7th Class Mathematics Sample Paper

done Maths Olympiad Model Test Paper-20 Total Questions - 50    [Download]

• question_answer1)
  Which of the following can be used to compute \[\left( 34\times 4\,\,\frac{1}{2} \right)\]?
  A)
   \[\left( 30\times 4 \right)+\left( 4\times 4\,\,\frac{1}{2} \right)\]
  done clear
  B)
   \[\left( 34\times \,\,\frac{1}{2} \right)+(30\times 4)+(4\times 4)\]
  done clear
  C)
   \[(34\times 40)+\left( 34\times \frac{1}{2} \right)\]
  done clear
  D)
   \[\left( 30\times 4\,\,\frac{1}{2} \right)+(4\times 4)\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer2)
  Which of the following numbers is divisible by 24?
  A)
   63810             
  done clear
  B)
   537804
  done clear
  C)
   35718             
  done clear
  D)
   3125736
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer3)
  What is the unit digit in \[\left\{ {{\left( 6374 \right)}^{1793}}\times {{\left( 625 \right)}^{317}}\times {{\left( 341 \right)}^{491}} \right\}\]?
  A)
   5                                
  done clear
  B)
   3
  done clear
  C)
   2                                
  done clear
  D)
   0
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer4)
  If \[9{{x}^{2}}+\left( p+20 \right)\,\,xy+49\,{{y}^{2}}\] is a perfect square, then find the value of p.
  A)
   49                               
  done clear
  B)
   39
  done clear
  C)
   22       
  done clear
  D)
   19
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer5)
  If \[\left( \frac{2x-y}{x+2y} \right)=\frac{1}{2},\] then find the value of \[\left( \frac{3x-y}{3x+y} \right).\]
  A)
   \[\frac{5}{7}\]                         
  done clear
  B)
   \[\frac{3}{7}\]
  done clear
  C)
   \[\frac{1}{5}\]                         
  done clear
  D)
   \[\frac{3}{5}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer6)
  If \[{{2}^{x}}={{3}^{y}}=\frac{1}{{{6}^{z}}},\] then solve \[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}.\]
  A)
   1                                
  done clear
  B)
   0
  done clear
  C)
   2                                
  done clear
  D)
   3
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer7)
  If \[{{a}^{2}}+{{b}^{2}}=117\] and \[ab=54,\] then find the value of \[\frac{a+b}{a-b}\].
  A)
   \[\frac{3}{5}\]                         
  done clear
  B)
   \[\frac{5}{3}\]
  done clear
  C)
   9                                
  done clear
  D)
   5
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer8)
  Simplify: \[\frac{\left[ 3\,\,\frac{1}{4}\div \left\{ 1\,\,\frac{1}{4}-0.5\left( 2\,\,\frac{1}{2}-\frac{1}{4}-\frac{1}{6} \right) \right\} \right]}{4\times \,\frac{1}{12}}\]
  A)
   234     
  done clear
  B)
   244
  done clear
  C)
   78                               
  done clear
  D)
   224
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer9)
  If\[{{3}^{x}}=900,\] then find the value of\[{{3}^{x+2}}-{{3}^{x-2}}\].
  A)
   1800               
  done clear
  B)
   8400
  done clear
  C)
   8200                           
  done clear
  D)
   8000
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer10)
  Evaluate: \[{{\left[ \frac{{{x}^{5y-5}}\times {{x}^{5-2y}}}{{{x}^{4y-6}}\times {{x}^{2y-9}}} \right]}^{\frac{-4}{3}}}\]
  A)
   \[{{x}^{3y+15}}\]                 
  done clear
  B)
   \[{{x}^{4y+18}}\]
  done clear
  C)
   \[{{x}^{4y-20}}\]
  done clear
  D)
   \[{{x}^{13-3y}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer11)
  \[\frac{1}{10}\] of a pole is coloured red, \[\frac{1}{20}\] white, \[\frac{1}{30}\] blue, \[\frac{1}{40}\] black, \[\frac{1}{50}\] violet, \[\frac{1}{60}\] yellow and the rest is green. If the length of the green portion of the pole is 12.08 meters, then find the length of the pole.
  A)
   16 m   
  done clear
  B)
   18 m
  done clear
  C)
   20 m                           
  done clear
  D)
   30 m
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer12)
  The base of parallelogram is thrice of its height. If the area of the parallelogram is 2187sq cm, then find its height.
  A)
   26 cm             
  done clear
  B)
   27 cm
  done clear
  C)
   29 cm             
  done clear
  D)
   35 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer13)
  The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of the third square whose area is equal to the difference of the areas of the two squares.
  A)
   56 cm             
  done clear
  B)
   38 cm
  done clear
  C)
   28 cm             
  done clear
  D)
   24 cm
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer14)
  A rectangular lawn 80 m \[\times \] 60 m has two roads each 10 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at Rs. 20 per\[{{m}^{2}}\].
  A)
   Rs. 35000                    
  done clear
  B)
   Rs. 39000
  done clear
  C)
   Rs. 26000        
  done clear
  D)
   Rs. 41000
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer15)
  In the figure given below ABCD is a rectangle. Find the area of the shaded portion in the given figure.
  A)
   \[280\text{ }c{{m}^{2}}\]                  
  done clear
  B)
   \[220\text{ }c{{m}^{2}}\]
  done clear
  C)
   \[180\text{ }c{{m}^{2}}\]      
  done clear
  D)
   \[156\text{ }c{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer16)
  In a certain school, 20% of students are below 8 years of age. The number of 2 students above 8 years of age is \[\frac{2}{3}\] of the number of students of 8 years age, which is 48. What is the total number of students in the school?
  A)
   72                               
  done clear
  B)
   80
  done clear
  C)
   100     
  done clear
  D)
   150
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer17)
  In a two digit number, the unit digit is equal to the square of tens digit. The difference between the original number and the number formed by interchanging the digits is 54. What is 60% of the original number?
  A)
   64                               
  done clear
  B)
   39
  done clear
  C)
   93                               
  done clear
  D)
   20
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer18)
  A piece of cloth which is 36 m in length is cut into two pieces such that the length of the one piece is equal to one-fifth the length of the other. Find the product lengths of the two pieces.
  A)
   \[64\text{ }{{m}^{2}}\]                      
  done clear
  B)
   \[150\text{ }{{m}^{2}}\]
  done clear
  C)
   \[180\text{ }{{m}^{2}}\]        
  done clear
  D)
   \[220\text{ }{{m}^{2}}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer19)
  The charges of a hired car are Rs. 4 per km for the first 60 km, Rs. 5 per km for the next 60 km and Rs. 8 for every 5 km for further journey. If the balance amount left over with Rohit is one-fourth of what he paid towards the charges of the hired car for travelling 320 km, how much money did he have initially with him?
  A)
   Rs. 1075
  done clear
  B)
   Rs. 1255
  done clear
  C)
   Rs. 1540                      
  done clear
  D)
   Rs. 1685
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer20)
  If \[p:q=2:3\]and \[q:r=4:5\], then find p : q: r.
  A)
   8 : 12 : 15       
  done clear
  B)
   2 : 3 : 4
  done clear
  C)
   1 : 2 : 3                       
  done clear
  D)
   4 : 5 : 6
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer21)
  In the given figure, ABCD is a quadrilateral. \[\angle ADB=60{}^\circ ,\] \[\angle DBC=30{}^\circ \] and \[\angle ACB\text{ }=\text{ }60{}^\circ \]. Find\[\angle DAC\].
  A)
   \[60{}^\circ \]                         
  done clear
  B)
   \[50{}^\circ \]
  done clear
  C)
   \[30{}^\circ \] 
  done clear
  D)
   \[20{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer22)
  In a group of three angles, the second angle is one-third of the compliment of the first angle. The third angle is half of the supplement of the first angle. The third angle is 6 times the second angle. Find the first angle.
  A)
   \[45{}^\circ \]                         
  done clear
  B)
   \[60{}^\circ \]
  done clear
  C)
   \[75{}^\circ \]                         
  done clear
  D)
   \[90{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer23)
  In the figure given below, find the values of \[x+y+z.\]
  A)
   \[180{}^\circ \]           
  done clear
  B)
   \[205{}^\circ \]
  done clear
  C)
   \[220{}^\circ \]
  done clear
  D)
   \[360{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer24)
  In the given figure AB| |CD, find the value of\[x\].
  A)
   \[75{}^\circ \] 
  done clear
  B)
   \[70{}^\circ \]
  done clear
  C)
   \[40{}^\circ \]                         
  done clear
  D)
   \[15{}^\circ \]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer25)
  Two pipes A and B can fill a tank in 6 hours and 3 hours respectively. Both the pipes are opened simultaneously and pipe A is closed after 1 hours. Find the time taken by B to fill the remaining part of the tank (in hours).
  A)
   1                                
  done clear
  B)
   \[1\frac{1}{2}\]
  done clear
  C)
   2                                
  done clear
  D)
   \[2\,\,\frac{1}{2}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer26)
  The average of three numbers is 77. The first number is twice the second and the second number is twice the third. The first number is
  A)
   33                               
  done clear
  B)
   66
  done clear
  C)
   77                               
  done clear
  D)
   132
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer27)
  Directions: Study the table carefully to answer the questions that follow:

  Percentage of Marks Obtained by Different Students in Different Subjects
  Students	Subjects marks
  	Hindi (100)	English (150)	Math?s (75)	Physics (150)	Chemistry (150)	Biology (75)	IT (50)
  Amit	67	88	92	88	58	60	98
  Ruchi	65	78	68	70	64	72	76
  Kanchan	89	66	76	76	72	68	76
  Prashant	88	80	72	68	62	64	72
  Mrinal	78	64	76	74	68	80	78
  Kunal	60	86	88	74	94	76	84
  Diksha	74	92	96	66	86	88	96

  How many marks did Kunal get in all the subjects together?
  A)
   562                             
  done clear
  B)
   558
  done clear
  C)
   634                             
  done clear
  D)
   606
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer28)
  What are the average marks obtained by all the students together in Chemistry?
  A)
   98                               
  done clear
  B)
   112
  done clear
  C)
   88                               
  done clear
  D)
   124
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer29)
  How many students have scored the highest marks in more than one Subject?
  A)
   Four                            
  done clear
  B)
   Three
  done clear
  C)
   Two    
  done clear
  D)
   One
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer30)
  Marks Obtained by Ruchi in Biology are what percent of marks obtained by Kanchan in the same subject? (rounded off to two digits after decimal)
  A)
   94.44%           
  done clear
  B)
   105.88%
  done clear
  C)
   113.13%                      
  done clear
  D)
   86.24%
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer31)
  Which number will come next in the following series? 3, 8, 5, 7, 8, 5, 12
  A)
   2        
  done clear
  B)
   3
  done clear
  C)
   4                                
  done clear
  D)
   1
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer32)
  Insert the missing number.
  A)
   10                               
  done clear
  B)
   16
  done clear
  C)
   18                               
  done clear
  D)
   20
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer33)
  Find the number pair/group which is different from others.
  A)
   \[12-72\]                      
  done clear
  B)
   \[24-48\]
  done clear
  C)
   \[60-74\]
  done clear
  D)
   \[84-96\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer34)
  Find the total number of triangles in the figure given below.
  A)
   26                               
  done clear
  B)
   32
  done clear
  C)
   36                               
  done clear
  D)
   38
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer35)
  From the four positions of a dice given below, find the colour which is opposite to yellow?
  A)
   Violet
  done clear
  B)
   Red
  done clear
  C)
   Rose                            
  done clear
  D)
   Blue
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer36)
  Given that

  1. A is the brother of B

  2. C is the father of A

  3. D is the brother of E

  4. E is the daughter of B

  Then, the uncle of D is

  A)
   A        
  done clear
  B)
   B
  done clear
  C)
   C                                
  done clear
  D)
   E
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer37)
  In a certain code language, 'WEAVE' is written as 'FEZVX'. How will 'ELEVATE' be written in that code language?
  A)
   ELFUATF                    
  done clear
  B)
   FLEAUTF
  done clear
  C)
   FLEUAFT                    
  done clear
  D)
   FLEUATF
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer38)
  Find out the missing letter in the following table
  A)
   R                                
  done clear
  B)
   N
  done clear
  C)
   M       
  done clear
  D)
   L
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer39)
  Which of the following numbers can be placed at the sign of question mark?

  7	49	7	98
  9	81	9	162
  6	36	6	72
  5	25	5	?

  A)
           80                               
  done clear
  B)
   65
  done clear
  C)
   60                               
  done clear
  D)
   50
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer40)
  Direction: In question two statements are given followed by two conclusions I and II. You have to consider the statements to be true even if the seen to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.

  Statements:

  1. All books are Literature.

  2. Some Literature are poems.

  Conclusions:

  I. Some books are poems.

  II. Some poems are literature.

  A)
   Only conclusion I follows
  done clear
  B)
   Neither I nor II follows
  done clear
  C)
   Both the conclusions I and II follow
  done clear
  D)
   Only conclusion II follows
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer41)
  Match the columns:

  Column - Ist		Column - IInd
  I.	\[\frac{2\times {{3}^{4}}\times {{2}^{5}}}{9\times {{4}^{2}}}\]	p.	98
  II.	\[\frac{{{12}^{4}}\times {{9}^{3}}\times 4}{{{6}^{3}}\times {{8}^{2}}\times 27}\]	q.	1
  III.	\[\frac{{{3}^{5}}\times {{10}^{5}}\times 25}{{{5}^{7}}\times {{6}^{5}}}\]	r.	36
  IV.	\[\frac{{{({{2}^{5}})}^{2}}\times {{7}^{3}}}{{{8}^{3}}\times 7}\]	s.	162

  A)
   \[(I)\to p,\,(II)\to q,\,(III)\to r,\,(IV)\to s\]
  done clear
  B)
   \[(I)\to r,\,(II)\to q,\,(III)\to p,\,(IV)\to s\]
  done clear
  C)
   \[(I)\to r,\,(II)\to s,\,(III)\to q,\,(IV)\to p\]
  done clear
  D)
   \[(I)\to s,\,(II)\to r,\,(III)\to q,\,(IV)\to p\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer42)
  Find the values of the given polynomials at \[m=1,\] \[n=-2\] and \[p=3\] then match the following.

  Column - I		Column - II
  I.	\[{{m}^{3}}+{{n}^{3}}+{{p}^{3}}\]	p.	\[-5\]
  II.	\[mn+np+pm\]	q.	49
  III.	\[{{m}^{3}}+{{n}^{3}}+{{p}^{3}}-3mnp\]	r.	20
  IV.	\[{{m}^{2}}{{n}^{2}}+{{n}^{2}}{{p}^{2}}+{{p}^{2}}{{m}^{2}}\]	s.	38

  A)
   \[(I)\to r,\,(II)\to q,\,(III)\to p,\,(IV)\to s\]
  done clear
  B)
   \[(I)\to s,\,(II)\to r,\,(III)\to q,\,(IV)\to p\]
  done clear
  C)
   \[(I)\to r,\,(II)\to p,\,(III)\to q,\,(IV)\to s\]
  done clear
  D)
   \[(I)\to r,\,(II)\to p,\,(III)\to s,\,(IV)\to q\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer43)
  Find the value of \[x\] from the following expression: \[\frac{7\,\,\frac{1}{2}-5\,\,\frac{3}{4}}{3\,\,\frac{1}{2}+x}\div \frac{\frac{1}{2}+1\,\,\frac{1}{4}}{1\,\,\frac{1}{5}+3\,\,\frac{1}{2}}=0.6\]
  A)
   \[4\,\,\frac{1}{3}\]                    
  done clear
  B)
   \[4\,\,\frac{1}{2}\]
  done clear
  C)
   \[4\,\,\frac{2}{3}\]                                
  done clear
  D)
   \[5\,\,\frac{2}{3}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer44)
  Consider the volume of the following shapes:

  1. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm.

  2. A cube of each side 4 cm.

  3. A cylinder of radius 3 cm and length 3 cm.

  4. A sphere of radius 3 cm.

  The volumes of these in the decreasing order is:

  A)
   1, 2, 3, 4                     
  done clear
  B)
   1, 3, 2, 4
  done clear
  C)
   4, 2, 3, 1                     
  done clear
  D)
   4, 3, 2, 1
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer45)
  A milk vendor has 2 cans of milk. The first contains 25 % water and rest the milk. The second contains 50 % water. How much milk should he mix from each of the containers so as to get 12 litres of milk, such that, the ratio of water to milk is 3 : 5 ?
  A)
   4 litres, 8 litres  
  done clear
  B)
   6 litres, 6 litres
  done clear
  C)
   5 litres, 7 litres  
  done clear
  D)
   7 litres, 5 litres
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer46)
  2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in:
  A)
   18 days                       
  done clear
  B)
   21 days
  done clear
  C)
   24 days                       
  done clear
  D)
   30 days
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer47)
  If the numerator of a fraction is increased by 2 and the denominator is increased by 3, the fraction becomes \[\frac{7}{9}\] and if both the numerator as well as the denominator are decreased by 1, the fraction becomes\[\frac{4}{5}\]. What is the original fraction?
  A)
   \[\frac{5}{6}\] 
  done clear
  B)
   \[\frac{9}{11}\]
  done clear
  C)
   \[\frac{13}{16}\]                                  
  done clear
  D)
   \[\frac{17}{21}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer48)
  From a number of apples, a man sells half the number of existing apples plus 1 to the first customer, \[\frac{1}{3}\,\,\text{rd}\]of the remaining apples plus 1 to the second customer and \[\frac{1}{5}\,\,\text{th}\]of the remaining apples plus 1 to the third customer. He then finds that he has 3 apples left. If number of apples the man sold to the first customer, second customer and third customer are P, Q and R respectively, then find the value of: \[\frac{{{(P+Q)}^{3}}+{{(P+R)}^{2}}}{(Q+R+2)}\]
  A)
   826                             
  done clear
  B)
   579
  done clear
  C)
   496                             
  done clear
  D)
   443
  done clear
  E)
   None of these
  done clear
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• question_answer49)
  Simplify: \[\frac{3}{2}\,\,\text{of}\,\,\left( \frac{4}{3}\div \frac{5}{7} \right)+\frac{1}{2}\div \,\,\left[ 3\,\,\frac{4}{5}-\,\,\left\{ \frac{2}{5}\div \left( \frac{1}{3}+\frac{1}{2}+\overline{\frac{1}{5}-\frac{1}{6}} \right) \right\} \right].\]
  A)
   \[1\,\,\frac{2061}{2170}\]                     
  done clear
  B)
   \[2\,\,\frac{1061}{2170}\]
  done clear
  C)
   \[2\,\,\frac{2061}{2170}\]         
  done clear
  D)
   \[3\,\,\frac{2061}{2170}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow

• question_answer50)
  If \[\sqrt[x\,]{\frac{{{25}^{\left( x+\frac{1}{4} \right)}}.\sqrt{{{5.5}^{-x}}}}{5.\sqrt{{{5}^{-x}}}}}=\text{P}\], then find the value of P.
  A)
   5                                
  done clear
  B)
   \[{{5}^{2}}\]
  done clear
  C)
   \[{{5}^{3}}\]                         
  done clear
  D)
   \[\sqrt[x]{5}\]
  done clear
  E)
   None of these
  done clear
  View Answer play_arrow