7th Class Mathematics Sample Paper

done Maths Olympiad Model Test Paper-1 Total Questions - 40    [Download]

• question_answer1)
  If \[A=9-25\,\,\{56-(47-13\div 26\times 4\,of\,2)\}\]and\[B=[13\times \{15+(3)\times (-5)\}]\] then find the value of \[A+B-{{B}^{2}}\]
  A)
   260                             
  done clear
  B)
   \[-316\]
  done clear
  C)
   153                             
  done clear
  D)
   316
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer2)
  What least value must be given to 'A' so that the number 5087A56 is divisible by 8?
  A)
   8                                
  done clear
  B)
   7
  done clear
  C)
   5                                
  done clear
  D)
   6
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer3)
  Simplify: \[\frac{35}{32}+\frac{15}{64}+\frac{65}{48}+\frac{75}{24}+\frac{25}{12}\]
  A)
   \[\frac{192}{5}\]                                  
  done clear
  B)
   \[\frac{6825}{4}\]
  done clear
  C)
   \[\frac{505}{64}\]        
  done clear
  D)
   \[\frac{13}{6825}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer4)
  If \[\sqrt{15}=3.88,\] then find the value of\[\sqrt{\frac{3125}{243}}\].
  A)
   3.4926            
  done clear
  B)
   4.5926
  done clear
  C)
   3.5926
  done clear
  D)
   5.5926
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)
  The value of \[1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}\] is:
  A)
   \[1\,\,\frac{1}{2}\]                                
  done clear
  B)
   \[1\,\,\frac{2}{3}\]
  done clear
  C)
   \[1\,\,\frac{3}{5}\]        
  done clear
  D)
   \[1\,\,\frac{3}{4}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer6)
  Find the product of \[\frac{15}{7}\times \frac{-21}{25}\times \frac{5}{18}\].
  A)
   \[\frac{17}{30}\]                                  
  done clear
  B)
   \[\frac{4}{-15}\]
  done clear
  C)
   \[\frac{-1}{2}\]
  done clear
  D)
   \[\frac{-7}{15}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer7)
  The product of two rational numbers is\[\frac{-33}{78}\]. If one of the number is \[\frac{15}{22},\]then find the other rational number.
  A)
   \[\frac{121}{195}\]                              
  done clear
  B)
   \[\frac{121}{-195}\]
  done clear
  C)
   \[\frac{122}{195}\]                              
  done clear
  D)
   \[\frac{-123}{-195}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer8)
  Which one of the following is a rational number?
  A)
   \[\frac{4}{7}\]
  done clear
  B)
   \[\pi \]
  done clear
  C)
   \[2\pi \]                        
  done clear
  D)
   \[\frac{\pi }{2}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  Evaluate: \[{{(27)}^{\frac{-2}{3}}}\times {{(81)}^{\frac{5}{4}}}\times {{\left( \frac{1}{3} \right)}^{3}}\]
  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_answer10)
  Evaluate: \[{{\left[ {{\left\{ {{\left( 81 \right)}^{-\frac{1}{3}}} \right\}}^{-\frac{1}{8}}} \right]}^{6}}\]
  A)
   2                                
  done clear
  B)
   3
  done clear
  C)
   4                                
  done clear
  D)
   5
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer11)
  Find the value of \[x\], if \[{{\left( \sqrt{6}+\sqrt{2}+\sqrt{7}+\sqrt{18}+\sqrt{6}+\frac{\sqrt{5\sqrt{5}}}{\sqrt{5}} \right)}^{x-2}}=1\]
  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_answer12)
  Find the value of \[4{{x}^{y}}+2 {{y}^{x}},\] if \[x=2\] and \[y=-2\].
  A)
  \[-9\]                           
  done clear
  B)
  9
  done clear
  C)
  3  
  done clear
  D)
  8
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer13)
  Expand: \[{{(4a-3b)}^{3}}\]
  A)
   \[64\,{{a}^{3}}+27\,{{b}^{3}}-144\,{{a}^{2}}b+108\,a{{b}^{2}}\]
  done clear
  B)
   \[64\,{{a}^{3}}-27\,{{b}^{3}}+144\,{{a}^{2}}b-108\,a{{b}^{2}}\]
  done clear
  C)
   \[64\,{{a}^{3}}-27\,{{b}^{3}}-144\,{{a}^{2}}b+108\,a{{b}^{2}}\]
  done clear
  D)
   \[64\,{{a}^{3}}-27\,{{b}^{3}}+144\,{{a}^{2}}b+108\,a{{b}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  Find the cube of\[x-2y\].
  A)
   \[{{x}^{3}}+8\,{{y}^{2}}+6\,{{x}^{2}}y-12\,x{{y}^{3}}\]
  done clear
  B)
   \[{{x}^{3}}-8\,{{y}^{2}}-6\,{{x}^{2}}y+12\,x{{y}^{2}}\]
  done clear
  C)
   \[{{x}^{2}}-87\,{{y}^{2}}+7\,xy-7\,xy\]
  done clear
  D)
   \[7\,x{{y}^{3}}+6\,x-74\,{{x}^{2}}y-2\,xy\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer15)
  Factorize:\[{{(5a+4b)}^{2}}-{{(3a-2b)}^{2}}\]
  A)
   \[4\,(a+3b)\,\,(4a+b)\]
  done clear
  B)
   \[2\,(a+3b)\,\,(4a+b)\]
  done clear
  C)
   \[3\,(a+3b)\,\,(4a+b)\]  
  done clear
  D)
   \[(a+3b)\,\,(4a+b)\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer16)
  Find the value of \[x\] which satisfies the equation\[\frac{{{x}^{2}}+5}{2-{{x}^{2}}}=\frac{-3}{2}\].
  A)
   \[x=\pm \,\,5\]             
  done clear
  B)
   \[x=\pm \,\,7\]
  done clear
  C)
   \[x=\pm \,\,4\] 
  done clear
  D)
   \[x=\pm \,\,9\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer17)
  The sum of three consecutive multiples of 6 is 1098. Find the numbers.
  A)
   360, 3686 and 370       
  done clear
  B)
   362, 368 and 370
  done clear
  C)
   360, 366 and 372         
  done clear
  D)
   360, 366 and 371
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer18)
  The daily pocket expenses of P and Q are Rs. 120 and Rs. 150 respectively. What is the ratio of their expenses in the simplest form?
  A)
   120 : 150                     
  done clear
  B)
   4 : 5
  done clear
  C)
   12 : 15            
  done clear
  D)
   5 : 4
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  The ratio of monthly income to the monthly savings of a family is 8 : 3. If the monthly income be Rs. 24, 000, then find the monthly expenses.
  A)
   Rs. 15000        
  done clear
  B)
   Rs. 9000
  done clear
  C)
   Rs. 6000                      
  done clear
  D)
   Rs. 7000
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer20)
  Due to increase of 30 % in the price of an air conditioner the sale is reduced by 40 %, then what will be the percentage change in income?
  A)
   18 % decrease  
  done clear
  B)
   18 % increase
  done clear
  C)
   22 % decrease
  done clear
  D)
   22 % increase
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer21)
  The population of a town is 16,000. If it increases at the rate of 10% per annum, then what will be its population after 2 years?
  A)
   18320             
  done clear
  B)
   19200
  done clear
  C)
   20620                         
  done clear
  D)
   19360
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  Find the selling price of an article if its cost price is Rs. 2500 and loss percent is \[11\frac{1}{5}\]%.
  A)
  Rs. 2000                      
  done clear
  B)
  Rs. 2200
  done clear
  C)
  Rs. 2250                      
  done clear
  D)
  Rs. 2220
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer23)
  A shopkeeper bought 240 cricket bats for Rs. 500 each. He sells 140 of them at the gain of 10%. At what gain percent must he sell the remaining so as to gain 20% on the whole transaction?
  A)
   44 %               
  done clear
  B)
   34 %
  done clear
  C)
   24 %               
  done clear
  D)
   25 %
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer24)
  Peter borrowed a sum of Rs. 2,00,000 from a money lender at 20 % per annum simple interest. After 3 years, he paid Rs. 1,80,000 and gave some ornaments of gold to clear off the debt. What is the cost of ornaments?
  A)
   Rs. 1,40,000    
  done clear
  B)
   Rs. 1,20,000
  done clear
  C)
   Rs. 1,50,000                
  done clear
  D)
   Rs. 1,60,000
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer25)
  Divide Rs. 21, 000 into two parts such that the simple interest on the first part for 3 years at 5% per annum is equal to the simple interest on the second part for 5 years at 4 % per annum.
  A)
   Rs. 8, 000 and Rs. 13, 000
  done clear
  B)
   Rs. 9, 000 and Rs. 12, 000
  done clear
  C)
   Rs. 11, 000 and Rs. 10, 000
  done clear
  D)
   Rs. 15, 000 and Rs. 6, 000
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer26)
  Two supplementary angles are in the ratio 7 : 8. Find the angles.
  A)
   \[105{}^\circ \,and\,\,75{}^\circ \]       
  done clear
  B)
   \[83{}^\circ \,and\,\,97{}^\circ \]
  done clear
  C)
   \[84{}^\circ \,and\,\,96{}^\circ \]         
  done clear
  D)
   \[85{}^\circ \,and\,\,95{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer27)
  In the figure given below \[AB\parallel CD\] and\[AE\parallel CF,\]\[\angle FCG=90{}^\circ \]and \[\angle BAC=120{}^\circ \]. Find the values of\[x\], \[y\] and z.
  A)
   \[x=60{}^\circ ,y=50{}^\circ \,and\,z=150{}^\circ \]
  done clear
  B)
   \[x=70{}^\circ ,y=30{}^\circ \,and\,z=150{}^\circ \]
  done clear
  C)
   \[x=60{}^\circ ,y=30{}^\circ \,and\,z=150{}^\circ \]
  done clear
  D)
   \[x=60{}^\circ ,y=30{}^\circ \,and\,z=120{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  The following figure is made by using two triangles. Find the value of \[\angle P+\angle Q+\angle R+\]\[\angle S+\angle T+\angle U\].
  A)
   \[180{}^\circ \]           
  done clear
  B)
   \[175{}^\circ \]
  done clear
  C)
   \[360{}^\circ \]
  done clear
  D)
   \[285{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer29)

  In the figure given below, CD is parallel to AB.

  The angle y is equal to:

   
  A)
  \[40{}^\circ \]                         
  done clear
  B)
  \[60{}^\circ \]
  done clear
  C)
  \[80{}^\circ \]                         
  done clear
  D)
  \[100{}^\circ \]
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer30)
  Two position of the dice are shown below. What number will be at top when 2 is at bottom?
  A)
   1                                
  done clear
  B)
   2
  done clear
  C)
   5        
  done clear
  D)
   4
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer31)
  The figure given below is a rectangular park of measure 20 m by 14 m. At each corner there is a grass bed in the form of quadrant of circle of radius 4 m. Also there is a grass bed in the form of a circle of radius 3 m in the middle of the park. Find the area of the remaining park.
  A)
   \[201.5\,{{m}^{2}}\]  
  done clear
  B)
   \[203.5\,{{m}^{2}}\]
  done clear
  C)
   \[201.75\,{{m}^{2}}\]            
  done clear
  D)
   \[205.5\,{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer32)
  In the figure given below, a circle of diametre 42 cm is given. Inside this circle, two another circles with diametres 28 cm and 14 cm have been drawn. Find the area of the shaded portion.
  A)
   \[625\,c{{m}^{2}}\]               
  done clear
  B)
   \[462\,c{{m}^{2}}\]
  done clear
  C)
   \[635\,c{{m}^{2}}\]               
  done clear
  D)
   \[605\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer33)
  Find the area of a rhombus, whose each side is of measure 20 cm and one of whose diagonals is 24 cm.
  A)
   \[192\,c{{m}^{2}}\]               
  done clear
  B)
   \[384\,c{{m}^{2}}\]
  done clear
  C)
   \[768\,c{{m}^{2}}\]               
  done clear
  D)
   \[480\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer34)
  The average of the following observations arranged in ascending order is 24, find\[x\]. 11, 12, 14, 18,\[x+2,\]\[x+4,\]30, 32, 35 and 40.
  A)
   9                                
  done clear
  B)
   20
  done clear
  C)
   21  
  done clear
  D)
   22
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer35)
  If \[\alpha \] means "walk", \[\beta \] means "stand", \[\gamma \] means "run" and \[\delta \] means "sit down", how many times does the following sequence of commands require sitting down? \[\alpha \,\beta \,\gamma \,\delta \,\beta \,\gamma \,\alpha \,\delta \,\delta \,\gamma \,\beta \,\beta \,\alpha \,\beta \,\delta \,\gamma \,\alpha \,\delta \,\delta \,\alpha \,\beta \,\gamma \]
  A)
   6        
  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_answer36)
  If ROSE is coded as 6821, CHAIR is coded as 73456 and PREACH is coded as 961473, what will be the code for SEARCH?
  A)
   246173            
  done clear
  B)
   214673
  done clear
  C)
   214763            
  done clear
  D)
   216473
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer37)
  The 124 employees of an industry contributed for an 'Accident Assistance Fund'. The management gave amount which was twice the amount collected by the employees. Thus the total fund became Rs. 22,320. What was the average contribution of each employee?
  A)
   Rs. 120            
  done clear
  B)
   Rs. 60
  done clear
  C)
   Rs. 180            
  done clear
  D)
   Rs. 240
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer38)
  At present, Gautam is older to Sitaram by 6 years. If after five years the ratio of their ages is 11 : 9, what will be the ratio of their present ages?
  A)
   6 : 4                            
  done clear
  B)
   5 : 3
  done clear
  C)
   14 : 11
  done clear
  D)
   6 : 1
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer39)
  The length of a rectangular plywood sheet is thrice its breadth. If the cost of painting one side of the sheet at Rs. 14 per sq. m comes to Rs. 60.48, what is the length of the sheet in metres?
  A)
   4.32 m            
  done clear
  B)
   1.44 m
  done clear
  C)
   2.4 m              
  done clear
  D)
   3.6 m
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer40)
  A village has a population of 4640 persons, out of which 25 per cent are voters. In an election, if 15 per cent voters did not vote, how many voters cast their vote?
  A)
   2958               
  done clear
  B)
   2784
  done clear
  C)
   696                             
  done clear
  D)
   986
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow