10th Class Mathematics Sample Paper

done Mathematics Sample Paper-5 Total Questions - 23    [Download]

• question_answer1)
  Identify the irrational number from the following.
  A)
  0.1010010001......
  done clear
  B)
       0.2020020002 ......
  done clear
  C)
  0.121121111211112......     
  done clear
  D)
  All of these
  done clear
  E)
  None of these
  done clear
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• question_answer2)
  Number \[\mathbf{1}.\mathbf{23}\overline{\mathbf{48}}\] is:
  A)
  an integer           
  done clear
  B)
      an irrational numbers
  done clear
  C)
  a rational number              
  done clear
  D)
  All of these
  done clear
  E)
  None of these
  done clear
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• question_answer3)
  If a and P are zeros of\[{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{5x}+\mathbf{8}\], the value of \[\left( \alpha +\beta  \right)\]is:
  A)
  8                     
  done clear
  B)
  ? 8          
  done clear
  C)
  5                     
  done clear
  D)
  ? 5
  done clear
  E)
  None of these
  done clear
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• question_answer4)
  If \[\sqrt{2}x-\sqrt{3}y=0\]and\[\sqrt{5}x+\sqrt{2}y=0\], then find the value of x and y.
  A)
  \[x=0\,and\,y=1\]   
  done clear
  B)
  \[x=1\,and\,y=0\]
  done clear
  C)
  \[x=-1\,and\,y=-1\]
  done clear
  D)
       \[x=0\text{ }and\text{ }y=0\]
  done clear
  E)
  None of these
  done clear
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• question_answer5)
  A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag.
  A)
  18                    
  done clear
  B)
  17       
  done clear
  C)
  14                    
  done clear
  D)
  15
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer6)
  If\[{{\mathbf{x}}^{n}}={{\mathbf{a}}^{n}}\,\mathbf{co}{{\mathbf{s}}^{4}}\theta \]and\[{{y}^{n}}={{b}^{m}}{{\sin }^{4}}\theta \], then which of the following will be the best choice?
  A)
  \[\frac{{{x}^{\frac{x}{2}}}}{{{a}^{\frac{m}{2}}}}+\frac{{{y}^{\frac{x}{2}}}}{{{b}^{\frac{m}{2}}}}=1\]           
  done clear
  B)
  \[\frac{{{x}^{n}}}{{{a}^{n}}}+\frac{{{y}^{n}}}{{{b}^{m}}}=1\]
  done clear
  C)
  \[\frac{{{x}^{\frac{n}{2}}}}{{{a}^{\frac{n}{2}}}}+\frac{{{y}^{\frac{n}{2}}}}{{{b}^{\frac{m}{2}}}}=1\]
  done clear
  D)
  All of these
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer7)
  If\[sin3\theta =cos\left( \theta -6{}^\circ  \right)\], where\[\mathbf{3}\theta \]and\[\left( \theta -\mathbf{6}{}^\circ  \right)\] are acute angles, then \[\theta \]=?
  A)
  \[24{}^\circ \]          
  done clear
  B)
  \[66{}^\circ \]        
  done clear
  C)
  \[36{}^\circ \]              
  done clear
  D)
  \[72{}^\circ \]
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer8)
  \[\mathbf{Tan5}{}^\circ \text{ }\mathbf{tan25}{}^\circ \text{ }\mathbf{tan30}{}^\circ \text{ }\mathbf{tan65}{}^\circ \text{ }\mathbf{tan85}{}^\circ \]= ?
  A)
  1                     
  done clear
  B)
  \[\frac{1}{\sqrt{3}}\]        
  done clear
  C)
  \[\sqrt{3}\]                  
  done clear
  D)
  \[\frac{1}{2}\]
  done clear
  E)
  None of these                                                         
  done clear
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• question_answer9)
  Two numbers are respectively 20% and 50% more than the third number. The ratio of the numbers is
  A)
  3:5                   
  done clear
  B)
  2:5     
  done clear
  C)
  4:5        
  done clear
  D)
  6:7
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer10)

  Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds.

  The ratio of their speed is:

  A)
  1 : 3                 
  done clear
  B)
  3 : 4       
  done clear
  C)
  3 : 2         
  done clear
  D)
  1: 4
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer11)
  In the following figure ABCD is a square of side 14 cm, with centers A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.
  A)
  \[40c{{m}^{2}}\]        
  done clear
  B)
  \[42c{{m}^{2}}\]    
  done clear
  C)
  \[38c{{m}^{2}}\]        
  done clear
  D)
  \[35c{{m}^{2}}\]
  done clear
  E)
  None of these
  done clear
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• question_answer12)
  If\[\alpha \]and\[\beta \]are the roots of the polynomial\[\mathbf{a}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{bx}+\mathbf{c}\], then find the value of\[{{\alpha }^{\mathbf{2}}}+{{\beta }^{\mathbf{2}}}\].
  A)
  \[\frac{b-2ac}{a}\]        
  done clear
  B)
  \[\frac{{{b}^{2}}+2ac}{{{a}^{2}}}\]
  done clear
  C)
  \[\frac{{{b}^{2}}-2ac}{{{a}^{2}}}\]
  done clear
  D)
  \[\frac{b+2ac}{a}\]
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer13)
  The median of the observations \[\mathbf{11},\mathbf{12},\mathbf{14},\mathbf{18},\text{ }\mathbf{x}+\mathbf{2},\text{ }\mathbf{x}+\mathbf{4},\text{ }\mathbf{30},\mathbf{32},\mathbf{35},\mathbf{41}\] arranged in ascending order is 24. Find the value of x.
  A)
  12         
  done clear
  B)
  19        
  done clear
  C)
  31                    
  done clear
  D)
  21
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer14)
  Two numbers a and b are such that one is odd and the other is even. Which statement is necessarily true?
  A)
  \[{{a}^{2b}}\]is even         
  done clear
  B)
  \[\left( a+b \right)\]is even
  done clear
  C)
  \[{{a}^{b}}\times {{b}^{a}}\]is even     
  done clear
  D)
    \[{{a}^{2}}-{{b}^{2}}\]is even
  done clear
  E)
  None of these
  done clear
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• question_answer15)
  A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Find the speed of the boat in still water.
  A)
  \[4km/h\]          
  done clear
  B)
  \[5km/h\]    
  done clear
  C)
  \[4.5km/h\]  
  done clear
  D)
  \[5.4km/h\]
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer16)
  If\[\mathbf{4}\text{ }\mathbf{tan}\text{ }\theta =\mathbf{3}\], then find the value of \[\frac{4\sin \theta -2cos\theta }{4sin\theta +3cos\theta }\]
  A)
  \[\frac{1}{4}\]              
  done clear
  B)
  \[\frac{1}{6}\]        
  done clear
  C)
  \[\frac{1}{8}\]              
  done clear
  D)
  \[\frac{3}{8}\]
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer17)
  In a \[\Delta \mathbf{ABC}\]if\[~\angle \mathbf{A}=\mathbf{30}{}^\circ ,\text{ }\angle \mathbf{B}=\mathbf{90}{}^\circ \]and\[~\mathbf{AC}=\mathbf{10cm}\], then find AB and BC.
  A)
  \[5\sqrt{2}cm,\,\,5cm\]     
  done clear
  B)
  \[5\sqrt{2}cm,\,\,3cm\]
  done clear
  C)
  \[5\sqrt{3}cm,\,\,3cm\]       
  done clear
  D)
    \[5\sqrt{2}cm,\,\,8cm\]
  done clear
  E)
  None of these
  done clear
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• question_answer18)
  In a class, there are 18 boys whose heights are more than 160 cm, which constitute three-fourths of the boys. If the total number of boys is two third of the total number of students in the class, then find the number of girls in the class.     
  A)
  6                     
  done clear
  B)
  18       
  done clear
  C)
  12          
  done clear
  D)
  24                
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer19)
  Find the value of\[\mathbf{x}+\mathbf{x}\left( {{\mathbf{x}}^{x}} \right)\]when\[\mathbf{x}=\mathbf{4}\].
  A)
  1160    
  done clear
  B)
      1360      
  done clear
  C)
  1640                
  done clear
  D)
       1028
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer20)
  If\[\mathbf{1}{{\mathbf{0}}^{\mathbf{2}y}}=\mathbf{25}\], then \[\mathbf{1}{{\mathbf{0}}^{-y}}\]is equals to ____.
  A)
  \[\frac{1}{625}\]
  done clear
  B)
       \[\frac{1}{50}\]
  done clear
  C)
  \[\frac{1}{25}\]             
  done clear
  D)
  \[\frac{1}{5}\]
  done clear
  E)
  None of these                                                          
  done clear
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• question_answer21)
  Two cubes each of volume\[~\mathbf{64c}{{\mathbf{m}}^{\mathbf{3}}}\] are joined end to end. Find the surface area of the resulting cuboid.                                                        
  A)
  \[160c{{m}^{2}}\]    
  done clear
  B)
  \[175c{{m}^{2}}\]
  done clear
  C)
  \[132c{{m}^{2}}\]               
  done clear
  D)
       \[164c{{m}^{2}}\]
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer22)
  The altitude AD of an isosceles\[\Delta \mathbf{ABC}\] with sides 2a, 2a and a, if\[\mathbf{AB}=\mathbf{AC}\] is:
  A)
  \[\frac{a\sqrt{5}}{3}\]   
  done clear
  B)
       \[\sqrt{15}\]
  done clear
  C)
  \[\frac{a\sqrt{15}}{4}\] 
  done clear
  D)
  \[\frac{a\sqrt{15}}{2}\]
  done clear
  E)
  None of these
  done clear
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• question_answer23)
  \[\mathbf{533}-\mathbf{463}-\mathbf{73}\]is dvisible by:
  A)
  6 and 9          
  done clear
  B)
  2 and 21
  done clear
  C)
  21 and 23           
  done clear
  D)
  Both [b] and [c]
  done clear
  E)
  None of these
  done clear
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