11th Class Mathematics Sample Paper

done Mathematics Olympiad - Sample Paper-3 Total Questions - 20    [Download]

• question_answer1)
  In a committee, 50 people speak Hindi, 20 speak English and 10 speak both Hindi and English then how many speak at least one of these two language?
  A)
   40                               
  done clear
  B)
   50           
  done clear
  C)
   60                               
  done clear
  D)
   80
  done clear
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• question_answer2)
  If A, B and C are non-empty subsets of a set, then \[\left( \mathbf{A}-\mathbf{B} \right)\cup \left( \mathbf{B}-\mathbf{A} \right)\] equal
  A)
   \[\left( A\cup B \right)-B\]          
  done clear
  B)
   \[A-\left( A\cap B \right)\]
  done clear
  C)
   \[\left( A\cup B \right)-\left( A\cap B \right)\]          
  done clear
  D)
   \[\left( A\cap B \right)\cup \left( A\cup B \right)\]
  done clear
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• question_answer3)
  \[\mathbf{P}\left( A \right)=\mathbf{0}.\mathbf{25}\]and \[\mathbf{P}\left( B \right)=\mathbf{0}.\mathbf{50}\]and \[\mathbf{P}\left( \mathbf{A}\cap \mathbf{B} \right)=\mathbf{0}.\mathbf{14}\]then \[\mathbf{P}\left( \mathbf{A}'\cap \mathbf{B}' \right)=?\]
  A)
   \[\frac{11}{100}\]                    
  done clear
  B)
   \[\frac{39}{100}\]
  done clear
  C)
   \[\frac{35}{100}\]                    
  done clear
  D)
   \[\frac{22}{100}\]
  done clear
  View Answer play_arrow

• question_answer4)
              The value of \[{{(e)}^{1/2}}\] will be
  A)
   1.444             
  done clear
  B)
   1.546         
  done clear
  C)
   1.349                          
  done clear
  D)
   1.648
  done clear
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• question_answer5)
  The coefficient of \[{{\mathbf{x}}^{\mathbf{3}}}\]in \[{{\left( \sqrt{{{\mathbf{x}}^{\mathbf{5}}}}+\frac{3}{\sqrt{{{x}^{3}}}} \right)}^{6}}\]  is
  A)
   120                             
  done clear
  B)
   540          
  done clear
  C)
   150                             
  done clear
  D)
   250
  done clear
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• question_answer6)
  The modulus of \[\frac{{{(3+2i)}^{2}}}{4-3i}\]is
  A)
   \[\frac{13}{5}\]                        
  done clear
  B)
   \[\frac{11}{5}\]            
  done clear
  C)
   \[\frac{9}{5}\]                         
  done clear
  D)
   \[\frac{7}{5}\]
  done clear
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• question_answer7)
  The interior angles of a polygon are in arithmetic progression. The smallest angle is \[\mathbf{12}{{\mathbf{0}}^{{}^\circ }}\] and the common difference is\[{{\mathbf{5}}^{{}^\circ }}\]. What will be the number of sides of the polygon
  A)
    8                  
  done clear
  B)
   9              
  done clear
  C)
   10                               
  done clear
  D)
   7
  done clear
  View Answer play_arrow

• question_answer8)
  \[\underset{x\to \infty }{\mathop{lim}}\,{{\left( cos\frac{x}{n} \right)}^{n}}\] is equal to
  A)
   e                     
  done clear
  B)
   \[\frac{1}{e}\]             
  done clear
  C)
   0                                
  done clear
  D)
   1
  done clear
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• question_answer9)
  \[\frac{{{d}^{2}}x}{d{{y}^{2}}}\] equal to
  A)
   \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{-1}}\]                  
  done clear
  B)
   \[-{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{-1}}.{{\left( \frac{dy}{d{{x}^{2}}} \right)}^{-3}}\]
  done clear
  C)
   \[\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)\times {{\left( \frac{dy}{dx} \right)}^{2}}\]
  done clear
  D)
   \[-\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right).{{\left( \frac{dy}{dx} \right)}^{-3}}\]
  done clear
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• question_answer10)
  If \[\mathbf{y=1}{{\mathbf{0}}^{\mathbf{x}}}\] is the reflection of \[\mathbf{y}=\mathbf{lo}{{\mathbf{g}}_{10}}\mathbf{x}\] in the line whose equations is:
  A)
   \[\mathbf{y}=-x\]                    
  done clear
  B)
   \[\mathbf{y}=x\]         
  done clear
  C)
   \[x-2y=0\]       
  done clear
  D)
   \[x+2y=0\]
  done clear
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• question_answer11)
  The length of major axis of ellipse is 26 and its foci is \[\left( \pm \text{ }\mathbf{5},\mathbf{0} \right)\] then equation of ellipse be
  A)
   \[\frac{{{x}^{2}}}{144}+\frac{{{y}^{2}}}{169}=1\]
  done clear
  B)
          \[\frac{{{x}^{2}}}{169}-\frac{{{y}^{2}}}{144}=-1\]
  done clear
  C)
   \[\frac{{{x}^{2}}}{169}+\frac{{{y}^{2}}}{144}=-1\]          
  done clear
  D)
   \[-\frac{{{x}^{2}}}{169}-\frac{{{y}^{2}}}{144}=-1\]
  done clear
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• question_answer12)
  The equation of the common tangent to the curves \[{{y}^{2}}=8x\] and \[\mathbf{xy}\text{=}-\mathbf{1}\]is-
  A)
   \[2y=x+8\]                  
  done clear
  B)
   \[y=x+2\]     
  done clear
  C)
   \[y=2x+1\]      
  done clear
  D)
   \[3y=9x+2\]
  done clear
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• question_answer13)
  If the quadratic equations \[{{x}^{2}}+ax+b=0\]and \[{{\mathbf{x}}^{2}}+\mathbf{bx}+\mathbf{a}=\mathbf{0}\]have a common root then the numerical value of \[\left( \mathbf{a}+\mathbf{b} \right)\] is:
  A)
   1                   
  done clear
  B)
   \[-1\]             
  done clear
  C)
   0                                
  done clear
  D)
   2
  done clear
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• question_answer14)
  The points \[\left( \mathbf{3},\mathbf{3} \right),\left( \mathbf{h},\mathbf{0} \right)\]and \[\left( \mathbf{0},\mathbf{k} \right)\]are collinear if
  A)
   \[\frac{1}{h}+\frac{1}{k}=\frac{1}{3}\]                       
  done clear
  B)
   \[\frac{1}{k}-\frac{1}{h}=\frac{1}{3}\]
  done clear
  C)
   \[h+k=3\]                    
  done clear
  D)
   \[\frac{1}{h}-\frac{1}{k}=\frac{1}{3}\]
  done clear
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• question_answer15)
  If \[y=si{{n}^{-1}}\left( \frac{5x+12\sqrt{1-{{x}^{2}}}}{13} \right)\] then \[\frac{dy}{dx}\]is equa.to
  A)
   \[\frac{1}{\sqrt{1-{{x}^{2}}}}\]                      
  done clear
  B)
   \[\frac{-1}{\sqrt{1-{{x}^{2}}}}\]
  done clear
  C)
   \[\frac{2}{\sqrt{1-{{x}^{2}}}}\]                      
  done clear
  D)
   \[\frac{-2}{\sqrt{1-{{x}^{2}}}}\]
  done clear
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• question_answer16)
  If \[\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\phi =\mathbf{2ta}{{\mathbf{n}}^{\mathbf{2}}}\phi +1\],then \[cos2\phi +si{{n}^{2}}\phi \]is equal to
  A)
   0                                
  done clear
  B)
   \[-1\]
  done clear
  C)
   1                                
  done clear
  D)
   2  
  done clear
  View Answer play_arrow

• question_answer17)
  The most stable measure of the central tendency Is:
  A)
   the mode                     
  done clear
  B)
   the mean      
  done clear
  C)
   the median       
  done clear
  D)
   None of these
  done clear
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• question_answer18)
  A group of 10 items has A.M 6, if the arithmetic mean of 4 of these items Is 7.5 the of the remaining items is:
  A)
   5                   
  done clear
  B)
   3               
  done clear
  C)
   3.5                              
  done clear
  D)
   4.5
  done clear
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• question_answer19)
  The value of k for which the circles \[{{x}^{2}}+{{y}^{2}}-~3x+ky-5=0\]and \[4{{x}^{2}}+4{{y}^{2}}-12x-y-9=0\]became concentric is
  A)
   \[-\frac{1}{6}\]                        
  done clear
  B)
   \[\frac{1}{6}\]             
  done clear
  C)
   \[-\frac{1}{4}\]                        
  done clear
  D)
   \[\frac{1}{4}\]
  done clear
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• question_answer20)
  If \[\mathbf{f}\left( \mathbf{x} \right)=\frac{\mathbf{1}-\mathbf{cosx}}{\mathbf{1}-\mathbf{sinx}}\] then \[f'\left( \frac{\pi }{2} \right)\]is equal to
  A)
   1                                
  done clear
  B)
          0              
  done clear
  C)
          \[\infty \]                                  
  done clear
  D)
          does not exist
  done clear
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