JEE Main & Advanced Sample Paper

done JEE Main Sample Paper-42 Total Questions - 105   

• question_answer1)
  A boat takes 2 h to travel 8 km and back in still water, if the velocity of water is 4 km/h the time taken for going upstream 8 km and coming back is
  A)
  2h
  done clear
  B)
  2 h 40 min
  done clear
  C)
  1 h 20 min
  done clear
  D)
  Cannot be estimated from the information given
  done clear
  View Answer play_arrow

• question_answer2)
  The rms speed of a certain gas is v at 400 K. The temperature at which the rms speed becomes two times, will be
  A)
  800 K                          
  done clear
  B)
  1600 K
  done clear
  C)
  1200 K                        
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer3)
  The kinetic energy of an electron with de-Broglie wavelength of 0.3 nm is
  A)
  0.168 eV         
  done clear
  B)
  16.8 eV
  done clear
  C)
  1.68 eV                       
  done clear
  D)
  2.5 Ev
  done clear
  View Answer play_arrow

• question_answer4)
  A body cools from \[100{}^\circ C\] to \[90{}^\circ C\] in 20 min, it will cool down from \[110{}^\circ C\] to \[100{}^\circ C\] in [Assume same surroundings]
  A)
   20 min                       
  done clear
  B)
   less than 20 min
  done clear
  C)
   more than 20 min      
  done clear
  D)
   30 min
  done clear
  View Answer play_arrow

• question_answer5)
  Consider two observers moving with respect to each other at a speed v along a straight line. They observe a block of mass m moving a distance I on a rough surface. The following quantities will be same as observed by the two observers
  A)
   kinetic energy of the block at time t
  done clear
  B)
   work done by friction
  done clear
  C)
   total work done on the block
  done clear
  D)
   acceleration of the block
  done clear
  View Answer play_arrow

• question_answer6)
  An astronaut has left the international space station to test a new space scooter. His partner measures the following velocity changes which take place in 10 s interval. Find the magnitude and direction of average acceleration. At the beginning of 10 s interval the astronaut is moving towards positive x-axis at 10 m/s and at the end of, 10 s he is moving towards negative x-axis at 5 m/s.
  A)
   15 m/s2, along positive x-axis
  done clear
  B)
   15 m/s2, along negative x-axis
  done clear
  C)
   1.5 m/s2, along negative x-axis
  done clear
  D)
   1.5 m/s2, along positive x-axis
  done clear
  View Answer play_arrow

• question_answer7)
  A particle of mass 10 kg starts from point A, with an initial velocity of 3m/s towards negative x-axis, it has been acted by a force of 10 N towards positive x-axis. Find the distance travelled by particle in 4 s.
  A)
   4 m                            
  done clear
  B)
   0.5 m
  done clear
  C)
   4.5m                          
  done clear
  D)
   5m
  done clear
  View Answer play_arrow

• question_answer8)
  Find the charge on \[5\mu F\]capacitor.
  A)
   5.45 \[\mu C\]            
  done clear
  B)
   16.37 \[\mu C\]
  done clear
  C)
   10.9\[\mu C\]             
  done clear
  D)
   18 \[\mu C\]
  done clear
  View Answer play_arrow

• question_answer9)
  A uniform slender rod 1m long is initially standing vertically on a smooth, horizontal surface. It is struck by a sharp horizontal blow at the top end, with the blow directed at right angles to the rod axis. As a result, the rod acquires an angular velocity of 3.00 rad/s. What is the translational velocity of the centre of mass of the rod after the blow?
  A)
   0.25 m/s                     
  done clear
  B)
   0.64 m/s
  done clear
  C)
   0.5 m/s                       
  done clear
  D)
   1.2 m/s
  done clear
  View Answer play_arrow

• question_answer10)
  Mark the incorrect option.
  A)
   During the discharging of battery, the battery supplies electrical energy at the rate of \[VI=EI-{{I}^{2}}r\]. Here, El represent the rate at which non-electrical energy is converted to electrical energy
  done clear
  B)
   During the charging of battery, the battery consumes energy at the rate of \[VI=EI+{{I}^{2}}r\]. Here, El represents the rate at which electrical energy is converted to non-electrical energy
  done clear
  C)
   In both the above cases the term \[{{I}^{2}}r\]represents the rate of dissipation of energy in the internal resistance of battery
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer11)
  Why does a glass sometimes break, if we quickly pour boiling water into it?
  A)
   Hot water expands, pushing the glass out
  done clear
  B)
   The hot water cools when it touches the glass, shrinking and pulling the glass in
  done clear
  C)
   The glass becomes hot and expands, causing the molecules to break
  done clear
  D)
   The inside of the glass expands faster than the outside of the glass, causing the glass to break
  done clear
  View Answer play_arrow

• question_answer12)
  Find the equivalent capacitance between A and B.
  A)
  \[\frac{2}{3}\mu F\]              
  done clear
  B)
  \[1\mu F\]
  done clear
  C)
  \[\frac{4}{3}\mu F\]              
  done clear
  D)
  \[6\mu F\]
  done clear
  View Answer play_arrow

• question_answer13)
  A 0.5 kg ball is dropped from rest at a point 1.20 m above the floor. The ball rebounds straight upward to a height of 0.7 m. What is the magnitude and the direction of the impulse of the net force applied to the ball during the collision with the floor?
  A)
   4.28 N-s, upward  
  done clear
  B)
   4.28 N-s, downward
  done clear
  C)
   8.56 N-s, upward  
  done clear
  D)
   8.56 N-s, downward
  done clear
  View Answer play_arrow

• question_answer14)
  A body is moving with uniform speed v in a horizontal circle in anticlockwise direction as shown in figure. The motion starts from point A, find the change in velocity in second quarter of revolution.
  A)
  \[\sqrt{2}vN-W\]                     
  done clear
  B)
  \[0.64m/s\]
  done clear
  C)
  \[0.5m/s\]                    
  done clear
  D)
  \[1.2m/s\]
  done clear
  View Answer play_arrow

• question_answer15)
  The statement "For a given body resistance is unique" is
  A)
   true                            
  done clear
  B)
   false
  done clear
  C)
   Cannot be predicted
  done clear
  D)
   None of the above        
  done clear
  View Answer play_arrow

• question_answer16)
  The block which is moving with constant speed 4 m/s with respect to ground is observed from two reference frames A and B. The frame A is non-inertial while B is inertial, then
  A)
   acceleration of block, with respect to A as well as with respect to B is zero
  done clear
  B)
   acceleration of block, with respect to A is non-zero while with respect to B is zero
  done clear
  C)
   acceleration of block with respect to A may be zero while with respect to B may be non-zero
  done clear
  D)
   acceleration of block with respect to both reference frames A and B would be non-zero
  done clear
  View Answer play_arrow

• question_answer17)
  N moles of an ideal diatomic gas are in a cylinder at temperature T. If we supply some heat to; it, then N/3 moles of gas dissociates into atoms while temperature remains constant. Heat supplied to the gas is
  A)
   NRT/6                        
  done clear
  B)
   5NRT/2
  done clear
  C)
   5.6 NRT                     
  done clear
  D)
   8NRT/3
  done clear
  View Answer play_arrow

• question_answer18)
  Electrons having KE 15 eV is collided with hydrogen atom and 80.6% of it is used to excite the electrons from its ground state. Find the number of emitted wavelengths.
  A)
   1                                
  done clear
  B)
   2
  done clear
  C)
   3                                
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer19)
  A pistol fires a 3g bullet with a speed of 400 m/s. The pistol barrel is 13 cm long. How (much energy is given to the bullet? Also, calculate the average force acted on the bullet while it was moving down the barrel.          
  A)
   140 J, 1846 N            
  done clear
  B)
   240 J, 184.6 N       
  done clear
  C)
   240 J, 1846 N            
  done clear
  D)
   240 J, 1746 N    
  done clear
  View Answer play_arrow

• question_answer20)
      If a charged conductor is not isolated and other conducting bodies are approaching towards it, then the
  A)
   capacitance of conductor will change as potential of conductor changes due to induction phenomenon
  done clear
  B)
   capacitance of conductor remains constant as it is depending on shape and size of conductor
  done clear
  C)
   capacitance of conductor will change due to redistribution of charge on approaching bodies                       
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer21)
  A person of mass m is standing a on a structure made up of pulley, strings and platform as shown in figure. Find the force exerted by the person on the rope, so that the system (person structure) remains in equilibrium.          
  A)
   mg                             
  done clear
  B)
  \[(m+M'+M)g\]
  done clear
  C)
  \[\frac{(M+M'+m)g}{2}\]     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  Find the distance between the object and its doubly magnified real image by a concave mirror of focal length f.
  A)
   2f                               
  done clear
  B)
  \[\frac{3f}{2}\]
  done clear
  C)
  \[\frac{5f}{2}\]                                   
  done clear
  D)
   3f
  done clear
  View Answer play_arrow

• question_answer23)
  A point source of light is taken away from the experimental set up of photoelectric effect, then which is the most appropriate statement?
  A)
   Saturation photo current remains same, while stopping potential increases.
  done clear
  B)
   Saturation photocurrent and stopping potential both decrease.
  done clear
  C)
   Saturation photocurrent decreases while stopping potential remains same.
  done clear
  D)
   Saturation photocurrent decreases and stopping potential increases.
  done clear
  View Answer play_arrow

• question_answer24)
  \[{{\text{X}}_{\text{ }\!\!\beta\!\!\text{ }}}\]X-ray of argon has wavelength 0.36 nm, the minimum energy needed to ionize an argon atom is 16 eV. Find the energy needed to knock out an electron from K shell of an argon atom.
  A)
   16 eV                         
  done clear
  B)
   3.45 keV
  done clear
  C)
   3.47 keV       
  done clear
  D)
   3.43 keV
  done clear
  View Answer play_arrow

• question_answer25)

  Directions: Assertion - Reaction type. Each of these contains tow statements:  Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below:

  Statement I: When speed of projection of a body is made n times, its time of flight becomes n times.

  Statement II: At this speed the range of projectile becomes n times.

  A)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I,
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer26)

  Directions: Assertion - Reaction type. Each of these contains tow statements:  Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below:

  Statement I: No diffraction is produced in sound waves near a very small opening.

  Statement II: For diffraction to take place the aperture of opening should be of the same order as wavelength of the waves.

  A)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I,
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer27)
  Two identical p-n junctions may be connected in series with a battery in three ways as shown in figure. The potential differences across the two p-n junctions are equal in       
  A)
  circuit 1 and circuit 2
  done clear
  B)
  circuit 2 and circuit 3
  done clear
  C)
  circuit 3 and circuit 1
  done clear
  D)
  circuit 1 only
  done clear
  View Answer play_arrow

• question_answer28)
  The electric field associated with a monochromatic beam becomes zero 2.4 x 1015 times per second. Find the maximum KE of the photoelectrons when this light falls on a metal surface whose work function is 2 eV.
  A)
   7.95 eV                      
  done clear
  B)
   17.9 eV
  done clear
  C)
   2.96 eV                      
  done clear
  D)
   4.96 Ev
  done clear
  View Answer play_arrow

• question_answer29)
  A radioactive sample whose half-life is 40 h has 18 times too much activity for safety, then after how many half-lives will the radioactive sample will be safe?        
  A)
   4                                
  done clear
  B)
   5
  done clear
  C)
   40                              
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer30)

  Direction: Question based on the following paragraph.

  Two rods 1 and 2 are released from rest as shown in figure.

  Given:\[{{l}_{1}}=4l,{{m}_{1}}=2m,{{l}_{2}}=2l\]and\[{{m}_{2}}=m.\]There is no friction between the two rods. If \[\alpha \]be the angular acceleration of rod 1 just after the rods are released. Then

  What is the normal reaction between the two rods at this instant?
  A)
  \[16\sqrt{3}\,ml\alpha \]                     
  done clear
  B)
  \[\frac{4ml\alpha }{\sqrt{3}}\]
  done clear
  C)
  \[\frac{32ml\alpha }{3\sqrt{3}}\]                  
  done clear
  D)
  \[12\sqrt{3}\,ml\alpha \]
  done clear
  View Answer play_arrow

• question_answer31)

  Direction: Question based on the following paragraph.

  Two rods 1 and 2 are released from rest as shown in figure.

  Given:\[{{l}_{1}}=4l,{{m}_{1}}=2m,{{l}_{2}}=2l\]and\[{{m}_{2}}=m.\]There is no friction between the two rods. If \[\alpha \]be the angular acceleration of rod 1 just after the rods are released. Then

  What is the horizontal force on rod 1 by hinge A at this instant?
  A)
  \[\left( \frac{32-12\sqrt{3}}{3\sqrt{3}} \right)ml\alpha \]      
  done clear
  B)
  \[\left( \frac{16-2\sqrt{3}}{\sqrt{3}} \right)ml\alpha \]
  done clear
  C)
  \[(14+2\sqrt{3})ml\alpha \]    
  done clear
  D)
  \[\sqrt{3}ml\alpha \]
  done clear
  View Answer play_arrow

• question_answer32)

  Direction: Question based on the following paragraph.

  Two rods 1 and 2 are released from rest as shown in figure.

  Given:\[{{l}_{1}}=4l,{{m}_{1}}=2m,{{l}_{2}}=2l\]and\[{{m}_{2}}=m.\]There is no friction between the two rods. If \[\alpha \]be the angular acceleration of rod 1 just after the rods are released. Then

  What is initial angular acceleration of rod 2 in terms of the given parameters in the question?
  A)
  \[\left[ \frac{2\sqrt{3}g}{2l}+2\sqrt{3}\alpha  \right]\]          
  done clear
  B)
  \[\left[ \frac{3\sqrt{3}g}{l}-\sqrt{3}\alpha  \right]\]
  done clear
  C)
  \[\left[ \frac{6\sqrt{3}g}{8l}+5\sqrt{3}\alpha  \right]\]          
  done clear
  D)
  \[\left[ \frac{3\sqrt{3}g}{8l}-\frac{8}{\sqrt{3}}\alpha  \right]\]
  done clear
  View Answer play_arrow

• question_answer33)
  For the given combination of gates, if the logic states of inputs A, B, C are as follows A = B = C = 0 and A = 5 = 1, C = 0, then the logic states of output D are
  A)
   0, 0                            
  done clear
  B)
   0, 1
  done clear
  C)
   1, 0                            
  done clear
  D)
   1, 1
  done clear
  View Answer play_arrow

• question_answer34)
  A person tries to find the value of unknown resistance using potentiometer as shown in the diagram below.                           He uses a resistance of \[5\Omega ,\]unknown resistance X and a battery of 5 V in secondary circuit. He touches the jockey\[{{\text{J}}_{\text{1}}}\]on potentiometer wire to get the point P, so that there is no deflection in \[{{G}_{1}}\] then he locates the point Q, so that \[{{G}_{2}}\] shows zero deflection. It is found that \[AP=\frac{AQ}{3}.\] Value of X is
  A)
  \[5\,\Omega \]                         
  done clear
  B)
  \[15\,\Omega \]
  done clear
  C)
  \[10\,\Omega \]
  done clear
  D)
   This method won't works
  done clear
  View Answer play_arrow

• question_answer35)
  A rain drop of radius 0.2 cm is falling through air with a terminal velocity of 8.7 m/s. The viscosity of air in SI units is [Take \[{{\text{ }\!\!\rho\!\!\text{ }}_{\text{water}}}\] = 1000 kg/m3 and \[{{\text{ }\!\!\rho\!\!\text{ }}_{\text{air}}}=1\text{kg/}{{\text{m}}^{\text{3}}}]\]
  A)
   \[\text{1}{{\text{0}}^{-4}}\]poise             
  done clear
  B)
   \[\text{1}\times \text{1}{{\text{0}}^{-3}}\]poise
  done clear
  C)
   \[8.6\times \text{1}{{\text{0}}^{-3}}\]poise          
  done clear
  D)
   \[1.02\times \text{1}{{\text{0}}^{-3}}\]poise
  done clear
  View Answer play_arrow

• question_answer36)
  The non-existence of \[\text{Pb}{{\text{I}}_{\text{4}}}\]is due to
  A)
  small size of \[\text{P}{{\text{b}}^{\text{4+}}}\] ions and large size of \[{{\text{I}}^{-}}\]ions
  done clear
  B)
  high oxidising power\[\text{P}{{\text{b}}^{\text{4+}}}\]of ions
  done clear
  C)
  high reducing power of \[{{\text{I}}^{-}}\] ions
  done clear
  D)
  Both [b] and [c]
  done clear
  View Answer play_arrow

• question_answer37)
  An ore of tin containing \[\text{FeCr}{{\text{O}}_{\text{4}}}\]is concentrated by
  A)
   froth floatation process
  done clear
  B)
   magnetic separation method
  done clear
  C)
   electrostatic method
  done clear
  D)
   gravity separation method
  done clear
  View Answer play_arrow

• question_answer38)
  For the reaction \[A+BC+D,\]equilibrium  concentration of [C] =[D] = 0.5M if we start with 1 mole each of A and B. Percentage of A converted into C if we start with 2 moles of A and 1 mole of B, is
  A)
   25%                           
  done clear
  B)
   40%
  done clear
  C)
   66.66%                      
  done clear
  D)
   33.33%
  done clear
  View Answer play_arrow

• question_answer39)
  The molecule \[B{{F}_{3}}\] and \[N{{F}_{3}}\] both are covalent compounds, but \[B{{F}_{3}}\]is non-polar and \[N{{F}_{3}}\]is polar. The reason is that
  A)
   boron is a metal and nitrogen is a gas in uncombined state
  done clear
  B)
   \[B{{F}_{3}}\] bonds have no dipole moment whereas \[N{{F}_{3}}\] bond have dipole moment
  done clear
  C)
   atomic size of boron is smaller than that of nitrogen                                    
  done clear
  D)
   \[B{{F}_{3}}\] is symmetrical molecule whereas \[N{{F}_{3}}\]is unsymmetrical?
  done clear
  View Answer play_arrow

• question_answer40)
  The rate of effusion doesn't depend on
  A)
   the area of cross-section of hole
  done clear
  B)
   number of molecules per unit volume
  done clear
  C)
   the average molecular speed
  done clear
  D)
   size of the molecule
  done clear
  View Answer play_arrow

• question_answer41)
  The correct IUPAC name of complex \[Fe{{({{C}_{5}}{{H}_{5}})}_{2}}\]is
  A)
   Cyclopentadienyliron (II)
  done clear
  B)
   Bis (cyclopentadienyl) iron (II)
  done clear
  C)
   Dicyclopentadienylferrate (II)
  done clear
  D)
   Ferrocene
  done clear
  View Answer play_arrow

• question_answer42)
  Which of the following is an example of chlorodising roasting ?
  A)
  \[A{{g}_{2}}S+2NaCl\to 2AgCl+N{{a}_{2}}S\]
  done clear
  B)
  \[PbS+2{{O}_{2}}\to PbS{{O}_{4}}\]
  done clear
  C)
  \[2AgCl+4Hg\to 2AgHg+H{{g}_{2}}C{{l}_{2}}\]
  done clear
  D)
   Both [a] and [c]                          
  done clear
  View Answer play_arrow

• question_answer43)
  The  raw materials  required  for the manu facture of \[N{{a}_{2}}C{{O}_{3}}\]by Solvay process,  are
  A)
  \[CaC{{l}_{2}},{{(N{{H}_{4}})}_{2}}C{{O}_{3}},N{{H}_{3}}\]
  done clear
  B)
  \[N{{H}_{4}}Cl,NaCl,Ca{{(OH)}_{2}}\]
  done clear
  C)
  \[NaCl,{{(N{{H}_{4}})}_{2}}C{{O}_{3}},N{{H}_{3}}\]
  done clear
  D)
  \[NaCl,N{{H}_{3}},CaC{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer44)
  \[X\xleftarrow[{{H}_{2}}S{{O}_{4}},{{H}_{2}}O]{HgS{{O}_{4}}}\]1-pentyne\[\xrightarrow[OH_{,}^{-}{{H}_{2}}{{O}_{2}}]{B{{H}_{3}},THF}Y\]X and V cannot be distinguished by
  A)
   silver-mirror test         
  done clear
  B)
   io do form test
  done clear
  C)
  \[N{{H}_{2}}OH\]               
  done clear
  D)
  \[LiAl{{H}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer45)
  Which of the following is correct about A, B and C?
  A)
   A, B and C are anomers
  done clear
  B)
   A, B and C are metamers
  done clear
  C)
   Only A and C are anomers
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer46)
  Predominant product is
  A)
  .                                                          
  done clear
  B)
  
  done clear
  C)
  .                                          
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer47)
  Product is
  A)
                                                  
  done clear
  B)
  
  done clear
  C)
                                     
  done clear
  D)
   Both [a] and [c]
  done clear
  View Answer play_arrow

• question_answer48)
  AgCl is colourless whereas Agl is yellow because of
  A)
   Ag+ possess 18 electrons shell to screen  the nuclear charge
  done clear
  B)
   \[A{{g}^{+}}\]shows pseudo inert gas configuration
  done clear
  C)
   distortion of r is more pronounced than \[C{{l}^{-}}\]ion
  done clear
  D)
   existence of d-d transition
  done clear
  View Answer play_arrow

• question_answer49)

  Direction: Assertion- Reaction type. Each of these contains tow statements:  Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below:

  Statement I: N-atom in \[N{{H}_{3}}\] is \[s{{p}^{3}}\]hybridized and bond angle is \[107{}^\circ \].

  Statement II: \[lp-bp\] repulsion    (VSEPR) decreases bond angle to \[107{}^\circ \].

  A)
   Statement I is true; Statement II is true;  Statement II is not a correct explanation for  Statement I,
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer50)

  Direction: Assertion- Reaction type. Each of these contains tow statements:  Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below:

  Statement I: In vulcanisation of rubber, sulphur cross links are introduced.

  Statement II: Vulcanisation is a free radical initiated chain reaction.

  A)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I,
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer51)
  Total entropy change for a system which is  not isolated from the surroundings is given by \[\Delta {{S}_{total}}=\Delta {{S}_{system}}+\Delta {{S}_{surroundings}}.\]For the spontaneous process
  A)
  \[\Delta {{S}_{total}}=0,\] always
  done clear
  B)
  \[\Delta {{S}_{total}}=\] positive, always
  done clear
  C)
  \[\Delta {{S}_{total}}=\] negative, always
  done clear
  D)
   \[\Delta {{S}_{total}}\] will be positive or negative other than zero
  done clear
  View Answer play_arrow

• question_answer52)
  The osmotic pressure of blood is 7.65 atm at \[37{}^\circ C\]. How much glucose should be used per litre for an intravenous injection that is to have the same osmotic pressure as blood?
  A)
   180 g                         
  done clear
  B)
   54.2 g
  done clear
  C)
   86 g                           
  done clear
  D)
   111 g
  done clear
  View Answer play_arrow

• question_answer53)
  \[\Delta {{S}^{o}},\]change in entropy for the following cell reaction is \[2{{H}_{2}}+{{O}_{2}}\to 2{{H}_{2}}O\](Given :\[{{E}^{o}}_{cell}=1.23V,\] \[\Delta H_{f}^{o}({{H}_{2}}O)=-285.8\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\],\[\Delta {{G}^{o}}=-\,474.78\text{kJ}\,)\]
  A)
  \[-126.7\text{J}{{\text{K}}^{-1}}\]            
  done clear
  B)
  \[+126.7\,\text{J}{{\text{K}}^{-1}}\]
  done clear
  C)
  \[-324.9\,\text{J}{{\text{K}}^{-1}}\]                      
  done clear
  D)
  \[324.9\,\text{J}{{\text{K}}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer54)
  Molar conductance of a 1.5M solution of an electrolyte is found to be 138.9 S cm2. The specific conductance of this solution is
  A)
   0.208 S \[\text{c}{{\text{m}}^{-1}}\]        
  done clear
  B)
   0.102 S\[\text{c}{{\text{m}}^{-1}}\]
  done clear
  C)
   0.320 S \[\text{c}{{\text{m}}^{-1}}\]        
  done clear
  D)
   0.152 S \[\text{c}{{\text{m}}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer55)
  A metal X on heating in nitrogen gas gives Y. Y on treatment with H-f) gives a colourless gas which when passed through \[CuS{{O}_{4}}\] solution gives a blue colour. Y is
  A)
  \[Mg{{(N{{O}_{3}})}_{2}}\]                      
  done clear
  B)
  \[M{{g}_{3}}{{N}_{2}}\]
  done clear
  C)
  \[N{{H}_{3}}\]                                 
  done clear
  D)
  \[MgO\]
  done clear
  View Answer play_arrow

• question_answer56)
  If one litre of air is passed repeatedly over heated copper and magnesium till no further reduction in volume takes place, the volume finally obtained would be approximately
  A)
   800 mL                      
  done clear
  B)
   200 mL
  done clear
  C)
   10 mL                        
  done clear
  D)
   zero
  done clear
  View Answer play_arrow

• question_answer57)
  The predominant product is
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer58)
  Predominant product is
  A)
  \[\text{R }\!\!'\!\!\text{ -}\underset{\begin{smallmatrix}  \text{ }\!\!|\!\!\text{ } \\  \text{R }\!\!'\!\!\text{  }\!\!'\!\!\text{ } \end{smallmatrix}}{\overset{\begin{smallmatrix}  \text{R} \\  \text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}}\,\text{-C}{{\text{H}}_{\text{2}}}\text{OH}\]
  done clear
  B)
  \[\text{R-C}{{\text{H}}_{\text{2}}}\text{-}\underset{\begin{smallmatrix}  \text{ }\!\!|\!\!\text{ } \\  \text{R }\!\!'\!\!\text{  }\!\!'\!\!\text{ } \end{smallmatrix}}{\overset{\begin{smallmatrix}  \text{R }\!\!'\!\!\text{ } \\  \text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}}\,\text{-OH}\]
  done clear
  C)
  \[\text{R }\!\!'\!\!\text{ C}{{\text{H}}_{\text{2}}}\text{-}\underset{\begin{smallmatrix}  \text{ }\!\!|\!\!\text{ } \\  \text{R }\!\!'\!\!\text{  }\!\!'\!\!\text{ } \end{smallmatrix}}{\overset{\begin{smallmatrix}  \text{R} \\  \text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}}\,\text{-OH}\]
  done clear
  D)
  \[\text{R }\!\!'\!\!\text{ C}{{\text{H}}_{\text{2}}}\text{-}\underset{\begin{smallmatrix}  \text{ }\!\!|\!\!\text{ } \\  \text{R }\!\!'\!\!\text{ } \end{smallmatrix}}{\overset{\begin{smallmatrix}  \text{R} \\  \text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}}\,\text{-OH}\]
  done clear
  View Answer play_arrow

• question_answer59)
  Which of the following is correct order of basicity for these molecules?
  A)
   IV > II > I > III         
  done clear
  B)
   III > IV > I > II
  done clear
  C)
   I > IV > III > II         
  done clear
  D)
   III > I > II > IV
  done clear
  View Answer play_arrow

• question_answer60)
  The compound 'X yeas boiled under reflux for some time with a solution of sodium hydroxide. The solution was cooled, acidified with dilute nitric acid and then silver nitrate solution was added, a thick precipitate was formed, which one is incorrect as 'X' ?
  A)
  \[C{{H}_{3}}COCl\]            
  done clear
  B)
  \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}Cl\]
  done clear
  C)
  \[C{{H}_{2}}ClCOOH\]      
  done clear
  D)
  \[{{C}_{6}}{{H}_{5}}Cl\]
  done clear
  View Answer play_arrow

• question_answer61)
  In the reaction sequence\[X\xrightarrow[{}]{Ca{{(OH)}_{2}}}Y\xrightarrow[distillation]{Dry}Actetone\xrightarrow[{{H}_{2}}S{{O}_{4}}]{Conc.}Z;\]X. V and Z are
  A)
  \[C{{H}_{3}}CHO,\] aldol, phorone
  done clear
  B)
  \[HCOOH,{{(HCOO)}_{2}}Ca,\] mesityl oxide
  done clear
  C)
  \[C{{H}_{3}}COOH,{{(C{{H}_{3}}COO)}_{2}}Ca,\] mesityl oxide
  done clear
  D)
  \[C{{H}_{3}}COOH,{{(C{{H}_{3}}COO)}_{2}}Ca,\] pinacol
  done clear
  View Answer play_arrow

• question_answer62)
  The ratio of kinetic energy and potential energy of an electron in Bohr orbit of a hydrogen like species is
  A)
   1/2                             
  done clear
  B)
   -1/2
  done clear
  C)
   1                                
  done clear
  D)
   - 1
  done clear
  View Answer play_arrow

• question_answer63)
  To a 25 mL HaOa solution, excess of acidified solution of potassium iodide was added. The iodine liberated required 20 mL of 0.3 N sodium thiosulphate solution. The volume strength of \[{{H}_{2}}{{O}_{2}}\] solution is
  A)
   4.444                         
  done clear
  B)
   2.444
  done clear
  C)
   3.344                         
  done clear
  D)
   1.344
  done clear
  View Answer play_arrow

• question_answer64)
  Which of the following is not correctly matched?

  Colloidal solution	Type
  I Cheese	Gel
  II Hair cream	Emulsion
  III Mist	Aerosol
  IV Whipped cream	Solid foam

  A)
   I                                 
  done clear
  B)
   II
  done clear
  C)
   III                               
  done clear
  D)
   IV
  done clear
  View Answer play_arrow

• question_answer65)
  In a certain polluted atmosphere containing 03 at    a    steady    state    concentration of \[2.0\times {{10}^{-8}}\text{mol/L,}\] the hourly production of 03 by all sources was estimated as \[7.2\times {{10}^{-15}}\text{mol/L}\]. If the only mechanism for destruction of \[{{O}_{3}}\] is the second order reaction\[2{{O}_{3}}\to 3{{O}_{2}},\]what is the rate constant for the destruction reaction?
  A)
  \[1.3\times {{10}^{-3}}\text{L}\,\text{mo}{{\text{l}}^{-1}}{{\text{s}}^{-1}}\]
  done clear
  B)
  \[5\times {{10}^{-3}}\text{L}\,\text{mo}{{\text{l}}^{-1}}{{\text{s}}^{-1}}\]
  done clear
  C)
  \[1.9\times {{10}^{-3}}\text{L}\,\text{mo}{{\text{l}}^{-1}}{{\text{s}}^{-1}}\]
  done clear
  D)
  \[3.6\times {{10}^{-15}}\text{L}\,\text{mo}{{\text{l}}^{-1}}{{\text{s}}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer66)
  The chemical reaction \[2{{O}_{3}}\to 3{{O}_{2}}\] proceeds as follows \[{{O}_{3}}{{O}_{2}}+O\] .... (fast)\[O+{{O}_{3}}\to 2{{O}_{2}}\].... (slow), the rate law expression should be
  A)
  \[r=k{{[{{O}_{3}}]}^{2}}\]                     
  done clear
  B)
  \[r=k{{[{{O}_{3}}]}^{2}}{{[{{O}_{2}}]}^{-1}}\]
  done clear
  C)
  \[r=k[{{O}_{3}}][{{O}_{2}}]\]     
  done clear
  D)
   un predictable
  done clear
  View Answer play_arrow

• question_answer67)
  The sal; of which one of the following weak acids will be the most hydrolysed?
  A)
  \[HA:{{K}_{a}}=1\times {{10}^{-8}}\]   
  done clear
  B)
  \[HB:{{K}_{a}}=2\times {{10}^{-6}}\]
  done clear
  C)
  \[HC:{{K}_{a}}=3\times {{10}^{-8}}\]   
  done clear
  D)
  \[HD:{{K}_{a}}=4\times {{10}^{-10}}\]
  done clear
  View Answer play_arrow

• question_answer68)

  Directions: The decarboxylation of aromatic acids is most often carried out by heating with Cu-quinoline \[ArCOOH\xrightarrow[{}]{Cu-quinoline}ArH+C{{O}_{2}}\] Cuprous salts of aromatic acids, actually undergoes decarboxylation. However, two other methods can be used with certain substrates.

  Method 1: Salt of acid, \[ArCO{{O}^{-}}\]is heated (SE1)

  Step I:

  Step II:

  Method II: Carboxylic acid is heated with a strong acid, often sulphuric acid.

  Decarboxylation takes place by the arenium ion mechanism, with\[{{\text{H}}^{+}}\] electrophile. Evidently, the order of electrofugal ability is \[C{{O}_{2}}>{{H}^{+}}>COO{{H}^{+}}\]Rearrangements are also known to take place. For example,, when the phthalate ion is heated with catalytic amount of cadmium, the terephthalate ion is produced. In a similar process, potassium benzoate heated with cadmium salts disproportionates. The rearrangement is named as 'Henkel rearrangement'.

  Mark out the correct order of -G (functional group) according to their ease to facilitate the decarboxylation reaction.
  A)
  \[-N{{O}_{2}}>-CHO>-H>-Cl>-C{{H}_{3}}\]
  done clear
  B)
  \[-C{{H}_{3}}>-H>-Cl>-CHO>-N{{O}_{2}}\]
  done clear
  C)
  \[-C{{H}_{3}}>-Cl>-H>-N{{O}_{2}}>-CHO\]
  done clear
  D)
  \[-CHO>-N{{O}_{2}}>-H>-C{{H}_{3}}>-Cl\]
  done clear
  View Answer play_arrow

• question_answer69)

  Directions: The decarboxylation of aromatic acids is most often carried out by heating with Cu-quinoline \[ArCOOH\xrightarrow[{}]{Cu-quinoline}ArH+C{{O}_{2}}\] Cuprous salts of aromatic acids, actually undergoes decarboxylation. However, two other methods can be used with certain substrates.

  Method 1: Salt of acid, \[ArCO{{O}^{-}}\]is heated (SE1)

  Step I:

  Step II:

  Method II: Carboxylic acid is heated with a strong acid, often sulphuric acid.

  Decarboxylation takes place by the arenium ion mechanism, with\[{{\text{H}}^{+}}\] electrophile. Evidently, the order of electrofugal ability is \[C{{O}_{2}}>{{H}^{+}}>COO{{H}^{+}}\]Rearrangements are also known to take place. For example,, when the phthalate ion is heated with catalytic amount of cadmium, the terephthalate ion is produced. In a similar process, potassium benzoate heated with cadmium salts disproportionates. The rearrangement is named as 'Henkel rearrangement'.

  Mark out the correct order of -G (functional group) according to their ease to facilitate the decarboxylation reaction.
  A)
  \[-OC{{H}_{3}}>-N{{O}_{2}}>-F>-H>-C{{H}_{3}}\]
  done clear
  B)
  \[-N{{O}_{2}}>-F>-H>-C{{H}_{3}}>-OC{{H}_{3}}\]
  done clear
  C)
  \[-N{{O}_{2}}>-F>-OC{{H}_{3}}>-H>-C{{H}_{3}}\]
  done clear
  D)
  \[-OC{{H}_{3}}>-C{{H}_{3}}>-H>-F>-N{{O}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer70)

  Directions: The decarboxylation of aromatic acids is most often carried out by heating with Cu-quinoline \[ArCOOH\xrightarrow[{}]{Cu-quinoline}ArH+C{{O}_{2}}\] Cuprous salts of aromatic acids, actually undergoes decarboxylation. However, two other methods can be used with certain substrates.

  Method 1: Salt of acid, \[ArCO{{O}^{-}}\]is heated (SE1)

  Step I:

  Step II:

  Method II: Carboxylic acid is heated with a strong acid, often sulphuric acid.

  Decarboxylation takes place by the arenium ion mechanism, with\[{{\text{H}}^{+}}\] electrophile. Evidently, the order of electrofugal ability is \[C{{O}_{2}}>{{H}^{+}}>COO{{H}^{+}}\]Rearrangements are also known to take place. For example,, when the phthalate ion is heated with catalytic amount of cadmium, the terephthalate ion is produced. In a similar process, potassium benzoate heated with cadmium salts disproportionates. The rearrangement is named as 'Henkel rearrangement'.

  In the 'Henkel reaction' when potassium benzoate is heated with cadmium salts, the products are
  A)
  
  done clear
  B)
  
  done clear
  C)
  ?                                 
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer71)
  If a, b and c are distinct positive numbers, then the expression (b + c - a) (a + c - b) (a +b - c) - abc is
  A)
   positive                      
  done clear
  B)
   negative
  done clear
  C)
   non-positive   
  done clear
  D)
   non-negative
  done clear
  View Answer play_arrow

• question_answer72)
  If \[{{x}_{1}},{{x}_{2}},{{x}_{3}}\]as well as \[{{y}_{1}},{{y}_{2}},{{y}_{3}}\]are in GP with the same common ratio, then the points\[({{x}_{1}},{{y}_{1}}),({{x}_{2}},{{y}_{2}})\]and \[({{x}_{1}},{{y}_{1}}),({{x}_{2}},{{y}_{2}})\]
  A)
   lie on a straight line    
  done clear
  B)
   lie on an ellipse
  done clear
  C)
   lie on a circle
  done clear
  D)
   are vertices of a triangle
  done clear
  View Answer play_arrow

• question_answer73)
  If  \[6{{A}^{-1}}={{A}^{2}}+cA+dI,\] then  (c, d) is
  A)
   (-6, 11)                      
  done clear
  B)
   (-11,6)
  done clear
  C)
   (11,6)                         
  done clear
  D)
   (6,11)
  done clear
  View Answer play_arrow

• question_answer74)

  Directions: Question based on the following paragraph.

  If\[\cos \frac{\pi }{7},\cos \frac{3\pi }{7},\cos \frac{5\pi }{7}.\]are the roots of the equation \[8{{x}^{3}}-4{{x}^{b}}-4x+1=0\].

  Find the value of \[\sec \frac{\pi }{7}+\sec \frac{3\pi }{7}+\sec \frac{5\pi }{7}.\]
  A)
   2                                
  done clear
  B)
   4
  done clear
  C)
   8                                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer75)

  Directions: Question based on the following paragraph.

  If\[\cos \frac{\pi }{7},\cos \frac{3\pi }{7},\cos \frac{5\pi }{7}.\]are the roots of the equation \[8{{x}^{3}}-4{{x}^{b}}-4x+1=0\].

  Find the value of \[\frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}.\]
  A)
  \[\frac{1}{4}\]                        
  done clear
  B)
  \[\frac{1}{8}\]
  done clear
  C)
  \[\frac{\sqrt{7}}{4}\]                         
  done clear
  D)
  \[\frac{\sqrt{7}}{8}\]
  done clear
  View Answer play_arrow

• question_answer76)
  On the interval [0, 1] the function \[{{x}^{25}}{{(1-x)}^{75}}\]takes its maximum value at the point
  A)
   0                                
  done clear
  B)
   ¼
  done clear
  C)
   1/2                             
  done clear
  D)
   1/3
  done clear
  View Answer play_arrow

• question_answer77)
  The area enclosed between the curves y = ox2 and x = qy2 (a > 0) is 1 sq unit. Then, the value of 'a' is
  A)
  \[\frac{1}{\sqrt{3}}\]                         
  done clear
  B)
  \[\frac{1}{2}\]
  done clear
  C)
   1                                
  done clear
  D)
   1/3
  done clear
  View Answer play_arrow

• question_answer78)
  Let \[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\] three vectors such that \[\overrightarrow{a}\ne 0\] and \[\overrightarrow{a}\times \overrightarrow{b}=2\overrightarrow{a}\times \overrightarrow{c},\]\[|\overrightarrow{a}|=|\overrightarrow{c}|=1,\]\[|\overrightarrow{b}|=4\]and \[|\overrightarrow{b}\times \overrightarrow{c}|=\sqrt{15}.\]If \[\overrightarrow{b}-2\overrightarrow{c}=\lambda \overrightarrow{a},\]then \[\lambda \] is equal to
  A)
   -4                               
  done clear
  B)
   -2
  done clear
  C)
   1                                
  done clear
  D)
   3                   
  done clear
  View Answer play_arrow

• question_answer79)
  Chords of an ellipse are drawn through the positive end of the minor axis. Then, their mid point lies on
  A)
   a circle                       
  done clear
  B)
   a parabola
  done clear
  C)
   an ellipse       
  done clear
  D)
   a hyperbola
  done clear
  View Answer play_arrow

• question_answer80)
  Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangements is
  A)
  \[^{6}{{C}_{3}}{{\times }^{3}}{{C}_{2}}\]               
  done clear
  B)
  \[^{4}{{P}_{2}}{{\times }^{4}}{{P}_{3}}\]
  done clear
  C)
  \[^{4}{{C}_{2}}{{+}^{4}}{{P}_{3}}\]                       
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer81)
  For   any   integer   n   the   integral \[\int_{0}^{\pi }{{{e}^{{{\cos }^{2}}x}}}{{\cos }^{3}}(2n+1)xdx\]has the value
  A)
  \[\pi \]                          
  done clear
  B)
   1
  done clear
  C)
   0                                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer82)
  If x = 9 is the chord of the hyperbola x2 -y2 = 9, then the equation of the corresponding pair of tangents is
  A)
  \[9{{x}^{2}}-8{{y}^{2}}+18x-9=0\]
  done clear
  B)
  \[9{{x}^{2}}-8{{y}^{2}}-18x+9=0\]
  done clear
  C)
  \[9{{x}^{2}}-8{{y}^{2}}-18x-9=0\]
  done clear
  D)
  \[9{{x}^{2}}-8{{y}^{2}}+18x+9=0\]
  done clear
  View Answer play_arrow

• question_answer83)
  The number of all possible triplets \[({{a}_{1}},{{a}_{2}},{{a}_{3}})\]such that \[{{a}_{1}}+{{a}_{2}}\cos 2x+{{a}_{3}}{{\sin }^{2}}x=0,\forall x,\]is
  A)
   0                                
  done clear
  B)
   1
  done clear
  C)
   3                                
  done clear
  D)
   \[\infty \]
  done clear
  View Answer play_arrow

• question_answer84)
  The number of real solutions of\[{{\tan }^{-1}}\sqrt{x(x+1)}+{{\sin }^{-1}}\sqrt{{{x}^{2}}+x+1}=\frac{\pi }{2}\]
  A)
   0                                
  done clear
  B)
   1
  done clear
  C)
   2                                
  done clear
  D)
   \[\infty \]
  done clear
  View Answer play_arrow

• question_answer85)

  Direction: Assertion- Reaction type. Each of these contains tow statements:  Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below:

  Statement I: A coin is tossed 31 times. If the probability of getting number of heads more than the number of tails is equal to the probability of getting tails more than the number of heads, then the coin must be unbiased.

  Statement II: If p = q and p + q = 1, then coin is unbiased.

  A)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer86)

  Direction: Assertion- Reaction type. Each of these contains tow statements:  Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below:

  Statement I: If f(x) is odd function and g(x) is even function, then f(x)+ g(x) is neither even no odd.

  Statement II: Odd function is symmetrical at in opposite quadrants and even function is symmetrical about the y-axis.

  A)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer87)

  Direction: Assertion- Reaction type. Each of these contains tow statements:  Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below:

  Statement I: If normal at the ends of double ordinate x = 4 of parabola y2 = 4x meet the curve again at P and P' respectively, then PP' = 12unit.

  Statement II: If normal at \[{{\text{t}}_{\text{1}}}\] of y2 = 4ox meet the parabola again at \[{{\text{t}}_{2}},\] then \[{{\text{t}}_{2}}=-{{t}_{1}}\frac{2}{{{t}_{1}}}.\]

  A)
   Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I
  done clear
  B)
   Statement I is true; Statement II is false.
  done clear
  C)
   Statement I is false; Statement II is true.
  done clear
  D)
   Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
  done clear
  View Answer play_arrow

• question_answer88)
  The minimum value of \[{{x}^{2}}+\frac{1}{1+{{x}^{2}}}\] is at
  A)
   x = 0                         
  done clear
  B)
   x = 1
  done clear
  C)
   x = 4                         
  done clear
  D)
   x = 3
  done clear
  View Answer play_arrow

• question_answer89)
  10 different toys are to be distributed among 10 children. Total number of ways of distributing these toys, so that exactly 2 children do not get any toy, is equal to
  A)
  \[{{(10!)}^{2}}\left( \frac{2}{3!2!7!}+\frac{1}{{{(2!)}^{5}}6!} \right)\]
  done clear
  B)
  \[{{(10!)}^{2}}\left( \frac{1}{3!2!7!}+\frac{1}{{{(2!)}^{4}}6!} \right)\]
  done clear
  C)
  \[{{(10!)}^{2}}\left( \frac{1}{3!7!}+\frac{1}{{{(2!)}^{5}}6!} \right)\]
  done clear
  D)
  \[{{(10!)}^{2}}\left( \frac{1}{3!7!}+\frac{1}{{{(2!)}^{5}}(6!)} \right)\]
  done clear
  View Answer play_arrow

• question_answer90)
  If\[{{(1+x)}^{n}}=\sum\limits_{r=0}^{n}{^{n}{{C}_{r}}\,{{x}^{n}},}\]then\[\frac{^{n}{{C}_{0}}}{1.2}{{2}^{2}}+\frac{^{n}{{C}_{1}}}{2.3}{{2}^{3}}+\frac{^{n}{{C}_{2}}}{3.4}{{2}^{4}}+...\]\[+\frac{^{n}{{C}_{2}}}{(n+1).(n+2)}{{2}^{n+2}}\]is equal to
  A)
  \[\frac{{{3}^{n+2}}+2n-5}{(n+1)(n+2)}\]         
  done clear
  B)
  \[\frac{{{3}^{n+2}}-2n+5}{(n+1)(n+2)}\]
  done clear
  C)
  \[\frac{{{3}^{n+2}}-2n-5}{(n+1)(n+2)}\]           
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer91)
  The solution of the differential equation \[xdy-ydx=\sqrt{{{x}^{2}}+{{y}^{2}}}dx\]is
  A)
  \[x+\sqrt{{{x}^{2}}+{{y}^{2}}}=c{{x}^{2}}\]        
  done clear
  B)
  \[y-\sqrt{{{x}^{2}}+{{y}^{2}}}=cx\]
  done clear
  C)
  \[x-\sqrt{{{x}^{2}}+{{y}^{2}}}=cx\]    
  done clear
  D)
  \[y+\sqrt{{{x}^{2}}+{{y}^{2}}}=c{{x}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer92)
  If the base of a triangle and the ratio of the lengths of the other two un equals sides are given, then the vertex lies on a/an
  A)
   straight line                
  done clear
  B)
   circle
  done clear
  C)
   ellipse                         
  done clear
  D)
   parabola
  done clear
  View Answer play_arrow

• question_answer93)
  The tangent to the curve \[x=a(\theta -\sin \theta ),\]\[y=a(1+\cos \theta )\] at the points \[\theta =(2k+1)\pi ,k\in I\] are parallel to
  A)
  \[y=x\]            
  done clear
  B)
  \[y=-x\]
  done clear
  C)
  \[y=0\]            
  done clear
  D)
  \[x=0\]
  done clear
  View Answer play_arrow

• question_answer94)
  If the imaginary part of the expression \[\frac{x-1}{{{e}^{i\theta }}}+\frac{{{e}^{i\theta }}}{z-1}\] be zero, then the locus of z is
  A)
   a straight line parallel to the .x-axis
  done clear
  B)
   a circle of radius 1 and centre (1, 0)
  done clear
  C)
   a parabola                 
  done clear
  D)
   None of the above
  done clear
  View Answer play_arrow

• question_answer95)
  A parallelepiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelepiped is
  A)
   7                                
  done clear
  B)
   \[\sqrt{38}\]
  done clear
  C)
   \[\sqrt{155}\]                         
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer96)
  If a vertex of a triangle is (1, 1) and the mid points of two sides through this vertex are (-1,2) and (3,2), then the centroid of the triangle is
  A)
  \[\left( \frac{1}{3},\frac{7}{3} \right)\]                      
  done clear
  B)
  \[\left( 1,\frac{7}{3} \right)\]
  done clear
  C)
  \[\left( -\frac{7}{3},\frac{7}{3} \right)\]                    
  done clear
  D)
  \[\left( -1,\frac{7}{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer97)
  The expression \[{{\{x+{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}+\]\[{{\{x-{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}\] polynomial of degree
  A)
   5                                
  done clear
  B)
   6   
  done clear
  C)
   7                                
  done clear
  D)
   8
  done clear
  View Answer play_arrow

• question_answer98)
  If p, q, r are simple propositions, then \[(p\wedge q)(q\wedge r)\] is true, then
  A)
   p, q, r are all false
  done clear
  B)
   p, q, r are all true
  done clear
  C)
   p, q are true and r is false
  done clear
  D)
   p is true and q and r are false
  done clear
  View Answer play_arrow

• question_answer99)
  \[\underset{x\to 1}{\mathop{\lim }}\,\frac{\sqrt{1-\cos 2(x-1)}}{x-1}\] is equal to
  A)
   exists and it equals \[\sqrt{2}\]
  done clear
  B)
   exists and it equals \[-\sqrt{2}\]
  done clear
  C)
   does not exist because \[x-1\to 0\]
  done clear
  D)
   does not exist because left hand limit is not equal to right hand limit
  done clear
  View Answer play_arrow

• question_answer100)
  The value of\[\int_{{}}^{{}}{\frac{{{\sin }^{-1}}\sqrt{x}-{{\cos }^{-1}}\sqrt{x}}{{{\sin }^{-1}}\sqrt{x}+{{\cos }^{-1}}\sqrt{x}}dx}\]is
  A)
  \[\frac{2}{\pi }\{\sqrt{x-{{x}^{2}}}\}-(1+2x){{\sin }^{-1}}\sqrt{x}\}-x+c\]
  done clear
  B)
  \[\frac{2}{\pi }\{\sqrt{x-{{x}^{2}}}-(1-2x){{\sin }^{-1}}\sqrt{x}\}-x+c\]
  done clear
  C)
  \[\frac{2}{\pi }\{\sqrt{x-{{x}^{2}}}-(1-2x){{\sin }^{-1}}x\}-x+c\]
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer101)
  If\[a>2b>0,\]then positive value of m for which \[y=mx-b\sqrt{1+{{m}^{2}}}\]is a common tangent to \[{{x}^{2}}+{{y}^{2}}={{b}^{2}}\]and \[{{(x-a)}^{2}}+{{y}^{2}}={{b}^{2}},\]is
  A)
  \[\frac{2b}{\sqrt{{{a}^{2}}-4{{b}^{2}}}}\]                  
  done clear
  B)
  \[\frac{\sqrt{{{a}^{2}}-4{{b}^{2}}}}{2b}\]
  done clear
  C)
  \[\frac{2b}{a-2b}\]                
  done clear
  D)
  \[\frac{b}{a-2b}\]
  done clear
  View Answer play_arrow

• question_answer102)
  If \[{{a}_{r}}>0,r\in N\]and \[{{a}_{1}},{{a}_{2}}....,{{a}_{2n}}\]are in AP, then\[\frac{{{a}_{1}}+{{a}_{2n}}}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{{{a}_{2}}+{{a}_{2n+1}}}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\frac{{{a}_{3}}+{{a}_{2n-2}}}{\sqrt{{{a}_{3}}}+\sqrt{{{a}_{4}}}}+....+\]\[\frac{{{a}_{n}}+{{a}_{n+1}}}{\sqrt{{{a}_{n}}}+\sqrt{{{a}_{n+1}}}}\]
  A)
  \[n-1\]                         
  done clear
  B)
  \[\frac{n({{a}_{1}}+{{a}_{2n}})}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n+1}}}}\]
  done clear
  C)
  \[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n+1}}}}\]                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer103)
  If the ratio of the roots of \[\lambda {{x}^{2}}+\mu x+v=0\] is equal to the ratio of the roots of x2 + x + 1 = 0 then \[\lambda ,\mu ,v\]are in
  A)
   AP                             
  done clear
  B)
   GP
  done clear
  C)
   HP                             
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer104)
  PQ and RS are two perpendicular chords of the rectangular hyperbola If C is the centre of the rectangular hyperbola, then the product of the slopes of CP, CQ, CR and CS is equal to
  A)
  -1                                
  done clear
  B)
   1
  done clear
  C)
   0                                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer105)
  If\[\cos x-\frac{\cot \beta \sin x}{2}=\frac{\sqrt{3}}{2},\] then the value of \[\tan \frac{x}{2}\]is
  A)
  \[\tan \frac{\beta }{2}\tan {{15}^{o}}\]                 
  done clear
  B)
  \[\tan \frac{\beta }{2}\]
  done clear
  C)
  \[\tan {{15}^{o}}\]              
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow