Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2009

done J and K - CET Engineering Solved Paper-2009 Total Questions - 225

• question_answer1) The quantities RC and \[\left( \frac{L}{R} \right)\] ( where R, L and C stand   for   resistance,   inductance   and capacitance respectively ) have the dimensions of
  A)
   force         
  done clear
  B)
   linear momentum
  done clear
  C)
   linear velocity  
  done clear
  D)
   time
  done clear
  View Answer play_arrow

• question_answer2) The correct vector relation between linear velocity \[\vec{v}\] and angular velocity \[\vec{\omega }\] in rigid body dynamics is ( where \[\vec{r}\] is the postion vector)
  A)
   \[\vec{\omega }=\vec{v}\times \vec{r}\]
  done clear
  B)
   \[\vec{v}=\vec{r}/\vec{\omega }\]
  done clear
  C)
   \[\vec{v}=\vec{\omega }\times \vec{r}\]
  done clear
  D)
   \[\vec{r}=\vec{v}\times \vec{\omega }\]
  done clear
  View Answer play_arrow

• question_answer3) Which of the following cannot be speed-time graph?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
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• question_answer4) Magnitudes of four pairs of displacement vectors are given. Which pair of displacement vectors, under vector addition, fails to give a resultant vector of magnitude\[3\text{ }cm\]?
  A)
   \[2\text{ }cm,7\text{ }cm\]
  done clear
  B)
   \[1\text{ }cm,4\text{ }cm\]
  done clear
  C)
   \[2\text{ }cm,3\text{ }cm~\]
  done clear
  D)
   \[2\text{ }cm,4\text{ }cm\]
  done clear
  View Answer play_arrow

• question_answer5) The maximum range of a projectile is\[100\text{ }m\]. The maximum height reached by it is
  A)
   \[100\text{ }m\]        
  done clear
  B)
   \[\text{25 }m\]
  done clear
  C)
   \[\text{200 }m\]        
  done clear
  D)
   \[\text{75 }m\]
  done clear
  View Answer play_arrow

• question_answer6) The working principle of rocket propulsion is conservation of
  A)
   angular momentum
  done clear
  B)
   mass
  done clear
  C)
   linear momentum
  done clear
  D)
   kinetic energy
  done clear
  View Answer play_arrow

• question_answer7) In inelastic collision
  A)
   momentum, kinetic energy and total energy are conserved
  done clear
  B)
   momentum, kinetic energy and total energy are not conserved
  done clear
  C)
   momentum, and kinetic energy are conserved but total energy is not conserved
  done clear
  D)
   total energy and momentum are conserved but kinetic energy is not conserved
  done clear
  View Answer play_arrow

• question_answer8) A cricket ball of mass \[0.5\text{ }kg\]strikes a cricket bat normally with a velocity of \[20\text{ }m{{s}^{-1}}\] and rebounds with velocity of \[10\text{ }m{{s}^{-1}}\]. The impulse of the force exerted by the ball on the bat is
  A)
   \[15\text{ }Ns\]         
  done clear
  B)
   \[25\text{ }Ns\]
  done clear
  C)
   \[30\text{ }Ns\]         
  done clear
  D)
   \[10\text{ }Ns\]
  done clear
  View Answer play_arrow

• question_answer9) Assuming earth to be an inertial frame, an example for inertial frame observer is
  A)
   a driver in a train which is slowing down to stop
  done clear
  B)
   a person in a car moving with uniform velocity
  done clear
  C)
   a girl revolving in a merry-go-round
  done clear
  D)
   a passenger in an aircraft which is taking off
  done clear
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• question_answer10) If the force acting on a body is inversely proportional to its speed, then its kinetic energy is
  A)
   linearly related to time
  done clear
  B)
   inversely proportional to time
  done clear
  C)
   inversely proportional to the square of time
  done clear
  D)
   a constant
  done clear
  View Answer play_arrow

• question_answer11) A body, possessing kinetic energy T, moving on a rough horizontal surface, is stopped in a distance y. The frictional force exerted on the. body is
  A)
   \[Ty\]
  done clear
  B)
   \[\frac{\sqrt{T}}{y}\]
  done clear
  C)
   \[\frac{T}{y}\]
  done clear
  D)
   \[\frac{T}{\sqrt{y}}\]
  done clear
  View Answer play_arrow

• question_answer12) A particle is describing uniform circular motion. Its acceleration is
  A)
   along the radius of the circular path pointing towards the centre
  done clear
  B)
   along the tangent to the circular path
  done clear
  C)
   along the radius of the circular path pointing away from the centre
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer13) \[{{I}_{1}}\] and \[{{I}_{2}}\] are the moments of inertia of two circular discs about their central axes perpendicular to their surfaces. Their angular frequencies of rotation are \[{{\omega }_{1}}\] and \[{{\omega }_{2}}\] respectively. If they are brought into contact face to face with their axes of rotation coinciding with each other, the angular frequency of the composite disc will be
  A)
   \[\frac{{{I}_{1}}+{{I}_{2}}}{{{\omega }_{1}}+{{\omega }_{2}}}\]
  done clear
  B)
   \[\frac{{{I}_{2}}{{\omega }_{1}}-{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}-{{I}_{2}}}\]
  done clear
  C)
   \[\frac{{{I}_{2}}{{\omega }_{1}}+{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\]
  done clear
  D)
   \[\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer14) A child stands at one end of a boat moving with a speed v in still water. If the child starts running towards the other end of the boat with a speed u, the centre of mass of the system (boat and child) will move with a speed
  A)
   \[v-u\]          
  done clear
  B)
   \[v\]
  done clear
  C)
   \[u\]              
  done clear
  D)
   \[v+u\]
  done clear
  View Answer play_arrow

• question_answer15) In planetary motion, the quantity that remains unchanged is
  A)
   radius of the orbit
  done clear
  B)
   speed along the orbit
  done clear
  C)
   total angular momentum
  done clear
  D)
   angular speed
  done clear
  View Answer play_arrow

• question_answer16) Work done in taking a mass from one point to another in a gravitational field depends on
  A)
   the end points, only
  done clear
  B)
   the path followed
  done clear
  C)
   the velocity of the mass
  done clear
  D)
   both the length of the path and the and points
  done clear
  View Answer play_arrow

• question_answer17) A body is projected up from the surface of the earth with a velocity equal to \[\frac{3}{4}th\] of its escape velocity. If R be the radius of earth, the height it reaches is
  A)
   \[\frac{3R}{10}\]
  done clear
  B)
   \[\frac{9R}{7}\]
  done clear
  C)
   \[\frac{8R}{5}\]
  done clear
  D)
   \[\frac{9R}{5}\]
  done clear
  View Answer play_arrow

• question_answer18) A satellite moving round the earth in circular orbit of radius r and speed v suddenly loses some of its energy. Then,
  A)
   r will increase and v will decrease
  done clear
  B)
   both r and v will decrease
  done clear
  C)
   both r and v will increase
  done clear
  D)
   r will decrease and v will increase
  done clear
  View Answer play_arrow

• question_answer19) The stress required to double the length of wire of Young's modulus Y is
  A)
   \[\frac{Y}{2}\]              
  done clear
  B)
   \[2Y\]
  done clear
  C)
   \[Y\]              
  done clear
  D)
   \[4\,y\]
  done clear
  View Answer play_arrow

• question_answer20) Water flows through a pipe of varying cross-section. Then the ratio of the speeds of water at two points 1 and 2, where the radii of the pipe are \[{{r}_{1}}\] and \[{{r}_{2}}\] is
  A)
   \[\frac{r_{2}^{2}}{r_{1}^{2}}\]
  done clear
  B)
   \[\frac{{{r}_{2}}}{{{r}_{1}}}\]
  done clear
  C)
   \[\frac{r_{1}^{2}}{r_{2}^{2}}\]
  done clear
  D)
   \[\frac{{{r}_{1}}}{{{r}_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer21) A piece of ice, with a stone embedded inside it, is floating in water contained in a vessel. When the ice melts completely, the level of water in vessel
  A)
   remains unchanged
  done clear
  B)
   rises
  done clear
  C)
   falls
  done clear
  D)
    falls in the beginning and rises to the same level later
  done clear
  View Answer play_arrow

• question_answer22) The excess pressure inside a cylindrical drop of liquid or a cylindrical bubble of radius R in a liquid of surface tension T is
  A)
   \[\frac{T}{4R}\]
  done clear
  B)
   \[\frac{T}{R}\]
  done clear
  C)
   \[\frac{2T}{R}\]
  done clear
  D)
   \[\frac{4T}{R}\]
  done clear
  View Answer play_arrow

• question_answer23) Two small spheres of radii r and \[4r\] fall through a viscous liquid with the same 'terminal velocity. The ratio between the viscous forces acting on them is
  A)
   \[1:2\]           
  done clear
  B)
   \[4:1\]
  done clear
  C)
   \[1:16\]          
  done clear
  D)
   \[1:4\]
  done clear
  View Answer play_arrow

• question_answer24) A certain quantity of heat energy is given to a diatomic ideal gas which expands at constant pressure. The fraction of the heat energy that is converted into work is
  A)
   \[2/3\]           
  done clear
  B)
   \[2/7\]
  done clear
  C)
   \[1/5\]           
  done clear
  D)
   \[1/7\]
  done clear
  View Answer play_arrow

• question_answer25) When the temperature of a gas is increased
  A)
   its molecular kinetic energy increases
  done clear
  B)
   molecular potential energy decreases and molecular kinetic energy also decreases, total energy remaining constant
  done clear
  C)
   molecular potential energy increases and molecular kinetic energy decreases; total energy remaining constant
  done clear
  D)
   its molecular potential energy increases
  done clear
  View Answer play_arrow

• question_answer26) Two monoatomic ideal gases A and B occupying the same volume V, are at the same temperature T and pressure p. If they are mixed, the resultant mixture has volume V and temperature T. The pressure of the mixture is
  A)
   \[P\]               
  done clear
  B)
   \[\frac{P}{2}\]
  done clear
  C)
   \[4\,P\]            
  done clear
  D)
   \[2\,P\]
  done clear
  View Answer play_arrow

• question_answer27) The requirement for heat conduction to take place in a solid is
  A)
   density gradient
  done clear
  B)
   uniform density
  done clear
  C)
   temperature gradient
  done clear
  D)
   uniform temperature
  done clear
  View Answer play_arrow

• question_answer28) A Carnot's engine working between \[{{27}^{o}}C\] and \[{{127}^{o}}C\] has a work output of\[200\text{ }J/cycle\]. The energy supplied to the engine from the source in each cycle is
  A)
   \[400\text{ }J\]         
  done clear
  B)
   \[800\text{ }J\]
  done clear
  C)
   \[600\text{ }J\]         
  done clear
  D)
   \[500\text{ }J\]
  done clear
  View Answer play_arrow

• question_answer29) A particle is executing linear simple harmonic motion. The fraction of the total energy that is potential, when its displacement is \[\frac{1}{4}\] of the amplitude is
  A)
   \[1/16\]          
  done clear
  B)
   \[1/8\]
  done clear
  C)
   \[1/2\]            
  done clear
  D)
   \[1/4\]
  done clear
  View Answer play_arrow

• question_answer30) The equation \[y=A\,\,\sin \,k(vt-x)\] represents \[\left( k=\frac{2\pi }{\lambda } \right)\]
  A)
    a plane progressive wave travelling along negative X-direction
  done clear
  B)
   a plane progressive wave travelling along positive X-direction
  done clear
  C)
   a stationary wave
  done clear
  D)
   a plane progressive wave travelling along positive Y-direction
  done clear
  View Answer play_arrow

• question_answer31) The third overtone of an open organ pipe is in resonance with the second overtone of a closed organ pipe. If the length of the open pipe is \[8\text{ }cm,\] then the length of closed pipe is
  A)
   \[10\text{ }cm\]       
  done clear
  B)
   \[8\text{ }cm\]
  done clear
  C)
   \[12\,\,cm\]         
  done clear
  D)
   \[5\,\,cm\]
  done clear
  View Answer play_arrow

• question_answer32) When a wave undergoes refraction
  A)
   its frequency changes
  done clear
  B)
   its amplitude changes
  done clear
  C)
   its velocity changes
  done clear
  D)
   both amplitude and frequency change
  done clear
  View Answer play_arrow

• question_answer33) A sound wave with frequency \[256\text{ }Hz\]falls normally on a perfectly reflecting wall. The shortest distance from the wall at which the air particles will have maximum amplitude of vibrations is nearly ( velocity of sound in air is \[336\,m{{s}^{-1}}\])
  A)
   \[32.8\,\,cm\]       
  done clear
  B)
   \[50\,\,cm\]
  done clear
  C)
   \[65.8\,\,cm\]       
  done clear
  D)
   \[25\,\,cm\]
  done clear
  View Answer play_arrow

• question_answer34) When air medium in which two charges kept apart at a distance r is replaced by a dielectric medium of dielectric constant K, the force between the charges
  A)
   remains unchanged
  done clear
  B)
   decreases K times
  done clear
  C)
   increases K times
  done clear
  D)
   increases \[{{K}^{2}}\]times
  done clear
  View Answer play_arrow

• question_answer35) The magnitude of electric field E required to balance an oil drop of mass m, carrying charge q is (g = acceleration due to gravity)
  A)
   \[\frac{q}{m}\]
  done clear
  B)
   \[\frac{mg}{{{q}^{2}}}\]
  done clear
  C)
   \[mgq\]
  done clear
  D)
   \[\frac{mg}{q}\]
  done clear
  View Answer play_arrow

• question_answer36) Three charges \[-q,\] \[+Q\] and \[-q\] are placed in a straight line as shown. If the total potential energy of the system is zero, then the ratio \[\frac{q}{Q}\]is
  A)
   \[2\]
  done clear
  B)
   \[5.5\]
  done clear
  C)
   \[4\]
  done clear
  D)
    \[1.5\]
  done clear
  View Answer play_arrow

• question_answer37) Electric flux emanating through a surface element \[\overrightarrow{ds}=5\hat{i}\] placed in an electric field \[\vec{E}=4\hat{i}+4\hat{j}+4\hat{k}\] is
  A)
   \[10\text{ }units\]        
  done clear
  B)
   \[20\text{ }units\]
  done clear
  C)
   \[~4\text{ }units\]         
  done clear
  D)
   \[16\text{ }units\]
  done clear
  View Answer play_arrow

• question_answer38) A parallel plate capacitor is charged to a potential of V volt. The battery is then disconnected and the distance between the plates of the capacitor is increased using an insulating handle. The potential difference between the plates of the capacitor will
  A)
   increase       
  done clear
  B)
   decrease
  done clear
  C)
   not change     
  done clear
  D)
   become zero
  done clear
  View Answer play_arrow

• question_answer39) Energy stored per unit volume of a parallel plate capacitor having plate area A and plate separation d when charged to a potential of V volts is (air space in between the plates)
  A)
   \[\frac{1}{2}{{C}^{2}}{{V}^{2}}\]
  done clear
  B)
   \[\frac{{{q}^{2}}}{4\,C}\]
  done clear
  C)
   \[\frac{1}{2}{{E}_{0}}\left( \frac{V}{d} \right)\]
  done clear
  D)
   \[\frac{1}{2}{{E}_{0}}\left( \frac{{{V}^{2}}}{{{d}^{2}}} \right)\]
  done clear
  View Answer play_arrow

• question_answer40) The mutual electrostatic potential energy between two protons which are at a distance of  \[9\times 10{{-}^{15}}\text{ }m,\] in \[_{92}{{U}^{235}}\] nucleus is
  A)
   \[1.56\times {{10}^{-14}}J\]
  done clear
  B)
   \[5.5\times {{10}^{-14}}J\]
  done clear
  C)
   \[2.56\times {{10}^{-14}}J\]
  done clear
  D)
   \[4.56\times {{10}^{-14}}J\]
  done clear
  View Answer play_arrow

• question_answer41) The SI units of electron mobility are
  A)
   \[{{m}^{2}}{{s}^{-1}}{{V}^{-1}}\]    
  done clear
  B)
   \[ms\,\,{{V}^{-1}}\]
  done clear
  C)
   \[m{{s}^{-1}}\,\,V\]        
  done clear
  D)
   \[{{m}^{2}}{{s}^{-2}}\,\,{{V}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer42) A copper wire and a silicon wire are heated from room temperature to \[{{60}^{o}}C\]. Then
  A)
   resistance of both the wires decreases
  done clear
  B)
   resistance of both the wires increases
  done clear
  C)
   resistance of copper wire decreases and that of silicon wire increases
  done clear
  D)
   resistance of copper wire increases and that of silicon wire decreases
  done clear
  View Answer play_arrow

• question_answer43) The tungsten filaments of two electric bulbs are of the same length. If one of them gives \[25\text{ }W\]power and the other \[60\text{ }W\]power, then
  A)
   both the filaments are of same thickness
  done clear
  B)
   \[25\text{ }W\]bulb has thicker filament
  done clear
  C)
   \[60\text{ }W\] bulb has thicker filament
  done clear
  D)
   both the filaments have same cross-section area
  done clear
  View Answer play_arrow

• question_answer44) Heater coil A takes \[{{t}_{1}}\] second to boil certain quantity of water. Heater coil B takes 13 second to boil same quantity of water. If A and B are connected in series, the time taken to boil the same quantity of water by the combination is
  A)
   \[-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{2}\]
  done clear
  B)
   \[\frac{1}{\sqrt{2}},-\frac{1}{2},\frac{1}{2}\]
  done clear
  C)
   \[-\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]
  done clear
  D)
   \[\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer45) When the cold and hot junctions of a thermocouple are interchanged, the thermo emf
  A)
   changes sign   
  done clear
  B)
   remains the same
  done clear
  C)
   becomes zero  
  done clear
  D)
   is doubled
  done clear
  View Answer play_arrow

• question_answer46) A charge q coulomb makes n revolutions in one second in a circular orbit of radius r. The magnetic field at the centre of the orbit in \[N{{A}^{-1}}{{m}^{-1}}\]is
  A)
   \[\frac{2\pi rn}{q}\times {{10}^{-7}}\]
  done clear
  B)
   \[\left( \frac{2\pi q}{r} \right)\times {{10}^{-7}}\]
  done clear
  C)
   \[\frac{1}{2}({{t}_{1}}+{{t}_{2}})\]
  done clear
  D)
   s\[\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer47) In a moving coil galvanometer, to make the field radial
  A)
   coil is wound on wooden frame
  done clear
  B)
   magnetic poles are cylindrically cut
  done clear
  C)
   a horse-shoe magnet is used
  done clear
  D)
   the number of windings in the coil is decreased
  done clear
  View Answer play_arrow

• question_answer48) An electron travelling with velocity v, enters a region of space in which electric and magnetic fields exist. Then the electron goes uneffected for all values of fields
  A)
   if both electric and magnetic fields are normal to v
  done clear
  B)
   if the magnetic field alone in normal to v
  done clear
  C)
   if both electric and magnetic fields are parallel to v
  done clear
  D)
   if the electric field alone is normal to v
  done clear
  View Answer play_arrow

• question_answer49) Magnetic field at the centre of a coil in the form of a square of side \[2\text{ }cm\]carrying a current of \[1.414\text{ }A\]is
  A)
   \[8\times {{10}^{-5}}T\]
  done clear
  B)
   \[8\times {{10}^{-5}}T\]
  done clear
  C)
   \[1.5\times {{10}^{-5}}T\]
  done clear
  D)
   \[6\times {{10}^{-5}}T\]
  done clear
  View Answer play_arrow

• question_answer50) The resistance of an ideal voltmeter is
  A)
   zero          
  done clear
  B)
   low
  done clear
  C)
   high           
  done clear
  D)
   infinity
  done clear
  View Answer play_arrow

• question_answer51) The relation connecting magnetic susceptibility \[{{\chi }_{m}}\]and relative permeability \[{{\mu }_{r}}\] is
  A)
   \[{{\chi }_{m}}={{\mu }_{r}}+1\]
  done clear
  B)
   \[{{\chi }_{m}}={{\mu }_{r}}-1\]
  done clear
  C)
   \[{{\chi }_{m}}=\frac{1}{{{\mu }_{r}}}\]
  done clear
  D)
   \[{{\chi }_{m}}=3(1+{{\mu }_{r}})\]
  done clear
  View Answer play_arrow

• question_answer52) Whenever there is a relative motion between a coil and a magnet, the magnitude of induced emf set up in the coil does not depend upon the
  A)
   relative speed between the coil and magnet
  done clear
  B)
   magnetic moment of the coil
  done clear
  C)
   resistance of the coil
  done clear
  D)
   number of turns in the coil
  done clear
  View Answer play_arrow

• question_answer53) A uniformly wound coil of self-inductance \[1.2\times {{10}^{-4}}H\]and resistance \[3\Omega \]. is broken up into two identical coils. These coils are then connected parallel across a \[6V\]battery of negligible resistance. The time constant for the current in the circuit is (neglect mutual inductance)
  A)
   \[0.4\times {{10}^{-4}}s\]
  done clear
  B)
   \[0.2\times {{10}^{-4}}\text{ }s\]
  done clear
  C)
   \[0.5\times {{10}^{-4}}\text{ }s\]    
  done clear
  D)
   \[0.1\times {{10}^{-4}}\text{ }s\]
  done clear
  View Answer play_arrow

• question_answer54) In AC circuit Ohm's law is applicable for
  A)
   instantaneous values of current and voltage only
  done clear
  B)
   rms values of current and voltage only
  done clear
  C)
   peak values of current and voltage only
  done clear
  D)
   all values of current and voltage
  done clear
  View Answer play_arrow

• question_answer55) The average power dissipated in a pure capacitance AC circuit is
  A)
   \[CV\]           
  done clear
  B)
   zero
  done clear
  C)
   \[\frac{1}{C{{V}^{2}}}\]
  done clear
  D)
   \[\frac{1}{4}C{{V}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer56) The instantaneous values of current and  voltage in an AC circuit are given by \[I=6\,\,\sin \,\left( 100\,\pi t+\frac{\pi }{4} \right),\] \[V=5\,\,\sin \,\left( 100\,\pi t-\frac{\pi }{4} \right),\] then
  A)
   current leads the voltage by \[{{45}^{o}}\]
  done clear
  B)
   voltage leads the current by \[{{90}^{o}}\]
  done clear
  C)
   current leads the voltage by \[{{90}^{o}}\]
  done clear
  D)
   voltage leads the current by \[{{45}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer57) The velocity of an electromagnetic wave in vacuum can be changed by changing
  A)
   frequency     
  done clear
  B)
   amplitude
  done clear
  C)
   wavelength    
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer58) The relationship between phase difference \[\Delta \phi \] and the path difference \[\Delta x\] between two interfering waves is given by (\[\lambda \]= wavelength)
  A)
   \[\Delta x=\left( \frac{\lambda }{2\pi } \right)\Delta \phi \]
  done clear
  B)
   \[\Delta x=\left( \frac{2\pi }{\lambda } \right)\Delta \phi \]
  done clear
  C)
   \[\Delta \phi =\left( \frac{\pi }{\lambda } \right)\Delta x\]
  done clear
  D)
   \[\Delta \phi =(2\pi )\,\,\Delta x\]
  done clear
  View Answer play_arrow

• question_answer59) In Young's double slit experiment, the fringe width with light of wavelength \[6000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]is\[3\text{ }mm\]. The fringe width, when the wavelength of light is changed to \[4000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]is
  A)
    \[3\text{ }mm\]
  done clear
  B)
    \[1\text{ }mm\]
  done clear
  C)
   \[\text{2 }mm\]
  done clear
  D)
   \[\text{4 }mm\]
  done clear
  View Answer play_arrow

• question_answer60) If the width of the slit in single slit diffraction experiment is doubled, then the central maximum of diffraction pattern becomes
  A)
   broader and brighter
  done clear
  B)
   sharper and brighter
  done clear
  C)
   sharper and fainter
  done clear
  D)
   broader and fainter
  done clear
  View Answer play_arrow

• question_answer61) Transverse nature of light was confirmed by the phenomenon of
  A)
   refraction of light    
  done clear
  B)
   diffraction of light
  done clear
  C)
   dispersion of light
  done clear
  D)
   polarization of light
  done clear
  View Answer play_arrow

• question_answer62) If a transparent parallel plate of uniform thickness t and refractive index \[\mu ,\] is interposed perpendicularly in the path of a light beam, the optical path is
  A)
   increased by \[(\mu -1)\,t\]
  done clear
  B)
   decreased by \[\mu \,t\]
  done clear
  C)
   decreased by \[(\mu -1)\,t\]
  done clear
  D)
   increased by \[\mu \,t\]
  done clear
  View Answer play_arrow

• question_answer63) If the photoelectric work function for a metallic surface is \[4.125\text{ }eV,\]the cut-off wavelength for photoelectric phenomenon for the surface is
  A)
   \[4500\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]        
  done clear
  B)
   \[1700\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  C)
   \[2800\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]        
  done clear
  D)
   \[3000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,\]
  done clear
  View Answer play_arrow

• question_answer64) The masses of two particles having same kinetic energies are in the ratio\[1:2\]. Then their de-Broglie wavelengths are in the ratio
  A)
   \[2:1\]
  done clear
  B)
   \[1:2\]
  done clear
  C)
   \[\sqrt{2}:1\]          
  done clear
  D)
   \[\sqrt{3}:1\]
  done clear
  View Answer play_arrow

• question_answer65) Balmer series of hydrogen atom lies in
  A)
   microwave region                       .
  done clear
  B)
   visible region
  done clear
  C)
   ultraviolet region
  done clear
  D)
   infrared region
  done clear
  View Answer play_arrow

• question_answer66) The shortest wavelength of X-rays coming from an X-ray tube depends on the
  A)
   voltage applied to the tube
  done clear
  B)
   current in the tube
  done clear
  C)
   atomic number of target element
  done clear
  D)
   nature of gas in the tube
  done clear
  View Answer play_arrow

• question_answer67) The nuclear force
  A)
   is purely an electrostatic force
  done clear
  B)
   obeys inverse square law of distance
  done clear
  C)
   is equal in strength to gravitational force
  done clear
  D)
   is short range force
  done clear
  View Answer play_arrow

• question_answer68) A radioactive isotope A with a half-life of \[1.25\times {{10}^{10}}\text{ }yr\]decays into B which is stable. A sample of rock from a planet is found to contain both A and B present in the ratio\[1:15\]. The age of the rock is (in years)
  A)
   \[9.6\times {{10}^{10}}\]
  done clear
  B)
   \[4.2\times {{10}^{10}}\]
  done clear
  C)
   \[5\times {{10}^{10}}\]
  done clear
  D)
   \[1.95\times {{10}^{10}}\]
  done clear
  View Answer play_arrow

• question_answer69) Enriched uranium is used in nuclear reactors because, it contains greater proportion of
  A)
   \[{{U}^{238}}\]          
  done clear
  B)
   \[{{U}^{235}}\]
  done clear
  C)
   \[{{U}^{239~}}\]         
  done clear
  D)
   \[{{U}^{233}}\]
  done clear
  View Answer play_arrow

• question_answer70) The weakest bond in solids is
  A)
   van der Waals' 
  done clear
  B)
   metallic
  done clear
  C)
   covalent       
  done clear
  D)
   ionic
  done clear
  View Answer play_arrow

• question_answer71) In a semiconducting material \[1/5th\]of the total current is carried by the holes and the remaining is carried by the electrons. The drift speed of electrons is twice that of holes at this temperature, the ratio between the -number densities of electrons and holes is
  A)
   \[21/6\]          
  done clear
  B)
   \[5\]
  done clear
  C)
   \[3/8\]            
  done clear
  D)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer72) In a transistor, the base is
  A)
   a conductor with high conductivity
  done clear
  B)
   an insulator
  done clear
  C)
   an extrinsic semiconductor
  done clear
  D)
   an intrinsic semiconductor
  done clear
  View Answer play_arrow

• question_answer73) The following figure represents
  A)
   OR gate       
  done clear
  B)
   NOT gate
  done clear
  C)
   NOR gate     
  done clear
  D)
   AND gate
  done clear
  View Answer play_arrow

• question_answer74) In amplitude modulation, the bandwidth is
  A)
   twice the audio signal frequency
  done clear
  B)
   thrice the audio signal frequency
  done clear
  C)
   thrice the carrier wave frequency
  done clear
  D)
   twice the carrier wave frequency
  done clear
  View Answer play_arrow

• question_answer75) In a typical optical fibres, the difference between the refractive indices of core material and cladding material is of the order of
  A)
   \[{{10}^{-5}}\]           
  done clear
  B)
   \[{{10}^{-6}}\]
  done clear
  C)
   \[{{10}^{-1}}\]           
  done clear
  D)
   \[{{10}^{-3}}\]
  done clear
  View Answer play_arrow

• question_answer76) The   equivalent   mass   of   potassium permanganate in alkaline medium is its
  A)
   \[\frac{\text{molar}\,\text{mass}}{\text{5}}\]
  done clear
  B)
   \[\frac{\text{molar}\,\text{mass}}{3}\]
  done clear
  C)
   \[\frac{\text{molar}\,\text{mass}}{\text{2}}\]
  done clear
  D)
   molar mass itself
  done clear
  View Answer play_arrow

• question_answer77) The number of molecules in 18 mg of water in terms of Avogadro number N is
  A)
   \[{{10}^{-3}}N\]
  done clear
  B)
  \[{{10}^{-2}}N\]
  done clear
  C)
   \[{{10}^{-1}}N\]
  done clear
  D)
  \[10N\]
  done clear
  View Answer play_arrow

• question_answer78) If the de-Broglie wavelength of a particle of mass m is 100 times its velocity then its value in terms of its mass\[(m)\] and Plants constant \[(h)\] is
  A)
   \[\frac{1}{10}\sqrt{m/h}\]
  done clear
  B)
  \[10\sqrt{h/m}\]
  done clear
  C)
   \[\frac{1}{10}\sqrt{h/m}\]
  done clear
  D)
  \[10\sqrt{m/h}\]
  done clear
  View Answer play_arrow

• question_answer79) How much volume of oxygen at STP, in litre is required to burn 4g of methane gas completely?
  A)
   11.2            
  done clear
  B)
   5.6
  done clear
  C)
   2.8             
  done clear
  D)
   8
  done clear
  View Answer play_arrow

• question_answer80) The set of quantum numbers \[n=4,l=0\]and \[s=+\frac{1}{2}\] correspond to the most loosely bound, ground state electron of which one of the following atoms?
  A)
   \[Na\]
  done clear
  B)
  \[Cl\]
  done clear
  C)
   \[Cr\]
  done clear
  D)
  \[Rb\]
  done clear
  View Answer play_arrow

• question_answer81) The\[\beta \]decay of a radioactive element results in the formation of its
  A)
   isotope
  done clear
  B)
   isobar
  done clear
  C)
   isodiapher
  done clear
  D)
   nuclear isomer
  done clear
  View Answer play_arrow

• question_answer82) In the radioactive, decay, \[_{y}{{X}^{z}}\xrightarrow{(-8\alpha \,\text{and}\,\text{6}\beta )}{{\,}_{82}}P{{b}^{206}},x,y\]and \[z\]are
  A)
   U, 92 and 235
  done clear
  B)
   Th, 90 and 232
  done clear
  C)
   Pu, 94 and 238
  done clear
  D)
   U, 92 and 238
  done clear
  View Answer play_arrow

• question_answer83) In which one of the following equilibria, the increase of pressure over the equilibrium will favour the reaction?
  A)
   Pecomposition equilibrium of HI
  done clear
  B)
   Formation equilibrium of\[\text{S}{{\text{O}}_{\text{3}}}\]
  done clear
  C)
   Decomposition equilibrium of\[\text{N}{{\text{H}}_{3}}\]
  done clear
  D)
   Formation equilibrium of \[PC{{l}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer84)  Which one of the following is the correct quadratic form of the Ostwald's dilution law equation?
  A)
   \[{{\alpha }^{2}}C+\alpha K-K=0\]
  done clear
  B)
   \[{{\alpha }^{2}}C-\alpha K-K=0\]
  done clear
  C)
   \[{{\alpha }^{2}}C-\alpha K+K=0\]
  done clear
  D)
   \[{{\alpha }^{2}}C+\alpha K+K=0\]
  done clear
  View Answer play_arrow

• question_answer85) Which one of the following aqueous solutions of salts has the lowest, pH value?
  A)
  \[C{{H}_{3}}COONa\]
  done clear
  B)
  \[NaCl\]
  done clear
  C)
   \[N{{H}_{4}}OOCC{{H}_{3}}\]
  done clear
  D)
  \[N{{H}_{4}}Cl\]
  done clear
  View Answer play_arrow

• question_answer86) The solubility product of a sparingly soluble metal hydroxide \[\text{M(OH}{{\text{)}}_{\text{2}}}\]at 298 K is\[\text{5}\times \text{1}{{\text{0}}^{-16}}\,mo{{l}^{3}}\,d{{m}^{-9}}.\]The pH value of its aqueous and saturated solution is
  A)
   5               
  done clear
  B)
   9
  done clear
  C)
   11.5          
  done clear
  D)
   8.5
  done clear
  View Answer play_arrow

• question_answer87) In the synthesis of ammonia from nitrogen and hydrogen gases, if \[6\times {{10}^{-2}}\] moles of hydrogen disappears in 10 min, the number of moles of ammonia formed in 3 min is
  A)
  \[1.8\times {{10}^{-2}}\]     
  done clear
  B)
  \[1.2\times {{10}^{-2}}\]
  done clear
  C)
   \[4.0\times {{10}^{-2}}\]
  done clear
  D)
   \[3.6\times {{10}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer88) In a reversible reaction, the enthalpy change and the, activation energy in the forward direction  are  respectively \[-x\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\] and \[y\,kJ\,mo{{l}^{-1}},\]Therefore, the energy of activation in the backward direction in \[kJmo{{l}^{-1}},\]is
  A)
  \[(y-x)\]
  done clear
  B)
  \[(x+y)\]
  done clear
  C)
   \[(x-y)\]
  done clear
  D)
  \[-(x+y)\]
  done clear
  View Answer play_arrow

• question_answer89) The rate constant for a first order reaction is \[6.909\,{{\min }^{-1}},\]Therefore, the time required, in minute, for the participation of 75% of the initial reactant is
  A)
  \[2/3\text{ }log2\]     
  done clear
  B)
  \[~2/3\text{ }log\text{ }4\]
  done clear
  C)
  \[~3/2\text{ }log\,2\]       
  done clear
  D)
  \[~3/2\text{ }log\text{ }4\]
  done clear
  View Answer play_arrow

• question_answer90) A solution with negative deviation among the following is
  A)
   ethanol-acetone
  done clear
  B)
   chlorobenzene-bromobenzene
  done clear
  C)
   chloroform-acetone
  done clear
  D)
   benzene-toluene
  done clear
  View Answer play_arrow

• question_answer91) At 300 K, two pure liquids A and B have vapour pressures respectively 150 mm Hg and 100 mm Hg, In an equimolar liquid mixture of A and\[B,\] the mole fraction of B in the vapour mixture at this temperature is
  A)
   0.6             
  done clear
  B)
   0.5
  done clear
  C)
   0.8            
  done clear
  D)
   0,4
  done clear
  View Answer play_arrow

• question_answer92) The molar mass of the solute sodium hydroxide obtained from the measurement of the osmotic pressure of its aqueous solution at \[\text{27}{{\,}^{\text{o}}}\text{C}\]is\[25\,\text{g}\,\text{mo}{{\text{l}}^{-1}}.\]Therefore,    its    ionization percentage in this solution is
  A)
   75             
  done clear
  B)
   60
  done clear
  C)
   80            
  done clear
  D)
   70
  done clear
  View Answer play_arrow

• question_answer93) 25 g of a solute of molar mass \[250\,g\,mo{{l}^{-1}}\] is dissolved in 10 mL of water to obtain a solution whose density is \[1.25\,g{{(mL)}^{-1}}.\] The molarity and molality of the solution are respectively
  A)
   0.75 M and 1 m
  done clear
  B)
   0.8 M and 1 m
  done clear
  C)
   1 M and 0.8 m 
  done clear
  D)
   1 M and 0.75 m
  done clear
  E)
   None of These
  done clear
  View Answer play_arrow

• question_answer94) The standard enthalpies of formation of A \[A(N{{H}_{3}}),B(C{{O}_{2}}),C(HI)\]are respectively \[-\,46,19,-\text{ }393.4,+\,24,94\] and\[-296.9\,\text{kJmo}{{\text{l}}^{-1}},\]The increasing order of their stability is
  A)
   B < D < A < C
  done clear
  B)
   C < A < D < B
  done clear
  C)
   D < B < C < A
  done clear
  D)
   A < C < D < B
  done clear
  View Answer play_arrow

• question_answer95) When 400 mL of 0.2 N solution of a weak acid  is neutralised by a dilute aqueous solution of sodium hydroxide under standard conditions, \[4.4\,kJ\]amount of heat is liberated. Therefore, the standard enthalpy bf neutralisation of this weak acid, in \[kJ\,\text{equi}{{\text{v}}^{-1}},\]is
  A)
  \[-11\]           
  done clear
  B)
  \[-44\]
  done clear
  C)
  \[-\text{ }55\]          
  done clear
  D)
  \[~-22\]
  done clear
  View Answer play_arrow

• question_answer96) The incorrect statement among the following is
  A)
   The entropy of the universe remains constant
  done clear
  B)
   Heat can be completely converted into work only under specified conditions
  done clear
  C)
   The absolute entropy of a perfect crystalline    solid   at   absolute   zero temperature is zero
  done clear
  D)
   The total energy of an isolated system remains constant
  done clear
  View Answer play_arrow

• question_answer97) Which one of the following is always not negative?
  A)
   Enthalpy of combustion
  done clear
  B)
   Enthalpy of formation
  done clear
  C)
   Enthalpy of neutralisation
  done clear
  D)
   Lattice enthalpy
  done clear
  View Answer play_arrow

• question_answer98) The oxidation numbers of the sulphur atoms in peroxomonosulphuric acid\[({{H}_{2}}S{{O}_{5}})\]and peroxodisulphuric   acid  \[({{H}_{2}}{{S}_{2}}{{O}_{8}})\]  are respectively
  A)
   +8 and +7   
  done clear
  B)
   +3 and +3
  done clear
  C)
   +6 and +6   
  done clear
  D)
   +4 and +6
  done clear
  View Answer play_arrow

• question_answer99) In the electrolysis of aqueous solution of \[\text{CuS}{{\text{O}}_{\text{4}}}\] using copper electrodes, the process taking place at the anode is
  A)
  \[SO_{4}^{2-}\xrightarrow{{}}S{{O}_{4}}+2{{e}^{-}}\]
  done clear
  B)
  \[Cu\xrightarrow{{}}C{{u}^{+}}+{{e}^{-}}\]
  done clear
  C)
   \[2O{{H}^{-}}\xrightarrow{{}}{{H}_{2}}O+\frac{1}{2}{{O}_{2}}+2{{e}^{-}}\]
  done clear
  D)
   \[Cu\xrightarrow{{}}C{{u}^{2+}}+2{{e}^{-}}\]
  done clear
  View Answer play_arrow

• question_answer100) The correct expression in SI system relating the equivalent conductance\[({{\Lambda }_{c}}),\]specific conductance \[(\kappa )\]and equivalent concentration [C]  is  (where C is the number of gram-equivalents of the electrolyte in one litre of the solution)
  A)
   \[{{\Lambda }_{c}}=\frac{\kappa }{C}\]
  done clear
  B)
   \[{{\Lambda }_{c}}=\kappa \times \frac{1000}{c}\]
  done clear
  C)
   \[{{\Lambda }_{c}}=\kappa \times \frac{{{10}^{-3}}}{c}\]
  done clear
  D)
   \[{{\Lambda }_{c}}=\kappa \times \frac{{{10}^{6}}}{c}\]
  done clear
  View Answer play_arrow

• question_answer101) The standard reduction electrode potentials of the three electrodes P, Q and R are respectively \[-1.76\text{ }V,0.34\text{ }V\]and 0.8 V, then
  A)
   metal Q will displace the cation of P from its aqueous solution and deposit the metal P     
  done clear
  B)
   both metals Q-and R will displace the cation of P from its aqueous solution and deposit the metal P
  done clear
  C)
   metal R will displace the cation of P from its aqueous solution and deposit the metal P
  done clear
  D)
   metal P will displace the cation of R from its aqueous solution and deposit the metal R
  done clear
  View Answer play_arrow

• question_answer102) If the ratio of the rates of diffusion of two gase A and B is 4 :1, the ratio of their densities in the same order is
  A)
   16: 1        
  done clear
  B)
   1:4
  done clear
  C)
   4 : 1         
  done clear
  D)
   1 : 16
  done clear
  View Answer play_arrow

• question_answer103) The van der Waals' constants for four gases P Q, R and S are 4J7, 3.59, 6.71 and 3.8 atm\[{{L}^{2}}.mo{{l}^{-2}}.\] Therefore, the ascending order of their liquification is
  A)
   R < P < S < Q   
  done clear
  B)
   Q < S < R < P
  done clear
  C)
   Q < S < P < R   
  done clear
  D)
   R < P < Q < S
  done clear
  View Answer play_arrow

• question_answer104) The unit cell of a binary alloy composed of ,A and B metals, has a ccp structure with A atoms occupying the corners and B atoms occupying centres of each face of the cube. If during the crystallisation of this alloy, in the unit cell two A atoms are missed, the overall composition per unit cell is
  A)
  \[A{{B}_{6}}\]
  done clear
  B)
  \[A{{B}_{4}}\]
  done clear
  C)
   \[A{{B}_{8}}\]
  done clear
  D)
   \[{{A}_{5}}{{B}_{24}}\]
  done clear
  View Answer play_arrow

• question_answer105) When an excess and a very dilute aqueous solution of\[\text{KI}\]is added to a very dilute aqueous solution of silver nitrate, the colloidal particles of silver iodide are associated with the Helmholtz double layer
  A)
   \[AgI:A{{g}^{+}}:NO_{3}^{-}\]
  done clear
  B)
   \[AgI:{{K}^{+}}:NO_{3}^{-}\]
  done clear
  C)
   \[AgI:NO_{3}^{-}:A{{g}^{+}}\]
  done clear
  D)
   \[AgI:{{I}^{-}}:{{K}^{+}}\]
  done clear
  View Answer play_arrow

• question_answer106) In the Freundlich's adsorption isotherm equation \[\log \frac{x}{m}=\log k+\left( \frac{1}{n} \right)\log \,p,\] the value of n is
  A)
   any value from 0 to 1
  done clear
  B)
   a negative integer
  done clear
  C)
   a positive integer
  done clear
  D)
   a positive or a negative fractional number
  done clear
  View Answer play_arrow

• question_answer107) The polymer used in the manufacture of 'orlon is
  A)
   PTFE         
  done clear
  B)
   PAN
  done clear
  C)
   PMMA       
  done clear
  D)
   PVC
  done clear
  View Answer play_arrow

• question_answer108) Which one of the following is \['d'-\]block element?                
  A)
   Gd            
  done clear
  B)
   Hs
  done clear
  C)
   Es             
  done clear
  D)
   Cs
  done clear
  View Answer play_arrow

• question_answer109) The atom of smallest atomic radius among the following is
  A)
   Na             
  done clear
  B)
   K
  done clear
  C)
   Br             
  done clear
  D)
   Li
  done clear
  View Answer play_arrow

• question_answer110) The \['d'\]orbital involved in the hybridisation in the\[PC{{l}_{5}}\] molecule is
  A)
   \[3{{d}_{{{x}^{2}}-{{y}^{2}}}}\]
  done clear
  B)
  \[3{{d}_{{{z}^{2}}}}\]
  done clear
  C)
   \[3{{d}_{xy}}\]
  done clear
  D)
   \[4{{d}_{{{x}^{2}}-{{y}^{2}}}}\]
  done clear
  View Answer play_arrow

• question_answer111) The shape of \[\text{XeO}{{\text{F}}_{\text{2}}}\]on the basis of VSEPR theory is
  A)
   sea saw       
  done clear
  B)
   V-shaped
  done clear
  C)
   trigonal planar
  done clear
  D)
   T-shaped
  done clear
  View Answer play_arrow

• question_answer112) Among the following the molecule possessing highest dipole moment is
  A)
   \[C{{O}_{2}}\]
  done clear
  B)
  \[B{{F}_{3}}\]
  done clear
  C)
   \[S{{O}_{2}}\]          
  done clear
  D)
   Trans 2-butene
  done clear
  View Answer play_arrow

• question_answer113) Which one of the following molecules is paramagnetic?
  A)
  \[{{F}_{2}}\]
  done clear
  B)
  \[{{B}_{2}}\]
  done clear
  C)
  \[L{{i}_{2}}\]
  done clear
  D)
  \[{{N}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer114) Among the following the least thermally stable is
  A)
  \[{{K}_{2}}C{{O}_{3}}\]       
  done clear
  B)
  \[~N{{a}_{2}}C{{O}_{3}}\]
  done clear
  C)
  \[~BaC{{O}_{3}}\]       
  done clear
  D)
  \[~L{{i}_{2}}C{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer115) Which one of the following has the highest Lewis acid strength?
  A)
  \[B{{I}_{3}}\]            
  done clear
  B)
  \[~BB{{r}_{3}}\]
  done clear
  C)
  \[~B{{F}_{3}}\]           
  done clear
  D)
  \[~BC{{l}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer116) The most powerful oxidising agent of the following is     
  A)
  \[{{I}_{2}}\]
  done clear
  B)
  \[{{F}_{2}}\]
  done clear
  C)
  \[B{{r}_{2}}\]
  done clear
  D)
  \[C{{l}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer117) Which one of the following is non-reducing?
  A)
  \[{{H}_{2}}S\]           
  done clear
  B)
  \[~{{H}_{2}}Te\]
  done clear
  C)
  \[{{H}_{2}}Se\]          
  done clear
  D)
  \[~{{H}_{2}}\text{O}\]
  done clear
  View Answer play_arrow

• question_answer118) The atom of which one of the following elements has the highest number of unpaired electrons?
  A)
   \[{{\,}_{25}}Mn\]          
  done clear
  B)
  \[{{\,}_{24}}Cr\]
  done clear
  C)
  \[{{\,}_{96}}Cm\]          
  done clear
  D)
  \[{{~}_{26}}Fe\]
  done clear
  View Answer play_arrow

• question_answer119) The ion of least magnetic moment among the following is
  A)
   \[T{{i}^{3+}}\]
  done clear
  B)
  \[N{{i}^{2+}}\]
  done clear
  C)
   \[C{{o}^{2+}}\]
  done clear
  D)
   \[M{{n}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer120) The composition of Bell metal is
  A)
   \[Cu\text{ (}80%\text{)},\text{ }Zn\text{ (}20%\text{)}\]
  done clear
  B)
  \[~Cu\text{ (}60%\text{)},\text{ }Ni\text{ (}40%\text{)}\]   .
  done clear
  C)
  \[~Cu\text{ (}90%\text{)},\text{ }Sn\text{ (}10%\text{)}\]
  done clear
  D)
   \[Cu\text{ (}80%\text{)},\text{ }Sn\text{ (}20%\text{)}\]
  done clear
  View Answer play_arrow

• question_answer121) The amphoteric oxide among the following is
  A)
  \[C{{r}_{2}}{{O}_{3}}\]
  done clear
  B)
  \[M{{n}_{2}}{{O}_{7}}\]
  done clear
  C)
   \[{{V}_{2}}{{O}_{3}}\]
  done clear
  D)
   \[CrO\]
  done clear
  View Answer play_arrow

• question_answer122) The coordination compound of which one of the following compositions will produce two equivalents of AgCl on reaction with aqueous silver nitrate solution?
  A)
  \[CoC{{l}_{3}}.3N{{H}_{3}}\]   
  done clear
  B)
  \[~CoC{{l}_{3}}.6N{{H}_{3}}\]
  done clear
  C)
  \[CoC{{l}_{3}}.4N{{H}_{3}}\]   
  done clear
  D)
  \[~CoC{{l}_{3}}.5N{{H}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer123) The optically active coordination complex ion among the following is
  A)
   trans\[{{[Co{{(en)}_{2}}C{{l}_{2}}]}^{+}}\]
  done clear
  B)
   \[cis{{[Co(en){{(N{{H}_{3}})}_{2}}C{{l}_{2}}]}^{+}}\]
  done clear
  C)
   \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
  done clear
  D)
   \[{{[Fe(C{{N}_{6}})]}^{3-}}\]
  done clear
  View Answer play_arrow

• question_answer124) Which one of the following complex ions has the highest magnetic moment?
  A)
   \[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
  done clear
  B)
  \[{{[Fe{{(CN)}_{6}}]}^{3-}}\]
  done clear
  C)
   \[{{[Fe{{(CN)}_{6}}]}^{4-}}\]
  done clear
  D)
   \[{{[Zn{{(N{{H}_{3}})}_{6}}]}^{2+}}\]
  done clear
  View Answer play_arrow

• question_answer125) The non-existant metal carbonyl among the following is
  A)
   \[Cr{{(CO)}_{6}}\]      
  done clear
  B)
  \[Mn{{(CO)}_{5}}\]           
  done clear
  C)
  \[Ni{{(CO)}_{4}}\] 
  done clear
  D)
  \[Fe{{(CO)}_{5}}\]
  done clear
  View Answer play_arrow

• question_answer126) The auto reduction process is not used in the metallurgy of
  A)
   Hg            
  done clear
  B)
   Cu
  done clear
  C)
   Pb            
  done clear
  D)
   Fe
  done clear
  View Answer play_arrow

• question_answer127) The incorrect statement among the following  is
  A)
   hydrogen is used to reduce \[\text{NiO}\]
  done clear
  B)
   zirconium is refined by van-Arkel method
  done clear
  C)
   the sulphide ore galena is concentrated by hydraulic washing process
  done clear
  D)
   in the metallurgy of iron, the flux used is \[\text{Si}{{\text{O}}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer128) The percentage of carbon in cast iron is
  A)
  \[5-10\]           
  done clear
  B)
  \[~0.25-2.5\]
  done clear
  C)
  \[2.5-4.5\]         
  done clear
  D)
   \[0.12-0.2\]
  done clear
  View Answer play_arrow

• question_answer129) The IUPAC name of the molecule \[C{{H}_{3}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,=\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-OH\]
  A)
   4-oxo-2, 3-dimethyl pent-2-en-l-oic acid
  done clear
  B)
   2-carboxy-3 methyl pent-2-en-3-one
  done clear
  C)
   4-carboxy-3 methyl pent-3-en-2-one
  done clear
  D)
   2, 3-dimethyl-4-oxo pent-2-en-l-oic acid
  done clear
  View Answer play_arrow

• question_answer130) The ascending order of stability of the \[\bar{C}{{H}_{3}}(P),{{C}_{6}}{{H}_{5}}\bar{C}{{H}_{2}}(Q),\] \[{{(C{{H}_{3}})}_{2}}-CH(R)\]and \[{{H}_{2}}\bar{C}-CH=C{{H}_{2}}(S)\]is
  A)
   \[P<R<S<Q\]
  done clear
  B)
  \[R<P<S<Q\]
  done clear
  C)
   \[R<P<Q<S\]
  done clear
  D)
   \[P<R<Q<S\]
  done clear
  View Answer play_arrow

• question_answer131) The descending order of stability, of the carbonium ions \[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{C}}\,{{H}_{2}}(I),p(C{{H}_{3}}O){{C}_{6}}{{H}_{4}}\overset{+}{\mathop{C}}\,{{H}_{2}}(II),p(N{{O}_{2}})\] \[{{C}_{6}}{{H}_{4}}\overset{+}{\mathop{C}}\,{{H}_{2}}(III)\]and \[p(C{{H}_{3}}){{C}_{6}}{{H}_{4}}\overset{+}{\mathop{C}}\,{{H}_{2}}(IV)\]
  A)
   \[IV>II>I>III\]
  done clear
  B)
   \[II>IV>m>l\]
  done clear
  C)
   \[II>IV>I>III\]
  done clear
  D)
   \[IV>II>III>I\text{ }\]
  done clear
  View Answer play_arrow

• question_answer132) Which one of the following is aromatic?
  A)
   Cyclopentadienyl cation
  done clear
  B)
   Cyclooctatetraene
  done clear
  C)
   Cycloheptatriene
  done clear
  D)
   Cycloheptatrienylcation
  done clear
  View Answer play_arrow

• question_answer133) The total number of acyclic structural and optical isomers possible for a hydrocarbon of molecular formula \[{{C}_{7}}{{H}_{16}}\]is
  A)
   12            
  done clear
  B)
   8
  done clear
  C)
   10            
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer134) The optical rotaion of an optically active compound is
  A)
   directly proportional to the length of the polarimeter tube only
  done clear
  B)
   directly proportional to the molar concentration of the compound
  done clear
  C)
   independent of the length of the polarimeter tube and concentration of the compound
  done clear
  D)
   directly proportional to both the length of the polarimeter tube and the molar concentration of the compound
  done clear
  View Answer play_arrow

• question_answer135) The absolute configurations of the\[{{C}_{2}}\] and\[{{C}_{3}}\] atoms in the molecule with the structure is
  A)
   \[2S,3S\]
  done clear
  B)
  \[2R,3S\]
  done clear
  C)
   \[2S,3R\]
  done clear
  D)
   \[2R,3R\]
  done clear
  View Answer play_arrow

• question_answer136) Hydration of which one of the following yields a ketone
  A)
   Propyne       
  done clear
  B)
   Ethene
  done clear
  C)
   Prppene       
  done clear
  D)
   Ethyne
  done clear
  View Answer play_arrow

• question_answer137) The most easily hydrolysed molecule under \[{{\text{S}}_{\text{N}}}\text{1}\] conditions is
  A)
   allyl chloride
  done clear
  B)
   ethyl chloride
  done clear
  C)
   isopropyl chloride
  done clear
  D)
   benzyl chloride
  done clear
  View Answer play_arrow

• question_answer138) The most acidic among the following is
  A)
   p-cresol        
  done clear
  B)
   o-cresol
  done clear
  C)
   p-nitrophenol  
  done clear
  D)
   p-chlorophenol
  done clear
  View Answer play_arrow

• question_answer139) Which one of the following does not undergo iodoform reaction?
  A)
   Secondary butyl alcohol
  done clear
  B)
   Iso-propyl alcohol
  done clear
  C)
   Diethyl ketone
  done clear
  D)
   Ethyl alcohol
  done clear
  View Answer play_arrow

• question_answer140) Glycerol on oxidation with bismuth nitrate forms
  A)
   mesooxalic acid
  done clear
  B)
   glyceraldehyde
  done clear
  C)
   dihydroxy acotone
  done clear
  D)
   tartronic acid
  done clear
  View Answer play_arrow

• question_answer141) Among the following, the alkene on ozonolysis giving rise to only one aldehyde as the product is
  A)
   1-butene
  done clear
  B)
   propone
  done clear
  C)
   2-butene
  done clear
  D)
   a-methyl-prop-1-ene
  done clear
  View Answer play_arrow

• question_answer142) Which one of the following does not form sodium bisulphite addition product with sodium bisulphite solution?
  A)
   \[C{{H}_{2}}O\]
  done clear
  B)
  \[{{C}_{6}}{{H}_{5}}COC{{H}_{3}}\]
  done clear
  C)
  \[{{C}_{6}}{{H}_{5}}CHO\]
  done clear
  D)
  \[C{{H}_{3}}CHO\]
  done clear
  View Answer play_arrow

• question_answer143) The carboxylic acid of least strength among the following is
  A)
   p-nitrobenzoic acid
  done clear
  B)
   p-methylbenzoic acid
  done clear
  C)
   p-chlprobenzoic acid
  done clear
  D)
   p-methoxybenzoic acid
  done clear
  View Answer play_arrow

• question_answer144) The most reactive of the following is
  A)
   acetone       
  done clear
  B)
   benzophenone
  done clear
  C)
   benzaldehyde  
  done clear
  D)
   acetaldehyde
  done clear
  View Answer play_arrow

• question_answer145) Which of the following is not a resonating form of benzaldehyde?
  A)
   
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer146) The compound that does' not undergo Hell-Volhard Zelinsky reaction is
  A)
   ethanoicacid   
  done clear
  B)
   propionic acid
  done clear
  C)
   \[iso-\]butyric acid
  done clear
  D)
   trichloroacetic acid
  done clear
  View Answer play_arrow

• question_answer147) Nitrobenzene   can   be   converted   into hydrazobenzene by reduction with
  A)
   Zn and alcoholic NaOH
  done clear
  B)
   Zn and aqueous NaOH
  done clear
  C)
  \[\text{ }\!\!~\!\!\text{ N}{{\text{H}}_{\text{2}}}\text{N}{{\text{H}}_{\text{2}}}\] and alcoholic KOH
  done clear
  D)
   Zn and HCl
  done clear
  View Answer play_arrow

• question_answer148) Which of the following compounds gives carbylamine test?
  A)
   N-methyl-o-methyl aniline
  done clear
  B)
   N, N-dimethyl aniline
  done clear
  C)
   2, 4-diethyl aniline
  done clear
  D)
   p-methyl-N-methyl benzylamine
  done clear
  View Answer play_arrow

• question_answer149) By which of the following reagents, both the aldehyde and the primary alcoholic group of glucose are oxidized?
  A)
   Tollen?s reagent
  done clear
  B)
  \[B{{r}_{2}}+{{H}_{2}}O\]
  done clear
  C)
   \[HN{{O}_{3}}\]
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer150) Lactoflavin is
  A)
   Vitamin \[{{B}_{1}}\]
  done clear
  B)
   Vitamin C
  done clear
  C)
   Vitamin \[{{B}_{2}}\]
  done clear
  D)
   Vitamin \[{{B}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer151) If S is a set with 10 elements and \[A=\{(x,y):x,\,y\,\in S,\,x\ne y\},\] then the number of elements in A is
  A)
  \[100\]    
  done clear
  B)
   \[90\]
  done clear
  C)
   \[50\]
  done clear
  D)
   \[45\]
  done clear
  View Answer play_arrow

• question_answer152) The   domain   of  the   real   function  \[f(x)=\frac{1}{\sqrt{4-{{x}^{2}}}}\]is
  A)
   the set of all real numbers
  done clear
  B)
   the set of all positive real numbers
  done clear
  C)
   \[(-2,\,2)\]
  done clear
  D)
   \[[-2,\,2]\]
  done clear
  View Answer play_arrow

• question_answer153) If \[(3+i)\,(z+\bar{z})-(2+i)(z-\bar{z})+14i\,=0,\] then \[z\bar{z}\] is equal to
  A)
   \[5\]              
  done clear
  B)
   \[8\]
  done clear
  C)
   \[10\]            
  done clear
  D)
   \[40\]
  done clear
  View Answer play_arrow

• question_answer154) \[4+5{{\left( \frac{-1+i\sqrt{3}}{2} \right)}^{2008}}+3{{\left( \frac{-1+i\sqrt{3}}{2} \right)}^{2009}}\] is equal to
  A)
   \[-i\sqrt{3}\]
  done clear
  B)
   \[i\sqrt{3}\]
  done clear
  C)
   \[1-i\sqrt{3}\]
  done clear
  D)
   \[-1+i\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer155) If the equation \[(a+1){{x}^{2}}-(a+2)x+(a+3)=0\] has  roots equal in magnitude but opposite in signs, then the roots of the equation are           
  A)
   \[\pm \,\,a\]           
  done clear
  B)
   \[\pm \,\frac{1}{2}\,a\]
  done clear
  C)
   \[\pm \,\frac{3}{2}\,a\]
  done clear
  D)
   \[\pm \,2\,a\]
  done clear
  View Answer play_arrow

• question_answer156) If a and p are roots of the quadratic equation \[{{x}^{2}}+4x+3=0,\]then the equation whose roots are \[2\alpha \,\text{+}\,\beta \] and \[\alpha \,\text{+2}\,\beta \] is
  A)
   \[{{x}^{2}}-12x+35=0\]
  done clear
  B)
   \[{{x}^{2}}+12x-33=0\]
  done clear
  C)
   \[{{x}^{2}}-12x-33=0\]
  done clear
  D)
   \[{{x}^{2}}+12x+35=0\]
  done clear
  View Answer play_arrow

• question_answer157) If the sum to 2 n terms of the \[AP\text{ }2,\text{ }5,\text{ }8,11,...\]is equal to the sum to n terms of the \[AP\text{ }57,\text{ }59,\text{ }61,\text{ }63,\text{ }...\text{ },\]then n is equal to
  A)
   \[10\]            
  done clear
  B)
   \[11\]
  done clear
  C)
   \[12\]            
  done clear
  D)
   \[13\]
  done clear
  View Answer play_arrow

• question_answer158) If the third term of a GP is 3, then the product of its first 5 terms is
  A)
   15
  done clear
  B)
   \[81\]
  done clear
  C)
   \[243\]
  done clear
  D)
   Cannot be determined
  done clear
  View Answer play_arrow

• question_answer159) The term independent of x in the expansion of \[{{\left( \sqrt{\frac{x}{3}}+\frac{3}{2{{x}^{2}}} \right)}^{10}}\] is
  A)
   \[\frac{5}{4}\]
  done clear
  B)
   \[\frac{7}{4}\]
  done clear
  C)
   \[\frac{9}{4}\]
  done clear
  D)
   \[45\]
  done clear
  View Answer play_arrow

• question_answer160) \[\frac{^{8}{{C}_{0}}}{6}{{-}^{8}}{{C}_{1}}{{+}^{8}}{{C}_{2}}.6{{-}^{8}}{{C}_{3}}{{.6}^{2}}+....{{+}^{8}}{{C}_{8}}{{.6}^{7}}\] is equal to
  A)
   \[0\]
  done clear
  B)
   \[{{6}^{7}}\]
  done clear
  C)
   \[{{6}^{8}}\]
  done clear
  D)
   \[\frac{{{5}^{8}}}{6}\]
  done clear
  View Answer play_arrow

• question_answer161) The number of ways in which 5 boys and 5 girls can be seated for a photograph so that no two girls sit next to each other is
  A)
   \[6!\,5!\]          
  done clear
  B)
   \[{{(5!)}^{2}}\]
  done clear
  C)
   \[\frac{10!}{(5!)}\]             
  done clear
  D)
   \[\frac{10!}{{{(5!)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer162) The number of diagonals of a polygon of 20 sides is
  A)
   \[210\]           
  done clear
  B)
   \[190\]
  done clear
  C)
   \[180\]           
  done clear
  D)
   \[170\]
  done clear
  View Answer play_arrow

• question_answer163) The     sum     of     the     series  \[\left( 1+\frac{{{({{\log }_{e}}\,n)}^{2}}}{2!}+\frac{{{({{\log }_{e}}n)}^{4}}}{4!}+... \right)\]is
  A)
   \[n+\frac{1}{n}\]
  done clear
  B)
   \[\frac{n'}{2}+\frac{1}{2n}\]
  done clear
  C)
   \[{{\log }_{e}}\frac{1}{1-{{({{\log }_{e}}n)}^{2}}}\]
  done clear
  D)
   \[\frac{1}{2}{{\log }_{e}}\,\frac{1}{1-{{({{\log }_{e}}\,n)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer164) If \[{{x}_{1}},{{x}_{2}},......{{x}_{18}}\] are observations such, that \[\sum\limits_{j=1}^{18}{({{x}_{j}}-8)=9}\] and \[\sum\limits_{j=1}^{18}{{{({{x}_{j}}-8)}^{2}}=45,}\] then the standard deviation of these observations is
  A)
   \[\sqrt{\frac{81}{34}}\]           
  done clear
  B)
   \[5\]
  done clear
  C)
   \[\sqrt{5}\]
  done clear
  D)
   \[\frac{3}{2}\]
  done clear
  View Answer play_arrow

• question_answer165) If \[(3,\,\,3)\] is a vertex of a triangle and \[(-3,\,\,6)\] and \[(9,\,\,6)\] are the mid points of the two sides through this vertex, then the centroid of the triangle is
  A)
   \[(3,\,\,7)\]          
  done clear
  B)
   \[(1,\,\,7)\]
  done clear
  C)
   \[(-3,\,\,7)\]        
  done clear
  D)
   \[(-1,\,\,7)\]
  done clear
  View Answer play_arrow

• question_answer166) If the lines \[x+2ay+a=0,\,\,\,\,x+3by+b=0\] and \[x+4\,cy+c=0\] are concurrent, where a, b, c are non-zero real numbers, then
  A)
   \[\frac{1}{a},\frac{1}{b},\frac{1}{c}\]are in an AP
  done clear
  B)
   \[\frac{1}{a},\frac{1}{b},\frac{1}{c}\] are in a GP
  done clear
  C)
   a, b, c are in an AP
  done clear
  D)
   a, b, c are in a GP
  done clear
  View Answer play_arrow

• question_answer167)  If the - equation \[6{{x}^{2}}+11xy-10{{y}^{2}}+x+31y+c=0\]represent a pair of straight lines, then the value of c is
  A)
   \[\frac{125}{367}\]         
  done clear
  B)
   \[-\frac{125}{367}\]
  done clear
  C)
   \[15\]
  done clear
  D)
   \[-15\]
  done clear
  View Answer play_arrow

• question_answer168) If the equation \[\lambda \,\,{{x}^{2}}+(2\lambda -3){{y}^{2}}-4x-1=0\] represents a circle, then its radius is
  A)
   \[\frac{\sqrt{11}}{3}\]          
  done clear
  B)
   \[\frac{\sqrt{13}}{3}\]
  done clear
  C)
   \[\frac{\sqrt{7}}{3}\]
  done clear
  D)
   \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer169) The equation of the circle passing through the point \[(1,\,\,1)\] and through the points of intersection of the circles \[{{x}^{2}}+{{y}^{2}}=6\] and \[{{x}^{2}}+\text{ }{{y}^{2}}-6y+8=0\]is
  A)
   \[{{x}^{2}}+{{y}^{2}}+3y-13=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}-3y+1=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}-3x+1=0\]
  done clear
  D)
   \[5{{x}^{2}}+5{{y}^{2}}+6y+16=0\]
  done clear
  View Answer play_arrow

• question_answer170) If \[x+y=k\]is a tangent to the parabola \[{{y}^{2}}=12x,\]then k is equal to
  A)
   \[9\]               
  done clear
  B)
   \[-9\]
  done clear
  C)
   \[3\]               
  done clear
  D)
   \[-3\]
  done clear
  View Answer play_arrow

• question_answer171) If in a hyperbola, the distance between the foci is 10 and the transverse axis has length 8, then the length of its latuserectum is
  A)
   \[9\]
  done clear
  B)
   \[\frac{9}{2}\]
  done clear
  C)
   \[\frac{5}{4}\]
  done clear
  D)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer172) If \[\tan \theta =\frac{1}{\sqrt{7}},\]then \[\frac{(\text{cose}{{\text{c}}^{2}}\,\theta -{{\sec }^{2}}\theta )}{(\text{cose}{{\text{c}}^{2}}\,\theta +{{\sec }^{2}}\theta )}\] is equal to
  A)
   \[\frac{1}{2}\]               
  done clear
  B)
   \[\frac{3}{4}\]
  done clear
  C)
   \[\frac{5}{4}\]
  done clear
  D)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer173) When \[\theta \] varies over the real numbers, the maximum value of \[\cos \,\,\theta -\cos \,2\theta \] is
  A)
   \[2\]
  done clear
  B)
   \[\frac{7}{8}\]
  done clear
  C)
   \[\frac{5}{4}\]
  done clear
  D)
   \[2\]
  done clear
  View Answer play_arrow

• question_answer174) \[\sin \,\,{{47}^{o}}+\sin {{61}^{o}}-\sin {{11}^{o}}-\sin {{25}^{o}}\] is equal to
  A)
   \[\sin \,{{7}^{o}}\]          
  done clear
  B)
   \[\cos \,{{7}^{o}}\]
  done clear
  C)
   \[\sin \,{{36}^{o}}\]         
  done clear
  D)
   \[\cos \,{{36}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer175) In \[\Delta \,\,ABC\] if \[si{{n}^{2}}A+si{{n}^{2}}B+si{{n}^{2}}C=2,\]then the triangle is
  A)
   right angled, but need not be isosceles
  done clear
  B)
   right angled and isosceles
  done clear
  C)
   isosceles, but need not be right angled
  done clear
  D)
   equilateral
  done clear
  View Answer play_arrow

• question_answer176) In    \[\Delta \,\,ABC,\]if \[s=\frac{a+b+c}{2},\]then \[\left( b\,\,{{\cos }^{2}}\,\frac{C}{2}+c\,\,{{\cos }^{2}}\,\frac{B}{2} \right)\] is equal to
  A)
   \[s\]
  done clear
  B)
   \[2s\]
  done clear
  C)
   \[4\,s\]               
  done clear
  D)
   \[3\,s\]
  done clear
  View Answer play_arrow

• question_answer177) The number of solutions of the equation \[\sin \,x\,\,\cos \,\,3x=\sin \,3x\,\,\cos \,5x\]in \[\left[ 0,\frac{\pi }{2} \right]\] is
  A)
   \[3\]               
  done clear
  B)
   \[4\]
  done clear
  C)
   \[5\]                 
  done clear
  D)
   \[6\]
  done clear
  View Answer play_arrow

• question_answer178) The most general values of \[\theta \] satisfying \[\tan \theta +\tan \left( \frac{3\pi }{4}+\theta  \right)=2\] are given by
  A)
   \[2n\pi \pm \frac{\pi }{3},\,n\in Z\]
  done clear
  B)
   \[n\pi \pm \frac{\pi }{3},\,n\in Z\]
  done clear
  C)
   \[2n\pi \pm \frac{\pi }{6},\,n\in Z\]
  done clear
  D)
   \[n\pi \pm \frac{\pi }{6},\,n\in Z\]
  done clear
  View Answer play_arrow

• question_answer179) The value of \[{{\cos }^{-1}}\,\left( \sin \,\frac{7\pi }{6} \right)\] is equal to
  A)
   \[\frac{\pi }{3}\]
  done clear
  B)
   \[\frac{\pi }{6}\]
  done clear
  C)
   \[\frac{2\pi }{3}\]
  done clear
  D)
   \[-\frac{\pi }{3}\]
  done clear
  View Answer play_arrow

• question_answer180) If \[{{\tan }^{-1}}\,2\] and \[{{\tan }^{-1}}\,3\] are two angles of a triangle, then the third angle is
  A)
   \[\frac{\pi }{2}\]
  done clear
  B)
   \[\frac{\pi }{3}\]
  done clear
  C)
   \[\frac{\pi }{4}\]
  done clear
  D)
   \[\frac{\pi }{6}\]
  done clear
  View Answer play_arrow

• question_answer181) The value of \[\left| \begin{matrix}    {{\log }_{5}}\,\,729 & {{\log }_{3}}\,5  \\    {{\log }_{5}}\,27 & {{\log }_{9}}\,25  \\ \end{matrix} \right|\,.\,\,\left| \begin{matrix}    {{\log }_{3}}\,5 & {{\log }_{27}}\,\,5  \\    {{\log }_{5}}\,9 & {{\log }_{5}}\,9  \\ \end{matrix} \right|\] is equal to
  A)
   \[1\]
  done clear
  B)
   \[6\]
  done clear
  C)
   \[{{\log }_{5}}\,9\]
  done clear
  D)
   \[{{\log }_{3}}5.\,{{\log }_{5}}\,81\,\]
  done clear
  View Answer play_arrow

• question_answer182) If a, b,  c are all distinct and if \[\left| \begin{matrix}    1-{{a}^{3}} & {{a}^{2}} & a  \\    1-{{b}^{3}} & {{b}^{2}} & b  \\    1-{{c}^{3}} & {{c}^{2}} & c  \\ \end{matrix} \right|=0,\] then
  A)
   \[abc=1\]
  done clear
  B)
   \[abc=-1\]
  done clear
  C)
   \[a+b+c=0\]
  done clear
  D)
   \[a+b+c=\pm 1\]
  done clear
  View Answer play_arrow

• question_answer183) If the system of homogeneous equations \[2x-y+z=0,\,\,x-2y+z=0,\,\,\lambda \,\,x-y+2z=0\] has infinitely many solutions, then
  A)
   \[\lambda =5\]         
  done clear
  B)
   \[\lambda =-5\]
  done clear
  C)
   \[\lambda \ne \pm 5\]        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer184) If X and Y are \[2\times 2\] matrices such that \[2X+3Y=O\] and \[X+2Y=I,\]where \[O\] and \[I\] denote the \[2\times 2\] zero matrix and the \[2\times 2\] identity matrix, then X is equal to
  A)
   \[\left[ \begin{matrix}    1 & 0  \\    0 & 1  \\ \end{matrix} \right]\]
  done clear
  B)
   \[\left[ \begin{matrix}    2 & 0  \\    0 & 2  \\ \end{matrix} \right]\]
  done clear
  C)
   \[\left[ \begin{matrix}    -3 & 0  \\    0 & -3  \\ \end{matrix} \right]\]
  done clear
  D)
   \[\left[ \begin{matrix}    3 & 0  \\    0 & 3  \\ \end{matrix} \right]\]
  done clear
  View Answer play_arrow

• question_answer185) For \[0<\theta <\pi ,\] if  \[A=\left[ \begin{matrix}    \cos \theta  & -\sin \theta   \\    \sin \theta  & \cos \theta   \\ \end{matrix} \right],\]then
  A)
   \[{{A}^{T}}=A\]        
  done clear
  B)
   \[{{A}^{T}}=-A\]
  done clear
  C)
   \[{{A}^{2}}=I\]
  done clear
  D)
   \[{{A}^{T}}={{A}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer186) The matrix \[\left[ \begin{matrix}    \lambda  & 1 & 0  \\    0 & 2 & 3  \\    0 & 0 & \lambda   \\ \end{matrix} \right]\] is non-singular
  A)
   for all real values of \[\lambda \]
  done clear
  B)
   only when \[\lambda =\pm \frac{1}{\sqrt{2}}\]
  done clear
  C)
   only when \[\lambda \ne 0\]
  done clear
  D)
   only when \[\lambda =0\]
  done clear
  View Answer play_arrow

• question_answer187)  A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are respectively, \[4\hat{i}+3\hat{j}-\hat{k}\]and \[-3\hat{i}+\hat{j}+\hat{k},\] then\[\overrightarrow{DE}\] is equal to
  A)
   \[7\hat{i}+2\hat{j}-2k\]   
  done clear
  B)
   \[-7\hat{i}-2\hat{j}+\text{ }2\hat{k}\]
  done clear
  C)
   \[3\hat{i}-\hat{j}-\hat{k}\]     
  done clear
  D)
   \[-4\hat{i}-3\hat{j}+2\hat{k}\]
  done clear
  View Answer play_arrow

• question_answer188) If the position vectors of the vertices of triangle ABC   are   \[3\hat{i}+\hat{j}+2\hat{k},\,\,\,\hat{i}-2\hat{j}+7\hat{k}\]and \[-2\hat{i}+3\hat{j}+5\hat{k},\] then the triangle ABC is
  A)
   right angled and isosceles
  done clear
  B)
   right angled, but not isosceles
  done clear
  C)
   isosceles but not right angled
  done clear
  D)
   equilateral
  done clear
  View Answer play_arrow

• question_answer189) If \[4|\vec{a}|=12|\vec{b}|=3|\vec{c}|=12\] and \[\vec{a}+\vec{b}+\vec{c}=\vec{0},\] then \[\vec{a}\,\,.\,\,\vec{b}+\vec{b}\,.\,\,\vec{c}+\vec{c}\,.\,\,\vec{a}\] is equal to
  A)
   \[-8\]           
  done clear
  B)
   \[8\]
  done clear
  C)
   \[-13\]           
  done clear
  D)
   \[13\]
  done clear
  View Answer play_arrow

• question_answer190) If \[2\text{ }\vec{a}+3\text{ }\vec{b}+\vec{c}=0,\] then \[\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}\]is equal to
  A)
   \[6\,(\vec{b}\times \vec{c})\]       
  done clear
  B)
   \[3\,(\vec{b}\times \vec{c})\]
  done clear
  C)
   \[2\,(\vec{b}\times \vec{c})\]        
  done clear
  D)
   \[\vec{0}\]
  done clear
  View Answer play_arrow

• question_answer191) If  \[\hat{i}-\hat{k},\,\lambda \hat{i}+\hat{j}+(1-\lambda )\hat{k}\]  and \[\mu \hat{i}+\lambda \hat{j}+(1+\lambda -\mu )\hat{k}\]are three coterminal edges of a parallelopiped, then its volume depends on
  A)
   only \[\lambda \]          
  done clear
  B)
   only \[\mu \]
  done clear
  C)
   both \[\lambda \] and \[\mu \]
  done clear
  D)
   neither \[\lambda \] nor\[\mu \] 
  done clear
  View Answer play_arrow

• question_answer192) \[\vec{u}\] and \[\vec{v}\] are unit vectors such that \[\vec{u}\,\,.\vec{v}\]. If \[\vec{r}\]is any vector coplanar with \[\vec{u}\] and \[\vec{v}\] then the magnitude of the \[\vec{u}\] vector \[\vec{v},\]  is
  A)
  \[0\]              
  done clear
  B)
   \[1\]
  done clear
  C)
   \[|\vec{r}|\]             
  done clear
  D)
   \[2|\vec{r}|\]
  done clear
  View Answer play_arrow

• question_answer193) The point on the x-axis equidistant from the points \[(4,3,1)\]and \[(-2,\,-6,\,-2)\] is
  A)
   \[(0,\,-1,0)\]      
  done clear
  B)
   \[(0,\,1,-6)\]
  done clear
  C)
   \[\left( -\frac{3}{2},0,0 \right)\]     
  done clear
  D)
   \[\left( -\frac{1}{2},0,0 \right)\]
  done clear
  View Answer play_arrow

• question_answer194) A line makes an obtuse angle with the positive x-axis and angles \[\frac{\pi }{4}\] and \[\frac{\pi }{3}\] with the positive y and z axes respectively. Its direction cosine are
  A)
   \[\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{2}\]
  done clear
  B)
   \[\frac{1}{\sqrt{2}},-\frac{1}{2},\frac{1}{2}\]
  done clear
  C)
   \[-\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]
  done clear
  D)
   \[\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer195) The shortest distance between the straight line \[\frac{x-6}{1}=\frac{2-y}{2}=\frac{z-2}{2}\] and \[\frac{x+4}{3}-\frac{y}{-2}=\frac{1-z}{2}\] is
  A)
   \[9\]             
  done clear
  B)
   \[\frac{19}{3}\]
  done clear
  C)
   \[\frac{16}{3}\]
  done clear
  D)
   \[4\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer196) The image of the point \[(6,3,9)\]in the straight line \[x-2=\frac{1-y}{2}=\frac{z}{2}\]is
  A)
   \[\left( \frac{28}{9},\frac{83}{9},\frac{11}{9} \right)\]
  done clear
  B)
   \[(28,83,11)\]
  done clear
  C)
   \[(4,-3,4)\]
  done clear
  D)
   \[(2,-9,-1)\]
  done clear
  View Answer play_arrow

• question_answer197) The equation of the plane passing through the point \[(1,1,1)\] and containing the line of intersection of the planes \[x+y+z=6\] and \[2x+3y+4z=12\] is
  A)
   \[x+y+z=3\]
  done clear
  B)
   \[x+2y+3z=6\]
  done clear
  C)
   \[2x+3y+4z=9\]
  done clear
  D)
   \[3x+4y+5z=18\]
  done clear
  View Answer play_arrow

• question_answer198) The shortest distance from the plane  \[2x-y+2z=25\] to     the     sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2x-4y+2z-3=0\] is
  A)
   \[6\]              
  done clear
  B)
   \[9\]
  done clear
  C)
   \[12\]             
  done clear
  D)
   \[24\]
  done clear
  View Answer play_arrow

• question_answer199) If \[\vec{a}\] is a constant vector and p is a real constant with \[|\vec{a}{{|}^{2}}>p,\] then the locus of a point with position vector \[|\vec{r}|\] such that \[|\vec{r}{{|}^{2}}-2\,\,\vec{r}.\,\vec{a}\,+\,\,p=O\]is
  A)
   a sphere       
  done clear
  B)
   an ellipse
  done clear
  C)
   a circle          
  done clear
  D)
   a plane
  done clear
  View Answer play_arrow

• question_answer200) Consider the switching circuit given below The logical expression corresponding to the complementary to the above circuit is
  A)
   \[a'b'c'\]          
  done clear
  B)
   \[a+b+c'\]
  done clear
  C)
   \[a\,.\,b\,.\,c'\]         
  done clear
  D)
   \[a'+b'+c\]
  done clear
  View Answer play_arrow

• question_answer201) A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. The probability that they match is
  A)
   \[\frac{4}{9}\]
  done clear
  B)
   \[\frac{5}{8}\]
  done clear
  C)
   \[\frac{5}{9}\]
  done clear
  D)
   \[\frac{5}{12}\]
  done clear
  View Answer play_arrow

• question_answer202) Events A, B, C are mutually exclusive events such that \[P(A)=\frac{(3x+1)}{3},\,\,P(B)=\frac{(1-x)}{4}\] and \[P(C)=\frac{(1-2x)}{2}\].The set of possible values of x are in the interval
  A)
   \[\left[ \frac{1}{3},\frac{1}{2} \right]\]
  done clear
  B)
   \[\left[ \frac{1}{3},\frac{2}{3} \right]\]
  done clear
  C)
   \[\left[ \frac{1}{3},\frac{13}{3} \right]\]
  done clear
  D)
   \[[0,\,1]\]
  done clear
  View Answer play_arrow

• question_answer203) \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{{{e}^{{{x}^{2}}}}-\cos \,x}{{{x}^{2}}}\]is equal to
  A)
   \[0\]
  done clear
  B)
   \[1/2\]
  done clear
  C)
   \[1\]
  done clear
  D)
   \[3/2\]
  done clear
  View Answer play_arrow

• question_answer204) If \[0<a<b,\]then \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{a}^{n}}+{{b}^{n}}}{{{a}^{n}}-{{b}^{n}}}\]
  A)
   equals 0       
  done clear
  B)
   equals - 1
  done clear
  C)
   equals 1    
  done clear
  D)
   does not exist
  done clear
  View Answer play_arrow

• question_answer205) The   function \[f(x)\] is   defined   as \[f(x)=\frac{2x-{{\sin }^{-1}}x}{2x+{{\tan }^{-1}}x'}\], if \[x\ne 0\]. The value to be assigned to f at \[x=0\]so that the function is continuous there, is
  A)
   \[-\frac{1}{3}\]              
  done clear
  B)
   \[1\]
  done clear
  C)
   \[\frac{2}{3}\]
  done clear
  D)
   \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer206) The function \[f(x)=\left\{ \begin{matrix}    |x-3|, & if & x\ge 1  \\    \frac{{{x}^{2}}}{4}-\frac{3x}{2}+\frac{13}{4}, & if & x<1  \\ \end{matrix} \right.\]is
  A)
   continuous and differentiable at \[x=3\]
  done clear
  B)
   continuous at \[x=3,\] but not differentiable at \[x=3\]
  done clear
  C)
   continuous and differentiable everywhere
  done clear
  D)
   continuous at \[x=1,\]but not differentiable at \[x=1,\]
  done clear
  View Answer play_arrow

• question_answer207) If \[f(x)={{x}^{n}},\] then \[f(1)+\frac{f'(1)}{1!}+\frac{f'\,'(1)}{2!}+....+\frac{{{f}^{n}}(1)}{n!}\]is equal to
  A)
   \[\frac{n(n+1)}{2}\]
  done clear
  B)
   \[{{2}^{n}}\]
  done clear
  C)
   \[{{2}^{(n+1)}}\]
  done clear
  D)
   \[{{2}^{(n-1)}}\]
  done clear
  View Answer play_arrow

• question_answer208) If \[y=\log \,(\sin \,({{x}^{2}})),\] \[0<0<\frac{\pi }{2},\] then \[\frac{dy}{dx}\] at\[x=\frac{\sqrt{\pi }}{2}\]is
  A)
   \[0\]
  done clear
  B)
   \[1\]
  done clear
  C)
   \[\frac{\pi }{4}\]
  done clear
  D)
   \[\sqrt{\pi }\]
  done clear
  View Answer play_arrow

• question_answer209) Let \[x={{\log }_{e}}\,t,t>0\] and \[y+1={{t}^{2}}.\] Then, \[\frac{{{d}^{2}}x}{d{{y}^{2}}}\]is equal to
  A)
   \[4{{e}^{2x}}\]
  done clear
  B)
   \[-\frac{1}{2}\,{{e}^{-4x}}\]
  done clear
  C)
   \[-\frac{3}{4}\,{{e}^{-5x}}\]
  done clear
  D)
   \[4{{e}^{x}}\]
  done clear
  View Answer play_arrow

• question_answer210) \[f(x)={{\tan }^{-1}}\,(\sin x+\cos x),\,\,-\frac{\pi }{2}\le x\le \frac{\pi }{2},\]is increasing in
  A)
   \[\left( -\frac{\pi }{4},\frac{\pi }{4} \right)\]
  done clear
  B)
   \[\left( 0,\frac{\pi }{2} \right)\]
  done clear
  C)
   \[\left( -\frac{\pi }{2},-\frac{\pi }{4} \right)\]
  done clear
  D)
   \[\left( \frac{\pi }{4},\frac{\pi }{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer211) For the function \[f(x)=x{{e}^{x}}\]the point
  A)
   \[x=0\]is a maximum
  done clear
  B)
   \[x=0\]is a minimum
  done clear
  C)
   \[x=-1\] is a maximum
  done clear
  D)
   \[x=-1\] is a minimum
  done clear
  View Answer play_arrow

• question_answer212) Let \[f(x)={{x}^{3}}.\]. Use mean value theorem to write \[\frac{f(x+h)-f(x)}{h}=f'(x+\theta h)\]  , with \[0<\theta <1\]. If \[x\ne 0,\]then \[\underset{h\to 0}{\mathop{\lim }}\,\,\,\theta \] is equal to
  A)
   \[-1\]
  done clear
  B)
   \[-0.5\]
  done clear
  C)
   \[0.5\]
  done clear
  D)
   \[1\]
  done clear
  View Answer play_arrow

• question_answer213) If \[f\,(x)=\underset{y\to x}{\mathop{lim}}\,\,\frac{{{\sin }^{2}}y-{{\sin }^{2}}x}{{{y}^{2}}-{{x}^{2}}},\]then \[\int{4x\,\,f(x)\,\,dx}\]is equal to
  A)
   \[\cos \,\,2x+c\]      
  done clear
  B)
   \[2\,\cos \,\,2x+c\]
  done clear
  C)
   \[-\,\cos \,\,2x+c\]    
  done clear
  D)
   \[-2\,\cos \,\,2x+c\]
  done clear
  View Answer play_arrow

• question_answer214) \[\int_{0}^{a}{\sqrt{\frac{a-x}{x}}\,\,dx}\]is equal to
  A)
   \[\frac{\pi a}{2}\]
  done clear
  B)
   \[\frac{\pi a}{4}\]
  done clear
  C)
   \[\frac{\pi {{a}^{2}}}{4}\]
  done clear
  D)
   \[\frac{a}{2}\]
  done clear
  View Answer play_arrow

• question_answer215) \[\int_{0}^{x}{\log \,(\cot \,x\,+\,\tan t)\,dt}\]is equal to
  A)
   \[x\,\log \,(\sin \,x)\]
  done clear
  B)
   \[-x\,\log \,(\sin \,x)\]
  done clear
  C)
   \[x\,\log \,(cos\,x)\]
  done clear
  D)
   \[-x\,\log \,(cos\,x)\]
  done clear
  View Answer play_arrow

• question_answer216) The equation of the tangent to the curve \[y=\int_{{{x}^{2}}}^{{{x}^{3}}}{\frac{dt}{\sqrt{{{t}^{2}}+1}}}\] at \[x=1\] is
  A)
   \[y=\sqrt{3}x+1\]
  done clear
  B)
   \[x=\sqrt{3}y+1\]
  done clear
  C)
   \[x=\sqrt{2}y+1\]
  done clear
  D)
   \[y=\sqrt{3}(x+1)+1\]
  done clear
  View Answer play_arrow

• question_answer217) The area of the region bounded by the curves \[y={{2}^{x}}\] and \[y=2x-{{x}^{2}}\]between the ordinates \[x=0\]and \[x=2\]is
  A)
   \[\frac{2}{\log \,2}-\frac{4}{3}\]
  done clear
  B)
   \[\frac{3}{\log \,2}-\frac{4}{3}\]
  done clear
  C)
   \[\frac{1}{\log \,2}-\frac{4}{3}\]
  done clear
  D)
   \[\frac{4}{\log \,2}-\frac{3}{2}\]
  done clear
  View Answer play_arrow

• question_answer218) If c is a positive constant, then the differential equation of the family of the curves \[{{y}^{2}}=2c(x+\sqrt{c})\]has
  A)
   order 1 and degree 3
  done clear
  B)
   order 1 and degree 2
  done clear
  C)
   order 2 and degree 1
  done clear
  D)
   order 3 and degree 1
  done clear
  View Answer play_arrow

• question_answer219) The solution of the differential equation \[(1+{{y}^{2}})+(x-{{e}^{{{\tan }^{-1}}y}})\frac{dy}{dx}=0\]is
  A)
   \[2x{{e}^{{{\tan }^{-1}}y}}={{e}^{2\,{{\tan }^{-1}}y}}+c\]
  done clear
  B)
   \[x{{e}^{{{\tan }^{-1}}y}}={{\tan }^{-1}}y+c\]
  done clear
  C)
   \[x{{e}^{2\,{{\tan }^{-1}}y}}={{e}^{{{\tan }^{-1}}y}}+c\]
  done clear
  D)
   \[(x-2)=c{{e}^{-{{\tan }^{-1}}}}y\]
  done clear
  View Answer play_arrow

• question_answer220) P and Q are two like parallel forces. If Q is moved parallel to itself through a distance x, then the resultant of P and Q moves through a distance
  A)
   \[Q(P+Q)X\]
  done clear
  B)
   \[\frac{QX}{(P+Q)}\]
  done clear
  C)
   \[\frac{PX}{(P+Q)}\]
  done clear
  D)
   \[\frac{(P+Q)X}{(P-Q)}\]
  done clear
  View Answer play_arrow

• question_answer221) The greatest and the least magnitudes of the resultant of two forces of constant magnitudes are F and G. when the forces act at an angle \[2\alpha ,\] the magnitude of the resultant is equal to
  A)
   \[\sqrt{{{F}^{2}}\,{{\cos }^{2}}\,\alpha \,+{{G}^{2}}\,{{\sin }^{2}}\alpha }\]
  done clear
  B)
   \[\sqrt{{{F}^{2}}\,{{\sin }^{2}}\alpha +{{G}^{2}}\,{{\cos }^{2}}\alpha }\]
  done clear
  C)
   \[\sqrt{{{F}^{2}}+{{G}^{2}}}\]
  done clear
  D)
   \[\sqrt{{{F}^{2}}-{{G}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer222) The magnitude of moment of a couple in certain direction is G and in a direction orthogonal to this direction (anti-clockwise) is H. The magnitude of moment of couple in anti-clockwise direction at an angle \[\theta \] to the critical direction is given by
  A)
   \[G\,\cos \,\theta -H\,\sin \theta \]
  done clear
  B)
   \[-G\,\cos \,\theta +H\,\sin \theta \]
  done clear
  C)
   \[G\,\cos \,\theta +H\,\sin \theta \]
  done clear
  D)
   \[G\,sin\,\theta +H\,\cos \theta \]
  done clear
  View Answer play_arrow

• question_answer223) The amount of force that is needed to accelerate a truck of mass \[36000\,kg\]from rest to a velocity of \[60\,km/h\]in \[20\,s\] is
  A)
   \[6\,kN\]
  done clear
  B)
    \[30\,kN\]
  done clear
  C)
   \[60\,kN\]
  done clear
  D)
   \[30000\,kN\]
  done clear
  View Answer play_arrow

• question_answer224) A body id falling freely under gravity starting from a point O.it passes through two points A and B. If \[OA=\,2AB,\] then the ratio of time takes by the body to cover the distance OA and AB is
  A)
   \[2\,\pm \,\sqrt{6}\]
  done clear
  B)
   \[\sqrt{2}\]
  done clear
  C)
   \[2+\sqrt{2}\]
  done clear
  D)
   \[2+\sqrt{6}\]
  done clear
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• question_answer225) A particle is projected from a point on the horizontal plane so as to just clear two walls each of height \[20\,m\]at distance \[30\,m\] and \[170\,m\] respectively from the point of projection. If \[\alpha \] is the angle projection then
  A)
   \[40\,\,\tan \,\alpha =51\]
  done clear
  B)
   \[40\,\,\cot \,\alpha =51\]
  done clear
  C)
   \[30\,\,tan\,\alpha =23\]
  done clear
  D)
   \[30\,\,\cot \,\alpha =23\]
  done clear
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