JEE Main & Advanced Sample Paper

done JEE Main Sample Paper-43 Total Questions - 90   

• question_answer1)
  Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is
  A)
  \[\frac{\sqrt{3}}{4}N\]          
  done clear
  B)
   \[\sqrt{3}\,N\]
  done clear
  C)
   0.5 N             
  done clear
  D)
   1.5N
  done clear
  View Answer play_arrow

• question_answer2)
  A uniform metal disc of radius R is taken and out of it a disc of diameter R/2 is cut-off from the end. The centre of mass of the remaining part will be
  A)
   \[\frac{R}{4}\]from the centre           
  done clear
  B)
   \[\frac{R}{3}\]from the centre
  done clear
  C)
   \[\frac{R}{5}\]from the centre           
  done clear
  D)
  \[\frac{R}{6}\]from the centre
  done clear
  View Answer play_arrow

• question_answer3)
  A tank is filled with water of density \[1\text{ }g/c{{m}^{3}}\] and oil of density \[0.9\text{ }g/c{{m}^{3}}\] . The height of water layer is 100 cm and of the oil layer is 400 cm. lf \[g=980\text{ }cm/{{s}^{2}}\] , then the velocity of efflux from an opening in the bottom of the tank is
  A)
   \[\sqrt{900\times 980}\,\,cm/s\]         
  done clear
  B)
   \[\sqrt{100\times 980}\,\,cm/s\]
  done clear
  C)
   \[\sqrt{920\times 980}\,\,cm/s\]         
  done clear
  D)
   \[\sqrt{950\times 980}\,\,cm/s\]
  done clear
  View Answer play_arrow

• question_answer4)
  A charge \[Q\] is divided into two parts q and q' and separated by a distance R. The force of repulsion between them will be maximum, when
  A)
   \[q=\frac{Q}{4}\]                
  done clear
  B)
   \[q=\frac{Q}{2}\]
  done clear
  C)
   \[q=Q\]                     
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)
  A parallel plate capacitor has plates with area A and separation between it is d. A battery charges the plates to a potential difference\[{{V}_{0}}\]The battery is then disconnected and a dielectric slab of thickness d is introduced. The ratio of energy stored in the capacitor before and after the slab is introduced is
  A)
   K                                
  done clear
  B)
   \[\frac{1}{K}\]
  done clear
  C)
   \[\frac{A}{{{d}^{2}}K}\]              
  done clear
  D)
   \[\frac{{{d}^{2}}K}{A}\]
  done clear
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• question_answer6)
  You are given n resistors, each of resistance r. They are first combined to get minimum possible resistance, then they are connected to get maximum possible resistance. The ratio between minimum to maximum resistances is
  A)
  \[\frac{1}{n}\]                        
  done clear
  B)
   \[n\]
  done clear
  C)
   \[{{n}^{2}}\]                                  
  done clear
  D)
   \[\frac{1}{{{n}^{2}}}\]
  done clear
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• question_answer7)
  A rectangular coil of 100 turns and size \[0.1m\times 0.05\,m\] is placed perpendicular to amagnetic field of 0.1 T. The induced \[emf\] when the field drops to 0.05 T is 0.05 s is
  A)
   0.5V              
  done clear
  B)
   1.0V
  done clear
  C)
   1.5V              
  done clear
  D)
   2.0V
  done clear
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• question_answer8)
  A bomb is dropped from an aeroplane when it is at a height h directly above the target. If the aero plane is moving horizontally at a speed v, the distance by which bomb will miss the target is given by
  A)
   \[2v\sqrt{\frac{h}{g}}\]                    
  done clear
  B)
   \[v\sqrt{\frac{h}{g}}\]
  done clear
  C)
   \[v\sqrt{\frac{2h}{g}}\]        
  done clear
  D)
   \[v\sqrt{\frac{h}{2g}}\]
  done clear
  View Answer play_arrow

• question_answer9)
  A block B is pushed momentarily along a horizontal surface with an initial velocity \[v\]. If \[\mu \] is the coefficient of sliding friction between B and the surface, block B will come to rest after a time
  A)
   \[\frac{g\mu }{v}\]                            
  done clear
  B)
   \[\frac{g}{v}\]
  done clear
  C)
   \[\frac{v}{g}\]                                   
  done clear
  D)
   \[\frac{v}{g\mu }\]
  done clear
  View Answer play_arrow

• question_answer10)
  A machine which is 80% efficient, uses 20 J of energy in lifting up a 2 kg mass through a certain distance. The mass is then allowed to fall through that distance. The velocity at the end of its fall is
  A)
   \[h\]                            
  done clear
  B)
   \[\frac{3}{4}h\]
  done clear
  C)
   \[\frac{1}{2}h\]                                 
  done clear
  D)
   \[\frac{1}{4}h\]
  done clear
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• question_answer11)
  A cylinder of height h is placed on an inclined plane, the angle of inclination of which is slowly increased. It begins to slip when the angle of inclination is \[45{}^\circ \]. What is the radius of the cylinder?
  A)
   h                                
  done clear
  B)
   \[\frac{3}{4}h\]
  done clear
  C)
   \[\frac{1}{2}h\]                                 
  done clear
  D)
   \[\frac{1}{4}h\]
  done clear
  View Answer play_arrow

• question_answer12)
  A person feels 2.5% difference of frequency of a motorcar horn. If the motorcar is moving to the person and the velocity of sound is 320 m/s, then the velocity of car will be
  A)
   8 m/s (approx)           
  done clear
  B)
   800 m/s          
  done clear
  C)
   7 m/s             
  done clear
  D)
   6 m/s (approx)
  done clear
  View Answer play_arrow

• question_answer13)
  Two concentric spheres of radii R and r have similar charges with same surface charge densities\[(\sigma )\]. What is the electric potential at their common centre?
  A)
   \[\frac{\sigma }{{{\varepsilon }_{0}}}\]                             
  done clear
  B)
   \[\frac{\sigma }{{{\varepsilon }_{0}}}\,(R-r)\]
  done clear
  C)
   \[\frac{\sigma }{{{\varepsilon }_{0}}}\,(R+r)\]                  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  A transformer is used to step-up an transformation \[emf\] of 220 V to 4.4 kV in order to transmit 6.6 kV of power. If the primary coil has 100 turns, what is the number of turns in the secondary?
  A)
   20                              
  done clear
  B)
   200             
  done clear
  C)
   2000                          
  done clear
  D)
   20000
  done clear
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• question_answer15)
  A body is projected vertically upwards. If \[{{t}_{1}}\] and \[{{t}_{2}}\] be the instants at which it is at a height h above the point of projection, while ascending and descending respectively, then
  A)
   \[h=g{{t}_{1}}{{t}_{2}}\]             
  done clear
  B)
  \[h=2g{{t}_{1}}{{t}_{2}}\]
  done clear
  C)
   \[h=\frac{1}{2}\,g{{t}_{1}}{{t}_{2}}\]                
  done clear
  D)
   \[h=\frac{1}{4}g{{t}_{1}}{{t}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer16)
  A particle of mass 4m at rest explodes into three fragments. Two of the fragments each of mass m move with speed v at right angles to each other. The kinetic energy released in the process is
  A)
   \[2\,m{{v}^{2}}\]               
  done clear
  B)
   \[\frac{3}{2}\,m{{v}^{2}}\]
  done clear
  C)
   \[\frac{1}{2}\,m{{v}^{2}}\]                      
  done clear
  D)
   \[3\,m{{v}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer17)
  In figure, if the surfaces are frictionless, the ratio \[{{T}_{1}}:{{T}_{2}}\] is
  A)
   \[\sqrt{3}:2\]              
  done clear
  B)
   \[1:\sqrt{3}\]
  done clear
  C)
   1 : 5                           
  done clear
  D)
   5 : 1
  done clear
  View Answer play_arrow

• question_answer18)
  A chord is used to lower vertically a block of mass M a distance d at a constant downward acceleration of \[\frac{g}{4}\]. Then, the work done by the chord on the block is
  A)
   \[\frac{Mgd}{4}\]                  
  done clear
  B)
   \[\frac{-Mgd}{4}\]
  done clear
  C)
   \[\frac{3Mgd}{4}\]                
  done clear
  D)
   \[\frac{-3Mgd}{4}\]
  done clear
  View Answer play_arrow

• question_answer19)
  A bar of mass \[m\] length \[l\] is in pure translator motion with its centre of mass velocity \[v\]. It collides with and sticks to another identical bar at rest as shown in figure. Assuming that after collision it becomes one composite bar of length \[2l\], the angular velocity of the composite bar will be
  A)
   \[\frac{3v}{4l}\], anti-clockwise                       
  done clear
  B)
   \[\frac{4v}{3l},\]anti-clockwise
  done clear
  C)
   \[\frac{3v}{4l},\]clockwise
  done clear
  D)
   \[\frac{4v}{3l},\]clockwise
  done clear
  View Answer play_arrow

• question_answer20)
  An U tube of uniform bore of cross-sectional area A is set up vertically with open ends up. A liquid of mass M and density d is poured into it. The liquid column will oscillate with a period
  A)
   \[2\pi \,\sqrt{\frac{M}{g}}\]              
  done clear
  B)
   \[2\pi \,\sqrt{\frac{MA}{dg}}\]
  done clear
  C)
   \[2\pi \,\sqrt{\frac{M}{Adg}}\]                      
  done clear
  D)
   \[2\pi \,\sqrt{\frac{M}{2Adg}}\]
  done clear
  View Answer play_arrow

• question_answer21)
  In a ball, a person receives direct sound waves from a source 120 m away. He also receives wave from the same source which reach him after being reflected from one 25 m high ceiling at a point half-way between them. The two waves interfere constructively for wavelengths (in metre) of
  A)
   \[10,5,\,\frac{5}{2},\,...\]                   
  done clear
  B)
   \[20,\,\frac{20}{3},\,\frac{20}{5},\,...\]
  done clear
  C)
   30, 20, 10, ?            
  done clear
  D)
   35, 25, 15, ?
  done clear
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• question_answer22)
  A dip circle lying initially in the magnetic meridian is rotated through angle \[\theta \] is the horizontal plane. The tangent of angle of dip is increased in the ratio 
  A)
  \[\cos \,\theta :1\]                     
  done clear
  B)
   \[\sin \,\theta :1\]
  done clear
  C)
   \[1:\,\cos \,\theta \]                  
  done clear
  D)
   \[1:\,\sin \,\theta \]
  done clear
  View Answer play_arrow

• question_answer23)
  A rectangular coil of single turn, having area A, rotates in a uniform magnetic field B with an angular velocity \[\omega \]about an axis perpendicular to the field. If initially the plane of the coil is perpendicular to the field, then the average induced \[emf\] when it has rotated through \[90{}^\circ \]. is
  A)
   \[\frac{\omega BA}{\pi }\]             
  done clear
  B)
   \[\frac{\omega BA}{2\pi }\]
  done clear
  C)
  \[\frac{\omega BA}{4\pi }\]               
  done clear
  D)
   \[\frac{2\omega BA}{\pi }\]
  done clear
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• question_answer24)
  A 60 W bulb is placed at a distance of 4 m from you. The bulb is emitting light of wavelength 600 nm uniformly in all directions. In 0.1 s, how many photons enter your eye if the pupil of the eye is having a diameter of 2 mm? [Take, he =1240 eV-nm]
  A)
   \[2.84\times {{10}^{12}}\]             
  done clear
  B)
   \[2.84\times {{10}^{11}}\]
  done clear
  C)
   \[9.37\times {{10}^{11}}\]             
  done clear
  D)
   \[6.48\times {{10}^{11}}\]
  done clear
  View Answer play_arrow

• question_answer25)
  Two identical non-relativistic particles A and 6 move at right angles to each other, possessing de-Broglie wavelengths \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] respectively. The de-Broglie wavelength of each particle in their C frame of reference is
  A)
   \[{{\lambda }_{1}}+{{\lambda }_{2}}\]               
  done clear
  B)
   \[\frac{2{{\lambda }_{1}}{{\lambda }_{2}}}{\sqrt{\lambda _{1}^{2}+\lambda _{2}^{2}}}\]
  done clear
  C)
   \[\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{\sqrt{|\lambda _{1}^{2}+\lambda _{2}^{2}|}}\]                  
  done clear
  D)
   \[\frac{{{\lambda }_{1}}+{{\lambda }_{2}}}{2}\]
  done clear
  View Answer play_arrow

• question_answer26)
  When the voltage applied to an X-rays tube increases from \[{{V}_{1}}=10kV\]to \[{{V}_{2}}=20\,kV\], the wavelength interval between \[{{K}_{\alpha }}\] line and cut-off wavelength of continuous spectrum increases by a factor of 3. Atomic number of the metallic target is
  A)
   28                              
  done clear
  B)
   29              
  done clear
  C)
   65                              
  done clear
  D)
   66
  done clear
  View Answer play_arrow

• question_answer27)
  The binding energy of an electron in the ground state of He-atom is equal to \[{{E}_{0}}=24.6\,eV\].The energy required to remove both the electrons from the atom is
  A)
   24.6eV          
  done clear
  B)
   79.0 eV          
  done clear
  C)
   54.4 eV                      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  A photosensitive material is at 9 m to the left of the origin and the source of light is at 7 m to the right of the origin along \[x\]-axis. The photosensitive material and the source of light start from rest and moves with 8i m/s and 4i m/s respectively. The ratio of intensity at \[t=0\] to\[t=3\]s as received by the photosensitive material is
  A)
   16: 1                          
  done clear
  B)
   1 : 16           
  done clear
  C)
   2 : 7                           
  done clear
  D)
   7 : 2
  done clear
  View Answer play_arrow

• question_answer29)
  Hydrogen atoms in a sample are excited to \[n=5\]  states and it is found that photons of all possible wavelengths are present in emission spectra. The minimum number of hydrogen atoms in the sample would be
  A)
   5                                
  done clear
  B)
   6                  
  done clear
  C)
   10                              
  done clear
  D)
   infinite
  done clear
  View Answer play_arrow

• question_answer30)
  A parallel beam of light of intensity \[l\] and frequency\[v\]is incident on a solid sphere of radius R as shown in the figure For this situation mark out the correct statement. 
  A)
   The force exerted by light on the sphere is the greatest when surface of sphere is perfectly reflecting and is equal to  \[\frac{2l\times \pi {{R}^{2}}}{c}\]
  done clear
  B)
   The force exerted by light on the sphere is independent of the nature of surface, i.e.. it is same for perfect reflector, perfect absorber, and is partially reflecting and for all it is equal to \[\frac{l\times \pi {{R}^{2}}}{c}\].
  done clear
  C)
   The force exerted by light on sphere is least when surface of the sphere a is perfect absorber, and is equal to \[\frac{l\times \pi {{R}^{2}}}{c}\].
  done clear
  D)
   Both [a] and [c] are correct.
  done clear
  View Answer play_arrow

• question_answer31)
  A gaseous substance \[A{{B}_{2}}(g)\] converts to \[AB\,(g)\] in the presence of solid \[A(s)\] as \[A{{B}_{2}}(g)+A(s)\,\,AB(g)\] The initial pressure and equilibrium pressure are 0.7 and 0.95 bar. Now the equilibrium mixture is expanded reversibly and isothermally till the gas pressure falls to 0.4 bar. The volume percentage of \[AB(g)\] the final equilibrium is
  A)
   67.5                           
  done clear
  B)
   32.5              
  done clear
  C)
   45.3                           
  done clear
  D)
   63.1
  done clear
  View Answer play_arrow

• question_answer32)
  A open manometer attached to a flask containing ammonia gas have no difference in mercury level initially as shown in fig. After sparking into the flask, ammonia is partially dissociated as  \[2N{{H}_{3}}\,(g)\,\xrightarrow{\,}\,{{N}_{2}}\,(g)\,+3{{H}_{2}}\,(g)\]. Now it have difference of 18cm in mercury level into columns, what is partial pressure of \[{{H}_{2}}(g)\] at equilibrium?                                                         
  A)
   9 cm Hg                     
  done clear
  B)
   18 cm Hg
  done clear
  C)
   27 cm Hg                   
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer33)
  An inorganic red colored compound [A] on heating gives a compound [B] and a gas [C].[A] on treatment with cone. \[HN{{O}_{3}}\]gives compound [D]. brown colour substance [E] and neutral oxide [F]. Compound [D] on warming gives off again gas [C]. Then [E] will be
  A)
   \[M{{n}_{3}}{{O}_{4}}\]              
  done clear
  B)
   \[Pb{{O}_{2}}\]
  done clear
  C)
   \[P{{b}_{3}}{{O}_{4}}\]              
  done clear
  D)
   \[F{{e}_{2}}{{O}_{3}}\]
  done clear
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• question_answer34)
  Which of the following are optically active?

  (I)

  (II)

  (III)

  (IV)

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

• question_answer35)
  In which of the following pairs, both the species have same hybridization and shape?
  A)
   \[S{{F}_{4}},\,\,Xe{{F}_{4}}\]                  
  done clear
  B)
   \[l_{3}^{-},\,Xe{{F}_{2}}\]
  done clear
  C)
   \[lCl_{4}^{+},\,\,SiC{{l}_{4}}\]               
  done clear
  D)
  \[ClO_{3}^{-},\,\,PO_{4}^{3-}\]
  done clear
  View Answer play_arrow

• question_answer36)
  At what temperature will the translational kinetic energy of H-atom equal to that for H-atom of first line Lyman transition? (Given \[{{N}_{A}}=6\times {{10}^{23}}\])
  A)
   780 K                         
  done clear
  B)
   \[1.32\times {{10}^{5}}\,K\]
  done clear
  C)
   \[7.84\times {{10}^{4}}K\]            
  done clear
  D)
   \[1900\,K\]
  done clear
  View Answer play_arrow

• question_answer37)
  The correct order of bond angles in \[N{{H}_{3}},\,\,N{{F}_{3}}\] and \[NC{{l}_{3}}\] are
  A)
   \[N{{H}_{3}}>N{{F}_{3}}>NC{{l}_{3}}\]
  done clear
  B)
   \[N{{H}_{3}}>NC{{l}_{3}}>N{{F}_{3}}\]
  done clear
  C)
   \[NC{{l}_{3}}>N{{H}_{3}}>N{{F}_{3}}\]
  done clear
  D)
   \[N{{F}_{3}}>NC{{l}_{3}}>N{{H}_{3}}\]
  done clear
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• question_answer38)
  At \[25{}^\circ C\] the vapour pressure of pure liquid A (mol. wt. = 40) is 100 torr and that of pure liquid B (mol. wt. =80) is 60 torr. Find the vapour pressure of solution at \[25{}^\circ C\] if the mole ratio of A and B in vapour phase is 2 : 3.
  A)
   60.3 torr                     
  done clear
  B)
   65.7 torr
  done clear
  C)
   71.42 ton-                  
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer39)
  The tautomerism involving (1, 5) migration of hydrogen atom can be observed in
  A)
   I and II                       
  done clear
  B)
   II and III
  done clear
  C)
   II, III and IV                
  done clear
  D)
   I, II and III
  done clear
  View Answer play_arrow

• question_answer40)
  In which of the following Aufbau principle and Hund's rule is violated?
  A)
              
  done clear
  B)
   
  done clear
  C)
              
  done clear
  D)
    
  done clear
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• question_answer41)
  Which of the following order are correct?

  (i) Solubility in water\[LiOH<NaOH<KOH<RbOH<CsOH\]

  (ii) Thermal stability\[BeS{{O}_{4}}<MgS{{O}_{4}}<CaS{{O}_{4}}<SrS{{O}_{4}}<BaS{{O}_{4}}\]

  (iii) Melting point \[NaCl>KCl>RbCl>CsCl>LiCl\]

  (iv) Solubility in water \[L{{i}_{2}}C{{O}_{3}}<N{{a}_{2}}C{{O}_{3}}<{{K}_{2}}C{{O}_{3}}<R{{b}_{2}}C{{O}_{3}}\]

  A)
   I, II and III                  
  done clear
  B)
   I, II and IV      
  done clear
  C)
   II, III and IV                
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer42)
  The product obtained from the following reaction is
  A)
    
  done clear
  B)
   
  done clear
  C)
    
  done clear
  D)
    
  done clear
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• question_answer43)
  A metal complex of coordination number six having three different types of ligands a, band c of composition \[M{{a}_{2}}{{b}_{2}}{{c}_{2}}\] can exist in several geometrical isomeric forms; the total number of such isomer is
  A)
   3                                
  done clear
  B)
   5                 
  done clear
  C)
   7                                
  done clear
  D)
   9
  done clear
  View Answer play_arrow

• question_answer44)
  Which of the following is incorrect about the following?
  A)
   I and II are geometrical isomers          
  done clear
  B)
   I and III are geometrical isomers
  done clear
  C)
   II and III are optically active              
  done clear
  D)
   II and III are same
  done clear
  View Answer play_arrow

• question_answer45)
  The number of geometrical isomers shown by the following compound is
  A)
   4                                
  done clear
  B)
   6               
  done clear
  C)
   8                                
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer46)
  A reaction \[A\to B\] involves the following mechanism

  Step 1 \[2A\xrightarrow{{{k}_{1}}}C\] (fast)

  Stem 2 \[C\xrightarrow{{{k}_{2}}}D\] (slow)

  Step3 \[3D\,\xrightarrow{{{k}_{3}}}B\] (fast)

  The rate law of the reaction may be given as
  A)
   rate\[={{k}_{1}}{{[A]}^{2}}\]                
  done clear
  B)
   rate
  done clear
  C)
   rate\[={{k}_{2}}[C]\,\,[D]\]
  done clear
  D)
   rate\[={{k}_{1}}{{k}_{2}}{{k}_{3}}\,[C]\,\,[D]\]
  done clear
  View Answer play_arrow

• question_answer47)
  Identify the correct statement.
  A)
   \[{{P}_{4}}{{O}_{11}}\]contains peroxide linkages
  done clear
  B)
   \[{{P}_{4}}{{O}_{10}}\]contains\[p\pi -d\pi \] back bonding
  done clear
  C)
   In \[{{P}_{4}}{{O}_{10}}\] each P atom is bonded to three oxygen atoms
  done clear
  D)
   \[{{P}_{4}}{{O}_{10}}\]hydrolyze in water forming phosphorous acid
  done clear
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• question_answer48)
  
  A)
       
  done clear
  B)
   
  done clear
  C)
               
  done clear
  D)
   None of these
  done clear
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• question_answer49)
  The following graph is obtained when the fraction of molecules is plotted against velocity. The profile curve will be same for the gases.

  (I) Oxygen gas at T temperature

  (II) Hydrogen gas at 2T temperature

  (III) Helium gas at 2T temperature

  (IV) Sulphur dioxide gas at 2T temperature

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

• question_answer50)
  A reactant  forms two products

  \[A\xrightarrow{{{k}_{1}}}B\] Activation energy \[{{E}_{{{a}_{1}}}}\]

  \[A\xrightarrow{{{k}_{2}}}C\] Activation energy \[E{{\,}_{{{a}_{2}}}}\]

  If \[{{E}_{{{a}_{2}}}}=2{{E}_{{{a}_{1}}}},\] then \[{{k}_{1}}\] and \[{{k}_{2}}\] will be related as
  A)
   \[{{k}_{2}}={{k}_{1}}{{e}^{-{{E}_{{{a}_{1}}}}/RT}}\]    
  done clear
  B)
   \[{{k}_{2}}={{k}_{1}}{{e}^{-{{E}_{{{a}_{2}}}}/RT}}\]
  done clear
  C)
  \[{{k}_{1}}={{k}_{2}}{{e}^{-{{E}_{{{a}_{1}}}}/RT}}\]     
  done clear
  D)
   \[{{k}_{1}}=2{{k}_{2}}{{e}^{{{E}_{{{a}_{2}}}}/RT}}\]
  done clear
  View Answer play_arrow

• question_answer51)
  The halogen oxide used for the estimation of carbon monoxide in automobile exhaust gases is
  A)
   \[C{{l}_{2}}{{O}_{7}}\]               
  done clear
  B)
   \[{{l}_{2}}{{O}_{5}}\]
  done clear
  C)
   \[Cl{{O}_{2}}\]                   
  done clear
  D)
   \[Br{{O}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer52)
  During the electrolysis of concentrated aqueous solution of sodium chloride, the pH of solution (electrolyte)
  A)
   increases                    
  done clear
  B)
   decreases        
  done clear
  C)
   remains same            
  done clear
  D)
   Non-e of these
  done clear
  View Answer play_arrow

• question_answer53)
  Which of the following can give iodo form test?

  (I) \[C{{H}_{3}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]	(II) \[{{C}_{6}}{{H}_{5}}-C{{H}_{2}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]
  (III) \[C{{H}_{3}}-CHO\]	(IV) \[{{C}_{6}}{{H}_{5}}-\overset{\begin{smallmatrix}  O \\  || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]

  A)
   Only IV                      
  done clear
  B)
   III and IV          
  done clear
  C)
   III and IV                    
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer54)
  The mono chlorinated products obtained from the reaction is
  A)
   4                                
  done clear
  B)
   5
  done clear
  C)
   6                                
  done clear
  D)
   7
  done clear
  View Answer play_arrow

• question_answer55)
  Oxygen atoms forms fee unit cell with 'A' atoms occupying all tetrahedral voids and 'B' atoms occupying all octahedral voids. If atoms are removed from two of the body diagonals then determine the formula of resultant compound formed.
  A)
   \[{{A}_{4}}{{B}_{4}}{{O}_{7}}\]                      
  done clear
  B)
   \[{{A}_{8}}{{B}_{6}}{{O}_{7}}\]
  done clear
  C)
   \[{{A}_{8}}{{B}_{8}}{{O}_{7}}\]                      
  done clear
  D)
   \[{{A}_{6}}{{B}_{8}}{{O}_{6}}\]
  done clear
  View Answer play_arrow

• question_answer56)
  Which of the following compounds will not undergo tautomerism?

  (I)

  (II)

  (III)

  (IV)

  A)
   (II) and (III)                
  done clear
  B)
   (I), (II) and
  done clear
  C)
   (III) Only (I)                
  done clear
  D)
   All of these
  done clear
  View Answer play_arrow

• question_answer57)
  To 100 mL of 0.1 M solution of sodium dihydrogen phosphate 75 mL of 0.1 M sodium phosphate is added. Calculate the pH when 25 mL of 0.1 M HCI is added to the above solution (stepwise acid dissociation constant for phosphoric acid are \[{{10}^{-3}},\,\,{{10}^{-6}}\] and \[{{10}^{-13}}\])
  A)
  6
  done clear
  B)
  4
  done clear
  C)
  8.5
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer58)
  The optically active compound among the following is
  A)
  
  done clear
  B)
    
  done clear
  C)
  
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer59)
  Flocculating value of ion depends on
  A)
  the shape of flocculating ion
  done clear
  B)
  the amount of flocculating ion
  done clear
  C)
  nature of the charge on the flocculating ion
  done clear
  D)
  both; the nature and magnitude of the charge of the flocculating ion
  done clear
  View Answer play_arrow

• question_answer60)
  The product 'B' on reaction with base \[O{{H}^{\odot -}}\] can undergo
  A)
   cross aldol condensation                
  done clear
  B)
   intra mole cular aldol condensation
  done clear
  C)
   cross Cannizzaro's reaction              
  done clear
  D)
   intra molecular Cannizzaro's reaction
  done clear
  View Answer play_arrow

• question_answer61)
  If\[kr+r\times a=b,\] where \[k\] is non-zero scalar and a,b are two given vectors, then will be
  A)
  \[\frac{1}{{{k}^{2}}+{{a}^{2}}}\,\left( kb+\frac{a\cdot b}{k}a+a\times b \right)\]
  done clear
  B)
   \[\frac{1}{{{k}^{2}}+{{a}^{2}}}\,\left( kb-\frac{a\cdot b}{k}a+a\times b \right)\]
  done clear
  C)
  \[\frac{1}{{{k}^{2}}+{{a}^{2}}}\,\left( kb-\frac{a\cdot b}{k}a-a\times b \right)\]
  done clear
  D)
   \[\frac{1}{{{k}^{2}}-{{a}^{2}}}\,\left( kb-\frac{a\cdot b}{k}-a\times b \right)\]
  done clear
  View Answer play_arrow

• question_answer62)
  The value of \[{{\tan }^{-1}}({{e}^{i\theta }})\] is equal to
  A)
   \[\frac{n\pi }{2}+\frac{\pi }{4}+\frac{i}{2}\log \,\tan \,\left( \frac{\pi }{4}+\frac{\theta }{2} \right)\]
  done clear
  B)
   \[\frac{n\pi }{2}-\frac{\pi }{4}-\frac{i}{2}\log \,\tan \,\left( \frac{\pi }{4}+\frac{\theta }{2} \right)\]
  done clear
  C)
   \[\frac{n\pi }{2}+\frac{\pi }{4}+\frac{i}{2}\log \,\tan \,\left( \frac{\pi }{4}-\frac{\theta }{2} \right)\]
  done clear
  D)
   \[\frac{n\pi }{2}+\frac{\pi }{4}+\frac{i}{2}\log \,\tan \,\left( \frac{\pi }{4}+\frac{\theta }{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer63)
  \[\sum\limits_{i=1}^{n}{{{a}_{i}}=0,}\] where \[|{{a}_{i}}|\,=1,\,\,\forall \,i,\] then the value of \[\sum\limits_{1\le i\le }{\,\sum\limits_{j<n}{{{a}_{i}}\cdot {{a}_{j}}}}\] is
  A)
   \[-\frac{n}{2}\]                                 
  done clear
  B)
   \[-n\]
  done clear
  C)
   \[\frac{n}{2}\]                                   
  done clear
  D)
   \[n\]
  done clear
  View Answer play_arrow

• question_answer64)
  If \[{{\sin }^{2}}\,x+{{\cos }^{2}}\,y=2\,\,{{\sec }^{2}}\,z,\] then values of and \[x,\,\,y\]and\[z\]are respectively (where, \[m,\,\,n,\,r\,\,\in l)\]
  A)
   \[\left( \left( n+\frac{1}{2} \right)\,\pi ,\,m\pi ,\,r\pi  \right)\]  
  done clear
  B)
   \[\left( (n-1)\,\frac{\pi }{2},\,\,m\pi ,\,\,r\pi  \right)\]
  done clear
  C)
   \[\left( (2n-1)\,\frac{\pi }{3},\,\,m\pi ,\,\,\frac{r\pi }{2} \right)\]
  done clear
  D)
   \[\left( (n+1)\,\frac{\pi }{2},\,\,m\pi ,\,r\pi  \right)\]
  done clear
  View Answer play_arrow

• question_answer65)
  If \[\alpha ,\,\,\beta \] and \[\gamma \] are the altitudes of the \[\Delta ABC\] from the vertices A, B and C respectively, then value of \[4{{\Delta }^{2}}\,\left( \frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}}+\frac{1}{{{\gamma }^{2}}} \right)\] is
  A)
   \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]            
  done clear
  B)
   \[\frac{1}{2}\,({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\]
  done clear
  C)
   \[{{a}^{2}}-{{b}^{2}}+{{c}^{2}}\]              
  done clear
  D)
   \[\frac{3}{\Delta }\]
  done clear
  View Answer play_arrow

• question_answer66)
  The number of real solutions of\[(x,\,\,y),\] where \[y=\,|\], \[\sin \,x\,|,\,\,y={{\cos }^{-1}}(\cos \,x),\]\[-2\pi \le \,x\le 2\pi ,\] is
  A)
   2                                
  done clear
  B)
   1                 
  done clear
  C)
   3                                
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer67)
  If p, q and r are simple propositions, then\[(p\hat{\ }q)\,\,\hat{\ }\,(q\,\hat{\ }r)\] is true, then
  A)
   p, q and r are all false                     
  done clear
  B)
   p, q and r are all true
  done clear
  C)
   p and 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_answer68)
  Probability of product of a perfect square when two dice are thrown together
  A)
   \[\frac{1}{9}\]                                   
  done clear
  B)
   \[\frac{2}{13}\]
  done clear
  C)
   \[\frac{2}{9}\]                                   
  done clear
  D)
   \[\frac{4}{9}\]
  done clear
  View Answer play_arrow

• question_answer69)
  The minimum value of \[|{{z}_{1}}-{{z}_{2}}|\] and \[{{z}_{1}}\]and\[{{z}_{2}}\] vary over the curve \[|\sqrt{3}\,(1-2z)\,+2i\,|\,=2\sqrt{7}\] and \[|\sqrt{3}\,(-1-z)\,-2i\,|\,=\,|\,\,\sqrt{3}\,(9-z)+18i\,\,|,\] respectively.
  A)
   \[\frac{7\sqrt{7}}{2\sqrt{3}}\]                     
  done clear
  B)
   \[\frac{5\sqrt{7}}{\sqrt{3}}\]
  done clear
  C)
   \[\frac{14\sqrt{7}}{\sqrt{3}}\]                     
  done clear
  D)
   \[\frac{7\sqrt{7}}{5\sqrt{3}}\]
  done clear
  View Answer play_arrow

• question_answer70)
  There are 10 girls and 8 boys in a classroom including Mr Ravi, Ms Rani and Ms Radha. A list of speakers consisting of 8 girls and 6 boys has to be prepared Mr Ravi refuses to speak. If Mr Ravi refuses to speak, if Ms Rani is a speaker. The number of ways the list can be prepared is
  A)
   202                            
  done clear
  B)
   308  
  done clear
  C)
   567                            
  done clear
  D)
   952
  done clear
  View Answer play_arrow

• question_answer71)
  The value of the integral \[\int\limits_{0}^{2}{\frac{\log \,({{x}^{2}}+2)}{{{(x+2)}^{2}}}\,dx}\] is
  A)
   \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}+\frac{5}{12}\,\log \,2-\frac{1}{4}\,\log \,3\]
  done clear
  B)
   \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}-\frac{5}{12}\,\log \,2-\frac{1}{12}\,\log \,3\]
  done clear
  C)
   \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}+\frac{5}{12}\,\log \,2+\frac{1}{4}\,\log \,3\]
  done clear
  D)
  \[\frac{\sqrt{2}}{3}{{\tan }^{-1}}\sqrt{2}-\frac{5}{12}\,\log \,2+\frac{1}{\sqrt{12}}\,\log \,3\]
  done clear
  View Answer play_arrow

• question_answer72)
  Let \[f:\,R\to R\] be defined by \[f(x)=2x+\sin \,x\]for \[x\,\in R\]. Then, \[f\] is
  A)
   one-one and onto                      
  done clear
  B)
   one-one but not onto
  done clear
  C)
   onto but not one-one                   
  done clear
  D)
   neither one-one nor onto
  done clear
  View Answer play_arrow

• question_answer73)
  Let M be a \[3\times 3\] non-singular matrix with\[|M|\,=\alpha \]. If \[{{M}^{-1}}\]\[adj\,\,(adj\,M)=kl,\] then the value of k is
  A)
   1                                
  done clear
  B)
   \[\alpha \]
  done clear
  C)
   \[{{\alpha }^{2}}\]             
  done clear
  D)
   \[{{\alpha }^{3}}\]
  done clear
  View Answer play_arrow

• question_answer74)
  If \[{{y}^{x}}-{{x}^{y}}=1,\] then the value of \[\frac{dy}{dx}\] at \[x=1\] is
  A)
   \[2(1-\log \,2)\]           
  done clear
  B)
   \[2(1+\,\log \,2)\]
  done clear
  C)
   \[2-\log \,2\]                
  done clear
  D)
   \[2+\log \,2\]
  done clear
  View Answer play_arrow

• question_answer75)
  In the interval \[\left[ 0,\frac{\pi }{2} \right]\], the equation \[{{\cos }^{2}}x-\cos \,x-x=0\] has
  A)
   no solution                              
  done clear
  B)
   exactly one solution
  done clear
  C)
   exactly two solutions                     
  done clear
  D)
   more than two solutions
  done clear
  View Answer play_arrow

• question_answer76)
  Let\[(0,\,1)\to \,(0,1)\]be a differential function such that \[f'(x)\ne 0\] for all \[x\,\in (0,\,\,1)\]and \[f\,\left( \frac{1}{2} \right)=\frac{\sqrt{3}}{2}\]. Suppose for all \[x\],

  \[\underset{t\to x}{\mathop{\lim }}\,\,\frac{\int\limits_{0}^{t}{\sqrt{1-{{\{f(S)\}}^{2}}}\,dS-\int\limits_{0}^{x}{\sqrt{1-{{\{f(S)\}}^{2}}}dx}}}{f(t)-f(x)}\]

  Then, the value of \[f\left( \frac{1}{4} \right)\] belongs to
  A)
   \[\left\{ \sqrt{7},\,\,\sqrt{15} \right\}\]            
  done clear
  B)
   \[\left\{ \frac{\sqrt{7}}{2},\,\,\frac{\sqrt{15}}{2} \right\}\]
  done clear
  C)
   \[\left\{ \frac{\sqrt{7}}{3},\,\,\frac{\sqrt{15}}{3} \right\}\]              
  done clear
  D)
   \[\left\{ \frac{\sqrt{7}}{4},\,\,\frac{\sqrt{15}}{4} \right\}\]
  done clear
  View Answer play_arrow

• question_answer77)
  The set of all \[2\times 2\] matrices which commute with the matrix with respect to matrix\[\left[ \begin{matrix}    1 & 1  \\    1 & 0  \\ \end{matrix} \right]\]multiplication is
  A)
   \[\left\{ \left[ \begin{matrix}    a & b  \\    c & a-b  \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}\]
  done clear
  B)
   \[\left\{ \left[ \begin{matrix}    a & b  \\    b & c  \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}\]
  done clear
  C)
  \[\left\{ \left[ \begin{matrix}    a-b & b  \\    b & c  \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}\]
  done clear
  D)
   \[\left\{ \left[ \begin{matrix}    a & b  \\    b & a-b  \\ \end{matrix} \right];\,\,a,\,\,b\,\,\in \,R \right\}\]
  done clear
  View Answer play_arrow

• question_answer78)
  Let, a be a non-zero real number and a, p be the roots of the equation \[a{{x}^{2}}+5x+2=0\].Then, the absolute value of the difference of the roots of the equation\[{{a}^{3}}{{(x+5)}^{2}}-25a(x+5)+50=0\]
  A)
   \[|{{\alpha }^{2}}-{{\beta }^{2}}|\]     
  done clear
  B)
   \[|\alpha \beta \,({{\alpha }^{2}}-{{\beta }^{2}})|\]
  done clear
  C)
  \[\left| \frac{{{\alpha }^{2}}-{{\beta }^{2}}}{\alpha \beta } \right|\]                
  done clear
  D)
   \[\left| \frac{{{\alpha }^{2}}-{{\beta }^{2}}}{{{\alpha }^{2}}{{\beta }^{2}}} \right|\]
  done clear
  View Answer play_arrow

• question_answer79)
  Suppose an ellipse and a hyperbola have the same pair of foci on the x-axis with centers at the origin and that they intersect at (2, 2). If the eccentricity of the ellipse is \[\frac{1}{2},\] then the eccentricity of the hyperbola is
  A)
   \[\sqrt{\frac{7}{4}}\]                        
  done clear
  B)
   \[\sqrt{\frac{7}{3}}\]
  done clear
  C)
  \[\sqrt{\frac{5}{4}}\]                         
  done clear
  D)
   \[\sqrt{\frac{5}{3}}\]
  done clear
  View Answer play_arrow

• question_answer80)
  The equation of the circle which cuts each of the three circles \[{{x}^{2}}+{{y}^{2}}=4,\]\[{{(x-1)}^{2}}+{{y}^{2}}=4\] and \[{{x}^{2}}+{{(y-2)}^{2}}=4\] orthogonally is
  A)
   \[{{x}^{2}}+{{y}^{2}}+x+2y+4=0\]
  done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}+x-2y+4=0\]
  done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}-x-2y+4=0\]
  done clear
  D)
   \[{{x}^{2}}+{{y}^{2}}-x+2y+4=0\]
  done clear
  View Answer play_arrow

• question_answer81)
  The number of solutions of the equation \[{{\cos }^{2}}\,\left( x+\frac{\pi }{6} \right)+{{\cos }^{2}}x-2\cos \,\left( x+\frac{\pi }{6} \right)\cos \,\frac{\pi }{6}={{\sin }^{2}}\frac{\pi }{6}\]
  A)
   0                                
  done clear
  B)
   1                 
  done clear
  C)
   2                                
  done clear
  D)
   3
  done clear
  View Answer play_arrow

• question_answer82)
  Let \[f(x)=\,\left\{ \begin{matrix}    |x|, & \text{for}\,\,0<\,|x|\,\le 2  \\    {} & \text{for}\,x=0  \\ \end{matrix} \right.\]. Then at \[x=0,\] f has
  A)
   a local maximum       
  done clear
  B)
   no local minimum
  done clear
  C)
   a local minimum        
  done clear
  D)
   no extremism
  done clear
  View Answer play_arrow

• question_answer83)
  The value of the sum of the series\[3{{\cdot }^{n}}{{C}_{0}}-8{{\cdot }^{n}}{{C}_{1}}+13{{\cdot }^{n}}{{C}_{2}}-18{{\,}^{n}}{{C}_{3}}+...\]
  A)
   0                                
  done clear
  B)
   \[{{3}^{n}}\]
  done clear
  C)
   \[{{5}^{n}}\]                      
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer84)
  Let \[f(\theta )=\frac{1}{{{\tan }^{9}}\theta }\,{{\{1+\tan \theta )}^{10}}+\,(2+\tan \theta )\]\[+...+{{(20+\tan \theta )}^{10}}\}-20\,\tan \theta \]
  A)
   1900                          
  done clear
  B)
   2000            
  done clear
  C)
   2100                          
  done clear
  D)
   2200
  done clear
  View Answer play_arrow

• question_answer85)

  Direction: Let ABC be a triangle, R be the circumradius of the triangle. Also, given \[{{R}^{2}}=\frac{1}{8}\,({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\],  then

  Which of the following is true?
  A)
   \[\sum{\cos \,2A=-1}\]          
  done clear
  B)
   \[\sum{\cos \,2A=1}\]
  done clear
  C)
   \[\sum{\sin \,2A=1}\]
  done clear
  D)
   \[\sum{\sin \,2A=-1}\]
  done clear
  View Answer play_arrow

• question_answer86)

  Direction: Let ABC be a triangle, R be the circumradius of the triangle. Also, given \[{{R}^{2}}=\frac{1}{8}\,({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\],  then

  Hence, the ABC can be
  A)
   equilateral
  done clear
  B)
   isosceles and scalene
  done clear
  C)
   cannot say                             
  done clear
  D)
   right angled
  done clear
  View Answer play_arrow

• question_answer87)

  Direction: Let a, b and c are three non-coplanar vectors, i.e., \[[a\,b\,c]\,\ne 0\]. The three new vectors \[a',\,\,b'\] and c' defined by the equation \[a'=\frac{b\times c}{[a\,\,b\,\,c]},\,\,b'=\frac{c\times a}{[a\,\,b\,\,c]}\]and\[c'=\frac{a\times b}{[a\,\,b\,\,c]}\] are called reciprocal system to the vectors a, b and c.

  If a, b, c and a', b', c' are reciprocal system of vectors, then the value of\[a\times a'+b\times b'+c\times c'\] is
  A)
   \[a\times a'+b\times b'+c\times c'\]   
  done clear
  B)
   \[2\,(a'\times b'\times c')\]
  done clear
  C)
   \[\frac{[a\,\,b\,\,c]}{2}\]
  done clear
  D)
   0
  done clear
  View Answer play_arrow

• question_answer88)

  Direction: Let a, b and c are three non-coplanar vectors, i.e., \[[a\,b\,c]\,\ne 0\]. The three new vectors \[a',\,\,b'\] and c' defined by the equation \[a'=\frac{b\times c}{[a\,\,b\,\,c]},\,\,b'=\frac{c\times a}{[a\,\,b\,\,c]}\]and\[c'=\frac{a\times b}{[a\,\,b\,\,c]}\] are called reciprocal system to the vectors a, b and c.

  The reciprocal set of the vectors \[2i+3j-k,\]\[i-j-2k\] and \[-i+2j+2k\] are
  A)
   \[\frac{2i+k}{3},\,\,\frac{-8i+3j-7k}{3},\,\,\frac{7i+3j+5k}{3}\]
  done clear
  B)
   \[\frac{2i+k}{3},\,\,\frac{-8i+3j+7k}{3},\,\,\frac{7i+3j+5k}{3}\]
  done clear
  C)
  \[\frac{2i+k}{3},\,\,\frac{-8i+3j+7k}{3},\,\,\frac{7i-3j+5k}{3}\]
  done clear
  D)
   \[\frac{2i+k}{3},\,\,\frac{-8i+3j-7k}{3},\,\,\frac{-7i+3j-5k}{3}\]
  done clear
  View Answer play_arrow

• question_answer89)

  Direction: For the following questions, choose the correct answer from the codes [a], [b], [c] and [d] defined as follows.

  Let us define the function as \[{{\cos }^{-1}}\,(\cos \theta )=\theta \]and\[2{{\tan }^{-1}}x=\frac{2x}{1-{{x}^{2}}}\].

  Statement I If \[\sin \,[2\,{{\cos }^{-1}}\{\cot \,(2\,{{\tan }^{-1}}x)\}]=0,\] then \[x=\pm 1,\,\,\pm \,(1\pm \sqrt{2})\]

  Statement II \[\cot \,\,(2\,{{\tan }^{-1}}x)=\frac{1-{{x}^{2}}}{2x}\]

  A)
   Statement I is true. Statement II is also true and Statement II is the correct explanation of Statement I.
  done clear
  B)
   Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I.
  done clear
  C)
   Statement I is true. Statement II is false.
  done clear
  D)
   Statement I is false. Statement II is true.
  done clear
  View Answer play_arrow

• question_answer90)

  Direction: For the following questions, choose the correct answer from the codes [a], [b], [c] and [d] defined as follows.

  Consider the identify \[\frac{\sin \,\frac{\theta }{2}-\sin \,\frac{\phi }{2}}{\cos \,\frac{\theta }{2}+\cos \,\frac{\theta }{2}}=\tan \,\frac{\theta -\phi }{4}\].

  Statement I \[{{\left( \frac{\cos A+\cos B}{\sin A-\sin B} \right)}^{n}}+{{\left( \frac{sinA+sinB}{\cos A-\cos B} \right)}^{n}}\] \[=\left\{ \begin{matrix}    2{{\cot }^{n}}\frac{A-B}{2}, & \text{if}\,\text{n}\,\text{is}\,\text{odd}  \\    0, & \text{if}\,\text{n}\,\text{is}\,\text{seven}  \\ \end{matrix} \right.\]

  Statement II \[\frac{\cos \,A+\cos \,B}{\sin \,A-\sin \,B}=\cot \,\frac{A-B}{2}\].

  A)
   Statement I is true. Statement II is also true and Statement II is the correct explanation of Statement I.
  done clear
  B)
   Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I.
  done clear
  C)
   Statement I is true. Statement II is false.
  done clear
  D)
   Statement I is false. Statement II is true.
  done clear
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