8th Class Mathematics Sample Paper

done Maths Olympiad Model Test Paper-19 Total Questions - 50    [Download]

• question_answer1)
  Which one among the following pair of numbers are co-prime?
  A)
   204 and 189                
  done clear
  B)
   444 and 203
  done clear
  C)
   319 and 407                
  done clear
  D)
   221 and 143
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer2)
  A number is formed by repeating a three digit number. For example, 567567 or 234234 etc. Any number of this form is always exactly divisible by _______.
  A)
   1001    
  done clear
  B)
   17
  done clear
  C)
   13 only                        
  done clear
  D)
   11 only
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer3)
  The greatest five digit number exactly divisible by 7 and 23 both is_______.
  A)
   99995             
  done clear
  B)
   99981
  done clear
  C)
   99974             
  done clear
  D)
   99988
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer4)
  By what number should \[{{\left( \frac{1}{27} \right)}^{\frac{-1}{2}}}\] be multiplied so that its product becomes \[{{\left( \frac{8}{11} \right)}^{\frac{-1}{2}}}\]?
  A)
   \[\frac{\sqrt{66}}{36}\]
  done clear
  B)
   \[\frac{\sqrt{66}}{18}\]
  done clear
  C)
   \[\frac{\sqrt{44}}{22}\]            
  done clear
  D)
   \[\frac{\sqrt{22}}{44}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)
  Solve: \[\frac{{{(320)}^{2}}-{{(310)}^{2}}}{63}\].
  A)
   1                                
  done clear
  B)
   10
  done clear
  C)
   100     
  done clear
  D)
   1000
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer6)
  Which one of the following statements is true?
  A)
   \[\sqrt[3]{5832}\]is equal to 28
  done clear
  B)
   If\[{{2}^{m}}=1024,\]then \[{{2}^{m-4}}=32\]
  done clear
  C)
   The LCM of the least two digit number and the greatest two digit number is 990
  done clear
  D)
   All of the above
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer7)
  One of the factors of \[6-m-2{{m}^{2}}\] is________.
  A)
   \[(m+6)\]                     
  done clear
  B)
   \[(2m+3)\]
  done clear
  C)
   \[(-2m+3)\]
  done clear
  D)
   \[(-2m+6)\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer8)
  Cost of two chairs and three tables is Rs. 3320, while the cost of one chair and two tables is Rs. 2020. Find the cost of each chair.
  A)
   Rs. 680            
  done clear
  B)
   Rs. 620
  done clear
  C)
   Rs. 580
  done clear
  D)
   Rs. 720
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  If \[a+\frac{2}{a}=1,\]then find the value of \[\frac{{{a}^{2}}+a+2}{{{a}^{2}}(1-a)}\].
  A)
   \[2\]                            
  done clear
  B)
   \[-1\]
  done clear
  C)
   \[1\]    
  done clear
  D)
   \[-2\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer10)
  What must be added to the following expression to make it a perfect square? \[\frac{3{{x}^{2}}}{16}+\frac{23}{9}-\frac{\sqrt{78}x}{3}\]
  A)
   \[\frac{1}{3}\]                         
  done clear
  B)
   \[\frac{13}{9}\]
  done clear
  C)
   \[8\]                            
  done clear
  D)
   \[9\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer11)
  48 women can do a piece of work in 18 days. How many women would be required to do the same work in 24 days?
  A)
   42                               
  done clear
  B)
   36
  done clear
  C)
   28                               
  done clear
  D)
   32
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer12)
  Two numbers p and q are in the ratio \[\frac{3}{4}:\frac{4}{3},\] respectively. By what percent is q more than p?
  A)
  \[152.\overline{8}\]%            
  done clear
  B)
  \[122.\overline{2}\]%
  done clear
  C)
  \[120\]%         
  done clear
  D)
  \[135\]%
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer13)
  If \[p:q=4:5,\] \[q:r=6:7\] and \[r:s=3:4,\]then on dividing Rs. 7733 among p, q, r and \[s\],the amount of q will be
  A)
  Rs. 1710
  done clear
  B)
  Rs. 1468
  done clear
  C)
  Rs. 1620            
  done clear
  D)
  Rs. 1805
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer14)
  Prabhav borrowed a sum of Rs. 2500 from Rishabh at the simple rate of 6 p.c.p.a. for 3 years. He then added some more money to the borrowed sum and lent it to Rishabh for the same time at 8 p.c.p.a. at simple interest. If Prabhav gains Rs. 438 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum (in Rs.) lent by him to Rishabh?
  A)
   2700               
  done clear
  B)
   3300
  done clear
  C)
   3700   
  done clear
  D)
   3900
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer15)

  Direction : Study the pie charts carefully to answer the questions that follow:

  What is the number of girls in school R?
  A)
   160                             
  done clear
  B)
   260
  done clear
  C)
   360                             
  done clear
  D)
   460
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer16)

  Direction : Study the pie charts carefully to answer the questions that follow:

  What is the total number of boys from schools P and T together?
  A)
   904     
  done clear
  B)
   824
  done clear
  C)
   924                             
  done clear
  D)
   804
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer17)

  Direction : Study the pie charts carefully to answer the questions that follow:

  The number of girls from school Q form what percent of total number of students from that school? (Rounded off to two digits after decimal)
  A)
   68.37              
  done clear
  B)
   71.43
  done clear
  C)
   70.21              
  done clear
  D)
   74.28
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer18)

  Direction : Study the pie charts carefully to answer the questions that follow:

  What is the respective ratio of boys and girls in the school S?
  A)
   74 : 115          
  done clear
  B)
   15 : 23
  done clear
  C)
   37 : 58            
  done clear
  D)
   19 : 29
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  Teacher gives some notebooks to Robert and Thomas and asked them to share among themself in the ratio\[9:7\]. If Robert gets 16 notebooks more than Thomas, then find the number of notebooks given by the teacher to them.
  A)
   112                             
  done clear
  B)
   122
  done clear
  C)
   118                             
  done clear
  D)
   128
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer20)
  The difference between the C.I. and S.I. on a certain sum for 2 years at 7.5% p.a. is Rs. 360. The sum is_______.
  A)
   Rs. 640            
  done clear
  B)
   Rs. 6400
  done clear
  C)
   Rs. 64,000       
  done clear
  D)
   Rs. 5400
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer21)
  Find the area of the shaded region given in the figure of a circle of radius 4 cm with centre O.
  A)
   \[2\pi \,\,c{{m}^{2}}\]
  done clear
  B)
   \[3\pi \,\,c{{m}^{2}}\]
  done clear
  C)
   \[4\pi \,\,c{{m}^{2}}\]                        
  done clear
  D)
   \[\pi \,\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  In a rectangle, if the difference between the sum of the adjacent sides and the diagonal is \[\frac{2}{5}\] of the length of the longer side, what is the ratio of the shorter to the longer side?
  A)
   \[3:4\]              
  done clear
  B)
   \[8:15\]
  done clear
  C)
   \[5:12\]            
  done clear
  D)
   \[7:24\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer23)
  For any two non-empty sets P and Q, if \[P-Q=P\] and \[Q-P=Q,\] then _______.
  A)
   \[(P\cup Q)'=\phi \]                   
  done clear
  B)
   \[P\cap Q=\phi \]
  done clear
  C)
   \[P\subset Q\]               
  done clear
  D)
   \[Q\subset P\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer24)
  If \[n\,\,(A\times B)-52,\] \[n\,\,(B\times C)=68\]and \[n\,\,(B)=4,\], then \[n\,\,(A\times C)=?\]
  A)
   118                             
  done clear
  B)
   121
  done clear
  C)
   221     
  done clear
  D)
   218
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer25)
  A set of concentric squares are shown in the figure given below. If the side of the innermost square is \[\sqrt{2}\,\,m,\]and if the distance between the corresponding corners of any two successive squares is 1 m, then find the difference between the areas of the eighth and the seventh square, counting from the innermost square.
  A)
   \[30\,\,{{m}^{2}}\]    
  done clear
  B)
   \[25\,\,\sqrt{2}\,\,{{m}^{2}}\]
  done clear
  C)
   \[35\,\,{{m}^{2}}\]                
  done clear
  D)
   \[20\,\sqrt{2}\,{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer26)
  In a class of 60 students, 35 students have passed in English and 42 students have passed in Mathematics. Then the number of students who have passed in Mathematics only is _______.
  A)
   15                               
  done clear
  B)
   20
  done clear
  C)
   25
  done clear
  D)
   30
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer27)
  In a cricket team of 11 players, 8 players were at least 21 years old and 6 players were almost 32 years old. The ages of how many players were from 21 years to 32 years (both inclusive)?
  A)
   1                                
  done clear
  B)
   2
  done clear
  C)
   3        
  done clear
  D)
   4
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  A cube has a total surface area of \[432\,\,c{{m}^{2}}\]. Find the height of the cube (in cm).
  A)
   \[3\,\sqrt{2}\]               
  done clear
  B)
   \[4\,\sqrt{2}\]
  done clear
  C)
   \[5\,\sqrt{2}\]               
  done clear
  D)
   \[6\,\sqrt{2}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer29)
  Find the number of coins, 4 cm in diameter and 2 cm in thickness to be melted to form a right circular cylinder of height 10 cm and diameter 8 cm.
  A)
   10                               
  done clear
  B)
   12
  done clear
  C)
   15       
  done clear
  D)
   18
  done clear
  E)
   16
  done clear
  View Answer play_arrow

• question_answer30)
  At what rate of percent per annum at compound interest will the sum of Rs. 625 amount to Rs. 1715 in 3 years?
  A)
   25                               
  done clear
  B)
   20
  done clear
  C)
   40       
  done clear
  D)
   30
  done clear
  E)
   None of these   
  done clear
  View Answer play_arrow

• question_answer31)
  Raman is driving towards West. What sequence of directions should he follow to drive towards South?
  A)
   Left, Right, Right           
  done clear
  B)
   Right, Left, Right
  done clear
  C)
   Right, Right, Right
  done clear
  D)
   Left, Left, Left
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer32)
  If in a certain language, FASHION is coded as FOIHSAN, how is PROBLEM coded in that code?
  A)
   PELBROM                   
  done clear
  B)
   PRBOELM
  done clear
  C)
   PELBORM       
  done clear
  D)
   RPBOELM
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer33)
  If \['M+N'\] means \['M'\] is the brother of \[N'\] \['M-N'\] means \['M'\]is the sister of \[N'\], \['M\times N'\] means \['M'\] is the mother of \[N'\]and \['M\div N'\] means \['M'\] is father of \[N'\], then which of the following would mean \['E\] is the paternal aunt of \[F'\]?
  A)
   \[E-G\div F\]
  done clear
  B)
   \[E+G\times F\]
  done clear
  C)
   \[E\times F-G\]              
  done clear
  D)
   \[F\times G+E\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer34)
  Deepak ranks seventh from the top and twenty eight from the bottom in a class. How many students are there in the class?
  A)
   37                               
  done clear
  B)
   36
  done clear
  C)
   35                               
  done clear
  D)
   34
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer35)
  How many 6's are there in the following number sequence which are immediately preceded by 9 but not immediately followed by 4? 5 6 4 3 2 9 6 3 1 6 4 9 6 4 2 1 5 9 6 7 2 1 4 7 4 9 6 4 2
  A)
   One                            
  done clear
  B)
   Two
  done clear
  C)
   Three              
  done clear
  D)
   Four
  done clear
  E)
   More than four
  done clear
  View Answer play_arrow

• question_answer36)
  Insert the missing number in place of the question mark (?).
  A)
   23                               
  done clear
  B)
   25
  done clear
  C)
   27                               
  done clear
  D)
   21
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer37)
  A detective agency uses a certain code to represent their mission to its employees. If some of the codes used by them are SAT = 154, SET = 134, TEN = 231, respectively, then what digit will represent the code "SEA" in their language?
  A)
   342                             
  done clear
  B)
   534
  done clear
  C)
   431                             
  done clear
  D)
   413
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer38)

  The numbers are arranged in the diagram as shown below:

  If the number in any box is equal to the sum of the numbers in the boxes immediately below it, like \[X=a+b,\] \[a=c+24\] and so on. Find the value of\['X'\].

  A)
   100                             
  done clear
  B)
   64
  done clear
  C)
   88       
  done clear
  D)
   90
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer39)
  If \['\times '\] means 'added to', \['\div '\] means 'multiplied by', \['+'\]means ?subtracted from' and \['-'\] means ?divided by', then \[48+72-24\times 16\div 8=\] ?
  A)
   72                               
  done clear
  B)
   173
  done clear
  C)
   153                             
  done clear
  D)
   148
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer40)
  Which should be the fifth letter to the right of 16th letter from the right end? A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
  A)
   N                                
  done clear
  B)
   M
  done clear
  C)
   P        
  done clear
  D)
   Q
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer41)
  If \[p+q+r=0,\]then find the value of \[\frac{{{p}^{2}}+{{q}^{2}}+{{r}^{2}}}{{{p}^{2}}-qr}\].
  A)
   \[-\,2\]                         
  done clear
  B)
   1
  done clear
  C)
   2        
  done clear
  D)
   \[-\,1\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer42)
  How many ways are possible to choose a white square and black square on a chessboard so that the squares must not lie in the same row or column?
  A)
   768                 
  done clear
  B)
   576
  done clear
  C)
   512                             
  done clear
  D)
   1024
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer43)
  When 27 is divided by x, the remainder is\[x-3\]. If \[x\] must be an integer, what are all the possible values of\[x\]?
  A)
   4                    
  done clear
  B)
   5
  done clear
  C)
   6  
  done clear
  D)
   7
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer44)
  Which one of the following is correct for the given statements?

  Statement I: \[{{37}^{24}}>{{124}^{16}}\]

  Statement II: \[{{50}^{18}}<{{210}^{12}}\]

  Statement III: \[12344\times 12350>{{(12347)}^{2}}\]

  A)
   Only statement I is true
  done clear
  B)
   Only statements I and II are true
  done clear
  C)
   All the statements I, II and III are true
  done clear
  D)
   Only statement II is true
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer45)
  If n is the smallest positive integer such that for any integer \[m\ge n,\] the quantity \[{{m}^{3}}-7{{m}^{2}}+11m-5\] is positive, then what is the value of n?
  A)
   3                                
  done clear
  B)
   5
  done clear
  C)
   7                                
  done clear
  D)
   9
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer46)

  Consider the figure given below:

  If b = 10, then find the value of a.

  A)
   9                                
  done clear
  B)
   11
  done clear
  C)
   14                               
  done clear
  D)
   16
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer47)
  In how many ways 1105 can be expressed as the sum of two squares of natural numbers?
  A)
   1                                
  done clear
  B)
   2
  done clear
  C)
   3                                
  done clear
  D)
   4
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer48)
  If P is an integer between 1 and 9,\[R-P=16229\]and R is divisible by 11, then find the value \[\frac{P+R-1}{3}\].
  A)
   5014               
  done clear
  B)
   4514
  done clear
  C)
   5414
  done clear
  D)
   5114
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer49)
  If p, q, r and s are four different positive integers selected from 1 to 200, then find the highest possible value of\[\frac{(p+q)+(r+s)}{(p+q)+(r-s)}.\]
  A)
   201                             
  done clear
  B)
   251
  done clear
  C)
   401     
  done clear
  D)
   451
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer50)
  Find the least number of cuts required which can cut a cube into 60 identical pieces?
  A)
   9        
  done clear
  B)
   12
  done clear
  C)
   15                               
  done clear
  D)
   5
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow