11th Class Mathematics Sample Paper

done Mathematics Olympiad - Sample Paper-8 Total Questions - 20    [Download]

• question_answer1)
  tan \[\left[ \mathbf{ilog}\frac{a-ib}{a+ib} \right]\]is equal to.
  A)
   \[\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\]                      
  done clear
  B)
   \[\frac{{{a}^{2}}-{{b}^{2}}}{2ab}\]
  done clear
  C)
   \[\frac{2ab}{{{a}^{2}}-{{b}^{2}}}\]            
  done clear
  D)
   \[ab\]
  done clear
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• question_answer2)
  A speaks truth in 60% of the cases and B in boy of the case. The percentage of cases they are likely to contradict each other in stating the same fact is
  A)
    36%               
  done clear
  B)
   42%         
  done clear
  C)
   48%                            
  done clear
  D)
   None of these
  done clear
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• question_answer3)
  The number of odd numbers between 60 & 360 is
  A)
   148                 
  done clear
  B)
   150          
  done clear
  C)
   160                             
  done clear
  D)
   153
  done clear
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• question_answer4)
  If \[\mathbf{sinx}+\mathbf{cosx}=\mathbf{a}\]then. \[si{{r}^{6}}x+co{{s}^{6}}x\]is equal to.
  A)
   \[\frac{1}{4}(4+3.({{a}^{2}}-{{1}^{2}}))\]   
  done clear
  B)
   \[\frac{1}{4}[4-3.({{a}^{2}}-{{1}^{2}})]\]            
  done clear
  C)
   \[\frac{1}{4}[4-2.({{a}^{2}}+{{1}^{2}})]\]   
  done clear
  D)
   \[\frac{1}{4}[4-3.{{({{a}^{2}}+1)}^{2}}]\]  
  done clear
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• question_answer5)
  If \[\mathbf{f}\left( \mathbf{2} \right)=\mathbf{2},\mathbf{f}'\left( \mathbf{2} \right)=1\]then \[\underset{x\to 2}{\mathop{Lt}}\,\frac{2{{x}^{2}}-4f(x)}{x-2}\]is equal to
  A)
   4                                
  done clear
  B)
   \[-2\]             
  done clear
  C)
  \[-4\]                            
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer6)
  If \[y=\frac{\cos x}{1+\sin x}\]then \[\frac{dy}{dx}\]at \[x=\frac{\pi }{2}\]is equal to.
  A)
   \[\frac{1}{2}\]                         
  done clear
  B)
   \[\frac{-1}{2}\]            
  done clear
  C)
   -1                               
  done clear
  D)
   0
  done clear
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• question_answer7)
  What will be the equation of a straight which is equidistant from parallel lines \[\mathbf{9x}+\mathbf{6y}-\mathbf{7}=\mathbf{0}\] and \[\mathbf{3x}+\mathbf{2y}+\mathbf{6}=\mathbf{0}.\]
  A)
   \[21x+18y+11=0\]      
  done clear
  B)
  \[18x+21y-11=0\]
  done clear
  C)
  \[18x+21y+11=0\]                     
  done clear
  D)
   \[21x+18y-11=0\]
  done clear
  View Answer play_arrow

• question_answer8)
  The solution of \[\mathbf{6}+\mathbf{x}-{{\mathbf{x}}^{\mathbf{2}}}>\mathbf{0}\]is
  A)
   \[-1<x<2\]      
  done clear
  B)
  \[~-2<x<3\]
  done clear
  C)
   \[-2<x<-1\]            
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  A man has gat 6 friends. Then the number of ways in which the can invite or of his friends to dinner, is
  A)
   63                               
  done clear
  B)
   65           
  done clear
  C)
   61                               
  done clear
  D)
   60
  done clear
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• question_answer10)
  The sum of the series \[\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}......\] up to \[\infty \] is equal to.
  A)
   \[lo{{g}_{e}}2\]                       
  done clear
  B)
  \[lo{{g}_{e}}2-1\]      
  done clear
  C)
   \[2.lo{{g}_{e}}2\]       
  done clear
  D)
   \[2.lo{{g}_{e}}2-1\]
  done clear
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• question_answer11)
  A set contains n elements. The power set contains -
  A)
   n elements       
  done clear
  B)
   \[{{2}^{n}}\]elements   
  done clear
  C)
   \[{{n}^{2}}\]elements             
  done clear
  D)
   \[{{2}^{(n-1)}}\]elements
  done clear
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• question_answer12)
  If \[f(x)=\frac{\mathbf{3x}+\mathbf{1}}{\mathbf{5x}-\mathbf{3}}\].then
  A)
   \[{{f}^{-1}}(x)=-f(x)\]            
  done clear
  B)
   \[f\,of\left( x \right)=f\left( x \right)\]
  done clear
  C)
   \[{{f}^{-1}}(x)=-f(x)\]            
  done clear
  D)
   \[{{f}^{-1}}(x)=\frac{1}{20}f(x)\]
  done clear
  View Answer play_arrow

• question_answer13)
  Sum of the absolute deviation about median is-
  A)
   least                
  done clear
  B)
   zero           
  done clear
  C)
   greatest                        
  done clear
  D)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  Coefficient of x4 in the expansion of \[{{\left( \mathbf{1}+\mathbf{x}+{{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{x}}^{\mathbf{4}}} \right)}^{\mathbf{11}}}\] is -
  A)
   605                             
  done clear
  B)
   810          
  done clear
  C)
   990                             
  done clear
  D)
   910
  done clear
  View Answer play_arrow

• question_answer15)
  The slope of the normal at the point \[\left( \mathbf{a}{{\mathbf{t}}^{\mathbf{2}}},\mathbf{2at} \right)\] of the parabola \[{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{4ax}\] is
  A)
   \[\frac{1}{t}\]                          
  done clear
  B)
   t               
  done clear
  C)
   \[-t\]                            
  done clear
  D)
   \[{{t}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer16)
  The roots of the equation \[{{2}^{x+2}}{{.3}^{\frac{3x}{x-1}}}=9\]are given by
  A)
   \[lo{{g}_{2}}\left( \frac{2}{3} \right),-2\]           
  done clear
  B)
   \[-3,3\]          
  done clear
  C)
   \[-2,1-\frac{\log 3}{\log 2}\]       
  done clear
  D)
   \[-2,1-{{\log }_{2}}3\]
  done clear
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• question_answer17)
  A coin & a dice is thrown. If A denotes the event head & even face and B denotes the event tail & multiple of 3. Then-
  A)
   \[P(A)=\frac{1}{4}\]                
  done clear
  B)
   \[P(B)=\frac{1}{5}\]       
  done clear
  C)
   \[P(A)=\frac{1}{3}\]                
  done clear
  D)
   \[P(B)=\frac{2}{3}\] 
  done clear
  View Answer play_arrow

• question_answer18)
  \[\underset{x\to 0}{\mathop{Lt}}\,\frac{{{e}^{{{x}^{2}}}}-\cos x}{{{x}^{2}}}\]is
  A)
   \[\frac{2}{3}\]                         
  done clear
  B)
   \[\frac{1}{2}\]              
  done clear
  C)
   \[\frac{3}{2}\]                         
  done clear
  D)
   2
  done clear
  View Answer play_arrow

• question_answer19)
  If w is an imaginary cube root of unity then \[\left( 1-w \right)\left( 1-{{w}^{2}} \right)\left( 1-{{w}^{4}} \right)\left( 1-{{w}^{5}} \right)\]is equal to
  A)
    3                  
  done clear
  B)
   6             
  done clear
  C)
   9                                
  done clear
  D)
   12
  done clear
  View Answer play_arrow

• question_answer20)
  Root of the equation- \[{{\mathbf{3}}^{\mathbf{x-1}}}\mathbf{+}{{\mathbf{3}}^{\mathbf{1-x}}}\mathbf{=2}\]
  A)
   \[x=0\]                        
  done clear
  B)
   \[x=1\]        
  done clear
  C)
   \[x=2\]                        
  done clear
  D)
   \[x=-1\]
  done clear
  View Answer play_arrow