1. Fill in the blanks:
(a) 1 lakh = _______ ten thousand.
(b) 1 million = _______ hundred thousand.
(c) 1 crore = _______ ten lakh.
(d) 1 crore = _______ million.
(e) 1 million = _______ lakh.

2. A book exhibition was held for four days in a school. The number of tickets sold
at the counter on the first, second, third and final day was respectively 1094,
1812, 2050 and 2751. Find the total number of tickets sold on all the four days.

3. Estimate each of the following using general rule:
(a) 730 + 998 (b) 796 – 314 (c) 12,904 +2,888 (d) 28,292 – 21,496
Make ten more such examples of addition, subtraction and estimation of their outcome.

4. Write in Roman Numerals (a) 69 (b) 98.

5. Write the next three natural numbers after 10999.

6. Write the three whole numbers occurring just before 10001.

7. Which is the smallest whole number?

8. How many whole numbers are there between 32 and 53?

9. Write the successor of :

(a) 2440701 (b) 100199 (c) 1099999 (d) 2345670

10. Write the predecessor of :

(a) 94 (b) 10000 (c) 208090 (d) 7654321
11. Find the sum by suitable rearrangement:
(a) 837 + 208 + 363 (b) 1962 + 453 + 1538 + 647

12. Find the product by suitable rearrangement:
(a) 2 × 1768 × 50 (b) 4 × 166 × 25 (c) 8 × 291 × 125
(d) 625 × 279 × 16 (e) 285 × 5 × 60 (f) 125 × 40 × 8 × 25

13. Find the value of the following:
(a) 297 × 17 + 297 × 3 (b) 54279 × 92 + 8 × 54279
(c) 81265 × 169 – 81265 × 69 (d) 3845 × 5 × 782 + 769 × 25 × 218

14. If the product of two whole numbers is zero, can we say that one or both of them will
be zero? Justify through examples.

15. Write all the factors of the following numbers :

(a) 24 (b) 15 (c) 21
(d) 27 (e) 12 (f) 20
(g) 18 (h) 23 (i) 36

16. Write first five multiples of :
(a) 5 (b) 8 (c) 9

17. What is the sum of any two (a) Odd numbers? (b) Even numbers?

18. State whether the following statements are True or False:
(a) The sum of three odd numbers is even.
(b) The sum of two odd numbers and one even number is even.
(c) The product of three odd numbers is odd.
(d) If an even number is divided by 2, the quotient is always odd.
(e) All prime numbers are odd.
(f) Prime numbers do not have any factors.
(g) Sum of two prime numbers is always even.
(h) 2 is the only even prime number.
(i) All even numbers are composite numbers.
(j) The product of two even numbers is always even.

19. Using divisibility tests, determine which of the following numbers are divisible by 2;
by 3; by 4; by 5; by 6; by 8; by 9; by 10 ; by 11 (say, yes or no):
128,990,1586,275,639210,6686, 429714,2856,3060,406839

20. Find the common factors of :
(a) 4, 8 and 12 (b) 5, 15 and 25

21. Which of the following statements are true?
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) A number is divisible by 18, if it is divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

22. Find the HCF of the following numbers :
(a) 18, 48 (b) 30, 42 (c) 18, 60 (d) 27, 63
(e) 36, 84 (f) 34, 102 (g) 70, 105, 175
(h) 91, 112, 49 (i) 18, 54, 81 (j) 12, 45, 75

23. Find the LCM of 40, 48 and 45.

24. Renu purchases two bags of fertiliser of weights 75 kg and 69 kg. Find the maximum
value of weight which can measure the weight of the fertiliser exact number of times.

25. Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm
and 77 cm respectively. What is the minimum distance each should cover so that all
can cover the distance in complete steps?

26. Use the figure to name :
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments

27. Draw rough diagrams to illustrate the following :
(a) Open curve (b) Closed curve.

28. Draw rough diagrams of two angles such that
they have
(a) One point in common.
(b) Two points in common.
(c) Three points in common.
(d) Four points in common.
(e) One ray in common.

29. Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point
Q in its exterior. Is the point A in its exterior or in its interior?

30. Draw a rough sketch of a quadrilateral PQRS. Draw
its diagonals. Name them. Is the meeting point of
the diagonals in the interior or exterior of the
quadrilateral?

31. From the figure, identify :
(a) the centre of circle (b) three radii
(c) a diameter (d) a chord
(e) two points in the interior (f) a point in the exterior
(g) a sector (h) a segment

32. (a) Is every diameter of a circle also a chord? (b) Is every chord of a circle also a diameter?

33. What is the disadvantage in comparing line segments by mere observation?

34. Why is it better to use a divider than a ruler, while measuring the length of a line segment?

35. What fraction of a clockwise revolution does the hour hand of a clock turn through,
when it goes from
(a) 3 to 9 (b) 4 to 7 (c) 7 to 10
(d) 12 to 9 (e) 1 to 10 (f) 6 to 3

36. Match the following :
(i) Straight angle (a) Less than one-fourth of a revolution
(ii) Right angle (b) More than half a revolution
(iii) Acute angle (c) Half of a revolution
(iv) Obtuse angle (d) One-fourth of a revolution
(v) Reflex angle (e) Between1/4 and 1/2 of a revolution
(f) One complete revolution

37. What is the measure of (i) a right angle? (ii) a straight angle?

38. Say True or False :
(a) The measure of an acute angle < 90°.
(b) The measure of an obtuse angle < 90°.
(c) The measure of a reflex angle > 180°.
(d) The measure of one complete revolution = 360°.
(e) If m∠A = 53° and m∠B = 35°, then m∠A > m∠B.

39. Which of the following are models for perpendicular lines :
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter ‘L’.
(d) The letter V.

40. Let PQ be the perpendicular to the line segment XY. Let PQ and XY intersect
in the point A. What is the measure of ∠PAY?

41. Name the types of following triangles :
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) ΔABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) ΔPQR such that PQ = QR = PR = 5 cm.
(d) ΔDEF with m∠D= 90°
(e) ΔXYZ with m∠Y= 90° and XY = YZ.
(f) ΔLMN with m∠L = 30°, m∠M = 70° and m∠N= 80°.

42. Say True or False :
(a) Each angle of a rectangle is a right angle.
(b) The opposite sides of a rectangle are equal in length.
(c) The diagonals of a square are perpendicular to one another.
(d) All the sides of a rhombus are of equal length.
(e) All the sides of a parallelogram are of equal length.
(f) The opposite sides of a trapezium are parallel.

43. Draw a rough sketch of a regular hexagon. Connecting any three of its vertices,
draw a triangle. Identify the type of the triangle you have drawn.

44. What shape is
(a) Your instrument box? (b) A brick?
(c) A match box? (d) A road-roller?
(e) A sweet laddu?

45. Write opposites of the following :
(a) Increase in weight (b) 30 km north (c) 326 BC
(d) Loss of Rs 700 (e) 100 m above sea level 

46. Using the number line write the integer which is :
(a) 3 more than 5
(b) 5 more than –5
(c) 6 less than 2
(d) 3 less than –2

47. Find
(a) 35 – (20) (b) 72 – (90)
(c) (– 15) – (– 18) (d) (–20) – (13)
(e) 23 – (– 12) (f) (–32) – (– 40)

48. What fraction of a day is 8 hours? Find the equivalent fraction of 2/5 with numerator 6.

49. Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After
4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal
used up 40 pencils. What fraction did each use up? Check if each has used up an
equal fraction of her/his pencils?

50. Reduce the following fractions to simplest form :
(a)48/60

51.  In a class A of 25 students, 20 passed in first class; in another class B of 30
students, 24 passed in first class. In which class was a greater fraction of students
getting first class?

52. Javed was given 5/7 of a basket of oranges. What fraction of oranges was left in
the basket? Jaidev takes 11/5 minutes to walk across the school ground. Rahul takes 7/4 minutes
to do the same. Who takes less time and by what fraction?

53. Write each of the following as decimals :
(a) 30 + 6 + 2/10
Write the following decimals in the place value table.
(a) 19.4 (b) 0.3 (c) 10.6 (d) 205.9
Write the following decimals as fractions. Reduce the fractions to lowest form.
(a) 0.6 (b) 2.5 (c) 1.0 (d) 3.8 (e) 13.7 (f) 21.2 (g) 6.4
Write each of the following decimals in words.
(a) 0.03 (b) 1.20 (c) 108.56 (d) 10.07 (e) 0.032 (f) 5.008
Write the following decimals in the place value table.
(a) 0.29 (b) 2.08 (c) 19.60 (d) 148.32 (e) 200.812
Which is greater?
(a) 1 or 0.99 (b) 1.09 or 1.093
1. Express as rupees using decimals.
(a) 5 paise (b) 75 paise (c) 20 paise
(d) 50 rupees 90 paise (e) 725 paise
Find the sum in each of the following :
(a) 0.007 + 8.5 + 30.08
(b) 15 + 0.632 + 13.8
(c) 27.076 + 0.55 + 0.004
(d) 25.65 + 9.005 + 3.7
(e) 0.75 + 10.425 + 2
(f) 280.69 + 25.2 + 38

54. 1. Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for her trouser. Find
the total length of cloth bought by her.
2. Naresh walked 2 km 35 m in the morning and 1 km 7 m in the evening. How much
distance did he walk in all?
3. Aakash bought vegetables weighing 10 kg. Out of this, 3 kg 500 g is onions, 2 kg 75 g
is tomatoes and the rest is potatoes. What is the weight of the potatoes?
4. Subtract :
(a) Rs 18.25 from Rs 20.75
(b) 202.54 m from 250 m
(c) Rs 5.36 from Rs 8.40
(d) 2.051 km from 5.206 km
(e) 0.314 kg from 2.107 kg

55. Total number of animals in five villages are as follows :
Village A : 80 Village B : 120
Village C : 90 Village D : 40
Village E : 60
Prepare a pictograph of these animals using one symbol to represent 10 animals
and answer the following questions :
(a) How many symbols represent animals of village E?
(b) Which village has the maximum number of animals?
(c) Which village has more animals : village A or village C?

56. Total number of students of a school in different years is shown in the following table
Years Number of students
1996 400
1998 535
2000 472
2002 600
2004 623
A. Prepare a pictograph of students using one symbol to represent 100 students and
answer the following questions:
(a) How many symbols represent total number of students in the year 2002?
(b) How many symbols represent total number of students for the year 1998?
B. Prepare another pictograph of students using any other symbol each representing 50
students. Which pictograph do you find more informative?

57. 1.Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular
park with length 60 m and breadth 45 m. Who covers less distance?
2. Bob wants to cover the floor of a room 3 m wide and 4 m long
by squared tiles. If each square tile is of side 0.5 m, then find the number of
tiles required to cover the floor of the room.
3. A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the
floor. Find the area of the floor that is not carpeted.
4. The side of an equilateral triangle is shown by l. Express the
perimeter of the equilateral triangle using l.
5. Give expressions in the following cases.
(a) 11 added to 2m (b) 11 subtracted from 2m
(c) 5 times y to which 3 is added (d) 5 times y from which 3 is subtracted
(e) y is multiplied by – 8
(f) y is multiplied by – 8 and then 5 is added to the result
(g) y is multiplied by 5 and the result is subtracted from 16
(h) y is multiplied by – 5 and the result is added to 16.

58. 1. (a) Take Sarita’s present age to be y years
(i) What will be her age 5 years from now?
(ii) What was her age 3 years back?
(iii) Sarita’s grandfather is 6 times her age. What is the age of her grandfather?
(iv) Grandmother is 2 years younger than grandfather. What is grandmother's age?
(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father's age?
2. A bus travels at v km per hour. It is going from Daspur to Beespur. After the
bus has travelled 5 hours, Beespur is still 20 km away. What is the distance
from Daspur to Beespur? Express it using v.
3. State which of the following are equations (with a variable). Give reason for
your answer. Identify the variable from the equations with a variable.
(a) 17 = x + 7 (b) (t – 7) > 5 (c)4/2= 2
(d) (7 × 3) – 19 = 8 (e) 5 × 4 – 8 = 2 x (f ) x – 2 = 0
(g) 2m < 30 (h) 2n + 1 = 11 ( i) 7 = (11 × 5) – (12 × 4)
( j) 7 = (11 × 2) + p (k) 20 = 5y ( l )3/2q< 5
(m) z + 12 > 24 (n) 20 – (10 – 5) = 3 × 5
(o) 7 – x = 5
4.Length and breadth of a rectangular field are 50 m and 15 m
respectively. Find the ratio of the length to the breadth of the field.
5. If the cost of a dozen soaps is Rs 153.60, what will be the cost
of 15 such soaps?
6. Write True ( T ) or False ( F ) against each of the following statements :
(a) 16 : 24 :: 20 : 30 (b) 21: 6 :: 35 : 10 (c) 12 : 18 :: 28 : 12
7.Are the following statements true?
(a) 40 persons : 200 persons = Rs 15 : Rs 75
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
(c) 99 kg : 45 kg = Rs 44 : Rs 20
(d) 32 m : 64 m = 6 sec : 12 sec
(e) 45 km : 60 km = 12 hours : 15 hours

59. 1. If the cost of a dozen soaps is Rs 153.60, what will be the cost of 15 such soaps?
2. Cost of 4 dozens bananas is Rs 60. How many bananas can be purchased for Rs 12.50?
3. On a squared paper, sketch the following:
(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry.
(b) A quadrilateral with both horizontal and vertical lines of symmetry.
(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.
(d) A hexagon with exactly two lines of symmetry.
(e) A hexagon with six lines of symmetry.
(Hint : It will be helpful if you first draw the lines of symmetry and then complete
the figures.)
4. With the same centre O, draw two circles of radii 4 cm and 2.5 cm.
5. Construct a line segment of length 5.6 cm using ruler and compasses.
6. Draw any line segment PQ. Without measuring PQ, construct a copy of PQ.
7. Draw any line segment PQ. Take any point R not on it. Through R, draw a perpendicular to PQ. (use ruler and set-square)
8. Draw the perpendicular bisector of XY whose length is 10.3 cm.
(a) Take any point P on the bisector drawn. Examine whether PX = PY.
(b) If M is the mid point of XY, what can you say about the lengths MX and XY?

60. 0.Draw AB of length 7.3 cm and find its axis of symmetry.
1. Draw ∠POQof measure 75° and find its line of symmetry.
2. Draw an angle of measure 147° and construct its bisector.
3. Draw a right angle and construct its bisector.
4. Draw an angle of measure 153° and divide it into four equal parts.
5. Construct with ruler and compasses, angles of following measures:
(a) 60° (b) 30° (c) 90° (d) 120° (e) 45° (f) 135°
6. Draw an angle of measure 45° and bisect it.
7. Draw an angle of measure 135° and bisect it.
8. Draw an angle of 70o. Make a copy of it using only a straight edge and compasses.
9. Draw an angle of 40o. Copy its supplementary angle.