10th Class Mathematics Sample Paper

done Maths Olympiad Model Test Paper-1 Total Questions - 40    [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
  View Answer play_arrow

• question_answer2)
  In a school, there are two sections A and B in which 32 students are in section A and 36 students are in section B. What is the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B.
  A)
   280                             
  done clear
  B)
   290
  done clear
  C)
   288     
  done clear
  D)
   295
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer3)
  A rectangular field is 1872 cm long and 1320 cm broad. It is to be paved with square tiles of the same size. Find the least possible numbers of such tiles.
  A)
   4250               
  done clear
  B)
   4290
  done clear
  C)
   4225                           
  done clear
  D)
   4195
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer4)
  If \[\alpha \] and \[\beta \] are the zeroes of the polynomial\[f(x)={{x}^{2}}-px+q,\]then find the value of\[{{\alpha }^{2}}+{{\beta }^{2}}\].
  A)
   \[{{p}^{2}}+q\]                    
  done clear
  B)
   \[{{p}^{2}}-2q\]
  done clear
  C)
   \[{{p}^{2}}+{{q}^{2}}\]                 
  done clear
  D)
   \[{{p}^{2}}-5q\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)
  If \[\alpha \] and \[\beta \] are roots of the polynomial\[p(s)=3{{s}^{2}}-6s+4,\] then find the value of\[\frac{\alpha }{\beta }+\frac{\beta }{\alpha }+2\,\,\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)+3\alpha \beta \].
  A)
   8        
  done clear
  B)
   2
  done clear
  C)
   6                                
  done clear
  D)
   0
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer6)
  If 5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46, find the cost of one pen.
  A)
   Rs. 5   
  done clear
  B)
   Rs. 6
  done clear
  C)
   Rs. 2                           
  done clear
  D)
   Rs. 4
  done clear
  E)
   None of these.
  done clear
  View Answer play_arrow

• question_answer7)
  Solve: \[\frac{x}{a}+\frac{y}{b}=a+b\] and \[\frac{x}{{{a}^{2}}}+\frac{y}{{{b}^{2}}}=2\]  
  A)
   \[x={{a}^{2}}\,\,and\,\,y={{b}^{2}}\]
  done clear
  B)
   \[x=1\,\,and\,\,y=ab\]
  done clear
  C)
   \[x=a\,\,and\,\,y={{b}^{2}}\]
  done clear
  D)
   \[x={{a}^{2}}\,\,and\,\,y=b\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer8)
  For what value of a will the equations \[x+2y+7=0\] and \[2x+ay+14=0\] represent coincident lines?
  A)
   4
  done clear
  B)
   5
  done clear
  C)
   0                                
  done clear
  D)
   2
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  If twice the son's age in years is added to the father's age, the sum becomes 70. But if twice the father's age is added to the son's age, the sum is 95. Find the age of son.
  A)
   15 years          
  done clear
  B)
   20 years
  done clear
  C)
   17 years                      
  done clear
  D)
   12 years
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer10)
  The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, area is increased by 67 square units. The length and breadth of the rectangle are respectively:
  A)
   15 units and 9 units
  done clear
  B)
   17 units and 9 units
  done clear
  C)
   20 units and 7 units       
  done clear
  D)
   17 units and 5 units
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer11)
  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)
   \[\frac{1}{4}\,\,or\,4\]               
  done clear
  D)
   \[\frac{3}{4}\,\,or\,\,\frac{4}{3}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer12)
  One - fourth of a herd of camels were seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the number of camels.
  A)
   24                               
  done clear
  B)
   49
  done clear
  C)
   36
  done clear
  D)
   64
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer13)
  A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B alone to finish the work.
  A)
   25 days                       
  done clear
  B)
   27 days
  done clear
  C)
   32 days                       
  done clear
  D)
   30 days
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  If mth term of an A.P. is \[\frac{1}{n}\] and nth term is \[\frac{1}{m}\] then find its (mn)th term:
  A)
   2                                
  done clear
  B)
   \[-\,1\]
  done clear
  C)
   0                                
  done clear
  D)
   1
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer15)
  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_answer16)
  Find the 31st term of A.P., if its 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_answer17)
  What will be the A.P look like whose 3rd term is 16 and 7th term exceeds the 5th term by 12?
  A)
   4, 8, 12, 16.......           
  done clear
  B)
   3, 6, 9, 12......
  done clear
  C)
   2, 4, 6, 8......               
  done clear
  D)
   4, 10, 16, 22......
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer18)
  The radii of two spheres are in the ratio 1 : 2. Find the ratio of their surface areas.
  A)
   1 : 4    
  done clear
  B)
   2 : 3
  done clear
  C)
   5 : 4                            
  done clear
  D)
   6 : 1
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  A chord AB of a circle of radius 9 cm makes a right angle at the centre of the circle. Find the area of major segment of the circle.
  A)
   \[231.43\,c{{m}^{2}}\]                       
  done clear
  B)
   \[254.34\,c{{m}^{2}}\]
  done clear
  C)
   \[190.93\,c{{m}^{2}}\]                       
  done clear
  D)
   \[63.585\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer20)
  In a bullet gun powder is to be filled into a metallic enclosure. The metallic enclosure is made up of a cylindrical base and a conical top, each having a radius of 5 cm. If the ratio of the height of the cylindrical part to that of the conical part is 3 : 2, then the ratio of their volumes will be:
  A)
   3 : 4                            
  done clear
  B)
   9 : 2
  done clear
  C)
   7 : 8                            
  done clear
  D)
   9 : 11
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer21)
  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)
   \[48\,c{{m}^{2}}\]                 
  done clear
  B)
   \[42\,c{{m}^{2}}\]
  done clear
  C)
   \[36\,c{{m}^{2}}\]                 
  done clear
  D)
   \[56\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  If \[\Delta \,ABC\sim \Delta \,QRP\] and AB = 6 cm, BC = 4 cm, AC = 8 cm, QR = 6 cm, then PQ + QR is equal to:
  A)
   9 cm                           
  done clear
  B)
   14 cm
  done clear
  C)
   7.5 cm            
  done clear
  D)
   12 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer23)
  A vertical stick 12 m long casts a shadow 8 m long on the ground. At the same time, a tower casts the shadow 40 m long on the ground. Find the height of the tower.
  A)
   55 m               
  done clear
  B)
   51 m
  done clear
  C)
   60 m
  done clear
  D)
   62 m
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer24)
  From the figure given below find the length of QR, if\[\Delta \,ABR\sim \Delta \,PQR\].
  A)
   4.1 cm
  done clear
  B)
   4.5 cm
  done clear
  C)
   5.3 cm            
  done clear
  D)
   6.4 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer25)
  If angle subtended by two tangents at the centre with the radii drawn through their point of contacts is \[130{}^\circ \], then find the angle subtended between these tangents outside the circle.
  A)
   \[55{}^\circ \]                         
  done clear
  B)
   \[50{}^\circ \]
  done clear
  C)
   \[45{}^\circ \]                         
  done clear
  D)
   \[65{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer26)
  Two circles intersect at M and N. IMNK and MNLJ are the quadrilaterals inscribed in the two circles as shown in the figure given below. If \[\angle I=95{}^\circ ,\] and \[\angle K=65{}^\circ ,\] then the values of x and y are respectively:
  A)
   \[65{}^\circ \,\,and\,\,135{}^\circ \]     
  done clear
  B)
   \[85{}^\circ \,\,and\,\,115{}^\circ \]
  done clear
  C)
   \[55{}^\circ \,\,and\,\,145{}^\circ \]     
  done clear
  D)
   \[75{}^\circ \,\,and\,\,125{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer27)
  In a right angled triangle ABC, \[\angle B\]is right angle side AB is half of the hypotenuse. AE is parallel to median BD and CE is parallel to BA. What is the ratio of length of BC to that of EC?
  A)
   \[\sqrt{2}:1\]                
  done clear
  B)
   \[\sqrt{3}:2\]
  done clear
  C)
   \[\sqrt{5}:\sqrt{3}\]                   
  done clear
  D)
   \[\sqrt{3}:4\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  If \[\cos \,(\alpha +\beta )=0\] and \[\sin \,(\alpha -\beta )=\frac{1}{2},\] then find the value of\[\frac{\cos 2\beta }{\sin \,(\alpha /2)}\].
  A)
   0                                
  done clear
  B)
   1
  done clear
  C)
   \[-\,1\]                         
  done clear
  D)
   4
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer29)
  If \[\sin \,A+{{\sin }^{2}}\text{A}=1,\] then \[(co{{s}^{2}}A+{{\cos }^{4}}A)\]  is equal to:
  A)
   1        
  done clear
  B)
   \[\frac{1}{2}\]
  done clear
  C)
   2                                
  done clear
  D)
   3
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer30)
  If q is an acute angle such that \[{{\tan }^{2}}q=\frac{8}{7},\] then the value of \[\frac{(1+sin\theta )(1-sin\theta )}{(1+cos\theta )(1-cos\theta )}\]  is:
  A)
   \[\frac{7}{8}\] 
  done clear
  B)
   \[\frac{8}{7}\]
  done clear
  C)
   \[\frac{7}{4}\]                         
  done clear
  D)
   \[\frac{64}{49}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer31)
  The shadow of a tower standing on a level ground is found to be 40 m longer when Sun's altitude is \[30{}^\circ \] than when it was \[60{}^\circ \]. What is the height of the tower?
  A)
   \[15\,\sqrt{3}m\]                       
  done clear
  B)
   \[20\,\sqrt{3}m\]
  done clear
  C)
   \[20\,\sqrt{3}m\]                       
  done clear
  D)
   \[18\,\sqrt{3}m\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer32)
  Find the lengths of the median AD of the \[\Delta \,ABC\]whose vertices are A (7, 3), B (5, 3) and \[C\,\,\left( 3,-1 \right),\] where D is the mid-point of the side BC.
  A)
   \[\sqrt{5}\]                               
  done clear
  B)
   \[\sqrt{6}\]
  done clear
  C)
   \[\sqrt{13}\]     
  done clear
  D)
   3
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer33)
  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)
   \[{{\tan }^{-1}}\left( \frac{2}{9} \right)\]          
  done clear
  D)
   \[\sqrt{3}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer34)
  If the point (x, y) is equidistant from (4, 3) and (0, 3), then the value of x is:
  A)
   2
  done clear
  B)
   4
  done clear
  C)
   5                                
  done clear
  D)
   3
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer35)
  If \[\sum{{{f}_{i}}{{x}_{i}}=35,}\] \[\sum{{{f}_{i}}=4p-63}\] and mean = 7, then p is equal to:
  A)
   12                               
  done clear
  B)
   13
  done clear
  C)
   14                               
  done clear
  D)
   17
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer36)
  What is the median of the following distribution:

  x	1	2	3	4	5	6	7	8	9
  f	8	10	11	16	20	25	15	9	6

  A)
   5
  done clear
  B)
   6
  done clear
  C)
   4                                
  done clear
  D)
   2
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer37)
  There are twenty books in a library numbered 61 to 80 on their cover page. What is the probability of getting a book having a multiple 8 or a prime number on its cover page?
  A)
   \[\frac{1}{5}\]                         
  done clear
  B)
   \[\frac{2}{5}\]
  done clear
  C)
   \[\frac{3}{80}\]                        
  done clear
  D)
   \[\frac{1}{10}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer38)
  There are fifteen horses in a stable, of which 5 are black, 2 are red, 6 are white and 2 are of mixed colors. All the black and mixed color horses are hybrid. If one horse is chosen at random, find that it is a hybrid horse.
  A)
   \[\frac{9}{15}\]                        
  done clear
  B)
   \[\frac{1}{5}\]
  done clear
  C)
   \[\frac{7}{15}\]
  done clear
  D)
   \[\frac{1}{3}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer39)
  Katherine studies in a senior secondary school. A math test was conducted as a part of monthly routine and she scores 50 marks, getting 4 marks for each correct answer and losing 2 marks for each wrong answer. Had she been awarded 5 marks for each correct answer and deducted 3 marks for each wrong answer, she would have scored 60 marks. The total number of questions in the test was
  A)
   25                               
  done clear
  B)
   5
  done clear
  C)
   15                               
  done clear
  D)
   20
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer40)
  If \[\alpha ,\] \[\beta ,\] \[\gamma \] are the roots of the equation\[{{z}^{3}}-4z+2=0,\] then the value of \[(\alpha -3)\]\[(\beta -3)\]\[(\gamma -3)\] is given by:
  A)
   \[-\,9\]                         
  done clear
  B)
   \[-\,14\]
  done clear
  C)
   \[-\,12\]                        
  done clear
  D)
   \[-\,17\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow