7th Class Mathematics Sample Paper

done Maths Olympiad Model Test Paper-10 Total Questions - 40    [Download]

• question_answer1)
  A bird is flying at the height of 750 m above the lake surface. At a particular point it is exactly above a fish swimming 120 m below the lake surface. What is the vertical separation between the bird and the fish?
  A)
   150 m             
  done clear
  B)
   350 m
  done clear
  C)
   870 m 
  done clear
  D)
   630 m
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer2)
  In a population of 1000, 640 are male. Find the percentage of female.
  A)
   36%                
  done clear
  B)
   40%
  done clear
  C)
   32%                            
  done clear
  D)
   48%
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer3)
  If \[{{(-24)}^{-1}}\] is divided by \[\left( {{3}^{-1}} \right)\] then the quotient will be _______
  A)
   \[\frac{-1}{8}\]
  done clear
  B)
   \[\left( -8 \right)\]
  done clear
  C)
   8                                
  done clear
  D)
   \[\frac{1}{8}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer4)
  Simplify: \[\frac{{{\left( q+\frac{1}{p} \right)}^{m}}{{\left( q-\frac{1}{p} \right)}^{m}}}{{{\left( p+\frac{1}{q} \right)}^{m}}{{\left( p-\frac{1}{q} \right)}^{m}}}\]
  A)
   0                                
  done clear
  B)
   1
  done clear
  C)
   \[{{\left( \frac{p}{q} \right)}^{2m}}\]               
  done clear
  D)
   \[{{\left( \frac{q}{p} \right)}^{2m}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)
  What should be subtracted from \[\left( 2\,a+8\,b+10 \right)\] to get\[\left( -\,3a+7\,b+16 \right)\]?
  A)
   \[5\,a-b-6\]                   
  done clear
  B)
   \[-\,5\,a-b+6\]
  done clear
  C)
   \[5\,a+b-6\]     
  done clear
  D)
   All of these
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer6)
  The Ratio between two quantities is 7 : 9. If the first quantity is 511 then find the other quantity.
  A)
   655                             
  done clear
  B)
   555
  done clear
  C)
   657     
  done clear
  D)
   656
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer7)
  A candidate must get 33 % marks to pass. He gets 220 marks and fails by 11 marks. What is the maximum marks of the exam?
  A)
   500                             
  done clear
  B)
   689
  done clear
  C)
   711                             
  done clear
  D)
   700
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer8)
  A certain sum becomes $ 7350 in 4 years and $ 8575 in 5 years. Find the rate of interest per annum.
  A)
   \[16\,\,\frac{2}{3}%\]   
  done clear
  B)
   \[\frac{51}{3}%\]
  done clear
  C)
   52%                            
  done clear
  D)
   \[14%\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  Determine x, if AB is parallel to CD in the adjoining figure.
  A)
   \[63{}^\circ \]                         
  done clear
  B)
   \[78{}^\circ \]
  done clear
  C)
   \[93{}^\circ \] 
  done clear
  D)
   \[112{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer10)
  In the adjoining figure, ABCD is a square and EBC is an equilateral triangles. The measure of \[\angle EAB\] is equal to_________.
  A)
   \[15{}^\circ \] 
  done clear
  B)
   \[30{}^\circ \]
  done clear
  C)
   \[{{\left( 22\frac{1}{2} \right)}^{{}^\circ }}\]              
  done clear
  D)
  \[45{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer11)

  Draw a line 8 cm long and draw its perpendicular bisector.

  Which one of the following steps of construction is incorrect?

  A)
   Draw a line segment \[AB=8\]cm
  done clear
  B)
   With A as centre and radius equal to less than half of AB, draw two arc one above AB and other below AB
  done clear
  C)
   With B as centre and radius is more than the half of AB, draw two arcs, cutting the previously drawn arcs at points C and D respectively
  done clear
  D)
   Join CD, intersecting AB at a point P then CD bisects AB at the point P
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer12)
  The diagonals of a rhombus are 24 cm and 10 cm. Find the perimetre of rhombus.
  A)
   52 cm
  done clear
  B)
   58 cm
  done clear
  C)
   99 cm             
  done clear
  D)
   81 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer13)
  Find the multiplicative inverse of \[{{\left( 7\times \frac{1}{12} \right)}^{-1}}\]
  A)
   \[{{7}^{-1}}\times {{12}^{-1}}\]                   
  done clear
  B)
   \[7\times {{12}^{-1}}\]
  done clear
  C)
   \[{{7}^{-1}}\times 12\]                       
  done clear
  D)
  \[(1/7)\,\times \,{{12}^{-1}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  The length of the minute hand of a clock is 10.5 cm long. Find the area swept by the minute hand in 10 minutes.
  A)
   \[57.75\,\,c{{m}^{2}}\]
  done clear
  B)
   \[95.75\,\,c{{m}^{2}}\]
  done clear
  C)
   \[85.78\,\,c{{m}^{2}}\]                      
  done clear
  D)
   \[99.99\,\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer15)
  Find out the marks in Hindi from pie chart given below, if the total marks is 540.
  A)
   168     
  done clear
  B)
   126
  done clear
  C)
   102                             
  done clear
  D)
   144
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer16)
  Given that the total number of students in 30 classes is 960. Find the probability that a student randomly chosen from these 30 classes is left handed.

  Number of Classes	1	2	5	12	8	2
  No. of Left Handed Students	0	2	10	36	32	10

  A)
   \[\frac{3}{32}\]
  done clear
  B)
   \[\frac{1}{4}\]
  done clear
  C)
   \[\frac{7}{35}\]                        
  done clear
  D)
   \[\frac{5}{33}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer17)
  Which one of the following rational number has non - terminating and non - repeating decimals.
  A)
   \[\frac{75}{64}\]                                  
  done clear
  B)
   \[\frac{14}{230}\]
  done clear
  C)
   \[\frac{35}{128}\]                                
  done clear
  D)
   \[\frac{33}{640}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer18)
  If the difference between half of Peter's age two years from now and one third of his age two years ago is 7 years then the present age of Peter will be?
  A)
   23 years                      
  done clear
  B)
   31 years
  done clear
  C)
   33 years                      
  done clear
  D)
   32 years
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  John scored 20% less marks than Catherine. How much percentage marks Catherine gets more than John?
  A)
   20 %               
  done clear
  B)
   25 %
  done clear
  C)
   30 %               
  done clear
  D)
   35 %
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer20)
  Two hundred students of class 7th and 8th were asked to name their favourite colour for their school building. The results are shown in the following bar graph. The most preferred colour is:
  A)
   Blue                
  done clear
  B)
   Green
  done clear
  C)
   Red                             
  done clear
  D)
   Yellow
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer21)
  Arrange the following in descending order\[\frac{4}{17},\frac{7}{15},\frac{3}{16},\frac{5}{19},\frac{21}{49}\]
  A)
   \[\frac{3}{16},\frac{4}{17},\frac{5}{19},\frac{7}{15},\frac{21}{49}\]    
  done clear
  B)
   \[\frac{7}{15},\frac{21}{49},\frac{5}{19},\frac{4}{17},\frac{3}{16}\]
  done clear
  C)
   \[\frac{7}{15},\frac{3}{16},\frac{4}{17},\frac{5}{19},\frac{21}{49}\]    
  done clear
  D)
   \[\frac{7}{15},\frac{21}{49},\frac{5}{19},\frac{3}{16},\frac{4}{17}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  If \[{{\left( \frac{5}{3} \right)}^{-5}}\times {{\left( \frac{5}{3} \right)}^{-11}}={{\left( \frac{5}{3} \right)}^{8a}}\]then the value of a is equal to?
  A)
   2                                
  done clear
  B)
   \[-2\]
  done clear
  C)
   \[-3\]                           
  done clear
  D)
   \[-1\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer23)

  In the adjoining figure the base of an isosceles triangle is 24 cm and its area is 192 \[c{{m}^{2}}\].

  Then the perimetre of the triangle is

  A)
   64 cm 
  done clear
  B)
   63 cm
  done clear
  C)
   62 cm             
  done clear
  D)
   61 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer24)
  Ram borrows two amounts. One amount is Rs. 15000 at the rate of 12% simple interest per annum, for 2 years. The other amount is at the rate of 15% per annum for same period. The total interest paid by him is Rs. 9000. Find the second amount borrowed by him.
  A)
   Rs. 10, 000                  
  done clear
  B)
   Rs. 16, 000
  done clear
  C)
   Rs. 18, 000      
  done clear
  D)
   Rs. 32, 000
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer25)
  The sum of the digits of a two digit number is 10. If the order of digit is reversed, the number is decreased by 54. Find the number.
  A)
   73                               
  done clear
  B)
   82
  done clear
  C)
   91                               
  done clear
  D)
   64
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer26)
  Find the area of shaded region.
  A)
   \[21.35\,c{{m}^{2}}\]
  done clear
  B)
   \[18.56\,c{{m}^{2}}\]
  done clear
  C)
   \[24.76\,c{{m}^{2}}\]            
  done clear
  D)
   \[28.36\,c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer27)
  What will be the compound interest on sum Rs. 15, 000 after 3 years at the rate of 10% per annum, compounded annually?
  A)
   Rs. 4956                      
  done clear
  B)
   Rs. 4965
  done clear
  C)
   Rs. 4865                      
  done clear
  D)
   Rs. 4685
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  Find the value of x from the figure given below.
  A)
  \[{{24}^{0}}\]   
  done clear
  B)
  \[{{26}^{0}}\]
  done clear
  C)
  \[{{25}^{0}}\]                
  done clear
  D)
   \[{{32}^{0}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer29)
  If mean is 8 and median is 10 then mode will be?
  A)
   10                               
  done clear
  B)
   14
  done clear
  C)
   16                               
  done clear
  D)
   18
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer30)
  Factorize: \[{{x}^{3}}-3{{x}^{2}}+3x-1\]
  A)
  \[{{\left( x-1 \right)}^{3}}\]                  
  done clear
  B)
  \[\left( x-1 \right)\,\,\left( x-3 \right)\]
  done clear
  C)
  \[\left( x+1 \right)\,\,\left( x-3 \right)\]       
  done clear
  D)
  \[{{\left( x-1 \right)}^{2}}\,\,\left( x-3 \right)\]
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer31)
  Find the discount percent on an article whose marked price is Rs. 1260 and is sold at Rs. 960.
  A)
   23.8 %
  done clear
  B)
   24.2 %
  done clear
  C)
   20 %               
  done clear
  D)
   26.8 %
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer32)
  The HCF of two number is 2 and also their difference is 12. The numbers are?
  A)
   (78, 66)                       
  done clear
  B)
   (82, 70)
  done clear
  C)
   (106, 94)                     
  done clear
  D)
   Both (b) and (c)
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer33)
  Find the mean of following distribution.

  x	5	10	15	20	25	30	35	40	45
  f	1	2	5	7	4	6	3	8	9

  A)
   27.63              
  done clear
  B)
   27.34
  done clear
  C)
   30       
  done clear
  D)
   27.27
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer34)
  If\[a-\frac{1}{a}=5\] the value of \[{{a}^{3}}-\frac{1}{{{a}^{3}}}\]is ­­­­_______.
  A)
   142                             
  done clear
  B)
   140
  done clear
  C)
   172                             
  done clear
  D)
   125
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer35)
  The volume of ice-cream cone whose radius is 5 cm and height is 7 cm is _____­­­___.
  A)
   \[445.24\,\,c{{m}^{3}}\]         
  done clear
  B)
   \[446.26\,\,c{{m}^{3}}\]
  done clear
  C)
   \[448.42\,\,c{{m}^{3}}\]                     
  done clear
  D)
   \[440.24\,\,c{{m}^{3}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer36)
  The ratio of income to the saving of a family is\[8:3\]. If monthly income is Rs. 24,000, 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_answer37)
  Find the cube of\[x-2y\].
  A)
   \[{{x}^{3}}+8\,{{y}^{2}}+6\,{{x}^{2}}y-12\,x{{y}^{3}}\]
  done clear
  B)
   \[{{x}^{3}}-8{{y}^{2}}-6\,{{x}^{2}}y+12\,x{{y}^{3}}\]
  done clear
  C)
   \[{{x}^{2}}+87y+7xy-7xy\]
  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_answer38)
  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_answer39)
  Steve and Jack borrowed Rs. 2000 and Rs. 2350 respectively at simple interest, at the same rate of interest, for 5 years. If the interest paid by Jack is Rs. 60 more than that paid by Steve, find the rate of interest per annum for Jack.
  A)
   3.4 %
  done clear
  B)
   8 %
  done clear
  C)
   5.2 %              
  done clear
  D)
   20 %
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer40)
  If \[x+1/x=4\]then value of \[{{x}^{3}}+1/{{x}^{3}}\] is?
  A)
   64                               
  done clear
  B)
   52
  done clear
  C)
   72                               
  done clear
  D)
   76
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow