{({{z}_{1}}+{{z}_{2}})({{z}_{1}}{{z}_{2}}-1)}\]is equal to
  A)
   \[\tan \left( \frac{\alpha +\beta }{2} \right)\,\,\tan \left( \frac{\alpha -\beta }{2} \right)\]
  done clear
  B)
   \[\cot \left( \frac{\alpha +\beta }{2} \right)\,\,\cot \left( \frac{\alpha +\beta }{2} \right)\]
  done clear
  C)
   \[\cot \left( \frac{\alpha -\beta }{2} \right)\,\,\cot \left( \frac{\alpha +\beta }{2} \right)\]
  done clear
  D)
   \[\cot \left( \frac{\alpha +\beta }{2} \right)\,\,\cot \left( \frac{\alpha +\beta }{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer172) \[\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{0+2+4+6+....+2n}{1+3+5+7+....+(2n-1)}\] is equal to
  A)
   \[0\]                 
  done clear
  B)
   \[1\]
  done clear
  C)
   \[2\]                 
  done clear
  D)
   Does not exist
  done clear
  View Answer play_arrow

• question_answer173) In a \[\Delta ABC,\] if \[\sin (A)=\frac{5}{13}\] and \[\sin (B)=\frac{99}{101},\] then the value of \[(1313\,\cos \,(C))\] is
  A)
   \[255\]                
  done clear
  B)
   \[265\]
  done clear
  C)
   \[275\]                
  done clear
  D)
   \[770\]
  done clear
  View Answer play_arrow

• question_answer174) Out of 64 students in a class, the number of students taking Mathematics is 55 and the number of students taking both Mathematics and Physics is 10. If all the students take either Mathematics or Physics or both, then the number of students taking only Physics is
  A)
   \[19\]              
  done clear
  B)
   \[20\]
  done clear
  C)
   \[15\]               
  done clear
  D)
   \[25\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer175) The derivative of sin x with respect to \[cos\text{ }x\]is
  A)
   \[sin\,\,x\]              
  done clear
  B)
   \[-cos\,x\]
  done clear
  C)
   \[tan\,\,x\]              
  done clear
  D)
   \[-cot\,x\]
  done clear
  View Answer play_arrow

• question_answer176) In how many ways, you can choose one or more identical balls out of six identical balls?
  A)
   \[31\]     
  done clear
  B)
   \[32\]     
  done clear
  C)
   \[63\]     
  done clear
  D)
   \[64\]
  done clear
  View Answer play_arrow

• question_answer177) If M is a \[3\times 3\]skew symmetric matrix, then det (M)is
  A)
   \[-1\]    
  done clear
  B)
   \[0\]
  done clear
  C)
   \[4\]     
  done clear
  D)
   \[1\]
  done clear
  View Answer play_arrow

• question_answer178) Length of the segment of the normal at the point \[(1,1)\] to the curve given by \[{{y}^{2}}(2-x)={{x}^{3}}\] between X-axis and the point is
  A)
   \[\frac{\sqrt{5}}{2}\]     
  done clear
  B)
   \[\sqrt{5}\]
  done clear
  C)
    \[2\sqrt{5}\]    
  done clear
  D)
   \[\sqrt{2}\]
  done clear
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• question_answer179) If the direction ratios of a line are \[(\lambda +1,\,1-\lambda ,2)\]and the line makes an angle 60° with the Y-axis, then a value of \[\lambda \] is
  A)
   \[1+\sqrt{3}\]             
  done clear
  B)
   \[2-\sqrt{3}\]
  done clear
  C)
   \[3+\sqrt{5}\]             
  done clear
  D)
   \[2-\sqrt{5}\]
  done clear
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• question_answer180) Value of \[\cos \,\left( {{\sin }^{-1}}\left( \frac{2}{5} \right) \right)\] is
  A)
   \[\frac{17}{25}\]
  done clear
  B)
   \[-\frac{51}{135}\]
  done clear
  C)
   \[\frac{-2\sqrt{18}}{120}\]
  done clear
  D)
   \[\frac{9\sqrt{21}}{125}\]
  done clear
  View Answer play_arrow