JEE Main & Advanced Sample Paper

done JEE Main - Mock Test - 2 Total Questions - 75    [Download]

• question_answer1)
  The moment of inertia of a uniform disc about an axis passing through its centre and perpendicular to its plane is 1 kg \[{{m}^{2}}\]. It is rotating with an angular velocity 100 rad \[{{s}^{-1}}\]. Another identical disc is gently placed on it so that their centres coincide. Now these two discs together continue to rotate about the same axis. Then the loss in kinetic energy in kilojoules is
  A)
  2.5
  done clear
  B)
  3.0   
  done clear
  C)
  3.5      
  done clear
  D)
  4.0
  done clear
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• question_answer2)
  In the given figure, the equivalent capacitance between points A and B is
  A)
  1.5 C
  done clear
  B)
  2 C
  done clear
  C)
  3 C
  done clear
  D)
  6 C
  done clear
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• question_answer3)
  An ideal gas is taken through a cyclic thermodynamic process through four steps. The amount of heat involved in these steps are \[{{Q}_{1}}=5960J,{{Q}_{2}}=-5585J,{{Q}_{3}}=-2980J\] and \[{{Q}_{4}}=3645J\] respectively. The corresponding quantities of work involved are \[{{W}_{1}}=2200J,{{W}_{2}}=-825J,\]\[{{W}_{3}}=-1100J\]  and \[{{W}_{4}}\] respectively. Find the value of \[{{W}_{4}}.\].  What is the efficiency of the cycle?
  A)
  3.33%   
  done clear
  B)
  6.76%
  done clear
  C)
  5.91%             
  done clear
  D)
  10.83%
  done clear
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• question_answer4)
  Three long, straight parallel wires, carrying current, are arranged as shown in figure. The force experienced by a 25 cm length of wire C is.
  A)
  \[{{10}^{-3}}N\]         
  done clear
  B)
  \[2.5\times {{10}^{-3}}N\]
  done clear
  C)
  \[zero\]
  done clear
  D)
  \[1.5\times {{10}^{-3}}N\]
  done clear
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• question_answer5)

  Of the following quantities which one has the dimensions different from the remaining three?

  (i) Energy density

  (ii) Force per unit area

  (iii) Product of charge per unit volume and voltage

  (iv) Angular momentum per unit mass

   
  A)
  (i)                   
  done clear
  B)
  (ii)  
  done clear
  C)
  (iii)                  
  done clear
  D)
  (iv)
  done clear
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• question_answer6)
  A magnetic flux through a stationary loop with a resistance R varies during the time interval \[\tau \]as \[\phi =at(\tau -t)\]. What is the amount of heat generated in the loop during that time?
  A)
  \[\frac{{{a}^{2}}{{\tau }^{3}}}{4R}\]                       
  done clear
  B)
  \[\frac{{{a}^{2}}{{\tau }^{3}}}{3R}\]
  done clear
  C)
  \[\frac{{{a}^{2}}{{\tau }^{3}}}{6R}\]                       
  done clear
  D)
  \[\frac{{{a}^{2}}{{\tau }^{3}}}{2R}\]
  done clear
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• question_answer7)
  A block of mass \[{{m}_{1}}\] lies on a smooth horizontal table and is connected to another freely hanging block of mass \[{{m}_{2}}\] by a light inextensible string passing over a smooth fixed pulley situated at the edge of the table as shown in the figure. Initially the system is at rest with \[{{m}_{1}}\] at a distance d from the pulley. The time taken for \[{{m}_{1}}\] to reach the pulley is
  A)
  \[\frac{{{m}_{2}}g}{{{m}_{1}}+{{m}_{2}}}\]
  done clear
  B)
  \[\sqrt{\frac{2d({{m}_{1}}+{{m}_{2}})}{{{m}_{2}}g}}\]
  done clear
  C)
  \[\sqrt{\frac{2{{m}_{2}}d}{({{m}_{1}}+{{m}_{2}})g}}\]        
  done clear
  D)
  \[\frac{4d({{m}_{1}}+{{m}_{2}})}{3g{{m}_{1}}}\]
  done clear
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• question_answer8)
  Two identical charged spheres suspended from a common point by two massless strings of length \[l\] are initially a distance d(d < < \[l\]) apart because of their mutual repulsion. The spheres begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them
  A)
  \[v\propto {{x}^{-1/2}}\]         
  done clear
  B)
  \[v\propto {{x}^{-1}}\]
  done clear
  C)
  \[v\propto {{x}^{1/2}}\]
  done clear
  D)
  \[v\propto x\]
  done clear
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• question_answer9)
  A stone of mass 2 kg is projected upward with kinetic energy of 98 J. The height at which the kinetic energy of the stone becomes half its original value, is given by
  A)
  5 m
  done clear
  B)
  2.5 m
  done clear
  C)
  1.5 m   
  done clear
  D)
  0.5 m
  done clear
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• question_answer10)
  In a series LCR circuit, different physical quantities vary with frequency v. Which of the following curves represent correct frequency variation of the corresponding quantity?
  A)
  Curve I for R and curve III for\[{{X}_{L}}\]
  done clear
  B)
  Curve II for current I
  done clear
  C)
  Curve III for \[{{X}_{L}}\] and curve IV for R
  done clear
  D)
  Curve IV for \[{{X}_{C}}\]
  done clear
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• question_answer11)
  The wavelengths and frequencies of photons in transitions 1, 2, and 3 for hydrogen like atom are \[{{\lambda }_{1}},{{\lambda }_{2}},{{\lambda }_{3}};{{\upsilon }_{1}},{{\upsilon }_{2}}\] and \[{{\upsilon }_{3}}\] respectively. Then
  A)
  \[{{\upsilon }_{3}}={{\upsilon }_{1}}-{{\upsilon }_{2}}\]          
  done clear
  B)
  \[{{\lambda }_{3}}={{\lambda }_{1}}+{{\lambda }_{2}}\]
  done clear
  C)
  \[{{\lambda }_{3}}=\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{{{\lambda }_{1}}+{{\lambda }_{2}}}\]
  done clear
  D)
  \[{{\upsilon }_{3}}=\frac{{{\upsilon }_{1}}{{\upsilon }_{2}}}{{{\upsilon }_{1}}+{{\upsilon }_{2}}}\]
  done clear
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• question_answer12)
  A lift is tied with thick iron wire and its mass is 1000 kg. The minimum diameter of the wire if the maximum acceleration of the lift is \[1.2m{{s}^{-2}}\]and the maximum safe stress is \[1.4\times {{10}^{8}}N\text{ }{{m}^{-}}^{2}\], is (Take \[g=9.8\text{ }m\text{ }{{s}^{-}}^{2}\])       
  A)
  0.00141 m
  done clear
  B)
  0.00282 m       
  done clear
  C)
  0.005m           
  done clear
  D)
  0.01m           
  done clear
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• question_answer13)
  Resolving power of reflecting type telescope increases with                             
  A)
   decrease in wavelength of incident light
  done clear
  B)
  increase in wavelength of incident light
  done clear
  C)
  increase in diameter of objective mirror
  done clear
  D)
   both [a] and [c].
  done clear
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• question_answer14)
  The surface energy of a liquid drop is u. It is splatted into 1000 equal droplets. Then its surface energy becomes
  A)
  u              
  done clear
  B)
  10 u
  done clear
  C)
  100 u
  done clear
  D)
  1000 u
  done clear
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• question_answer15)
  2 kg of ice at \[-20{}^\circ C\] is mixed with 5 kg of water at \[20{}^\circ C\] in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. (Given : Specific heat capacities of water and ice are \[1\,\,ca\operatorname{l}\,{{g}^{-1}}{}^\circ {{C}^{-1}}\]and \[0.5\text{ }cal\text{ }{{g}^{-}}^{1}{}^\circ {{C}^{-}}^{1}\] respectively. Latent heat of fusion of ice \[=80\,cal\,{{g}^{-1}})\]
  A)
  7 kg
  done clear
  B)
  6 kg
  done clear
  C)
  4 kg        
  done clear
  D)
  2 kg
  done clear
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• question_answer16)
  To get an output Y = 1 from circuit of figure, the inputs must be  
  A)

  A	B	C
  0	1	0

  done clear
  B)

  A	B	C
  0	0	1

  done clear
  C)

  A	B	C
  1	0	0

  done clear
  D)

  A	B	C
  1	0	1

  done clear
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• question_answer17)
  The escape velocity for a planet is \[{{v}_{e}}\]. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be
  A)
  \[{{v}_{e}}\]                
  done clear
  B)
  \[\frac{{{v}_{e}}}{\sqrt{2}}\]
  done clear
  C)
  \[\frac{{{v}_{e}}}{2}\]             
  done clear
  D)
  zero
  done clear
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• question_answer18)
  In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of \[2\times {{10}^{10}}\] Hz and amplitude 54 V \[{{\text{m}}^{-1}}\].
  A)
  The amplitude of oscillating magnetic field will be \[18\times {{10}^{-7}}\text{Wb}\,{{\text{m}}^{-2}}\].
  done clear
  B)
  The amplitude of oscillating magnetic field will be \[18\times {{10}^{-8}}\text{Wb}\,{{\text{m}}^{-2}}\].
  done clear
  C)
  The wavelength of electromagnetic wave is 1.5 m.
  done clear
  D)
  The wavelength of electromagnetic wave is 1.5 cm.
  done clear
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• question_answer19)
  A uniform rod of mass m and length \[{{l}_{0}}\]is pivoted at one end and is hanging in the vertical direction. The period of small angular oscillations of the rod (if displaced slightly from its position) is
  A)
  \[3\pi \sqrt{\frac{2{{l}_{0}}}{3g}}\]      
  done clear
  B)
  \[4\pi \sqrt{\frac{{{l}_{0}}}{g}}\]
  done clear
  C)
  \[2\pi \sqrt{\frac{{{l}_{0}}}{3g}}\]        
  done clear
  D)
  \[2\pi \sqrt{\frac{2{{l}_{0}}}{3g}}\]
  done clear
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• question_answer20)
  Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0, number of P species are \[4{{N}_{0}}\]and that of Q are \[{{N}_{0}}\]. Half-life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. Initially no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be
  A)
  \[2{{N}_{0}}\]             
  done clear
  B)
  \[3{{N}_{0}}\]
  done clear
  C)
  \[\frac{9{{N}_{0}}}{2}\]                      
  done clear
  D)
  \[\frac{5{{N}_{0}}}{2}\]
  done clear
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• question_answer21)
  A particle is projected from a horizontal plane with velocity of \[5\sqrt{2}\,m{{s}^{-1}}\]at an angle. If at highest point its velocity is found to be \[5\,m\,{{s}^{-1}}\]. Then its range ______ m.           (Take\[g=10\,m\,{{s}^{-2}}\])
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• question_answer22)
  In the given circuit diagram, the current passing through wire CD is _________A.
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• question_answer23)
  For a certain organ pipe, three successive resonance frequencies are observed at 425, 595 and 765 Hz respectively. Taking the speed of sound in air to be \[340\,m\,{{s}^{-1}}\], the length of the pipe will be ___ m.
  View Answer play_arrow

• question_answer24)
  A fish at a depth of 12 cm in water is viewed by an observer on the bank of a lake. The image of fish is raised by height ___ cm. (Refractive index of lake water \[=\frac{4}{3}\])
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• question_answer25)
  If the ratio of the de Broglie wavelength of a proton and an \[\alpha \]-particle of same kinetic energy is x : 1, then the value of x is ___.
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• question_answer26)
  The number of isomers for the complexes X and Y are, respectively, \[X={{[Pt(N{{H}_{3}})(N{{H}_{2}}OH)(N{{O}_{2}})(py)]}^{\oplus }}\] \[Y=\left[ Cr \right[\left( N{{H}_{3}} \right){{\left( OH \right)}_{2}}C{{l}_{3}}]\]
  A)
  2 and 3
  done clear
  B)
  3 and 3        
  done clear
  C)
  3 and 4              
  done clear
  D)
  4 and 3
  done clear
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• question_answer27)
  The correct decreasing order of \[E_{{{M}^{3+}}/{{M}^{2+}}}^{\Theta }\] values for the following elements is

  I. Co (Z = 27)

  II. Mn (Z = 25)

  III. Fe (Z = 26)

  IV. Cr (Z = 24)

   
  A)
  I > II > III > IV  
  done clear
  B)
  IV >III > II > I   
  done clear
  C)
  II > I > III > IV  
  done clear
  D)
  III >IV > I > II
  done clear
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• question_answer28)
  The compound A, B and C are
  A)
  A - \[F{{e}_{2}}{{O}_{3}}\]                B - \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]                   C - \[C{{r}_{2}}{{O}_{3}}\]
  done clear
  B)
  A - \[C{{r}_{2}}{{O}_{3}}\]                 B - \[N{{a}_{2}}C{{r}_{2}}{{O}_{7}}\]                   C - \[F{{e}_{2}}{{O}_{3}}\]
  done clear
  C)
  A - \[FeO\,\,C{{r}_{2}}{{O}_{3}}\]      B - \[C{{r}_{2}}{{O}_{3}}\]                C - \[N{{a}_{2}}C{{r}_{2}}{{O}_{7}}\]
  done clear
  D)
  A - \[FeC{{r}_{2}}{{O}_{4}}\]          B - \[N{{a}_{2}}C{{r}_{2}}{{O}_{7}}\]              C - \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]
  done clear
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• question_answer29)
  Which of the following statement is CORRECT?  
  A)
  A gas can be liquefied at when \[T={{T}_{C}}\] and \[p<{{p}_{c}}\]
  done clear
  B)
  The gas gets heated if its temperature is less than its inversion temperature in Joule-Thomson effect.
  done clear
  C)
  It is possible to liquefy an ideal gas.
  done clear
  D)
  Average speed of molecules of a gas in a container moving only in one dimension will be zero.
  done clear
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• question_answer30)
  The CORRECT statements about NO  molecule and \[N{{O}^{\oplus }}\] ion is/are, respectively,

  I. Bond orders are 3 and 2.5 respectively.

  II. NO is paramagnetic and \[N{{O}^{\oplus }}\] ion is diamagnetic.

  III. \[NO\left( g \right)\]is obtained by the reaction of dil. \[HN{{O}_{3}}\]with Zn.

  IV. \[N{{O}^{\oplus }}\] is more stable than NO molecule.

  A)
  I, II                     
  done clear
  B)
  II, III                   
  done clear
  C)
  II, IV       
  done clear
  D)
  I, IV
  done clear
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• question_answer31)
  Which of the following is INCORRECT statement about inert gases?
  A)
  Helium has high thermal conductivity, low viscosity and density. With\[{{O}_{2}}\], it is used for deep sea diving.
  done clear
  B)
  Neon exist in stellar atmosphere. It is used in discharge tubes and fluorescent bulbs for advertising display purposes.
  done clear
  C)
  Argon is derived from Greek word which means 'stranger'. It doesn't forms clatherate compounds.
  done clear
  D)
  Xenon has highest ease of liquefication. It forms clatherate compounds and react with \[Pt{{F}_{6}}\]to give orange red ionic solid.
  done clear
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• question_answer32)
  Number of water molecules coordinated to the central metal ion to form complexes in (I) Blue vitriol, (II) White vitriol and (III) Green vitriol are, respectively,
  A)
  4, 4 and 6           
  done clear
  B)
  5, 5 and 7          
  done clear
  C)
  6, 6 and 4           
  done clear
  D)
  7, 5 and 5
  done clear
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• question_answer33)
  Identify (X) and (Y) respectively. \[Colemanite+N{{a}_{2}}C{{O}_{3}}\xrightarrow{{}}(X)+.........\] \[(X)+(Y)+5{{H}_{2}}O\xrightarrow{{}}2N{{a}_{2}}S{{O}_{4}}+..........\]
  A)
  \[{{B}_{2}}{{H}_{6}},S{{O}_{2}}\]          
  done clear
  B)
   \[{{B}_{2}}{{O}_{3}},\text{ }S{{O}_{3}}\]
  done clear
  C)
  \[N{{a}_{2}}{{B}_{4}}{{O}_{7}},{{H}_{2}}\text{S}{{\text{O}}_{4}}\text{ }\]
  done clear
  D)
  \[{{H}_{3}}B{{O}_{3}},{{H}_{2}}S\]
  done clear
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• question_answer34)
  Which of the following relations is INCORRECT?
  A)
  \[\int\limits_{{{U}_{1}}}^{{{U}_{2}}}{dU}={{U}_{2}}-{{U}_{1}}\]
  done clear
  B)
   \[\int\limits_{{{w}_{1}}}^{{{w}_{2}}}{dU}\ne {{w}_{2}}-{{w}_{1}}\]
  done clear
  C)
  \[{{P}_{(adiabatic\,\,expansion)}}<{{P}_{(isothermal\,\,expansion)}}\]
  done clear
  D)
  \[{{V}_{(adiabatic\,\,expansion)}}>{{V}_{(isothermal\,\,expansion)}}\]
  done clear
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• question_answer35)
  Number of significant figures in Loschmidt number and Boltzmann constant are, respectively,
  A)
  2 and 2               
  done clear
  B)
  3 and 3              
  done clear
  C)
  4 and 3    
  done clear
  D)
  3 and 4
  done clear
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• question_answer36)
  The quantum number of the last electron of an element are given below. Predict the atomic number and name of the element from the following quantum numbers \[n=3,l=2,m=0,s=-\frac{1}{2}\]
  A)
  23, V                 
  done clear
  B)
  21, Sc                 
  done clear
  C)
  29, Cu                   
  done clear
  D)
  28, Ni
  done clear
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• question_answer37)
  Nearest distance between two tetrahedral voids and between two octahedral voids are, respectively,
  A)
  \[\frac{a}{\sqrt{2}},\frac{\sqrt{3}}{2}a\]                       
  done clear
  B)
  \[\frac{\sqrt{3}}{4}a,\frac{\sqrt{3}}{2}a\]
  done clear
  C)
  \[\frac{\sqrt{3}}{2}a,\frac{a}{\sqrt{2}}\]           
  done clear
  D)
  \[\frac{\sqrt{3}}{2}a,\frac{\sqrt{3}}{4}a\]
  done clear
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• question_answer38)
  From the data given below, which of the following is most effective drying agent at\[0{}^\circ C\].

  I.	\[SrC{{l}_{2}}\cdot 6{{H}_{2}}O(s)\rightleftharpoons SrC{{l}_{2}}\cdot 2{{H}_{2}}O(s)+4{{H}_{2}}O(g)\]
  		\[{{K}_{p}}={{10}^{-12}}at{{m}^{4}}\]
  II.	\[N{{a}_{2}}HP{{O}_{4}}\cdot 12{{H}_{2}}O(s)\rightleftharpoons N{{a}_{2}}HP{{O}_{4}}\cdot 7{{H}_{2}}O(s)+5{{H}_{2}}O(g)\]
  		\[{{K}_{p}}=5.25\times {{10}^{-13}}at{{m}^{5}}\]
  III.	\[N{{a}_{2}}S{{O}_{4}}\cdot 10{{H}_{2}}O(s)\rightleftharpoons N{{a}_{2}}S{{O}_{4}}(s)+10{{H}_{2}}O(g)\]
  		\[{{K}_{p}}=4.08\times {{10}^{-25}}at{{m}^{10}}\]

  Given: The vapour pressure of water (i,e., \[P({{H}_{2}}O)at\,0{}^\circ C=6.0\times {{10}^{-3}}atm\]
  A)
  \[SrC{{l}_{2}}.2{{H}_{2}}O\] 
  done clear
  B)
  \[N{{a}_{2}}HP{{O}_{4}}.7{{H}_{2}}O\]
  done clear
  C)
  \[N{{a}_{2}}S{{O}_{4}}\]              
  done clear
  D)
  All of these
  done clear
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• question_answer39)
  From the given following sol, how many can coagulate the haemoglobin sol? \[Fe{{\left( OH \right)}_{3}},Ca{{\left( OH \right)}_{2}},\text{ }Al{{\left( OH \right)}_{3}},\text{ }starch,\text{ }clay,\]\[A{{s}_{2}}{{S}_{3}},CdS,\text{ }basic\text{ }dye\]
  A)
  1          
  done clear
  B)
  3                      
  done clear
  C)
  4              
  done clear
  D)
  8
  done clear
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• question_answer40)
  Trans-3, 6-dimethyloct-4-ene (A) exists in two diastereomers (I) and (II) Which of the following statements is CORRECT?
  A)
  Total number of stereoisomer for (A) is 6.
  done clear
  B)
   Both I and II are optically active.
  done clear
  C)
  If the stereochemistry about the double bond in (A) is cis, the total number of stereoisomers possible for (A) is 3.
  done clear
  D)
  If the stereochemistry about the double bond in (A) is trans, (II) is optically inactive due to presence of plane of symmetry.
  done clear
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• question_answer41)
  Which of the following reactions will not give a four membered cyclic compound?
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
      
  done clear
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• question_answer42)
  Compound \[(A)({{C}_{4}}{{H}_{8}}{{O}_{3}})\] reacts with \[NaHC{{O}_{3}}\]and evolves \[C{{O}_{2}}\left( g \right)\]. (A) reacts with LAH to give a compound (B) which is a chiral. The structure of (A) is
  A)
           
  done clear
  B)
  
  done clear
  C)
         
  done clear
  D)
  
  done clear
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• question_answer43)
  Consider the following reactions: Arrange the above reactions in the decreasing order of greater proportion of inverted product and select the correct answer.
  A)
  I>II>III>IV       
  done clear
  B)
  II>I>III>IV       
  done clear
  C)
  III>II>I>IV       
  done clear
  D)
  IV>III>II>I
  done clear
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• question_answer44)
  In the following Claisen-Schmidt reaction: The product (A) and number of product in (B) are respectively.
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
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• question_answer45)
  Which of the following does not undergo easy decarboxylation?
  A)
  \[MeCOC{{H}_{2}}COOH\]    
  done clear
  B)
  \[{{O}_{2}}N-COOH\]
  done clear
  C)
  \[C{{l}_{3}}C-COOH\]   
  done clear
  D)
  \[{{F}_{3}}C-COC{{H}_{2}}COOH\]
  done clear
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• question_answer46)
  The volume (in L) of 0.1 N \[FeS{{O}_{4}}\] can be oxidized by a current of 2 ampere hours is
  View Answer play_arrow

• question_answer47)
  The freezing point of the solution of compound \[(X)Co{{(N{{H}_{3}})}_{4}}C{{l}_{3}}\], containing 23.35 of solute per kg water is Given \[{{K}_{f}}=1.86{}^\circ \text{ }K\text{ }kg\text{ }mo{{l}^{-1}}\] Mwt of \[X=233.5\text{ }g\,\,mo{{l}^{-1}}\]
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• question_answer48)
  For a reaction, \[A\to B\], half-life time for a reaction at [A] = 0.1 M is 200 s and at [A] = 0.4 M it is 50 s. Thus, order of thereaction is
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• question_answer49)
  The total number of contributing structures showing hyperconjugation (involving C - H bonds) for the following carbocation is
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• question_answer50)
  How many of the following are condensation copolymers? Nylon-6, Nylon-66, Dacron, Glyptal, buna-S, ABS, neoprene, PHBV, perlon-U
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• question_answer51)
  For  \[x>0,\] \[\underset{x\to 0}{\mathop{\lim }}\,\,\left( {{\left( \sin x \right)}^{1/x}}+{{\left( \frac{1}{x} \right)}^{sin\,x}} \right)\]is
  A)
  \[0\]
  done clear
  B)
  \[-1\]
  done clear
  C)
  \[1\]
  done clear
  D)
  2
  done clear
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• question_answer52)
  If \[\tan \,\,{{q}_{1}}\]\[\tan \,\,{{q}_{2}}=-\frac{{{a}^{2}}}{{{b}^{2}}},\] then the chord joining two points \[(a\,\,\cos \,\,{{q}_{1}},\,\,b\,\,\sin \,\,{{q}_{1}}),\] and \[(a\,\,\cos \,\,{{q}_{2}},\,\,b\,\,\sin \,\,{{q}_{2}})\] on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] will subtend a right angle at
  A)
  Focus              
  done clear
  B)
  Centre
  done clear
  C)
  End of the major axes             
  done clear
  D)
  End of minor axes
  done clear
  View Answer play_arrow

• question_answer53)
  Domain of definition of the function\[f(x)=\frac{3}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x),\]is
  A)
  \[(-1,0)\cup (1,2)\cup (2,\infty )\]
  done clear
  B)
  \[(0,2)\]
  done clear
  C)
  \[(-1,0)\cup (0,2)\]       
  done clear
  D)
  \[(1,2)\cup (2,\infty )\]
  done clear
  View Answer play_arrow

• question_answer54)
  For positive numbers x, y, z, the numerical value of the determinant \[\left| \begin{matrix}    1 & {{\log }_{x}}y & {{\log }_{x}}z  \\    {{\log }_{y}}x & 1 & {{\log }_{y}}z  \\    {{\log }_{z}}x & {{\log }_{z}}y & 1  \\ \end{matrix} \right|\]is
  A)
  0                                 
  done clear
  B)
   1
  done clear
  C)
  2                                 
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer55)
  If \[S*(p,q,r)\] is the dual of the compound statement \[S(p,q,r)\]and \[S(p,q,r)=\,\sim p\wedge [\sim (q\vee r)]\] then \[S*(\sim p,\sim q,\sim r)\] is equivalent to-
  A)
  \[S(p,q,r)\]                   
  done clear
  B)
  \[\sim S(\sim p,\sim q,\sim r)\]
  done clear
  C)
  \[\sim S\,(p,q,r)\]                     
  done clear
  D)
  \[S*\,(p,q,r)\]
  done clear
  View Answer play_arrow

• question_answer56)
  The value of a so that the sum of the squares of the roots of the equation \[{{x}^{2}}-(a-2)x-a+1=0\] assume the least value, is
  A)
  2                     
  done clear
  B)
  1         
  done clear
  C)
  3                     
  done clear
  D)
  0
  done clear
  View Answer play_arrow

• question_answer57)
  Common roots of the equations \[2{{\sin }^{2}}x+{{\sin }^{2}}2x=2\] and \[2x+\cos 2x=\tan x,\] are
  A)
  \[x=(2n-1)\frac{\pi }{2}\]                  
  done clear
  B)
  \[x=(2n+1)\frac{\pi }{4}\]
  done clear
  C)
  \[x=(2n+1)\frac{\pi }{3}\]    
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer58)
  A particular solution of \[\log \,\left( \frac{dy}{dx} \right)=3x+4y,\] \[y(0)=0\] is
  A)
  \[{{e}^{3x}}+3{{e}^{-4y}}=4\]
  done clear
  B)
  \[4{{e}^{3x}}-3{{e}^{-4y}}=3\]
  done clear
  C)
  \[3{{e}^{3x}}+4{{e}^{4y}}=7\]
  done clear
  D)
  \[4{{e}^{3x}}+3{{e}^{-4y}}=7\]
  done clear
  View Answer play_arrow

• question_answer59)
  If \[f(x)=\frac{1}{2}x-1,\] then on the interval [0, n]
  A)
  \[\tan \,[f(x)]\] and \[1/f(x)\] are both continuous
  done clear
  B)
  \[\tan \,[f(x)]\]and \[1/f(x)\] are both discontinuous
  done clear
  C)
  \[\tan \,[f(x)]\] and \[{{f}^{-1}}(x)\]are both continuous
  done clear
  D)
  \[\tan \,[f(x)]\]is continuous but \[1/f(x)\] is not
  done clear
  View Answer play_arrow

• question_answer60)
  If  \[\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx},\] \[x\ne 0,\] then a, b, c, d, are in
  A)
  A. P.               
  done clear
  B)
  H.P.     
  done clear
  C)
  GP.                 
  done clear
  D)
  None
  done clear
  View Answer play_arrow

• question_answer61)
  The value of \[\int\limits_{2}^{4}{\{|x-2|+|x-3|\}dx}\]
  A)
  1                     
  done clear
  B)
  2        
  done clear
  C)
  3                     
  done clear
  D)
  5
  done clear
  View Answer play_arrow

• question_answer62)
  The angles of elevation of the top of a tower from the top and bottom at a building of height a are \[30{}^\circ \] and \[45{}^\circ \] respectively. If the tower and the building stand at the same level, then the height of the tower is
  A)
  \[a\sqrt{3}\]                            
  done clear
  B)
  \[\frac{a\sqrt{3}}{\sqrt{3}-1}\]
  done clear
  C)
  \[\frac{a(3+\sqrt{3})}{2}\]               
  done clear
  D)
  \[a(\sqrt{3}-1)\]
  done clear
  View Answer play_arrow

• question_answer63)
  The locus of the centres of the circles which touch externally the circles \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] and  \[{{x}^{2}}+{{y}^{2}}=4ax,\]will be
  A)
  \[12{{x}^{2}}-4{{y}^{2}}-24ax+9{{a}^{2}}=0\]
  done clear
  B)
  \[12{{x}^{2}}+4{{y}^{2}}-24ax+9{{a}^{2}}=0\]
  done clear
  C)
  \[12{{x}^{2}}-4{{y}^{2}}+24ax+9{{a}^{2}}=0\]
  done clear
  D)
  \[12{{x}^{2}}+4{{y}^{2}}+24ax+|9{{a}^{2}}=0\]
  done clear
  View Answer play_arrow

• question_answer64)
  The equation of the plane passing through the points \[(2,-1,0),\]\[(3,-4,5)\] and parallel to the line \[2x=3y=4z\] is
  A)
  \[29(x-2)+27(y+1)-22z=0\]
  done clear
  B)
  \[29(x-2)-27(y+1)-22z=0\]
  done clear
  C)
  \[29(x-2)+27(y+1)+22z=0\]
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer65)
  Let r be the range and \[{{S}^{2}}=\frac{1}{n-1}\sum\limits_{i=1}^{n}{{{\left( {{x}_{i}}-\bar{x} \right)}^{2}}}\]be the S.D. of a set of observations \[{{x}_{1}},{{x}_{2}},.....{{x}_{n}},\] then
  A)
  \[S\le r\sqrt{\frac{n}{n-1}}\]              
  done clear
  B)
  \[S=r\sqrt{\frac{n}{n-1}}\]
  done clear
  C)
  \[S\ge r\sqrt{\frac{n}{n-1}}\]             
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer66)
  If \[\vec{a}+\vec{b}+\vec{c}=0,\]\[|\vec{a}|\,=3,\] \[|\vec{b}|\,=5,\]\[|\vec{c}|\,=7,\] then the angle between a and b is:
  A)
  \[\frac{\pi }{4}\]                                 
  done clear
  B)
  \[\frac{\pi }{3}\]
  done clear
  C)
  \[\frac{2\pi }{3}\]                               
  done clear
  D)
  \[\frac{\pi }{6}\]
  done clear
  View Answer play_arrow

• question_answer67)
  If at least one value of the complex number \[z=x+iy\] satisfy the condition \[|z+\sqrt{2}|={{a}^{2}}-3a+2\] and the inequality \[|z+i\sqrt{2}|<{{a}^{2}},\] then
  A)
  \[a>2\]                       
  done clear
  B)
  \[a=2\]
  done clear
  C)
  \[a<2\]                       
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer68)
  A letter is known to have come either from LONDON or CLIFTON; on the postmark only the two consecutive letters ON are legible. The probability that it came from LONDON is
  A)
  \[\frac{5}{17}\]                                  
  done clear
  B)
  \[\frac{12}{17}\]
  done clear
  C)
  \[\frac{17}{30}\]                                
  done clear
  D)
  \[\frac{3}{5}\]
  done clear
  View Answer play_arrow

• question_answer69)
  If \[\int{f(x)}\,\sin x\,\,\cos x\,dx=\frac{1}{2({{b}^{2}}-{{a}^{2}})}{{\log }_{e}}\,\left( f(x) \right)+A\], \[b\ne \pm a,\] then \[{{\left\{ f(x) \right\}}^{-1}}\] is equal to
  A)
  \[{{a}^{2}}{{\sin }^{2}}x+{{b}^{2}}{{\cos }^{2}}x+C\]
  done clear
  B)
  \[{{a}^{2}}{{\sin }^{2}}x-{{b}^{2}}{{\cos }^{2}}x+C\]
  done clear
  C)
  \[{{a}^{2}}{{\cos }^{2}}x+{{b}^{2}}si{{n}^{2}}x+C\]
  done clear
  D)
  \[{{a}^{2}}{{\cos }^{2}}x-{{b}^{2}}si{{n}^{2}}x+C\]
  done clear
  View Answer play_arrow

• question_answer70)
  If \[f(x)\] is differentiable and strictly increasing function, then the value of \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{f({{x}^{2}})-f(x)}{f(x)-f(0)}\] is
  A)
  1                     
  done clear
  B)
  0    
  done clear
  C)
  -1                         
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer71)
  Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:
  View Answer play_arrow

• question_answer72)
  The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices \[(0,0),\] \[(0,21)\] (0,21) and \[(21,0),\] is
  View Answer play_arrow

• question_answer73)
  If a and b are the roots of the equation \[{{x}^{2}}-4x+1=0\] \[(a>b)\]then the value of \[f(\alpha ,\beta )=\frac{{{\beta }^{3}}}{2}\text{cose}{{\text{c}}^{2}}\left( \frac{1}{2}{{\tan }^{-1}}\frac{\beta }{\alpha } \right)+\frac{{{\alpha }^{3}}}{2}{{\sec }^{2}}\left( \frac{1}{2}{{\tan }^{-1}}\frac{\alpha }{\beta } \right)\]is
  View Answer play_arrow

• question_answer74)
  Find the number of irrational terms in the expansion of \[{{(\sqrt[8]{5}+\sqrt[6]{2})}^{100}}\]
  View Answer play_arrow

• question_answer75)
  The area enclosed by \[2|x|+3|y|\le 6\] is
  View Answer play_arrow