10th Class Mathematics Sample Paper

done Mathematics Sample Paper-2 Total Questions - 23    [Download]

• question_answer1)
  In a morning walk, three persons step off together, their steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that he can cover the distance in complete steps?
  A)
  122 m 40 cm    
  done clear
  B)
  120 m
  done clear
  C)
  121 m 42 cm    
  done clear
  D)
  129 m 50 cm
  done clear
  E)
  None of these
  done clear
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• question_answer2)
  If the zeroes of the polynomial\[f(x)={{x}^{2}}-12{{x}^{2}}\]\[+39x+k\] are in A.P., then find the value of k.
  A)
  \[-20\]               
  done clear
  B)
  \[-28\]
  done clear
  C)
  \[-30\]               
  done clear
  D)
  \[-26\]
  done clear
  E)
  None of these
  done clear
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• question_answer3)
  7 audio cassettes and 3 video cassettes cost Rs. 1110, while 5 audio cassettes and 4 video cassettes cost Rs. 1350. Find the cost of a video cassette.
  A)
  Rs. 300 
  done clear
  B)
  Rs. 250
  done clear
  C)
  Rs. 275
  done clear
  D)
  Rs. 325
  done clear
  E)
  None of these
  done clear
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• question_answer4)
  The sum of a number and its reciprocal is\[2\frac{1}{30}\]. Find the number.
  A)
  \[\frac{5}{6}or\frac{6}{5}\]       
  done clear
  B)
  \[\frac{7}{6}or\frac{6}{7}\]       
  done clear
  C)
  \[\frac{1}{4}or4\]          
  done clear
  D)
  \[\frac{3}{4}or\frac{4}{3}\]
  done clear
  E)
  None of these
  done clear
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• question_answer5)
  Rama saved Rs. 5 in the first week of the year and then increased her weekly savings by Rs. 1.75 each week. In what week will her weekly savings be Rs. 20.75?
  A)
  12th week         
  done clear
  B)
  10th week
  done clear
  C)
  11th week         
  done clear
  D)
  8th week
  done clear
  E)
  None of these
  done clear
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• question_answer6)
  Find the volume of a conical flask whose slant height is three times the radius of the cone and its curved surface area is\[462\,\,c{{m}^{2}}\].
  A)
  \[646.32c{{m}^{3}}\]  
  done clear
  B)
  \[~631.32c{{m}^{3}}\]
  done clear
  C)
  \[~1016.35c{{m}^{3}}\]         
  done clear
  D)
  \[685.32c{{m}^{3}}\]
  done clear
  E)
  None of these
  done clear
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• question_answer7)
  In \[\Delta ABC\] and\[\Delta DEF\], it is being given that AB = 5cm, BC = cm and CA = 4.2 cm, DE = 10 cm, EF = 8cm, and FD = 8.4cm. If \[AL\bot BC\]and\[DM\bot EF\], then AL : DM is equal to:
  A)
  2 : 1                 
  done clear
  B)
  3 : 2
  done clear
  C)
  1 : 2                 
  done clear
  D)
  2 : 3
  done clear
  E)
  None of these
  done clear
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• question_answer8)
  Find the area of the sector which subtend an angle \[{{120}^{o}}\] at the centre of the circle of radius 21 cm.
  A)
  \[221\,\,c{{m}^{2}}\]  
  done clear
  B)
  \[363\,\,c{{m}^{2}}\]
  done clear
  C)
  \[462\,\,c{{m}^{2}}\]  
  done clear
  D)
  \[248\,\,c{{m}^{2}}\]
  done clear
  E)
  None of these
  done clear
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• question_answer9)
  If q is an acute angle and\[\sin \,\,q=\cos \,\,q\], find the value of \[2{{\tan }^{2}}q+{{\sin }^{2}}q-1.\]
  A)
  \[\frac{2}{5}\]              
  done clear
  B)
  \[\frac{3}{2}\]
  done clear
  C)
  \[\frac{2}{3}\]              
  done clear
  D)
         \[\frac{4}{5}\]
  done clear
  E)
  None of these
  done clear
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• question_answer10)
  The ratio in which line \[y=x\] divides the line segment joining \[(-\text{ }2,2)\] and \[(4,-2)\] is:
  A)
  2 : 3                 
  done clear
  B)
  3 : 8
  done clear
  C)
  3 : 2                 
  done clear
  D)
  1 : 1
  done clear
  E)
  None of these
  done clear
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• question_answer11)
  In the graphical representation of a frequency distribution, if the distance between mode and mean is k times the distance between median and mean, then what is the value of k.
  A)
  2                     
  done clear
  B)
  3
  done clear
  C)
  0                     
  done clear
  D)
  \[-2\]
  done clear
  E)
  None of these
  done clear
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• question_answer12)
  What is the probability of an impossible event?
  A)
  0                     
  done clear
  B)
  1
  done clear
  C)
  \[\frac{1}{2}\]              
  done clear
  D)
  \[\frac{2}{1}\]
  done clear
  E)
  None of these
  done clear
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• question_answer13)
  Write the discriminant of the following quadratic equations. \[\sqrt{3}{{x}^{2}}-2\sqrt{2}x-2\sqrt{3}=0\]
  A)
  23                    
  done clear
  B)
  32
  done clear
  C)
  21                    
  done clear
  D)
  26
  done clear
  E)
  None of these
  done clear
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• question_answer14)
  Which term of the following \[-1,\text{ }3,\text{ }7,\text{ }11------\]is 95?
  A)
  n = 52 
  done clear
  B)
  n = 25
  done clear
  C)
  n = 32 
  done clear
  D)
  n = 23
  done clear
  E)
  None of these
  done clear
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• question_answer15)
  If \[2x,\,\,x+10,\,\,3x+2\] are in AP, find the value of\[x\].
  A)
  6         
  done clear
  B)
  4
  done clear
  C)
  10                    
  done clear
  D)
  7
  done clear
  E)
  None of these
  done clear
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• question_answer16)
  If \[\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}\]is the A.M. between a and b. Then, find the value of n.
  A)
  1                     
  done clear
  B)
  21
  done clear
  C)
  0                     
  done clear
  D)
  5
  done clear
  E)
  None of these
  done clear
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• question_answer17)
  In the adjoining figure, ABCD is a square of side 14 cm. With Centres 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)
  \[36\,\,c{{m}^{2}}\]    
  done clear
  B)
  \[48\,\,c{{m}^{2}}\]
  done clear
  C)
  \[56\,\,c{{m}^{2}}\]    
  done clear
  D)
  \[42\,\,c{{m}^{2}}\]
  done clear
  E)
  None of these
  done clear
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• question_answer18)
  If \[{{S}_{n}},\]the sum of first n terms of an A.P. is given by\[{{S}_{n}}=5{{n}^{2}}+3n\], then find its nth term.
  A)
  \[n2\]                
  done clear
  B)
  \[2n-10\]
  done clear
  C)
  \[10\,\,n2\]        
  done clear
  D)
  \[n+2\]
  done clear
  E)
  None of these
  done clear
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• question_answer19)
  Find the value of \[x\]in \[\tan \,~3x=\sin {{45}^{o}}\times \cos {{45}^{o}}+\sin {{30}^{o}}\]
  A)
  \[{{15}^{o}}\]            
  done clear
  B)
  \[{{51}^{o}}\]
  done clear
  C)
  \[{{25}^{o}}\]            
  done clear
  D)
  \[{{21}^{o}}\]
  done clear
  E)
  None of these
  done clear
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• question_answer20)
  The distance between the points \[(\cos \theta ,\,\,\sin \theta )\]and\[(\sin \theta ,-\cos \theta )\]is
  A)
  2                     
  done clear
  B)
  \[\sqrt{2}\]
  done clear
  C)
  1                     
  done clear
  D)
  \[\sqrt{3}\]
  done clear
  E)
  None of these
  done clear
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• question_answer21)
  Find the areas of the shaded region in the figure given below.
  A)
  \[308\,\,c{{m}^{2}}\]  
  done clear
  B)
  \[154\,\,c{{m}^{2}}\]
  done clear
  C)
  \[462\,\,c{{m}^{2}}\]  
  done clear
  D)
  \[159\,\,c{{m}^{2}}\]
  done clear
  E)
  None of these
  done clear
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• question_answer22)
  If an event cannot occur, then its probability is
  A)
  1                     
  done clear
  B)
  \[\frac{3}{4}\]
  done clear
  C)
  \[\frac{1}{2}\]              
  done clear
  D)
  0
  done clear
  E)
  None of these
  done clear
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• question_answer23)
  If the probability of an event is P. then, the probability of its complementary event will be
  A)
  \[P-1\]  
  done clear
  B)
  \[P\]
  done clear
  C)
  \[1-P\]              
  done clear
  D)
  \[1-\frac{1}{P}\]
  done clear
  E)
  None of these
  done clear
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