1 | Page Morning Glory School & College Study Material Class: VII Subject: Mathematics Manner: CQ and MCQ. Arithmetic 1. 0.000576 is a rational number . (a) What is the least number by which the given number will be multiplied so that the product will be a natural number? 1000000. (b) Find out the square root of the given number. 0.024. (c) Find out the square root of the number obtained in option (b) up to three decimal places. 0.155. 2. A troop can be arranged in 6, 7 and 8 rows, but not in a square from. (a) Find out the factors of 8. a) 1, 2, 4 and 8. (b) What is the least number by which the number in troop is to be multiplied so that the troop can be arranged in a square form? b) 42. (c) At least how many soldiers should have to join to arrange troops so obtained in a square from? c) 1. 3. 384 and 2187 are two numbers. (a) Verify with factors whether the first number is a perfect square or not. a) Not a perfect square . (b) If the second number is not a perfect square number, what is the least number is to be multiplied to get a perfect square number? what is the perfect square number? b) 3, 6561. (c) What is the least number is to be added to the second number so that the total sum will be a perfect square number? c) 22. 4. 21952 and 565 are two numbers. (a) Give reason whether the first number is perfect square number or not. a) Not a perfect square number for being the digit of unit place 2. (b) If the first number is not a perfect square number, what is the least number by which it will be divided to b) 7.
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Morning Glory School & College
Study Material
Class: VII
Subject: Mathematics
Manner: CQ and MCQ. Arithmetic
1. 0.000576 is a rational number .
(a) What is the least number by which the given number
will be multiplied so that the product will be a natural
number?
1000000.
(b) Find out the square root of the given number. 0.024.
(c) Find out the square root of the number obtained in
option (b) up to three decimal places.
0.155.
2. A troop can be arranged in 6, 7 and 8 rows, but not in a square from.
(a) Find out the factors of 8. a) 1, 2, 4 and 8.
(b) What is the least number by which the number in troop
is to be multiplied so that the troop can be arranged in
a square form?
b) 42.
(c) At least how many soldiers should have to join to
arrange troops so obtained in a square from?
c) 1.
3. 384 and 2187 are two numbers.
(a) Verify with factors whether the first number is a
perfect square or not.
a) Not a perfect
square .
(b) If the second number is not a perfect square number,
what is the least number is to be multiplied to get a
perfect square number? what is the perfect square
number?
b) 3, 6561.
(c) What is the least number is to be added to the second
number so that the total sum will be a perfect square
number?
c) 22.
4. 21952 and 565 are two numbers.
(a) Give reason whether the first number is perfect square
number or not.
a) Not a perfect
square
number for
being the
digit of unit
place 2.
(b) If the first number is not a perfect square number,
what is the least number by which it will be divided to
b) 7.
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get a perfect square number?
(c) What is the least number is to be added to the second
number so that the total sum will be a perfect square
number?
c) 20.
5. Suppose, your father told you to write a fixed fraction and
you wrote 3
.
(a) Turn the given fraction into improper fraction. a)
.
(b) Determine the square root of the given fraction. b) 1
.
(c) If the quotient of two numbers is the square root of the
given fraction and product of them is 364, determine
the numbers.
c) 26 and 14.
6. Suppose, you are told to write a number and you wrote 1.1025.
(a) Determine whether the number is rational or irrational. Rational.
(b) Determine the square root of the given number. 1.05.
(c) Determine the square root of the result obtained from
option (b) up to three decimal place.
1.025.
7. You are told to writhe a number and you wrote 0.00007225.
(a) What is the number by which the given number will be
multiplied to turn the number into an integer?
10,00,00,000.
(b) Determine the square root of the given number. 0.0085.
(c) Determine the square root of the number obtained
from option (b) up to three decimal place.
0.092.
8. Your mathematics teacher wrote a number 1328.6025 on the board.
(a) Determine whether the number 2.25 is perfect square
or not.
Perfect square
number.
(b) Determine the square root of the given number. 36.45,
(c) Determine the square root of the number obtained
from option (b) up to three decimal place.
6.037.
9. In a garden, there are 1024 nut trees.
(a) In each row, if there exits 8 nut trees, how many rows
are there in that garden?
a) 128.
(b) In each row along length and breadth of the garden, if
there are equal number of nut trees, how many nut
trees are there in each row?
b) 32.
(c) If the number of nut trees is 4210, at least, how many
nut trees will be added to the total number of nut trees
so that the number of nut trees in each row along
length and breadth will be equal?
c) 15.
10. A least perfect square number which is divisible by 9, 15 and 25?
(a) How many prime factors are there in 25? a) One .
(b) What is the least perfect square number? b) 225.
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(c) What is the largest number of three digits, which is
multiple of the least perfect square number obtained in
option (b)?
c) 900.
11. Product and quotient of two numbers are 288 and
respectively.
(a) Without dividing, how will you determine that the
number 288 is divisible by 3?
a) Sun of the
digits is
divisible by
3.
(b) What are the numbers? b) 16 and 18.
(c) If the digits of the product and numerator and
denominator of the quotient of the two numbers are
rearranged to their opposite order conversely
respectively, what will be the smaller number?
c) 28.
12. Each of the students of class VII of a Junior High School subscribes 5 times
the number of the students in Taka and total amount raised by Tk. 12500 .
(a) How many square numbers are there from 1 to 10? a) 3.
(b) Determine the number of students of class VII. b) 50.
(c) If 15 more students get themselves admitted to class
VII to that Junior High School and each student
subscribes Tk. 10, how much money will be raised?
c) Tk. 400.
13. Difference of squares of two consecutive numbers is 37.
(a) Determine the largest number of two digits, which is
multiple of 7?
a) 91.
(b) Determine the two numbers. b) 18 and 19.
(c) Without being the two numbers consecutive, if one
number is twice the other and difference of square of
them is 72, what will be the numbers?
c) 4 and 12.
14. A farmer buys 595 plants for making a garden. The price of each plant is
Tk.12.
(a) How much money did he spend to buy the plants? a) 7140.
(b) How many of the plants will be left if the number of
plants in each row of the garden is equal to the number
of rows?
b) 19.
(c) What is the least number which is to be added to the
difference of the number of spending of total taka and
the number of plants so that the sum will be a perfect
square number?
c) 16.
15. In a troop, there are 56728 soldiers.
(a) Without dividing directly, how will you conclude that
the number 56728 is divisible by 4?
(a) The number
formed by last
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two digit i.e. 28
is divisible by 4. (b) At least how many soldiers is to be removed so that
the soldiers can be arranged in the form of a square?
(b) 84.
(c) At least how many soldiers is to be added to the troop[
so that the soldiers can be arranged in the form of a
square?
c) 393.
16. Labours were employed to reap paddy from a paddy field. The daily wage of
each labour is 10 times of their numbers and the total daily wage is Tk.
6250.
(a) How many prime numbers are there from 1 to 10? (a) 4.
(b) Find the total number of labours. (b)25.
(c)What is the least number by which the number 6250
will be multiplied so the product will be a perfect square
number?
(c)10.
17. Each member of a cooperative society subscribes 20 times the number of the
members in Taka. The total amount raised being Tk.20480.
(a) How many prime numbers are there from 20 to 90? a) 16.
(b) Find the number of members of the society. b) 32.
(c) If Tk.20480 is the total number of people living in a
village, what is the least number of people should be
added to the total number of people so that the total
sum will be a perfect square number?
c) 256.
18. The monthly expenditure of each student is 10 times the total number
students living in a hostel and total monthly expenditure is Tk.6250.
(a) What is the square root of 81? a) 9.
(b) What is the number of students in that hostel? b) 25.
(c) If more 20 students join to that hostel and the monthly
expenditure of each of them becomes Tk. 350, what
will be the total monthly expenditure of that hostel?
c) Tk.13,250.
19. Your father wants to divide some taka among you, your younger sister and
your elder sister in such a way that the amount of your taka is
times as
amount of your younger sister and the amount of your younger sister is
times as the amount of your elder sister.
(a) Express
as the formation of ratio 1 : x. a) 1:
.
(b) Find the ratio of the amount of taka of you, your
younger sister and your elder sister.
b) 10: 15: 12.
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(c) If you get Tk. 50, how many Taka was your
father divided among you?
c) Tk. 1850.
20. The ratio of successful and unsuccessful students of a school of 1,800
students is 5: 4.
(a) Express the ratio 5 : 4 to be decimal fraction.
Answer: 1.25.
1.25.
(b) Find the number of successful and unsuccessful
students.
1000 and 800.
(c) How many students need to be more successful so
that the number of successful and unsuccessful
students will be 7 : 2?
400.
21. Three glasses of same size are full of mango juice. 1: 8 is the ratio of water
and mango in the first glass, 2: 7 is that in the second one and 4 : 5 is that in
the third one. The juice of three glasses was poured into another large
container.
(a) What is the compound ratio of the given ratios? 1 : 35.
(b) Find the ratio of water and syrup in the large
container.
7 :20.
(c) If the weight of water in the large container is 56
decagram, find the weight of water in gram.
1600 gram.
22. Product of the marginal quantities of a continued proportion is 36 and the
first marginal quantity is 9.
(a) What is the inverse ratio of the sub-duplicate
ratio of 9: 4?
2: 3.
(b) Find out the mid proportional and the second
marginal quantity.
6 and 4.
(c) Suppose, the sub-duplicate ratio of the first
marginal quantity and the second marginal
quantity of the continued proportion is the ratio
of the ages of father and his son. If the age of
son is 27 years, what will be the age of father?
54 years.
23. a: b: c = 2 : 3 : 5 and a = 12.
(a) What is the name of the ratio 2: 3: 5? Successive or
continuous
ratio.
(b) Find the value of b and c. b = 18 and c =
30.
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(c) If the value of b and c are the present age of 2
sons and
that of their father, find the ratio of the ages of
them after 10 years.
19 : 20.
24. Abul and Babul are two friends. They bought cow of Tk. 50,000 and sold
it by Tk. 76,900. Abul paid an amount of 1
times than that of Babul
during buying the cow.
(a) Express 1
as the formation of ratio 1 : x. 1 :
(b) How much money will Abul get from the profit? Tk. 11, 700.
(c) If the ratio of the capital of Abul and Babul for
buying the cow is the ratio of lengths of a square
and a rhombus having perimeter 80 cm, what is the
perimeter of the square?
180 cm.
25. a : b = 3 : 4
b : c = 4 : 5
(a) What is the duplicate ratio of 3 : 4? 9 : 16.
(b) If the mixed ratio of 3: 4 and 4 : 5 is the ratio of
the equal side and base of an isosceles triangle
of which perimeter is 33 metre, find the length
of equal side and length of the base of the
isosceles triangle.
9 m and 15m.
(c) If the ratio of a : c is the gold and silver of an
ornament having weight 40 gram, what is the
weight of gold that will be added to gold of the
ornament so that the ratio of gold and silver will
be c : a?
gram.
26. a : b = 1 : 2, b : c = 3 : 2, c : d = 2 : 5.
(a) What is the mixed ratio of 1: 2 and 3 : 2?
Answer: 3 : 4.
3 : 4.
(b) If the ratio of the lengths of four sides of a
quadrilateral is a: b: c : d and the perimeter of
the triangle is 69 cm, then find the lengths of the
four sides of the quadrilateral.
9 cm, 18 cm and
30 cm.
(c) If a: d is the ratio of present ages of daughter
and her mother and after 8 years the sum of the
ages of them is 68 years, find the present age of
mother.
40 years.
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27. Some labours come contact to finish a work in 18 days, but for being absent
of 9 labours among them, the work is finished in 36 days.
(a) Find a: b: c if a: b= 2: 3 and b: c = 2 : 3. 9 days.
(b) How many labours are come to contact to finish
the work in 18 days?
4 : 6 : 9.
(c) How many days will be required to finish work
by 36 labours?
18 labours.
28. Suppose, you have some takas. You want to divide that money among A, B,
C in such a way that, A gets 3 times more than the share of B and B gets 2
times more than the share of C.
(a) What is called ratio? The comparison
of two like
quantities is
called ratio.
(b) Find the ratio of the shares of A, B and C. 12: 3 : 1.
(c) If C gets Tk. 80, how many taka were there to
you?
Tk.1280.
29. Divide Tk. 2,040 among A, B, C and D in such a way that the portion of A
is
of the portion of B, the portion of B is
of the portion of C and the
portion of D is the sum of the portions of B and C.
(a) What is the mixed ratio of 4 : 5 and 8 : 9? 32: 45.
(b) Find the ratio of the portions of A, B, C and D. 4: 6: 9: 15.
(c) If the portions of B and A are interchanged and D
gives Tk. 60 to C, then find the ratio of the portion
of A, B, C and D.
3: 2: 5: 6.
30. Suppose, you have some taka. You want to divide your taka among A, B and
C in such a way that, 3 times of the share of A = 4 times the share of B = 2
times the share of C.
(a) What is the largest number of two digits multiple of 6
and 5?
90.
(b) Find the ratio of the shares of A, B and C. 4: 3: 6.
(c) If A gets Tk. 40 more than the share of B, then
determine the share of C.
Tk.240.
31. Suppose, you have some taka. You want to divide your taka among A, B and
C in such a way that, A gets 3 times the share of B and B gets 2 times the
share of C and A gets Tk. 270 more than the shares of B and C.
(a) What is the inverse ratio of the mixed ratio of 1: 2 and
2: 3?
3: 1
(b) Find the ratio of the shares of A, B and C. 6: 2 :1.
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(c) How many taka did you have? Tk. 810
32. Suppose, you have Tk. 800. You want to divide your taka among A, B and C
in such a way that, A gets 3 times the share of B and B and C together get
portion of the shares of A.
(a) Express the inverse ratio of 2: 3 into percentage.
20 : 15: 12
(b) Find the ratio of the shares of A, B and C.
3: 1 : 4.
(c) If C gives Tk. 100 to B and A gives Tk. 100 to B,
what will be the ratio of the shares of A, B and C?
2: 3: 3.
33. Suppose, you have Tk. 280. You want to divide your taka among A, B and C
in such a way that, A gets
portion of the sharesof B and C and A and C
gets
portion of the shares of A and B.
(a) What is the successive ratio of 3: 4 and 3: 5? 9 : 12 : 20.
(b) Find the share of A, B and C.. A = Tk. 120,
B = Tk. 80 and
C = Tk. 80
(c) If the ratio of the shares of A, B and C are the
ratio of the three sides of a triangle having
perimeter 28 meter, find the lengths of the three
sides of the triangle.
12 m, 8 m and 8
m.
34. Ratio of the shares of some taka of a business of three partners A, B and C is
and share of A is Tk. 2,500 more than that of B.
(a) Express
to be simple ratio. 20 : 15 : 12.
(b) Find the shares of A, B and C. A = Tk. 1,000,
B = Tk. 7,500
and C = Tk.
6000.
(c) How many taka will be given by B to A so that
the ratio of the share of A and B will be 3 : 2?
Tk. 2400.
35. A labour earns Tk. 540 in 24 days working 6 hours per day.
(a) How many prime numbers are there from 20 to 70? 11.
(b) How many takas can the labour earn in 30 days
working 8 hours per day? (Applying Multi
Expression or Rule of many)
Tk. 900.
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(c) If the taka obtained in option (b) is the sum of two
numbers having ratio of them 13: 5, find the two
numbers.
650 and 250.
36. 8 workers can finish a piece of work in 14 days working 7 hours per day.
(a) What is the smallest number of two digits multiple
of both 3 and 5?
90.
(b) In how many days 7 workers can finish that work
working 6 hours per day?(Applying Multi
Expression or Rule of many)
16 days.
(c) If the ratio of two numbers is equal to the ratio of
the least multiples of the required number days
obtained in option (b) and sum of the numbers is
27, find the two numbers.
9 and 18
37. In a hostel, 60 students have a stock of food for 25days. After 5 days,
20students moved to another place.
(a) How many prime factors are there in 60? 3
(b) How many days will run for the rest of the students
by the reaming food? [Use Rule of three]
30 days.
(c) If the ratio of the sum of the prime factors of 60
and number of prime numbers from 1 to 60 is the
ratio of number of female and male students of a
school and number of female students is 500, what
is the number of male students?
850.
38. Ratio of the weights of salt and sugar in 45 litre of saline of a vessel is 2 : 3.
(a) What is the value of x if 1: x = 1: 3? x = 3.
(b) Find the weights of guar salt and sugar. 18 gm and 27
gm.
(c) How much of salt should be mixed to saline of
the vessel to get the ratio 2: 3?
22.5 gm.
Algebra
39. A = , B = and C =
(a) Find the value of A – B. –2xy.
(b) Find the product of AB.
(c) Show that,
= 1.
40. A = , B = and C =
(a) Find the value of B – A. 2x.
(b) Prove that, AB = C.
(c) Putting x = –1, find the value of AB. 3.
41. P = 2a – 3b and Q = 3a + 2b.
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(a) Find the value of P + Q. 5a – b.
(b) Find the product of P and Q. 6 .
(c) Find the product of (Q–P) and (P–Q).
– 42. P = a + 1, Q = a – 1 and R = .
(a) Determine the value of P + Q. 2a.
(b) Prove that, PQ = R.
(c) Find the product of (P + Q) and (P–Q). 4a.
43. A = x + y, B = x–y and C = (a) Putting x = 1 and y = 1, find the value of A. 2.
(b) Prove that, AB = .
(c) Find the product of A, B and C. .
44. A = and B = x – y.
(a) If x = 1 and y = 1, prove that, the value of AB is zero.
(b) Prove that, AB = .
(c) Find the sum of A and Bx. 2 45. X = – and Y = a + b.
(a) If a = 1 and b = –1, find the value of Y. 0.
(b) Prove that, XY =
(c) Find the difference subtracting bY from X. 46. P = 3a + b, Q = 3a – b and R = 9
(a) What is the value of (P + Q)? 6a.
(b) Prove that PQ = R.
(c) What is the value of ( ) 4 47. 15 – and 5x –1 are two algebraic expressions.
(a) Subtract the second expression from the first
expression. 15 + 2x –1.
(b) Determine the product of the two expressions. 75 + 2.
(c) Putting x = 1, find the value of the product of the
given expressions.
80.
48. A = , B = and C = .
(a) A + B = what? 2 (b) Find the product of A and B.
.
(c) Determine AB–2C. .
49. P = and Q = 3 . (a) Which one of the above mentioned expression is
monomial?
Q.
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(b) Find the value of PQ in terms of a and b. 3 .
(c) Find the value of (P+ Q)(P–Q) in terms of a and x by
applying formula.
+ 81 .
50. and are two algebraic expressions.
(a) Find the difference subtracting the second expression
from the first one.
2x.
(b) Find the value of the square of the sum of the given
expressions if x = –1.
16.
(c) By applying formula, find the product of the given
expressions. +1
51. a + b = = 7 and ab = 9.
(a) What is the value of ( ) ? 49.
(b) Find the value of 31.
(c) Find the value of ( ) 13.
52. p –
= 8.
(a) What is the value of (
) ?
64.
(b) Prove that,
= 66.
(c) Find the value of (
)
60.
53. a + b = 4 and ab = 2.
(a) What is the value of 2a + 2b? 8.
(b) Find the value of ( ) . 8.
(c) Prove that, ( ) = 128.
54. a –
= 5.
(a) Find the value of 3a –
. 15.
(b) Prove that,
(c) Prove that,
55. A = 2x + 3y and B = 2x – 5y.
(a) What is the value of A + B? –2y.
(b) If x = 1 and y = –2, find the value of . 160.
(c) Simplify: . 64 .
56. a + b= 7 and ab = 3.
(a) What is the value of 2a + 2b? 14.
(b) Prove that, ( ) = 61.
(c) Prove that,
=
.
57. a + b = 5 and ab = 12.
(a) What is the value of 3a + 3b. 15.
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(b) Prove that,
(c) Prove that,
=
.
58. x +
= 5.
(a) What is the value of 2x +
? 10.
(b) Find the value of
. 23.
(c) Prove that, (
) = 525.
59. a + b = 8 and a – b = 4.
(a) What is the value of 5a + 5b? 40.
(b) What is the value of ab? 12.
(c) What is the value of 2( )? 40.
60. x + y = 7 and xy = 10.
(a) What is the value of 5xy? 50.
(b) What is the value of ( ) ? 29.
(c) What is the value of 79.
61. AB and CD are two parallel straight line and PQ is their transversal which
intersects the straight lines AB and CD at the points E and F.
(a) Draw the figure based on the stem.
(b) Prove that, AEF = alternate EFD.
(c) Prove that, BEF + EFD = 2 right angles.
62.
In the above mentioned figure, AB CD, BPE = and PQ = PR.
(a) Show that,
= .
(b) Determine the value of CQF. (c) Prove that, PQR is an equilateral triangle.
63. ABC is a triangle whose side BC is extended up to D and CE AB.
A B
E
F
C D
P
Q R
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(a) Draw the figure based on the above mentioned
information.
(b) Show that, ACD = A + B.
(c) Prove that, A + B + C = 2 right angles.
64. ABCD is a quadrilateral and AC is a diagonal of it.
(a) Draw the figure based on the stem.
(b) Prove that, A + B + C + D = 4 right angles.
(c) If CAB = ACB = 600, prove that, ABC = 120
0.
65. Two line segments PQ and RS intersect at O and L, M, E and F are four
points on them such that LM PQ.
(a) Draw the figure based on the stem.
(b) Prove that, MLO = FEO.
(c) Prove that, SEF = MLQ.
66. In ABC, AC BC; E is a point on AC produced.
ED AB is drawn to meet BC at O.
(a) draw the figure based on the stem.
(b) prove thatm, CEO = DBO.
(c) prove that, COD + CAD = 1800.
67. In ABC, AB>AC and the bisectors of the angle B and C intersect a the
point P.
(a) Draw the figure based on the information of the stem.
(b) Prove that, ACB > ABC.
(c) Prove that, PB> PC.
68. ABC is an isosceles triangle whose AB = AC. The side BC is extended up to
D.
(a) Draw the figure based on the information of the stem.
(b) Prove that, AD > AB.
(c) If BA is extended to E and AF BC, prove that,
CAE = 1800 –A.
69. In the quadrilateral ABCD, AB = AD, BC = CD and CD >AD.
(a) Draw the figure based on the information of the stem.
(b) Prove that, DAB>BCD.
(c) If B and D are joined, ABD = and CBD = , prove that, A +
C = . 70.
71.
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72. In ABC, ABC >ACB and D is the midpoint of BC.
(a) Draw the figure based on the information of the stem.
(b) Prove that, AC > AB.
(c) Prove that, AB + AC> 2AD.
73. In the ABC, AB = AC and D is a point of AC.
(a) Draw the figure based on the information of the stem.
(b) Prove that, AB> AD.
(c) If D is the midpoint of AC, Prove that, AB + BC >2BD.
74. In ABC, AB AC and D is a point on AC.
(a) Draw the figure based on the information of the stem.
(b) Prove that, BC> BD.
(c) Prove that, BC is the largest side of the right angled ABC.
75. In ABC, AC is the largest side.
(a) Draw the figure based on the information of the stem.
(b) Prove that, ABC is the largest angle.
(c) Prove that, AB + AC > BC.
76.
77.
In the above mentioned figure, QPM = RPM and
QPR = 900, PQ = 6 cm.
(a) Find the measure of the QPM. 450.
(b) What is the measure of the PQM and PRM? 450 and 45
0.
(c) Find the value of PR. 6 cm.
78. Two parallel straight lines AB and CE and he line PQ interests AB and CD
at E and F respectively.
(a) Draw the figure based on information.
(b) Show that, AEP = CFE.
(c) Prove that, AEF + CFE = 2 right angles.
Statistics
79. Following are the marks obtained on Mathematics by 60 students of a class