Q1. A Television set is sold for Rs 20000 cash or for Rs 6000 as cash down
payment followed by Rs 16800 after six months. Find the rate of interest charged under the
instalment plan.

Q2. A table fan is sold for Rs 450 cash or Rs 210 cash down payment followed by
two monthly instalments of Rs 125 each. Find the rate of interest charged under the instalment
plan.

Q3. A microwave oven is available for Rs9600 cash or for Rs4000 cash down
payment and 3 monthly instalments of Rs2000 each. Find the rate of interest charged under
the instalment plan.

Q4. A computer is sold for Rs30,000 cash or Rs18000 cash down payment and
6 monthly instalments of Rs2150 each. Find the rate of interest charged under the instalment
plan.

Q5. A ceiling fan is marked at Rs1940 cash or for Rs420 cash down payment
followed by three equal monthly instalments. If the rate of interest charged under the
instalment plan is 16% per annum, find the monthly instalment.

Q6. A computer is available for Rs34000 cash or Rs20000 cash down payment
together with 5 equal monthly instalments. If the rate of interest charged under the instalment
plan is 30% per annum, calculate the amount of each instalment.

Q7. The cost of a washing machine is Rs12000. The company asks for Rs5200
in advance and the rest to be paid in equal monthly instalments. The rate of interest to be
charged is 12% per annum. If a customer can pay Rs1400 each month, then how many
instalments he will have to pay?

Q8. A bicycle is sold for Rs500 cash down payment and Rs610 after one month.
If the rate of interest being charged is 20% p.a., find the cash price of the bicycle.

Q9. A camera is sold for Rs2500 as cash down payment and Rs2100 after 3
months. If the rate of interest charged is 20% p.a., find the cash price of the camera.

Q10. A mixi was purchased by paying Rs360 as cash down payment followed
by three equal monthly instalments of Rs390 each. If the rate of interest charged under
instalment plan is 16% p.a., find the cash price of the mixi.

Q11. A refrigerator is available for Rs12000 cash or Rs3600 cash down payment
along with 2 equal half yearly instalments. If the dealer charges an interest of 20% p.a.
compounded semi-annually, under the instalment plan, find the amount of each instalment.

Q12. A washing machine was available for Rs15000 cash but was purchased
under an instalment plan after paying Rs2250 as cash down payment followed by two
equal half yearly instalments. If interest charged was 8% per annum compounded semiannually,
find the value of each instalment.

Q13. A juicer is available for Rs3500 cash but was sold under instalment plan
where the purchaser agreed to pay Rs1500 cash down and 3 equal quarterly instalments.
If the dealer charges interest at 12% p.a. compounded quarterly, find the amount of each
instalment to the nearest rupee.

Q14. A television set is sold for Rs7110 cash down payment along with
2 equal monthly instalments of Rs5581.50 each. If the dealer charges interest at 20% p.a.
compounded monthly under the instalment plan, find the cash price of the television set.

Q15. A dealer offeres a micro-oven for Rs5800 cash. A customer agrees to pay
Rs1800 cash down and 3 equal annual instalments. If the dealer charges interest at 12%
p.a. compounded annually, what is the amount of each instalment.

Q16. A flat is available for Rs1600000 cash or Rs585500 cash down payment
and three equal half yearly instalments. If the interest charged is 16% per annum
compounded half yearly, calculate the value of each instalment. Find also the total interest
charged.
 

Q17. Shweta obtained 18 marks in a test of 25 marks. What was her percentage
of marks?.

Q18. One-fourth of the total number of shoes in a shop were on discount sale.
What percent of the shoes were there on normal price?

Q19. Out of 40 students in a class, 32 opted to go for a picnic. What percent of
students opted for picnic?

Q20. In the word ARITHMETIC, what percent of the letters are I’s?

Q21. A mixture of 80 litres, of acid and water, contains 20 litres of acid. What
percent of water is in the mixture?

Q22. In an examination, Neetu scored 62% marks. If the total marks in the
examination are 600, then what are the marks obtained by Neetu?

Q23. Naresh earns Rs 30800 per month. He keeps 50% for household expenses,
15% for his personal expenses, 20% for expenditure on his children and the rest he saves.
What amount does he save per month?

Q24. What percent of 360 is 144?

Q25. If 120 is reduced to 96, what is the reduction percent?

Q26. The cost of an article has increased from Rs 450 to Rs 495. By what percent
did the cost increased?

Q27. 60% of the students in a school are girls. If the total number of girls in the
school is 690, find the total number of students in the school. Also, find the number of boys
in the school.

Q28. A’s income is 25% more than that of B. B’s income is 8% more than that
of C. If A’s income is Rs 20250, then find the income of C.

Q29. A reduction of 10% in the price of tea enables a dealer to purchase 25 kg
more tea for Rs 22500. What is the reduced price per kg of tea? Also, find the original price
per kg.

Q30. A student got 45% marks in the first paper and 70% in the second paper.
How much percent should he get in the third paper so as to get 60% as overall score?

Q31. Find the sum which when increased by 15% becomes Rs 19320.

Q32. A shopkeeper buys an article for Rs. 360 and sells it for Rs. 270. Find his
gain or loss percent.

Q33. Sudha purchased a house for Rs 4,52,000 and spent Rs 28,000 on its
repairs. She had to sell it for Rs 4,92,000. Find her gain or loss percent.

Q34. By selling a book for Rs 258, a publisher gains 20%. For how much should
he sell it to gain 30%?

Q35. A man bought oranges at 25 for Rs 100 and sold them at 20 for Rs 100.
Find his gain or loss percent.

Q36. A man sold two horses for Rs 29700 each. On one he lost 10% while he
gained 10% on the other. Find his total gain or loss percent in the transaction.

Q37. The cost price of 15 articles is equal to the selling price of 12 articles. Find
the gain percent.

Q38. A watch was sold at a profit of 12%. Had it been sold for Rs 33 more, the
profit would have been 14%. Find the cost price of the watch.

Q39. A machine listed at Rs 8400 is available for Rs 6300. Find the rate of
discount offered.

Q40. A coat is marked at Rs 2400. Find its selling price if a discount of 12% is
offered.

Q41. A wholesaler’s list price of a fan is Rs 1250 and is available to a retailer at
a discount of 20%. For how much should the retailer sell it, to earn a profit of 15%.

Q42. A shopkeeper marks his goods 25% more than their cost price and allows
a discount of 10%. Find his gain or loss percent.

Q43. An article listed at Rs 5400 is offered at a discount of 15%. Due to festival
season, the shopkeeper allows a further discount of 5%. Find the selling price of the
article.

Q44. A retailer buys books from a wholesaler at the rate of Rs 300 per book and
marked them at Rs 400 each. He allows some discount and gets a profit of 30% on the cost
price. What percent discount does he allow to his customers?

Q45. Find at what rate of simple interest per annum will Rs 5000 amount to
Rs 6050 in 3 years.

Q46. A sum amounts to Rs 4875 at 12+1/2% simple interest per annum after 4 years. Find the sum.

Q47. In how many years will a sum of Rs 2000 yield an interest (Simple) of
Rs 560 at the rate of 14% per annum?

Q48. A certain sum of money at simple interest amounts to Rs 1300 in 4 years
and to Rs 1525 in 7 years. Find the sum and rate percent.

Q49. Out of Rs 70,000 to invest for one year, a man invests Rs 30,000 at 4% and
Rs 20,000 at 3% per annum simple interest. At what rate percent, should he lend the
remaining money, so that he gets 5% interest on the total amount he has?

Q50. Find the compound interest on a sum of Rs. 2000, for two years when the
interest is compounded annually at 10% per annum.

Q51. Calculate the compound interest on Rs 20,000 for 3 years at 5% per
annum, when the interest is compounded annually.

Q52. Calculate the compound interest on Rs 20,000 for 1+1/2years at the rate of
10% per annum, when the interest is compounded semi-annually.

Q53. Calculate the compound interest on Rs 20,000 for 9 months at the rate of
4% per annum, when the interest is compounded quarterly.

Q54. calculate the amount and compound interest on Rs 12000 for 1+1/2years at
the rate of 10% per annum compounded annually.

Q55. At what rate percent per annum, will a sum of Rs 15,625 become
Rs 17576 in three years, when the interest is compounded annually?

Q56. In how much time will a sum of Rs 8000 amount to Rs 9261 at 10% per
annum, compounded semi-annually?

Q57. Find the difference between simple interest and compound interest for1+1/2
years at 4% per annum, for a sum of Rs 24000, when the interest is compounded semiannually..

Q58. A sum of money is invested at compound interest for 1+1/2year at 4%
compounded annually. If the interests were compounded semi-annually, it would have
fetched Rs 20.40 more than in the previous case. Find the sum.

Q59. The population of a city is 9765625. What will be its population after 3
years, if the rate of growth of population is 4% per year?

Q60. The cost of a car was Rs 3,50,000 in January 2005. If the rate of depreciation
is 15% for the first year and 10% for the subsequent years, find its value after 3 years.

Q61. A plant gains its height at the rate of 2% per month of what was its height
in the beginning of the month. If its height was 1.2 m in the beginning of January 2008, find
its height in the beginning of April 2008, correct upto 3 places of decimal.

Q62. The virus of a culture decreases at the rate of 5% per hour due to a
medicine. If the virus count in the culture at 11.00 AM was 2.3 × 107, find the virus count
at 1.00 PM on the same day.

Q63. The sum of first three terms of an AP is 36 and their product is 1620. Find
the AP.

Q64. Find the sum of all natural numbers between 1 and 1000 which are divisible
by 7.

Q65. How may terms of the AP 2, 4, 6, 8, 10 .... are needed to get sum 210?

Q66. If p times the pth term of an AP is equal to q times the qth term, prove that
its (p + q)th term is zero, provided p ≠ q.

Q67. If the pth, qth and rth terms of an AP are x, y and z respectively, prove that:
x (q – r) + y (r – p) + z (p – q) = 0

Q68. The first term of an AP is – 2 and 11th term is 18. Find its 15thterm.

Q69. The common difference of an AP is 5 and 10th term is 43. Find its first
term.

Q70. The first term of an AP is – 3 and 12th term is 41. Determine the common
difference.

Q71. Find the 15th and nth terms of the AP

Q72. If 7 times the 7th term of an AP is equal to 11 times the 11th term, show that the 18th
term is zero.

Q73. The fourth term of an AP is equal to three times its first term and seventh term exceeds
twice the third term by 1. Find the first term and common difference.

Q74. The angles of a triangle are in AP. If the smallest angle is one-third the largest angle,
find the angles of the triangle.

Q75. If k + 2, 4k – 6 and 3k – 2 are three consecutive terms of an AP, find k.

Q76. Each term of an AP whose first term is a and common difference is d, is doubled. Is the
resulting pattern an AP? If so, find its first term and common difference.

Q77. Solve the equation (x – 4)(x + 3) = 0

Q78. Solve the equation 6x2 + 7x – 3 = 0 by factorisation.

Q79. Using quadratic formula, find the roots of the equation 6x2 – 19x + 15 = 0

Q80. Find the value of m sothat the equation 3x2 + mx – 5 = 0 has equal roots.

Q81. The sum of squares of two consecutive odd natural numbers is 74. Find the
numbers.

Q82. The sum of the areas of two square fields is 468 m2. If the difference of
their perimeter is 24 m, find the sides of the two squares.

Q83. The product of digits of a two digit number is 12. When 9 is added to the
number, the digits interchange their places. Determine the number.

Q84. The sum of two natural numbers is 12. If sum of their reciprocals is 9/4,find the numbers.

Q85. Twice a number subtracted from 15 is 7.

Q86. A motor boat uses 0.1 litres of fuel for every kilometer. One day, it made a trip of x
km. Form an equation in x, if the total consumption of fuel was 10 litres.

Q87. The length of rectangle is twice its width. The perimeter of rectangle is 96m. [Assume
width of rectangle as y m]

Q88. After 15 years, Salma will be four times as old as she is now. [Assume present age of
Salma as t years]

Q89. The present age of Jacob’s father is three times that of Jacob. After 5
years, the difference of their ages will be 30 years. Find their present ages.

Q90. The sum of three consecutive even integers is 36. Find the integers.

Q91. The length of a rectangle is 3 cm more than its breadth. If its perimeter is
34 cm find its length and breadth.

Q92. The sum of two integers is 15. Form a linear equation in two variables

Q93. The perimeter of a rectangular garden is 20 m. If the length is 4 m more
than the breadth, find the length and breadth of the garden.

Q94. Asha is five years older than Robert. Five years ago, Asha was twice as
old as Robert was then. Find their present ages.

Q95. Two places A and B are 100 km apart. One car starts from A and another
from B at the same time. If they travel in the same direction, they meet after 5 hours. If they
travel towards each other, they meet in 1 hour. What are the speeds of the two cars.
Assume that the speed of car at A is more than the speed of car at B.

Q96. The sum of the digits of a two-digit number is 11. If the digits are reversed, the new
number is 27 less than the original number. Find the original number.

Q97. Three years ago Atul's age was four times Parul's age. After 5 years from now, Atul's
age will be two times Parul's age. Find their present ages.

Q98. The perimeter of a rectangular plot of land is 32 m. If the length is increased by 2m and
breadth is decreased by 1 m, the area of the plot remains the same. Find the length and
breadth of the plot.

LAST UPDATED : 31/08/2021 | 06:30AM

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1Q. Questions Given Below :

2Q. Questions Given Below :

3Q. Questions Given Below :

4Q. Questions Given Below :

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.

1. In a survey of 600 students in a school, 150 students were found to be taking tea
and 225 taking coffee, 100 were taking both tea and coffee. Find how many
students were taking neither tea nor coffee?

2. If R is the set of real numbers and Q is the set of rational numbers, then what is
R – Q?

3. 9. Let R be the relation on Z defined by R = {(a,b): a, b Î Z, a – b is an integer}.
Find the domain and range of R.

4. The Cartesian product A × A has 9 elements among which are found (–1, 0) and
(0,1). Find the set A and the remaining elements of A × A.

5. Let A = {9,10,11,12,13} and let f : A ->N be defined by f (n) = the highest prime
factor of n. Find the range of f.

6. Let f be the subset of Z × Z defined by f = {(ab, a + b) : a, b E Z}. Is f a
function from Z to Z? Justify your answer.

7. The minute hand of a watch is 1.5 cm long. How far does its tip move in
40 minutes? (Use pi = 3.14).

8. If the arcs of the same lengths in two circles subtend angles 65°and 110°
at the centre, find the ratio of their radii.

9. If cot x = –5/12, x lies in second quadrant, find the values of other five
trigonometric functions.

10. cosec (– 1410°)

11. Prove that sin5x - 2sin3x + sinx /cos5x - cosx = tanx

12. Find the principal solutions of the equation tan x = −1/3.

13. (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0

14. For every positive integer n, prove that 7n – 3n is divisible by 4.

15. Prove that (1 + x)n ³ (1 + nx), for all natural number n, where x > – 1.

16. If 4x + i(3x – y) = 3 + i (– 6), where x and y are real numbers, then find
the values of x and y.

17. Express (5 – 3i)3 in the form a + ib.

18. Represent the complex number z =1+ i square root 3 in the polar form & arguments.

19. Find Roots : 21x2 − 28x +10 = 0

20. Solve 7x + 3 < 5x + 9. Show the graph of the solutions on number line.

21. How many 2 digit even numbers can be formed from the digits
1, 2, 3, 4, 5 if the digits can be repeated?

22. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the
digits can be repeated?

23. Using binomial theorem, prove that 6n–5n always leaves remainder
1 when divided by 25.

24. Compute (98)5

25. Which is larger (1.01)1000000 or 10,000?

26. In an A.P. if mth term is n and the nth term is m, where m is not equal to n, find the pth
term.

27. In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of
the next five terms. Show that 20th term is –112.

28. Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).

29. Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7),
(5, – 5) and (– 4, –2). Also, find its area.

30. Find the equation of the circle passing through the points (4,1) and (6,5) and
whose centre is on the line 4x + y = 16.

31. Find the equation of set of points P such that PA2 + PB2 = 2k2, where
A and B are the points (3, 4, 5) and (–1, 3, –7), respectively.

32. Find the derivative of f(x) = 1 + x + x2 + x3 +... + x50 at x = 1.

33. 

34. Write the negation of the following statements:
(i) p: For every positive real number x, the number x – 1 is also positive.
(ii) q: All cats scratch.
(iii) r: For every real number x, either x > 1 or x < 1.
(iv) s: There exists a number x such that 0 < x < 1.

35. The mean and variance of eight observations are 9 and 9.25, respectively. If six
of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

36. A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles
are drawn from the box, what is the probability that
(i) all will be blue? (ii) atleast one will be green?
 

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