10th Class Mathematics Sample Paper

done Mathematics Sample Paper-1 Total Questions - 23    [Download]

• question_answer1)
  Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively.
  A)
  11        
  done clear
  B)
         19        
  done clear
  C)
  17        
  done clear
  D)
  21
  done clear
  E)
  None of these
  done clear
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• question_answer2)
  If sum of the squares of zeroes of the polynomial \[f(x)={{x}^{2}}-8x+k\]is 40, then find the value of k.
  A)
  13                    
  done clear
  B)
  11
  done clear
  C)
  10                    
  done clear
  D)
  12
  done clear
  E)
  None of these
  done clear
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• question_answer3)
  On selling a T.V. at 5% gain and a refrigerator at 10% gain, a shopkeeper gains? 2000. But if he sells the T.V. at 10% gain and the refrigerator at 5% loss, he gains? 1500 on the transaction. Find the actual price of the refrigerator.
  A)
  Rs. 10000         
  done clear
  B)
  Rs. 15000
  done clear
  C)
  Rs. 7500           
  done clear
  D)
  Rs. 9000
  done clear
  E)
  None of these
  done clear
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• question_answer4)
  The sum of the squares of two consecutive natural numbers is 265. Find the numbers.
  A)
  13 and 14         
  done clear
  B)
  11 and 12
  done clear
  C)
  12 and 13         
  done clear
  D)
  14 and 15
  done clear
  E)
  None of these
  done clear
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• question_answer5)
  If 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term.
  A)
  160                  
  done clear
  B)
  175
  done clear
  C)
  162                  
  done clear
  D)
  169
  done clear
  E)
  None of these
  done clear
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• question_answer6)
  Three sphere whose radii is 3 cm, 4 cm and 5 cm are melted to form a big sphere. Then what is the radius of big sphere.
  A)
  6cm                 
  done clear
  B)
  7cm
  done clear
  C)
  8cm                 
  done clear
  D)
  9cm
  done clear
  E)
  None of these
  done clear
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• question_answer7)
  In\[\Delta ABC\], D and E are points on the sides AB and AC respectively such that\[DE\left| {} \right|BC\]. If AD=4 units, AE=8 units, DB= \[x-4\] units and EC=\[3x-19\]units, then x is equal to:
  A)
  7 units  
  done clear
  B)
  15 units
  done clear
  C)
  14 units
  done clear
  D)
  11 units
  done clear
  E)
  None of these
  done clear
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• question_answer8)
  Find the radius of in circle inscribed in a right triangle whose base and altitude are 7 cm and 24 cm respectively.
  A)
  \[{{30}^{o}}\]            
  done clear
  B)
  \[{{50}^{o}}\]
  done clear
  C)
  \[{{60}^{o}}\]            
  done clear
  D)
  \[{{90}^{o}}\]
  done clear
  E)
  None of these
  done clear
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• question_answer9)
  The value of \[(\tan {{1}^{o}}\tan {{2}^{o}}.........\tan {{89}^{o}})\]is :
  A)
  0                     
  done clear
  B)
  1
  done clear
  C)
  2                     
  done clear
  D)
  4
  done clear
  E)
  None of these
  done clear
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• question_answer10)
  Find the angle between the lines \[x+2y=1\]and \[x+4y=2.\]
  A)
  1         
  done clear
  B)
         \[\frac{1}{\sqrt{3}}\]
  done clear
  C)
  \[{{\tan }^{-1}}\left( \frac{4}{9} \right)\]           
  done clear
  D)
  \[\sqrt{3}\]
  done clear
  E)
  None of these
  done clear
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• question_answer11)
  The algebraic sum of the deviations of a frequency distribution from its mean is:
  A)
  always positive
  done clear
  B)
  0
  done clear
  C)
  always negative
  done clear
  D)
  1
  done clear
  E)
  None of these
  done clear
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• question_answer12)
  A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomly, then the probability that it is a black or red ball is:
  A)
  \[\frac{1}{3}\]              
  done clear
  B)
  \[\frac{1}{4}\]
  done clear
  C)
  \[\frac{5}{12}\]             
  done clear
  D)
  \[\frac{2}{3}\]
  done clear
  E)
  None of these
  done clear
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• question_answer13)
  Find the 14th term of an A.P. whose first term is 3 and the common difference is 2.
  A)
  33                    
  done clear
  B)
  28
  done clear
  C)
  29                    
  done clear
  D)
  15
  done clear
  E)
  None of these
  done clear
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• question_answer14)
  In an AP if a=\[-7.2\], d=3.6 and\[{{a}_{n}}\]=7.2, then find n.
  A)
  4                     
  done clear
  B)
  5
  done clear
  C)
  3                     
  done clear
  D)
  2
  done clear
  E)
  None of these
  done clear
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• question_answer15)
  Find the value of \[\sqrt{30+\sqrt{30+\sqrt{30+----\infty }}}\]
  A)
  5                     
  done clear
  B)
  6
  done clear
  C)
  4                     
  done clear
  D)
  7
  done clear
  E)
  None of these
  done clear
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• question_answer16)
  If a and B are the roots of the equation\[{{x}^{2}}-12x+32=0\], then find the value of\[\frac{{{\alpha }^{2}}+{{\beta }^{2}}}{\alpha +\beta }\]
  A)
  \[\frac{8}{3}\]              
  done clear
  B)
  \[\frac{-8}{3}\]
  done clear
  C)
  \[\frac{20}{3}\]             
  done clear
  D)
  \[\frac{-20}{3}\]
  done clear
  E)
  None of these
  done clear
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• question_answer17)
  If (\[x-2\]) is a factor of \[{{x}^{3}}+a{{x}^{2}}+bx+16\]and b=4a, then find the values of a and b.
  A)
  \[a=2,\text{ }b=-8\]
  done clear
  B)
         \[a=-2,b=8\]
  done clear
  C)
  \[a=-2,\text{ }b=-8\]
  done clear
  D)
  \[a=2,\text{ }b=8\]
  done clear
  E)
  None of these
  done clear
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• question_answer18)
  \[Cos(A+B)=\frac{1}{2}\]and\[sin(A-B)=\frac{1}{2},\,\,{{0}^{o}}<A+B<{{90}^{o}}\]and\[A-B>{{0}^{o}}\], find the values of \[\angle A\]and\[\angle B\].
  A)
  \[~\angle A={{60}^{o}}\,,\angle B={{30}^{o}}\]       
  done clear
  B)
  \[\angle A={{15}^{o}},\text{ }\angle B={{45}^{o}}\]
  done clear
  C)
  \[\angle A={{30}^{o}},\,\,\angle B={{15}^{o}}\]
  done clear
  D)
  \[\angle A=45{}^\circ ,\text{ }\angle B=15{}^\circ \]
  done clear
  E)
  None of these
  done clear
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• question_answer19)
  If \[\frac{x}{a}Sin\theta -\frac{y}{b}Cos\theta =1and\frac{x}{a}\ Cos\theta +\frac{y}{b}Sin\theta =1\]then the value of \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}\]is
  A)
  2                     
  done clear
  B)
  \[\frac{1}{a}+\frac{1}{b}\]
  done clear
  C)
  \[\sqrt[4]{4ab}\] 
  done clear
  D)
  0
  done clear
  E)
  None of these
  done clear
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• question_answer20)
  Find the angle between the lines x+2y=1 and x+4y=2
  A)
  1                     
  done clear
  B)
  \[\frac{1}{\sqrt{3}}\]
  done clear
  C)
  \[ta{{n}^{-1}}\left( \frac{2}{9} \right)\] 
  done clear
  D)
  \[\sqrt{3}\]
  done clear
  E)
  None of these
  done clear
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• question_answer21)
  If the cost price of a book is reduced by Rs. 5, a person can by 5 more books for Rs. 300. Find the original list price of the book.
  A)
  Rs. 10  
  done clear
  B)
  Rs. 20
  done clear
  C)
  Rs. 15  
  done clear
  D)
  Rs. 17
  done clear
  E)
  None of these
  done clear
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• question_answer22)
  lf\[\tan \theta +\frac{1}{\tan \theta }=2\],find the value of\[{{\tan }^{2}}\theta +\frac{1}{{{\tan }^{2}}\theta }\]
  A)
  4                     
  done clear
  B)
  2
  done clear
  C)
  7                     
  done clear
  D)
  3
  done clear
  E)
  None of these
  done clear
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• question_answer23)
  The value of \[(\tan {{1}^{o}}\tan {{2}^{o}}\tan {{3}^{o}}----\tan {{89}^{o}})\]is
  A)
  0                     
  done clear
  B)
  2
  done clear
  C)
  1                     
  done clear
  D)
  \[\frac{1}{2}\]
  done clear
  E)
  None of these
  done clear
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