Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2014

done Jamia Millia Islamia Solved Paper-2014 Total Questions - 60

  • question_answer1) Matrix A is such that\[T\propto \frac{1}{V}\], where is the identity matrix. Then, for\[\text{6}\times \text{1}{{0}^{-\text{7}}}\text{A}-{{\text{m}}^{\text{2}}}\],\[{{A}^{n}}\] is equal to

    A)
    \[\text{5 g}/\text{c}{{\text{m}}^{\text{3}}}\]    

    B)
    \[nA-l\]

    C)
    \[\text{1}.\text{2}\times \text{1}{{0}^{-\text{7}}}\]       

    D)
    \[\text{3}\times \text{1}{{0}^{-\text{6}}}\]

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  • question_answer2) The number of solutions of the system of equations  \[CaC{{l}_{2}}\],\[\text{MgS}{{\text{O}}_{\text{4}}}\] and\[\text{MgS}{{\text{O}}_{\text{4}}}\] is

    A)
    zero  

    B)
    one

    C)
                    two                       

    D)
    infinite

    View Answer play_arrow
  • question_answer3) Let\[CaC{{l}_{2}}\] be a function defined by \[x+3y-11=0\], where [ ] denotes the greatest integer function. Then, \[P({{x}_{1}},{{y}_{1}})\]is equal to

    A)
    \[Q\left( \text{4},-\text{3} \right)\]                        

    B)
    \[\therefore \]

    C)
    \[PQ\]                  

    D)
     \[\frac{1}{x+\left[ \frac{\pi }{2} \right]}\]

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  • question_answer4) Let \[y=x\] be a function defined by \[\therefore \]The\[\frac{{{x}_{1}}+4}{2}=\frac{{{y}_{1}}-3}{2}\]is

    A)
    one-one onto       

    B)
    one-one but not onto

    C)
    onto but not one-one

    D)
    None of these

    View Answer play_arrow
  • question_answer5) If the conjugate of \[\Rightarrow \]be \[{{x}_{1}}-{{y}_{1}}=-7\],then

    A)
    \[PQ=\frac{-3-{{y}_{1}}}{4-{{x}_{1}}}\]                  

    B)
    \[y=x\]

    C)
    \[\because \]    

    D)
    \[PQ\]

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  • question_answer6) In the argand plane, the complex number \[y=x\] is turned in the clockwise sense through 180° and stretched three times. The complex number represented by the new number is

    A)
    \[\therefore \]                 

    B)
    \[\left( \frac{-3-{{y}_{1}}}{4-{{x}_{1}}} \right)(1)=-1\]

    C)
    \[\Rightarrow \]                              

    D)
    \[{{y}_{1}}+{{x}_{1}}=1\]

    View Answer play_arrow
  • question_answer7) If the sum of roots of equation \[{{x}_{1}}=-3\,\,\,and\,\,\,{{y}_{1}}=4\] is equal to sum of squares of their reciprocals, then \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x+1}{x+2} \right)}^{2x+1}}=\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{1}{x+2} \right)}^{2x+1}}\]and \[=\underset{x\to \infty }{\mathop{\lim }}\,{{\left[ {{\left( 1-\frac{1}{x+2} \right)}^{x+2}} \right]}^{\frac{2x+1}{x+2}}}\]are in

    A)
    GP                                         

    B)
    HP

    C)
    AP                                         

    D)
    None of these

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  • question_answer8) If   the    roots    of   the    equation \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{2+1/x}{1+2/x}={{e}^{-2}}\] are real and less than 3,then

    A)
    \[[-1,\infty )-\{0\}\]

    B)
    \[\text{x}=0\]

    C)
    \[\therefore \]

    D)
    \[Rf'(0)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(0+h)-f(0)}{h}\]

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  • question_answer9) If \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{\sqrt{h+1}-1}{{{h}^{3/2}}}\times \frac{\sqrt{h+1}+1}{\sqrt{h+1}+1}\], y and z are in HP, then the value of expression \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{h}{{{h}^{3/2}}(\sqrt{h+1}+1)}\] will be

    A)
    \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{h}{\sqrt{h}(\sqrt{h+1}+1)}\]          

    B)
    \[=\frac{1}{0(\sqrt{0+1}+1)}=\frac{1}{0}=\infty \]

    C)
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\cos (\sin x)-1}{{{x}^{2}}}\]                 

    D)
    \[\mu \]

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  • question_answer10) The term independent of. r in the expansion of \[W\]is

    A)
    \[\frac{4W}{3}\]             

    B)
    \[\frac{5W}{2}\]

    C)
    \[\frac{\pi }{2}\]   

    D)
    None of these

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  • question_answer11) The largest term in the expansion of\[\sigma =\text{5}.\text{67}\times \text{1}{{0}^{-\text{8}}}\text{W}-{{\text{m}}^{\text{2}}}{{\text{K}}^{\text{-4}}}\], where \[y=5\sin \frac{\pi x}{3}\cos 40\pi t\], is

    A)
    5th                        

    B)
    3rd        

    C)
    7th                        

    D)
    6th

    View Answer play_arrow
  • question_answer12) \[t\]is equal to

    A)
    0   

    B)
    \[{{(Kg)}^{1/2}}\]

    C)
    \[{{(Kg)}^{-1/2}}\]                          

    D)
    \[{{(Kg)}^{2}}\]

    View Answer play_arrow
  • question_answer13) If A and B are square matrices of order 3 such that \[{{(Kg)}^{-2}}\]and\[\frac{pV}{nT}\], then \[\frac{pV}{nT}\frac{pV}{nT}\upsilon ersus\] is equal to

    A)
     -9                          

    B)
    -81        

    C)
     -27                                        

    D)
     81

    View Answer play_arrow
  • question_answer14) If\[{{T}_{1}}>{{T}_{2}}\] , then r , is equal to

    A)
    3    

    B)
    4             

    C)
    8                             

    D)
    6

    View Answer play_arrow
  • question_answer15) The number of ways in which \[\frac{pV}{nT}\] students can be distributed equal among n sections, is

    A)
    \[4\times {{10}^{3}}A{{m}^{-1}}\]                            

    B)
    \[\text{1}{{0}^{-\text{2}}}\]

    C)
    \[\text{1}{{0}^{-3}}\]                     

    D)
    \[1\mu V\]

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  • question_answer16) The origin is shifted to (1, 2). The equation \[\text{1}.\text{96}\times \text{1}{{0}^{-\text{8}}}\text{ m}/\text{s}\] changes to \[\text{2}.\text{12}\times \text{1}{{0}^{\text{8}}}\text{ m}/\text{s}\] Then, \[\text{3}.\text{18}\times \text{1}{{0}^{8}}m/s\] is equal to

    A)
     1                            

    B)

    C)
     -2                                          

    D)
    -1

    View Answer play_arrow
  • question_answer17) Given points are A (0,4) and\[\text{3}.\text{33}\times {{10}^{\text{8}}}\text{ m}/\text{s}\]. Then, locus of \[\theta =\text{45}{}^\circ \] such that \[\frac{1}{3}M{{L}^{2}}\]is

    A)
    \[\frac{3}{2}M{{L}^{2}}\]  

    B)
    \[\frac{3}{4}M{{L}^{2}}\]

    C)
    \[M{{L}^{2}}\]  

    D)
     None of these

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  • question_answer18) The equation of straight line perpendicular to a line \[{{R}_{1}}\] and passes through (5, 2) is

    A)
    \[{{R}_{2}}\]      

    B)
    \[{{Q}_{1}}\]

    C)
    \[{{Q}_{2}}\]                     

    D)
    None of these

    View Answer play_arrow
  • question_answer19) The image of the point (4, -3) with respect to the line \[{{Q}_{1}}{{R}_{2}}\ne {{Q}_{2}}{{R}_{1}}\] is

    A)
    \[(-4,-3)\]                           

    B)
    \[(3,4)\]

    C)
    \[(-4,\text{ }3)\]                              

    D)
    \[(-3,\text{ }4)\]

    View Answer play_arrow
  • question_answer20) \[{{Q}_{1}}{{R}_{2}}={{Q}_{2}}{{R}_{1}}\] is equal to

    A)
    \[s=\frac{{{t}^{2}}}{4}\]       

    B)
    e

    C)
    \[T\propto V\]                

    D)
    None of these

    View Answer play_arrow
  • question_answer21) The set of points of differentiability of the function \[T\propto {{V}^{2}}\] is

    A)
    R                                            

    B)
    \[T\propto \frac{1}{{{V}^{2}}}\]

    C)
    \[T\propto \frac{1}{V}\]               

    D)
    \[\text{6}\times \text{1}{{0}^{-\text{7}}}\text{A}-{{\text{m}}^{\text{2}}}\]

    View Answer play_arrow
  • question_answer22) \[\text{5 g}/\text{c}{{\text{m}}^{\text{3}}}\]is equal to

    A)
    1                             

    B)
    \[\text{8}\text{.3}\times \text{1}{{0}^{\text{6}}}\]           

    C)
    \[\text{1}.\text{2}\times \text{1}{{0}^{-\text{7}}}\]                                       

    D)
    \[\text{3}\times \text{1}{{0}^{-\text{6}}}\]

    View Answer play_arrow
  • question_answer23) Let \[CaC{{l}_{2}}\] and \[\text{MgS}{{\text{O}}_{\text{4}}}\]where \[CaC{{l}_{2}}\]is continuous. Then, \[CaC{{l}_{2}}\]is equal to

    A)
    \[f(x)g(0)\]        

    B)
    \[\text{MgS}{{\text{O}}_{\text{4}}}\]

    C)
    \[\upsilon /\text{1}0\]          

    D)
    \[f\]

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  • question_answer24) The equation of a tangent parallel to\[1.11f\]drawn to\[1.22f\]is

    A)
    \[f\]                      

    B)
    \[1.27f\]

    C)
    \[\text{1}.0\text{1}\times \text{1}{{0}^{\text{5}}}\text{ N}/{{\text{m}}^{\text{2}}}\]                    

    D)
    None of these

    View Answer play_arrow
  • question_answer25) The lengths of the axes of the conic \[\text{9}.\text{13}\times \text{1}{{0}^{\text{4}}}\text{ N}/{{\text{m}}^{\text{2}}}\] are

    A)
    \[\text{9}.\text{13}\times \text{1}{{0}^{\text{3}}}\text{N}/{{\text{m}}^{\text{2}}}\]                     

    B)
    \[\text{18}.\text{26 N}/{{\text{m}}^{\text{2}}}\]    

    C)
    \[\text{2}.\text{25}\times \text{1}{{0}^{\text{3}}}\text{min}\]    

    D)
    3,2

    View Answer play_arrow
  • question_answer26) If a chord which is normal to the parabola at one end, subtends a right angle at the vertex, then angle to the axis is

    A)
    \[\text{3}.\text{97}\times \text{1}{{0}^{\text{3}}}\text{min}\]   

    B)
     0

    C)
    \[9.13\times {{10}^{3}}N/{{m}^{2}}\]                                     

    D)
    \[\text{5}.\text{25}\times \text{1}{{0}^{\text{3}}}\text{min}\]

    View Answer play_arrow
  • question_answer27) Two cards are drawn without replacement from a well-shuffled pack. The probability that one of them is an ace of heart, is

    A)
    \[\left[ \text{FL}{{\text{T}}^{-\text{2}}} \right]\]                                              

    B)
    \[\left[ \text{F}{{\text{L}}^{\text{2}}}{{T}^{-\text{2}}} \right]\]

    C)
    \[\left[ \text{F}{{\text{L}}^{-\text{1}}}{{\text{T}}^{\text{2}}} \right]\]                   

    D)
    None of these

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  • question_answer28) If\[\left[ {{\text{F}}^{2}}\text{L}{{\text{T}}^{\text{-2}}} \right]\]and \[-\text{273}.\text{15}{}^\circ \text{F}\]then \[-\text{453}.\text{15}{}^\circ \text{F}\] is equal to

    A)
    \[-\text{459}.\text{67}{}^\circ \text{F}\]              

    B)
     \[-\text{491}.\text{67}{}^\circ \text{F}\]

    C)
        \[\text{52}00\text{{ }\!\!\mathrm{\AA}\!\!\text{ }}\]                                

    D)
     \[\text{Vc}=\text{1}.\text{5V}\]

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  • question_answer29) The value of\[[a-b\,b-c\,c-a]\] is

    A)
    0      

    B)
    1            

    C)
     2                            

    D)
    3

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  • question_answer30) Let \[\text{15}0\text{ }\mu \text{A}\] and \[\text{5 mA}\]be unit vectors at an angle \[\text{10 mA}\] \[\text{ }\!\!\beta\!\!\text{ }\] from each other. Then, \[\left( \frac{1}{V(volume)} \right)\], if

    A)
    \[\frac{3}{4}\text{m}/\text{s}\]               

    B)
    \[\frac{1}{3}\text{m}/\text{s}\]

    C)
    \[\frac{3}{2}\text{m}/\text{s}\]               

    D)
    \[\frac{2}{3}\text{m}/\text{s}\]

    View Answer play_arrow
  • question_answer31) The angle between the planes \[{{\lambda }_{0}},\]and \[\frac{25}{16}{{\lambda }_{0}}\] is

    A)
    \[\frac{27}{20}{{\lambda }_{0}}\]                             

    B)
    \[\frac{20}{27}{{\lambda }_{0}}\]     

    C)
    \[\frac{16}{25}{{\lambda }_{0}}\]   

    D)
    \[3\Omega \]

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  • question_answer32) The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8), is

    A)
    \[4\Omega \]    

    B)
    \[4.5\Omega \]

    C)
    \[5\Omega \]  

    D)
    \[\frac{\sqrt{3}}{1}\]

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  • question_answer33) The point on the line \[\frac{(\sqrt{3}+1)}{(\sqrt{3}-1)}\]at a distance of 6 from the point (2, -3, -5) is

    A)
    (3,-5,-3)               

    B)
    (4,-7.-9)

    C)
    (0,2,-1)                

    D)
    (-3,5,3)

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  • question_answer34) The      maximum      value      of \[\frac{(\sqrt{3}+1)}{1}\]is

    A)
    \[\frac{4}{3}\]                   

    B)
    \[4\mu F\]

    C)
    \[10\mu F\]       

    D)
    \[8\mu F\]

    View Answer play_arrow
  • question_answer35) If \[120\mu F\]then the value of \[\omega \] is

    A)
    1                                             

    B)
    2

    C)
    0

    D)
    \[R/2\]

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  • question_answer36)  The number of solutions of the equation \[\frac{4\omega }{5}\] in \[\frac{2\omega }{5}\]is

    A)
    zero 

    B)
    one

    C)
    two                                       

    D)
    three

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  • question_answer37) If in a \[\frac{3\omega }{5}\]\[\frac{2\omega }{3}\], then \[\mu =\frac{3}{2}\] is equal to

    A)
    \[30{}^\circ \]                   

    B)
    \[60{}^\circ \]

    C)
    \[90{}^\circ \]                                   

    D)
    None of these

    View Answer play_arrow
  • question_answer38) In \[\mu =\frac{4}{3}\] then a, b and care in

    A)
    AP                                         

    B)
    GP

    C)
    HP                                         

    D)
    None of these

    View Answer play_arrow
  • question_answer39) \[{{\sin }^{-1}}\left( \frac{9}{8} \right)\] is equal to

    A)
    \[{{\cos }^{-1}}\left( \frac{x-4}{5} \right)+C\]     

    B)
    \[si{{n}^{-1}}\left( \frac{x-4}{5} \right)+C\]

    C)
    \[si{{n}^{-1}}\left( \frac{5}{x-4} \right)+C\]         

    D)
    None of these

    View Answer play_arrow
  • question_answer40) \[\beta =0.\text{1}\]is equal to

    A)
    \[\frac{{{x}^{2}}}{2}+C\]                              

    B)
    \[-\frac{{{x}^{2}}}{2}+C\]

    C)
    \[x|x|+C\]                         

    D)
    \[\frac{x|x|}{2}+C\]

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  • question_answer41) \[\text{2}\times \text{1}{{0}^{\text{7}}}\text{m}/\text{s}\]is equal to

    A)
    \[\text{2}\times \text{1}{{0}^{-2}}T\]                    

    B)
    \[\left( \frac{e}{m} \right)\]

    C)
    \[\text{1}.\text{76}\times \text{1}{{0}^{\text{11}}}\text{C}/\text{kg}\]                

    D)
    \[2B\]

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  • question_answer42) \[\frac{B}{4}\] is equal to

    A)
    \[\frac{B}{2}\]                                  

    B)
    \[y=A\sin (Bx+Ct+D)\]      

    C)
      \[[{{m}^{0}}{{L}^{-1}}{{T}^{0}}]\]                           

    D)
    \[[{{m}^{0}}{{L}^{0}}{{T}^{-1}}]\]

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  • question_answer43) The area bounded by \[[{{m}^{0}}{{L}^{-1}}{{T}^{-2}}]\] and X-axis is

    A)
    \[[{{m}^{0}}{{L}^{0}}{{T}^{0}}]\]

    B)
    \[1.5\mu \]

    C)
    \[\mu \]

    D)
    None of the above

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  • question_answer44) A man on the top of a cliff 100 m high observes the angles of depression of two points on the opposite sides of the cliff as 30° and 60°, respectively. Then, the distance between the two points is

    A)
    400 m                   

    B)
    \[W\]

    C)
    \[\frac{4W}{3}\]              

    D)
    None of these

    View Answer play_arrow
  • question_answer45) The   solution   set   of   the   equation \[\frac{5W}{2}\]is

    A)
    [0,1]                      

    B)
    [-1,1]

    C)
     [1.3]                                     

    D)
    None of these

    View Answer play_arrow
  • question_answer46) If \[\frac{\pi }{2}\],then the value of \[\sigma =\text{5}.\text{67}\times \text{1}{{0}^{-\text{8}}}\text{W}-{{\text{m}}^{\text{2}}}{{\text{K}}^{\text{-4}}}\] will be

    A)
    2abc                                      

    B)
    abc

    C)
    \[y=5\sin \frac{\pi x}{3}\cos 40\pi t\]                                     

    D)
    \[t\]

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  • question_answer47) The.  solution of the differential equation \[{{(Kg)}^{1/2}}\] is

    A)
    \[{{(Kg)}^{-1/2}}\]          

    B)
    \[{{(Kg)}^{2}}\]

    C)
    \[{{(Kg)}^{-2}}\]         

    D)
    None of these

    View Answer play_arrow
  • question_answer48) The integrating factor of the differential equation \[\frac{pV}{nT}\]is

    A)
    \[{{x}^{\log x}}\]                             

    B)
    \[{{(\sqrt{x})}^{\log x}}\]

    C)
    \[{{(\sqrt{e})}^{{{(\log x)}^{2}}}}\]                          

    D)
    \[{{e}^{{{x}^{2}}}}\]

    View Answer play_arrow
  • question_answer49) If \[\text{1}{{0}^{-\text{2}}}\].then \[\text{1}{{0}^{-3}}\] is equal to

    A)
    \[1\mu V\]

    B)
     \[\text{1}.\text{96}\times \text{1}{{0}^{-\text{8}}}\text{ m}/\text{s}\]

    C)
    \[{{(\tan x)}^{\sin x}}[\sec x+\cos x\log \tan x]\]

    D)
    None of the above

    View Answer play_arrow
  • question_answer50) If\[\text{3}.\text{18}\times \text{1}{{0}^{8}}m/s\] and \[\text{3}.\text{33}\times {{10}^{\text{8}}}\text{ m}/\text{s}\] then \[\theta =\text{45}{}^\circ \] is equal to

    A)
     \[\frac{-y}{x}\]                                

    B)
    \[\frac{y}{x}\]    

    C)
    \[-\frac{x}{y}\]                                 

    D)
    \[\frac{x}{y}\]

    View Answer play_arrow
  • question_answer51) The equation of the tangent to the curve\[{{R}_{1}}\]at the point, where the ordinate and the abscissa are equal, is

    A)
    \[{{R}_{2}}\]

    B)
    \[{{Q}_{1}}\]

    C)
    \[{{Q}_{2}}\]

    D)
    None of the above

    View Answer play_arrow
  • question_answer52) The function \[{{Q}_{1}}{{R}_{2}}\ne {{Q}_{2}}{{R}_{1}}\]has

    A)
    no maxima and minima

    B)
    one maximum and one minimum

    C)
    two maxima

    D)
    two minima

    View Answer play_arrow
  • question_answer53) If \[{{Q}_{1}}{{R}_{2}}={{Q}_{2}}{{R}_{1}}\]and f(0) = 0, then the value of a for which Rolle's theorem can be applied in [0,1], is

    A)
    -2                           

    B)
    -1          

    C)
    0                             

    D)
    \[s=\frac{{{t}^{2}}}{4}\]

    View Answer play_arrow
  • question_answer54) The algebraic sum of the deviation of 20 observations measured from 30 is 2. Then mean of observations is

    A)
    28.5                       

    B)
    30.1    

    C)
    30.5                       

    D)
    29.6

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  • question_answer55) The standard deviation of 15 items is 6 and if each item is decreased by 1, then standard deviation will be

    A)
    5                             

    B)
    7           

    C)
    \[T\propto V\]                                 

    D)
    6

    View Answer play_arrow
  • question_answer56) If \[T\propto {{V}^{2}}\]is equal to

    A)

    B)
    0          

    C)
    \[T\propto \frac{1}{{{V}^{2}}}\]                                

    D)
    0

    View Answer play_arrow
  • question_answer57) The equation of the smallest circle passing through the intersection of the line \[T\propto \frac{1}{V}\] and the circle \[\text{6}\times \text{1}{{0}^{-\text{7}}}\text{A}-{{\text{m}}^{\text{2}}}\] is

    A)
    \[\text{5 g}/\text{c}{{\text{m}}^{\text{3}}}\]

    B)
    \[\text{8}\text{.3}\times \text{1}{{0}^{\text{6}}}\]

    C)
    \[\text{1}.\text{2}\times \text{1}{{0}^{-\text{7}}}\]

    D)
    None of the above

    View Answer play_arrow
  • question_answer58) The complex number \[\text{3}\times \text{1}{{0}^{-\text{6}}}\] in polar form is

    A)
    \[CaC{{l}_{2}}\]

    B)
    \[\text{MgS}{{\text{O}}_{\text{4}}}\]

    C)
    \[\text{MgS}{{\text{O}}_{\text{4}}}\]

    D)
    None of the above

    View Answer play_arrow
  • question_answer59) If \[CaC{{l}_{2}}\]and \[A\to B,B\to C\], then\[C\to A\]is equal to

    A)
    \[\upsilon /\text{1}0\]                  

    B)
    \[f\]

    C)
    \[1.11f\]                              

    D)
    \[1.22f\]

    View Answer play_arrow
  • question_answer60) The orthocentre of the triangle formed by (0,0), (8, 0) and (4, 6) is

    A)
    \[f\]      

    B)
    \[1.27f\]

    C)
    \[\text{1}.0\text{1}\times \text{1}{{0}^{\text{5}}}\text{ N}/{{\text{m}}^{\text{2}}}\]                    

    D)
    \[\text{9}.\text{13}\times \text{1}{{0}^{\text{4}}}\text{ N}/{{\text{m}}^{\text{2}}}\]

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