7th Class Mathematics Sample Paper

done Maths Olympiad Model Test Paper-8 Total Questions - 40    [Download]

• question_answer1)
  A tree is situated on the bank of river and its one branch is \[25\,\,\frac{2}{3}\] m above the water level of the river. A monkey is sitting on the branch and see the image of itself. Find the distance between the monkey and its image (suppose the surface of the water act like a plane mirror).
  A)
   50.33 m                      
  done clear
  B)
   51.33 m
  done clear
  C)
   25.66 m                      
  done clear
  D)
   30.66 m
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer2)
  If X and Y are two positive integers such that \[X>Y\] and P, Q are the multiplicative inverse of X and Y respectively, then which one of the following is a value of\[PY+QX\]?
  A)
   \[\frac{{{P}^{2}}+{{Q}^{2}}}{P+Q}\]                   
  done clear
  B)
   \[\frac{{{X}^{2}}+{{Y}^{2}}}{X+Y}\]
  done clear
  C)
   \[\frac{{{X}^{2}}+{{Y}^{2}}}{X\,Y}\]
  done clear
  D)
   \[\frac{{{P}^{2}}+{{Y}^{2}}}{Q\,Y}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer3)
  Anderson tries to use bracket for a mathematical expression "fifty one divided by the product of twelve and the difference between thirty six and fourteen". The correct representation is :
  A)
   \[51\div 12\times \left( 36-14 \right)\]
  done clear
  B)
   \[51\div \{12\times 36-14\}\]
  done clear
  C)
   \[51\div \{12\times (36-14)\}\]
  done clear
  D)
   \[\{51\div 12\}\times \{36-14\}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer4)
  The diametre of a circular park is 42 m. A 2.1 m wide road runs inside it. Find the cost of constructing the road at Rs. 50 per \[{{m}^{2}}\].
  A)
   Rs. 13206                    
  done clear
  B)
   Rs. 14216
  done clear
  C)
   Rs. 14206                    
  done clear
  D)
   Rs. 13167
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)
  Distance between \[-\,3\] and \[-\,7\] on the number line is:
  A)
   6 units             
  done clear
  B)
   2 units
  done clear
  C)
   4 units 
  done clear
  D)
   8 units
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer6)
  In the given figure, if POQ is a straight line then \[\angle POT\]is equal to :
  A)
   \[144{}^\circ \]           
  done clear
  B)
   \[45{}^\circ \]
  done clear
  C)
   \[68{}^\circ \]                         
  done clear
  D)
   \[33{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer7)
  On solving \[3\,\,\frac{5}{9}\,\,\times \,\,81\,\,\times \,\,\frac{17}{16}\] to its simplified form, we get:
  A)
   306     
  done clear
  B)
   316
  done clear
  C)
   206                             
  done clear
  D)
   305
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer8)
  Jasmine spends \[\frac{1}{4}\]th of her income on household articles and \[\frac{1}{5}\]th of the remaining income on her personal expenses. If her monthly income is Rs. 50,000 then her monthly savings is:
  A)
   \[\frac{2}{5}\] of her income
  done clear
  B)
   \[\frac{2}{5}\] of her remaining income
  done clear
  C)
   \[\frac{3}{5}\] of her monthly income
  done clear
  D)
   \[\frac{11}{20}\] of her income
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  We know that light year is the distance travelled by light in one year and the speed of light is \[3\times {{10}^{8}}\] metre per second. Express one light year into kilometre.
  A)
   \[9.46\times {{10}^{12}}\,km\]
  done clear
  B)
   \[9.46\times {{10}^{18}}\,km\]
  done clear
  C)
   \[9.46\times {{10}^{15}}\,km\]
  done clear
  D)
   \[9.46\times {{10}^{13}}\,km\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer10)
  Simplify:\[\frac{{{(0.99)}^{3}}+{{(0.98)}^{3}}}{0.99\times 0.99-0.99\times 0.98+0.98\times 0.98}\].
  A)
   1.85                            
  done clear
  B)
   1.97
  done clear
  C)
   2.15                            
  done clear
  D)
   0.97
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer11)
  Find the length of the side of a square in which an equilateral triangle is formed, as shown in the figure given below, whose perimeter is \[3\,\,\frac{12}{17}\]m
  A)
   \[3\,\,\frac{12}{17}\,\,m\]                     
  done clear
  B)
   \[\frac{412}{57}\,m\]
  done clear
  C)
   \[1\,\,\frac{4}{17}\,m\] 
  done clear
  D)
   \[\frac{57}{216}\,m\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer12)
  The real numbers are either rational or irrational. The irrational numbers are the numbers which are non - terminating and non - repeating. Identify the numbers given below as non - terminating and non - repeating.
  A)
   \[\frac{1}{7}\]                         
  done clear
  B)
   \[\frac{4}{5}\]
  done clear
  C)
   \[\frac{5}{2}\]                         
  done clear
  D)
   \[\frac{\sqrt{216}}{3}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer13)
  What number must be added to\[\left( -\frac{7}{8} \right)\] get \[\frac{4}{9}\]?
  A)
   \[\frac{95}{72}\]          
  done clear
  B)
   \[\frac{17}{62}\]
  done clear
  C)
   \[\frac{71}{63}\]                                  
  done clear
  D)
   \[\frac{81}{73}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  Find the value of \[x\] in the following figure if \[AD\bot BC\] and AE is the bisector of\[\angle BAC\].
  A)
   \[30{}^\circ \]                         
  done clear
  B)
   \[20{}^\circ \]
  done clear
  C)
   \[10{}^\circ \] 
  done clear
  D)
   \[60{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer15)
  Simplify: \[{{\left( \frac{{{x}^{-3}}}{{{y}^{2}}} \right)}^{-3}}{{\left( \frac{{{x}^{-3}}}{{{y}^{5}}} \right)}^{2}}\]
  A)
   \[\frac{1}{{{y}^{2}}}\]                                  
  done clear
  B)
   \[\frac{1}{{{y}^{4}}}\]
  done clear
  C)
   \[\frac{{{x}^{2}}}{{{y}^{3}}}\]                              
  done clear
  D)
   \[\frac{{{x}^{3}}}{{{y}^{4}}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer16)
  Evaluate: \[{{\left[ {{\left( \sqrt{\frac{2}{3}} \right)}^{2}}-\sqrt[3]{\frac{8}{27}} \right]}^{1000}}\]
  A)
   0        
  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_answer17)
  Simplify : \[{{(p+q-r)}^{2}}+{{(p-q-r)}^{2}}\]
  A)
   \[2\,[{{(p-r)}^{2}}+{{q}^{2}}]\]
  done clear
  B)
   \[2\,[{{(p-q)}^{2}}+{{r}^{2}}]\]
  done clear
  C)
   \[2\,[{{(q-p)}^{2}}+{{r}^{2}}]\]       
  done clear
  D)
   \[2\,[{{(p-q)}^{2}}+{{q}^{2}}]\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer18)
  Find the sum of the given algebraic expression. \[3\,{{p}^{2}}{{q}^{2}}-4\,pq+5,\]\[6+7\,{{p}^{2}}{{q}^{2}}-8\,pq,\]\[9\,{{p}^{2}}{{q}^{2}}-10+11\,pq\]
  A)
   \[18\,{{p}^{2}}{{q}^{2}}-3\,pq+1\] 
  done clear
  B)
   \[19\,{{p}^{2}}{{q}^{2}}-pq+1\]
  done clear
  C)
   \[20\,{{p}^{2}}{{q}^{2}}-5\,pq+1\] 
  done clear
  D)
   \[18\,{{p}^{2}}{{q}^{2}}-4\,pq+1\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  Find the least value of * so that \[97*3\] is divisible by 3 is:
  A)
   2        
  done clear
  B)
   3
  done clear
  C)
   1                                
  done clear
  D)
   0
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer20)
  David divides a piece of milky bar into two equal pieces and again divides one half into two equal parts weighing 40 gram each. If he has eight equal pieces of the bars all along with him, then how heavy is the original bar?
  A)
   120 gm            
  done clear
  B)
   160 gm
  done clear
  C)
   300 gm            
  done clear
  D)
   340 gm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer21)
  Harry wants to mix the flour of two different rates to sell them at the rate he wants. In what proportion he must mixes the flour of Rs. 16.6 / k with the flour of Rs. 16.45 / kg so that the mixture can be sold at the rate of Rs. 16.54 / kg.
  A)
   1 : 3                            
  done clear
  B)
   2 : 3
  done clear
  C)
   1 : 2                            
  done clear
  D)
   3 : 2
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  Find the mean of following distribution.

  x	10	15	20	25	30	35	40
  f	7	7	13	15	7	4	4

  A)
   23.4482           
  done clear
  B)
   23.34
  done clear
  C)
   23.48              
  done clear
  D)
   23.55
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer23)
  What is the total number of candidates appeared in an examination, if 20 % are failed and the number of passed candidates are 240 more than the number of failed candidates?
  A)
   600                             
  done clear
  B)
   400
  done clear
  C)
   300                             
  done clear
  D)
   500
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer24)
  Find the unit digit in the product of\[{{(9)}^{7}}\].
  A)
   1                                
  done clear
  B)
   6
  done clear
  C)
   3                                
  done clear
  D)
   9
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer25)
  A shopkeeper sold two televisions, one at the profit of 15% and other at the loss of 10%. If the cost price of each television is Rs. 12,000, then find his profit or loss on whole transaction.
  A)
   6 % loss                       
  done clear
  B)
   5.5 % gain
  done clear
  C)
   2.5 % gain       
  done clear
  D)
   3 % loss
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer26)
  Smith invested an amount of Rs. 12000 at the simple interest rate of 10 % and another amount at the simple interest rate of 20 % per annum. The total interest earned at the end of one year on the total amount invested became 14 % per annum. The total amount invested was:
  A)
   Rs. 24000                    
  done clear
  B)
   Rs. 18000
  done clear
  C)
   Rs. 25000                    
  done clear
  D)
   Rs. 20000
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer27)
  In the following figure, AOB is a straight line and OC is perpendicular to AOB. If OX and OY are bisector of\[\angle AOC\] and \[\angle BOC\] then find\[\angle XOY\].
  A)
   \[95{}^\circ \]                         
  done clear
  B)
   \[90{}^\circ \]
  done clear
  C)
   \[98{}^\circ \]                         
  done clear
  D)
   \[92{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  If \[x=2\] and \[y=3,\]then the value of \[{{x}^{x}}+{{y}^{y}}\] is:
  A)
   13                               
  done clear
  B)
   31
  done clear
  C)
   125                             
  done clear
  D)
   25
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer29)
  Find the value of x in the figure given below:
  A)
   35 cm             
  done clear
  B)
   70 cm
  done clear
  C)
   32 cm             
  done clear
  D)
   64 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer30)
  The value of the expression \[{{\left( \frac{105}{120} \right)}^{\frac{4}{3}}}\times {{\left( \frac{105}{120} \right)}^{\frac{5}{3}}}\] is equal to:
  A)
   \[\frac{125}{64}\]                                
  done clear
  B)
   \[\frac{{{7}^{2}}}{{{12}^{5}}}\]
  done clear
  C)
   \[\frac{49}{64}\]                                  
  done clear
  D)
   \[{{\left( \frac{7}{8} \right)}^{3}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer31)
  Find the total number of prime numbers upto 100.
  A)
   26                               
  done clear
  B)
   28
  done clear
  C)
   25       
  done clear
  D)
   27
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer32)
  What fraction of Rs. 3 is 40 paise?
  A)
   \[\frac{1}{5}\]                         
  done clear
  B)
   \[\frac{4}{9}\]
  done clear
  C)
   \[\frac{2}{15}\]
  done clear
  D)
   \[\frac{6}{11}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer33)
  Find the area of the shaded region in the following figure, if ABCD is a square of side 14 cm and APB and DPC are semicircles.
  A)
   \[94\,c{{m}^{2}}\]                 
  done clear
  B)
   \[21\,c{{m}^{2}}\]
  done clear
  C)
   \[43\,c{{m}^{2}}\]
  done clear
  D)
   \[63\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer34)
  A number A and B are respectively 20 % and 50% more than the number C. What percent is the number A of the number B?
  A)
   50 %               
  done clear
  B)
   70 %
  done clear
  C)
   80 %
  done clear
  D)
   90 %
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer35)
  The area of the shaded region in the following figure is:
  A)
   \[54\,c{{m}^{2}}\]                 
  done clear
  B)
   \[66\,c{{m}^{2}}\]
  done clear
  C)
   \[77\,c{{m}^{2}}\]
  done clear
  D)
   \[96\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer36)
  Find the value of\[\frac{1}{0.5}+\frac{1}{0.2}\].
  A)
   6                                
  done clear
  B)
   7
  done clear
  C)
   8                                
  done clear
  D)
   9
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer37)
  Find the additive inverse of the rational number\[\frac{45}{78}\].
  A)
   \[\frac{78}{45}\]                                  
  done clear
  B)
   \[\frac{-\,45}{78}\]
  done clear
  C)
   \[\frac{-78}{45}\]                                 
  done clear
  D)
   1
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer38)
  Factorize: \[{{x}^{2}}-14x+48\].
  A)
   \[\left( x+6 \right)\,\,\left( x-8 \right)\]       
  done clear
  B)
   \[\left( x-6 \right)\,\,\left( x+8 \right)\]
  done clear
  C)
   \[\left( x-6 \right)\,\,\left( x-8 \right)\]
  done clear
  D)
   \[\left( x+6 \right)\,\,\left( x+8 \right)\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer39)
  If \[ab=8\]and \[a+b=10\] then the value of \[{{a}^{2}}+{{b}^{2}}\]is:
  A)
   88                               
  done clear
  B)
   68
  done clear
  C)
   98                               
  done clear
  D)
   84
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer40)
  If the average of first nine prime number is multiplied by 9, then the number obtained will be:
  A)
   9                                
  done clear
  B)
   10
  done clear
  C)
   18                               
  done clear
  D)
   24
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow