10th Class Mathematics Sample Paper

done Maths Olympiad Model Test Paper-16 Total Questions - 40    [Download]

• question_answer1)
  If the HCF and LCM of two numbers are 9 and 924 respectively, then find the product of two numbers.
  A)
   8216               
  done clear
  B)
   8968
  done clear
  C)
   8316   
  done clear
  D)
   8896
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer2)
  Which one of the following is an irrational number?
  A)
   \[\sqrt{225}\]               
  done clear
  B)
   \[\sqrt{625}\]
  done clear
  C)
   \[\sqrt{28672}\]
  done clear
  D)
   \[\sqrt{2304}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer3)
  The least number which when divided by 12, 15, 18 leaves the remainders 3, 6, 9 respectively is:
  A)
   181                             
  done clear
  B)
   151
  done clear
  C)
   171     
  done clear
  D)
   161
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer4)
  The zeroes of the polynomials \[6{{x}^{2}}-x-2\] are:
  A)
   \[\frac{1}{3}\,\,and\,\,\frac{2}{3}\]                   
  done clear
  B)
   \[\frac{-1}{3}\,\,and\,\,\frac{1}{2}\]  
  done clear
  C)
   \[\frac{2}{3}\,\,and\,\,\frac{-1}{2}\]
  done clear
  D)
   \[\frac{-2}{3}\,\,and\,\,\frac{1}{2}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)
  When we divide \[(9{{x}^{4}}-4{{x}^{2}}+4)\] by \[(3{{x}^{2}}+x-1),\] then the quotient is:
  A)
   \[2{{x}^{2}}+x\]                   
  done clear
  B)
   \[3{{x}^{2}}-1\]
  done clear
  C)
   \[2x+1\]                      
  done clear
  D)
   \[3{{x}^{2}}-x\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer6)
  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
  View Answer play_arrow

• question_answer7)
  Find k such that \[5x+2y=k\] and \[10x+4y=3\]has infinitely many solutions.
  A)
   \[\frac{1}{2}\]                         
  done clear
  B)
   \[\frac{2}{3}\]
  done clear
  C)
   \[\frac{3}{2}\]
  done clear
  D)
   \[\frac{4}{9}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer8)
  Find the value of k such that \[kx-y=2\] and \[6x-2y=3\] has unique solution.
  A)
   \[k=2\]            
  done clear
  B)
   \[k\ne 3\]
  done clear
  C)
   \[k=5\]            
  done clear
  D)
   \[k\ne 7\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  Sum of two numbers is 35 and their difference is 13. Find the numbers.
  A)
   32 and 3                      
  done clear
  B)
   25 and 10
  done clear
  C)
   24 and 11
  done clear
  D)
   20 and 15
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer10)
  The value of k for which the equation\[{{k}^{2}}\,{{x}^{2}}-2\,\,(2k-1)x+4=0\] have real and equal roots is:
  A)
   \[\frac{1}{2}\]                         
  done clear
  B)
   \[\frac{1}{8}\]
  done clear
  C)
   \[\frac{1}{4}\]
  done clear
  D)
   \[\frac{1}{6}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer11)
  If \[\alpha \] and \[\beta \] are the roots of the equation\[{{x}^{2}}+3x-8=0,\] then the value of \[\alpha {{\beta }^{2}}+{{\alpha }^{2}}\beta \] is:
  A)
   \[-\,4\]                         
  done clear
  B)
   2
  done clear
  C)
   1                    
  done clear
  D)
   24
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer12)
  In a garden-bed there are 23 rose plants in the first row, twenty-one in the second row, nineteen in the third row and so on. There are five plants in the last row. How many rows are there?
  A)
   10       
  done clear
  B)
   12
  done clear
  C)
   14                               
  done clear
  D)
   9
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer13)
  If \[2x,\]\[x+10,\] \[3x+2\] are in A.P, then find the value of x.
  A)
   5                                
  done clear
  B)
   7
  done clear
  C)
   9                                
  done clear
  D)
   6
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  Find the 31st term of A.P., whose 11th term is 38 and the 16th term is 73.
  A)
   182                             
  done clear
  B)
   178
  done clear
  C)
   181                             
  done clear
  D)
   183
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer15)
  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)
   6 cm   
  done clear
  B)
   7 cm
  done clear
  C)
   8 cm                           
  done clear
  D)
   9 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer16)
  Find the cost of levelling the rectangular field whose longer side is 24 m and length of its diagonal is 26 m at the rate of Rs.\[25\,per\,{{m}^{2}}\].
  A)
   Rs. 5600                      
  done clear
  B)
   Rs. 6000
  done clear
  C)
   Rs. 5400                      
  done clear
  D)
   Rs. 4800
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer17)
  Find the value of x from the figure given below, if\[ST\parallel QR\].
  A)
   2                                
  done clear
  B)
   3
  done clear
  C)
   1        
  done clear
  D)
   4
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer18)
  In an equilateral triangle the length of the altitude is 6 cm, then find the area of the triangle.
  A)
   \[6\,\sqrt{3}\,c{{m}^{2}}\]                 
  done clear
  B)
   \[4\,\sqrt{3}\,c{{m}^{2}}\]
  done clear
  C)
   \[2\,\sqrt{3}\,c{{m}^{2}}\]                 
  done clear
  D)
   \[12\,\sqrt{3}\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  The perimetre of two similar triangles are 42 cm and 63 cm respectively. If one side of first triangle is 12 cm, then find the corresponding side of other triangle.
  A)
   12 cm             
  done clear
  B)
   16 cm
  done clear
  C)
   18 cm
  done clear
  D)
   9 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer20)
  It is given that \[\Delta \,ABC\sim \Delta \,PQR\] with \[\frac{BC}{QR}=\frac{1}{3}\]. Then \[\frac{ar\,(\Delta \,PRQ)}{ar\,(\Delta \,BCA)}\] is equal to:
  A)
   9        
  done clear
  B)
   3
  done clear
  C)
   \[\frac{1}{3}\]                         
  done clear
  D)
   \[\frac{1}{9}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer21)
  In the figure given below the value of y is:
  A)
   \[135{}^\circ \]           
  done clear
  B)
   \[45{}^\circ \]
  done clear
  C)
   \[120{}^\circ \]
  done clear
  D)
   \[115{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  Find the measure of \[\angle AOB+\angle COD\] from the figure given below if ABCD is a square.
  A)
   \[60{}^\circ \]                         
  done clear
  B)
   \[180{}^\circ \]
  done clear
  C)
   \[90{}^\circ \]                         
  done clear
  D)
   \[120{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer23)
  If \[\cos A=\frac{4}{5},\] then the value of tan A is:
  A)
   \[\frac{3}{5}\]                         
  done clear
  B)
   \[\frac{3}{4}\]
  done clear
  C)
   \[\frac{4}{3}\]                         
  done clear
  D)
   \[\frac{5}{3}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer24)
  The value of \[\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}\] is:
  A)
   \[\cot \theta -cosec\theta \]         
  done clear
  B)
   \[\text{cosec}\theta +\cot \theta \]
  done clear
  C)
   \[{{\operatorname{cosec}}^{2}}\theta +{{\cot }^{2}}\theta \] 
  done clear
  D)
   \[{{(cot\theta +\operatorname{cosec}\theta )}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer25)
  An observer 1.5 m tall is 28.5 m away from a tower, the angle of elevation of the top of the tower from her eyes is \[45{}^\circ \]. What is the height of the tower?
  A)
   35 m               
  done clear
  B)
   26 m
  done clear
  C)
   30 m               
  done clear
  D)
   34 m
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer26)
  Find the coordinates of the mid-point of the line segment joining the points \[A\,\,\left( -\,4,\text{8} \right)\] and \[B\,\,\left( 6,-\,16 \right)\].
  A)
   \[(4,-\,\,2)\]                   
  done clear
  B)
   \[(1,-\,\,6)\]
  done clear
  C)
   \[(1,-\,\,4)\]
  done clear
  D)
   \[(-\,\,3,4)\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer27)
  Find the coordinate of centroid of a triangle ABC whose vertices are A (1, 2), B (0, 6) and C (3, 3).
  A)
   \[\left( \frac{4}{3},5 \right)\]                  
  done clear
  B)
   \[(0,3)\]
  done clear
  C)
   \[\left( 2,\frac{11}{3} \right)\]                 
  done clear
  D)
   \[\left( \frac{4}{3},\frac{11}{3} \right)\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  Find the equation of the line passing through the points \[A\,\,\left( 3,-\,2 \right)\] and \[B\,\,\left( -\,1,\,\,4 \right)\].
  A)
   \[3x+2y=-13\]
  done clear
  B)
   \[3x-2y=13\]
  done clear
  C)
   \[3x-2y=-5\]                 
  done clear
  D)
   \[3x+2y=5\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer29)
  The value of \[2{{\sin }^{2}}\frac{3\pi }{4}+2{{\cos }^{2}}\frac{\pi }{4}+2{{\sec }^{2}}\frac{\pi }{3}\] is given by:
  A)
   1                                
  done clear
  B)
   5
  done clear
  C)
   10       
  done clear
  D)
   8
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer30)
  There are 20 tickets numbered from 1, 2, 3,..., 20 respectively. One ticket is drawn at random, what is the probability that the number on the ticket is a multiple of 3 or 5?
  A)
   \[\frac{1}{4}\]                         
  done clear
  B)
   \[\frac{9}{20}\]
  done clear
  C)
   \[\frac{2}{5}\]             
  done clear
  D)
   \[\frac{4}{10}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer31)
  If \[P\,\,\left( -\,3,2 \right),\] \[Q\,\,\left( -\,5,-\,5 \right),\] \[R\,\,\left( 2,-3 \right)\] and \[S\,\,\left( 4,\,\,4 \right)\] are the vertices of a quadrilateral, then the quadrilateral will be a:
  A)
   Rectangle                     
  done clear
  B)
   Trapezium
  done clear
  C)
   Rhombus         
  done clear
  D)
   Kite
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer32)
  The median of first five prime numbers is:
  A)
   5        
  done clear
  B)
   6
  done clear
  C)
   7                                
  done clear
  D)
   4
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer33)
  If the mode of a given data is 45 and mean is 27, then the median is:
  A)
   30                               
  done clear
  B)
   27
  done clear
  C)
   33       
  done clear
  D)
   41
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer34)

  Find x if mode of the following data is 25.

  15, 20, 25, 18, 14, 15, 25, 15, 18, 16, 20, 25, 20, x, 18

  A)
   22                               
  done clear
  B)
   25
  done clear
  C)
   27                               
  done clear
  D)
   29
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer35)
  The probability of getting a number between and 100 which is divisible by 1 and itself only is:
  A)
   \[\frac{29}{98}\]                                  
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   \[\frac{25}{98}\]          
  done clear
  D)
   \[\frac{23}{98}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer36)
  A bag contains 4 white balls, 6 red balls, 7 black balls and 3 blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is neither white nor black?
  A)
   \[\frac{11}{20}\]                                  
  done clear
  B)
   \[\frac{9}{20}\]
  done clear
  C)
   \[\frac{1}{2}\]                         
  done clear
  D)
   \[\frac{13}{20}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer37)
  In 56, 63, 70, .......,497 series. How many terms are there?
  A)
   56                               
  done clear
  B)
   46
  done clear
  C)
   64       
  done clear
  D)
   68
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer38)
  The sum of the numerator and denominator of a fraction is 8. If 3 is added to both the numerator and denominator, the fraction becomes \[\frac{3}{4}\]. Find the fraction.
  A)
   \[\frac{4}{5}\]                         
  done clear
  B)
   \[\frac{3}{5}\]
  done clear
  C)
   \[\frac{1}{7}\]                         
  done clear
  D)
   \[\frac{2}{7}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer39)

  Directions: Base on the following directions

  A man is facing North and turned to his right at an angle of \[180{}^\circ ,\] again he turned right at an angle of \[90{}^\circ \]. In which direction is he now?
  A)
   East                            
  done clear
  B)
   North
  done clear
  C)
   West   
  done clear
  D)
   South
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer40)

  Directions: Base on the following directions

  A, B, C, and D are playing cards. B is sitting in front of D. A is sitting to the right of D, facing C. D is facing South. Which direction is C facing?
  A)
   East                            
  done clear
  B)
   West
  done clear
  C)
   North              
  done clear
  D)
   South
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow