8th Mathematics MCQs

CHAPTER –1. 

RATIONAL NUMBERS.

 

Put a tick mark (√) on the correct answer :

Q1.Which of the following numbers is the additive inverse of 7/29
(i) 29/7
(ii)—29/7
(iii) –7/29
(iv) 7/29

Q2.Which of the following numbers is the multiplicative inverse of 15/31
(i) 31/15
(ii)—31/15
(iii) –15/31
(iv) 15/31

Q3.Which of the following numbers has no multiplicative inverse
(i) zero
(ii) 1
(iii) – 1
(iv) none of these

Q4. Which of the following numbers is the product of 6/13 & -- 26/3
(i) 1
(ii) —4
(iii) –266/133
(iv) 266/133

Q5.Which of the following numbers is its own reciprocal
(i) 10
(ii) zero
(iii) 1/5
(iv) 1

Q6.Which of the following numbers is the decimal form of 1/4
(i) -- 0.25
(ii) 2.5
(iii) 0.25
(iv) – 2.5

Q7.Which of the following numbers lies in the middle of 3/4 & 7/4
(i) 5.0
(ii) 3.0
(iii) 2.5
(iv) 1.25

Q8.Which pair of following numbers is respectively the additive & multiplicative identities.
(i) 2 & 0
(ii) 1 & --1
(iii) --1 & 0
(iv) 0 & 1

Q9.Which of the following numbers is the simplest form of 3/4 + ( -- 1/4) + (-- 5/4)
(i) 9/4
(ii) —3/4
(iii) -- 9/4
(iv) 7/4

Q10.Which of the following properties indicates the given operation
[( –1/5) + (--3/5) ] + (1/7) = (--1/5) + [ (--3/5)+ (1/7)]
(i) commutative
(ii) associative
(iii) distributive
(iv) none of these

 

 

Chapter 2 

Linear Equations in One Variable 

 

Question: A student has to secure 40% marks to pass. He got 40 marks and failed by 40 marks. The maximum number of marks is
a) 200
b) 160
c) 180
d) 320

Question: If the sum of three consecutive even numbers is 234, then the smallest among them is

a) 76
b) 80
c) 78
d) none

 

Question: Two angles in a triangle are in the ratio 4: 5. If the sum of these angles is equal to the third aJlglc, the third angle is

a) 90°
b) 40°
c) 180°
d) 50°

 

Question: The ratio of number of males to number of females in a club are 7 : 4. If there are 84 males in the club, the total number of members in the club are

a) 132
b) 148
c) 16
d) 136

 

Question: The prices of a scooter and cycle are in in the ratio 9 : 5. If a scooter costs Rs. 4200 more than a cycle. The price of cycle is

a) Rs. 5250
b) Rs.5000
c) Rs. 5200
d) Rs.4800

 

Question: The ratio of two numbers is 3: 8 and their difference is 115. The largest number is

a) 184
b) 69
c) 115
d) 230

 

Question: A number 351 is divided into two parts in the ratio 2 : 7. Find the product of the numbers.

a) 21294
b) 31294
c) 20294
d) 25295

 

Question: A boat goes downstream and covers the distance between two ports in 4 hrs while it covers the same distance upstream in 5 hrs. If the speed of the stream is 2 kmph, the speed of the boat in still water is

a) 18 km/hr
b) 20 km/hr
c) 15 km/hr
d) 24 km/hr

 

Question: If 2/3 of a number if 20 less than the original number, then the number is

a) 40
b) 120
c) 60
d) 80

 

Question: If 10 is added to four times a certain number the result is 5 less than five times the number. The number is

a) 10
b) 20
c) 15
d) 25

 

Question: If a number increased by 8% of itself gives 135, then that number is
a) 125
b) 112
c) 100
d) none

 

Question: A number consists of two digits whose sum is 8. If 18 is added to the number, its digits are interchanged. Find the number

a) 35
b) 63
c) 53
d) 92

 

Question: How much pure alcohol should be added to 400 ml of a 15% to make its strength 32%?

a) 100 ml
b) 150 ml
c) 50 ml
d) None of these

 

Question: By selling a bicycle for Rs.1885, a man gains 16%. At what price did he buy the bicycle?
a) Rs.1625
b) Rs.1825
c) None
d) Rs.2000

 

Question: X and Y together can do a piece of work in 8 days, which X alone can do in 12 days. In how many days can Y do the same work alone?
a) 24 days
b) 16 days
c) 12 days
d) 36 days

 

Question: A man can row at 8 kmph in still water. If the river is running at 2 kmph, it takes him 48 minutes to row to a place and back. How far is the place?
a) 3 km
b) 1 km
c) 2 km
d) 4 km

 

Question: If the angles of a triangle are in the ratio 2 : 3 : 4, then the difference between the greatest and smallest angles is

a) 40°
b) 20°
c) 10°
d) 30°

 

Question: The consecutive multiples of 3 whose sum is 51 are

a) 24, 27
b) 40, 11
c) 20, 31
d) 25, 26

 

Question: If the digit 1 is placed after a two digit number whose tens digit is ‘t’ and units digit is ‘u’, the new number is

a) 100t + 10u + 1
b) none
c) 10t + u + 1
d) t + u + 1

 

Question: The solution of X−5/2 − X−3/5 = 1/2 is 

a) x = 8
b) x = 7
c) x = 9
d) x = 5

  

Put a tick mark(√) on the correct answer :

Q1. If (x/3) + 1 = ( 7/15) then the value of ‘x’ is
(i) 22/5
(ii)—8/5
(iii) 7/5
(iv) 3

Q2.What is the degree of the equation x² + 2x – 3 = x² + 7x -- 23
(i) zero
(ii) one
(iii) two
(iv) three

Q3.What is the length of the rectangle whose breadth is 10 cm & perimeter 60 cm.
(i) 15cm
(ii) 16cm
(iii) 20cm
(iv) 25cm

Q4.What should be added to –3/5 to get – 7/5
(i) 4/5
(ii) 1
(iii) –4/5
(iv) 2

Q5.If x % of 50 is 10, then the value of ‘x’ is
(i) 30
(ii) 15
(iii) 10
(iv) 20

Q6.Two numbers are in the ratio 3: 5. If their sum is 64, then the numbers are
(i) 24 & 40
(ii) 1 5& 24
(iii) 10 & 24
(iv) 20 & 24

Q7.The sum of the ages of three persons is 100 years. What will be the sum of their ages after 5 years?
(i) 100 yrs.
(ii) 115 yrs.
(iii) 300 yrs.
(iv) 305yrs.

Q8. The sum of three consecutive multiples of ‘5’ is 45. Which is the smallest of the three multiples.
(i) 10
(ii) 15
(iii) 20
(iv) 25

Q9.If z/(z + 15) = 4/9 , then the value of ‘z’ is
(i) 11
(ii) 12
(iii) 13
(iv) 14

Q10.Sum of two numbers is 95.If one exceeds the other by 15 , then the numbers are
(i) 25 & 40
(ii) 50 & 65
(iii) 30 & 45
(iv) 40 & 55 

 

 1. A student has to secure 40% marks to pass. He got 40 marks and failed by 40 marks. The maximum number of marks is

(A) 160
(B) 180
(C) 200
(D) 320

2. If the sum of three consecutive even numbers is 234, then the smallest among them is
(A) 76
(B) 78
(C) 80
(D) none

3. Two angles in a triangle are in the ratio 4: 5. If the sum of these angles is equal to the third aJlglc, the third angle is
(A) 180°
(B) 40°
(C) 50°
(D) 90°

4. The ratio of number of males to number of females in a club are 7 : 4. If there are 84 males in the club, the total number of members in the club are
(A) 16
(B) 132
(C) 136
(D) 148

5. The prices of a scooter and cycle are in the ratio 9 : 5. If a scooter costs Rs. 4200 more than a cycle. The price of cycle is
(A) Rs. 5250
(B) Rs. 5200
(C)Rs.5000
(D)Rs.4800

6. The ratio of two numbers is 3: 8 and their difference is 115. The largest number is
(A) 69
(B) 115
(C) 184
(D) 230

7. A number 351 is divided into two parts in the ratio 2 : 7. Find the product of the numbers.
(A) 20294
(B) 21294
(C) 25295
(D) 31294

8. A boat goes downstream and covers the distance between two ports in 4 hrs while it covers the same distance upstream in 5 hrs. If the speed of the stream is 2 kmph, the speed of the boat in still water is
(A) 15 km/hr
(B) 20 km/hr
(C) 24 km/hr
(D) 18 km/hr

9. If 2/3 of a number if 20 less than the original number, then the number is
(A) 60
(B) 40
(C) 80
(D) 120

10. If 10 is added to four times a certain number the result is 5 less than five times the number. The number is
(A) 10
(B) 15
(C) 20
(D) 25

11. The solution of √3x = 2√3 + x
(a) 3 + √3
(b) 2√3/√3-1
(c) √3/√3-1
(d) None

12. If a number increased by 8% of itself gives 135, then that number is
(A) 112
(B) 100
(C) 125
(D) none

13. A number consists of two digits whose sum is 8. If 18 are added to the number, its digits are interchanged. Find the number
(A) 53
(B) 35
(C) 92
(D) 63

14. How much pure alcohol should be added to 400 ml of a 15% to make its strength 32%?
(A) 50 ml
(B) 75 ml
(C) 100 ml
(D) 150 ml

15. by selling a bicycle for Rs.1885, a man gains 16%. At what price did he buy the bicycle?
(A) Rs.1625
(B) Rs.1825
(C) Rs.2000
(D) None

16. X and Y together can do a piece of work in 8 days, which X alone can do in 12 days. In how many days can Y do the same work alone?
(A) 12 days
(B) 24 days
(C) 36 days
(D) 16 days

17. A man can row at 8 kmph in still water. If the river is running at 2 kmph, it takes him 48 minutes to row to a place and back. How far is the place?
(A) 1 km
(B) 2 km
(C) 3 km
(D) 4 km

18. The solution of (x + 4)3 – (x – 5)2 = 9 is
(A) 1
(B) 2
(C) 3
(D) 4

19. If the angles of a triangle are in the ratio 2 : 3 : 4, then the difference between the greatest and smallest angles is
(A) 10°
(B) 20°
(C) 30°
(D) 40°

20. The consecutive multiples of 3 whose sum is 51 are
(A) 24, 27
(B) 20, 31
(C) 40, 11
(D) 25, 26

21. If the digit 1 is placed after a two digit number whose tens digit is ‘t’ and units digit is ‘u’, the new number is
(A) 10t + u + 1
(B) 100t + 10u + 1
(C) t + u + 1
(D) none

22. The solution of x - 5 / 2, - x - 3 / 5 = 1/2 is
(A) x = 7
(B) x = 9
(C) x = 8
(D) x = 5

23. The solution of 2x - 1 / 3x - 1 = 3/2 is
(A) x = 1
(B) x = –1
(C) x = 2
(D) x = –3

24. In an examination a student was asked to find 3/14th of a certain number. By mistake, he found 3/4 or it. His answer was 150 more than the correct answer. The number given him is
(A) 290
(B) 280
(C) 240
(D) 180

25. 2/3rd of a number when multiplied by 3/4th of the same number make 338. The number is
(A) 18
(B) 24
(C) 36
(D) 26

26. A man is 5 years older than his wife and the wife is now thrice as old as their daughter, who is 10 years old. How old was the man when his daughter was born?
(A) 20 years
(B) 23 years
(C) 25 years
(D) 30 years

27. Twenty years ago, my age was 1/3rd of what it is now. My present age is
(A) 66 years
(B) 30 years
(C) 33 years
(D) 36 years

29. There were only two candidates in an election. One got 62% votes and was elected by a margin of
144 votes. The total number of voters were
(A) 500
(B) 600
(C) 700
(D) 800

30. When 75% of a number is added to 75 the result is the number again. The number is
(A) 150
(B) 300
(C) 100
(D) 450

31. Twenty years ago, my age was 1/3rd of what is it now. My present age is
(A) 66 years
(B) 30 years
(C) 33 years
(D) 36 years

32. If the angles of a triangle are in the ratio 2 : 3 : 4, then the difference between the greatest and smallest angles is
(A) 10°
(B) 20°
(C) 30°
(D) 40°

33. A 100 litres solution of acid and water contains 20 liters of acid. How much water must be added to make the solution 16% acidic?
(A) 20 litres
(B) 25 litres
(C) 30 litres
(D) 40 litres

34. The length of a rectangle is 6m less than the three times its breadth. The length and breadth of the rectangle if its perimeter is 148 m, is
(A) 54 m, 20 m
(C) 50 m, 30 m
(C) 40 m, 25 m
(D) 30 m, 20 m

35. by selling a bicycle for Rs. 1885, a man gains 16%. At what price did he buy the bicycle?
(A) Rs. 1625
(B) Rs. 1825
(C) Rs. 2000
(D) Rs. 1600

36. A boat goes downstream and covers the distance between two ports in 4 hours while it covers the same distance upstream in 5 hrs. If the speed of the stream is 2 kmph, then speed of the boat in still water is
(A) 15 km/hr
(B) 20 km/hr
(C) 24 km/hr
(D) 18 km/hr

37. Fifteen years from now Ravi’s age will be four times of age 15 years ago from now. The present age is
(A) 40 years
(B) 10 years
(C) 25 years
(D) 75 years

38. Two years ago, Dilip was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Then the present age of Dilip is
(A) 14 years
(B) 38 years
(C) 32 years
(D) 34 years

39. In a school 1/5th of the girls and 1/8th of the boys took part in a school camp. The fraction of the total strength took part in the camp is
(A) 2/13
(B) 2/7
(C) 3/11 
(D) 2/9

40. A man is 5 years older than his wife and the wife is now thrice as old as their daughter, who is 10 years old. How old was the man when his daughter was born?
(A) 20 years
(B) 23 years
(C) 25 years
(D) 30 years

41. from a group of boys and girls, 15 girls are left. There are then left two boys for each girl. After this 45 boys are left. There are then 5 girls for each boy. The number of girls in the beginning was
(A) 40
(B) 43
(C) 29
(D) 50

42. A student has to secure 40% marks to pass. He got 40 marks and failed by 40 marks. The maximum number of marks is
(A) 160
(B) 180
(C) 200
(D) 320

43. Division of 64 between A and B such that 3 times A’s share is greater than 4 times B’s share by 10 is
(A) 38, 26
(B) 32, 25
(C) 34, 22
(D) 35, 20

44. When 75% of a number is added to 75, then resultant number is the original number. The number is
(A) 150
(B) 300
(C) 100
(D) 450

45. A car leaves Jaipur at 11 am travelling 5 km/hr. If second car leaves Jaipur an hour later and over takes the first car at 5 pm then speed of second car is
(A) 60 km/hr
(B) 40 km/hr
(C) 30 km/hr
(D) 20 km/hr

46. The number which should be added to twice the rational number - (3/7) to get 7/3 is
(A) 105/21
(B) 100/21
(C) 107/21
(D) -(89/21)

47. Three fourths of a number is 60 more than its one-third. The number is
(A) 108
(B) 84
(C) 144
(D) 116

48. The sum of a number n and its reciprocal is 18. Then the equation showing this relation is
(A) n + 1/n = 18
(B) n - 18 = 1/n
(C) n+1/n = 18
(D) n + 18 = 1/n

49. The four consecutive numbers whose sum is 74 are
(A) 17, 18, 19, 20
(B) 1, 2, 3, 4
(C) 15, 16, 17, 18
(D) 10, 11, 12, 13

50. The value of x when α = 2x - 1 / 3, b = 7 - 3x / 4 and a - b / 5 = 1 is
(A) 4
(B) 5
(C) 3
(D) 2

51. 2/3rd of a number when multiplied by 3/3 of the same number make 338. The number is
(A) 18
(B) 24
(C) 36
(D) 26

52. The solution of √3x = 2√3 + x is
(A) 3 + √3
(B) 2√3/√3+1
(C) √3/√3-1
(D) 3 - √3

53. The value of x for which x + 6 / 4 + x - 3 / 5 = 5x - 4 / 8 is
(A) 2
(B) 4
(C) 6
(D) 8

54. The two consecutive multiples of 3 whose sum is 51 are
(A) 24, 27
(B) 20, 31
(C) 40, 11
(D) 25, 26

55. The solution of x-6/2 - x-3/5 = 1/2 is
(A) x = 7
(B) x = 9
(C) x = 8
(D) x = 5

56. Solution of the equation 6(3x + 2) – 5(6x – 1) = 6(x– 3) – 5(7x–6) + 12x is
(A) – 1
(B) 1
(C) 0
(D) 2

57. A number 351 is divided into two parts in the ratio 2 : 7. The product of the numbers is
(A) 20294
(B) 21294
(C) 25295
(D) 31294

58. If (1/2 + 1/2 + 1/2 +....... up to is times) + (5/2 + 5/2 + 5/2 + ........ up to (x - times) = (5/2) R then the value n ∈ N such that it is least positive integer
(A) 4
(B) 3
(C) 6
(D) 5

59. If 2/2rd of a number is 20 less than the original number, then the number is
(A) 60
(B) 40
(C) 80
(D) 120

60. The ratio of two numbers is 3 : 8 and their difference is 115. The largest number is
(A) 69
(B) 115
(C) 184
(D) 230

61. The perimeter of a rectangle is numerically equal to the area of rectangle. If width of rectangle is cm, then its length is
(A) (11/3) cm
(B) (22/3) cm
(C) 11 cm
(D) 10 cm

62. If 3(1/x) x 3(3/4) = 12(1/2 then the value 
(A) 1
(B) 1/3
(C) 2
(D) 3

63. The sum of two numbers is 15 and the difference of their squares is 15. The difference of the numbers is
(A) 0
(B) 1
(C) 4
(D) 6

64. The solution of (x + 4)2 – (x–5)2 = 9 is
(A) 1
(B) 2
(C) 3
(D) 4

65. The value of x for which 2x - 3 / 3x + 2 = -2/3 is
(A) 5/10
(B) 5/11
(C) 11/5
(D) 5/12

66. A man can row at 8 kmph in still water. If the river is running at 2 kmph, it takes him 48 minutes to row to a place and back. How far is the place?
(A) 1 km
(B) 2 km
(C) 3 km
(D) 4 km

67. A number consists of two digits whose sum is 8. If 18 is added to the number, its digits are interchanged. The number is
(A) 53
(B) 35
(C) 92
(D) 63

68. Ram has Rs. 27 in the form of fifty paise and twenty five paise coins. He has twice as many twenty-five paise coins as he has fifty paise coins. The number of coins of each kind are
(A) 22 and 50
(B) 27 and 54
(C) 20 and 50
(D) 30 and 40

69. There were only two candidates in an election. One got 62% votes and was elected by a margin of 144 votes. The total number of voters were
(A) 500
(B) 600
(C) 700
(D) 800

70. The age of a man is same as his wife’s age with the digits reversed. Then sum of their ages is 99 and the man is 9 years older than his wife. How old is the man?
(A) 50
(B) 49
(C) 54
(D) 44

71. Two angles in a triangle are in the ratio 4 : 5. If the sum of these angles is equal to the third angle, then third angle is
(A) 180°
(B) 40°
(C) 50°
(D) 90°

72. If the digit 1 is placed after a two digit number whose tens digit is t and units digit is u, the new number is
(A) 10 t + u + 1
(B) 100 t + 10 u + 1
(C) t + u + 1
(D) t + u – 1

73. Raman has 3 times as many two rupee coins as he has five rupee coins. If he has in all a sum of Rs. 77, how many coins of each denomination does he has?
(A) 7 two rupee coins and 21 five rupee coins
(B) 21 two rupee coins and 7 five rupee coins
(C) 11 two rupee coins and 11 five rupee coins
(D) 16 two rupee coins and 9 five rupee coins

74. If a number is increased by 8 % of itself gives 135, then that number is
(A) 112
(B) 100
(C) 125
(D) 50

75. The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5. The original number is
(A) - (5/8)
(B) 5/8
(C) 3/8
(D) - (3/8)

76. How much pure alcohol should be added to 400 ml of a 15% strength to make its strength 32%?
(A) 50 ml
(B) 75 ml
(C) 100 ml
(D) 150 ml

77. In an examination a student was asked to find 3/14th of a certain number. By mistake, he found 3/4 of it. His answer was 150 more than the correct answer. The number given to him is
(A) 290
(B) 280
(C) 240
(D) 180

78. The numerator of a rational number is less than its denominator by 3. If the numerator becomes three times and denominator is increased by 20, the new number becomes 1/8. The original number is
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1

79. The sum of the two numbers is 11 and their product is 30, then the numbers are
(A) 8, 3
(B) 9, 2
(C) 7, 4
(D) 6, 5

80. If one number is thrice the other and their sum is 20, then the numbers are
(A) 5, 15
(B) 4, 12
(C) 3, 9
(D) None of these

81. The distance between two stations is 340 km. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than that of other by 5 km/ hr. If the distance between the two trains after 2 hours of their start is 30 km., the speed of each train is
(A) 75 kmph, 80 kmph
(B) 60 kmph, 65 kmph
(C) 80 kmph, 85 kmph
(D) None of these

82. A streamer goes downstream and covers the distance between two ports in 4 hours while it covers the same distance upstream in 5 hours. If the speed of the stream is 2 km. per hour, then the speed of the streamer in still water is
(A) 20 km/hr
(B) 19 km/hr
(C) 18 km/hr
(D) 19.5 km/hr

83. The sum of two numbers is 2490 and if 6.5% of one number is equal to 8.5% of the other, then numbers are
(A) 1414, 1076
(B) 1411, 1097
(C) 1412, 1078
(D) None of these

84. There prizes are to be distributed in a quiz-contest. The value of the second prize is five-sixth of the value of the first price and the value of the third prize is four-fifth of that of the second prize. If the total value of the three prizes is Rs. 150, then the value of each price is respectively
(A) Rs. 60, Rs. 40, Rs. 50
(B) Rs. 55, Rs. 45, Rs. 50
(C) Rs. 50, Rs. 40, Rs. 60
(D) Rs. 60, Rs. 50, Rs. 40

85. Two planes start from a city and fly in opposite directions, one averaging a speed of 40 km/hr greater than the others. If they are 3400 km. apart after 5 hours, the average speeds respectively are
(A) 330, 370 kmph
(B) 320, 360 kmph
(C) 250, 290 kmph
(D) 300, 340 kmph

 

 

 

Chapter 3 

Understanding Quadrilaterals 

 

 

Various Types of Quadrilaterals

1. Quadrilateral: A closed figure bounded by four line segments is called a quadrilateral.
2. Types of quadrilaterals.
a) Parallelogram: In a parallelogram
i) the opposite sides are equal
ii) the opposite angles are equal
iii) each diagonal bisects the other.
b) Rectangle: A parallelogram is a rectangle if each of its angles is a right angle. A rectangle obeys all the properties of a parallelogram.
c) Square: A rectangle having all its sides equal is called a square.
d) Rhombus: A rectangle having all its sides equal is called a square.
e) Kite: Kite is a quadrilateral formed by two isosceles triangles standing on the opposite sides of a common base.
f) Trapezium: A quadrilateral in which one pair of opposite sides are parallel is called a trapezium.
Note: If the non-parallel sides of a trapezium are equal, it is called an isosceles trapezium 

Venn - diagram of Quadrilaterals

Q = set of all quadrilaterals in a given plane
T = set of all trapeziums in the given plane
P = set of all parallelograms in the given plane
S = set of all squares in the given plane
R = set of all rectangles in the given plane
H = set of all rhombuses in the given plane
K = set of all kites in the given plane. 

Question. The perimeter of a parallelogram is 180 cm. One side exceeds another by 10 cm. The sides of the parallelogram are
(A) 40 cm, 50 cm
(B) 45 cm each
(C) 50 cm each
(D) cannot be determined

 

Question. One of the diagonals of a rhombus is equal to a side of the rhombus. The angles of the rhombus are
(A) 60° and 80°
(B) 60° and 120°
(C) 120° and 240°
(D) 100° and 120°

 

Question. In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. Then ABCD is a
(A) square
(B) parallelogram
(C) rhombus
(D) trapezium

 

Question. ABCD is a parallelogram as shown in figure. IF AB = 2AD and P is midpoint of AB, then <CPD is equal to 

(A) 90°
(B) 60°
(C) 45°
(D) 135°

 

Question. In a parallelogram ABCD, if AB = 2x + 5, CD = y + 1, AD = y + 5 and BC = 3x – 4 then ratio of AB : BC
(A) 71 : 21
(B) 12 : 11
(C) 31 : 35
(D) 4 : 7

 

Question. If ABCD is an isosceles trapezium, ∠C is equal to
(A) ∠B
(B) ∠A
(C) ∠D
(D) 90°

 

Question. The diagonals of a parallelogram ABCD intersect at O. If ∠BOC - 90° and ∠BDC = 50°, then ∠AOB is
(A) 10°
(B) 40°
(C) 50°
(D) 90°

 

Question. A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is
(A) 25°
(B) 40°
(C) 50°
(D) 55°

 

Question. ABCD is a rhombus. IF ∠ACB = 40°, then ∠ADB is
(A) 40°
(B) 45°
(C) 50°
(D) 60°

 

Question. The quadrilateral formed by joining the mid points of the sides of a quadrilateral PQRS, taken in order, is a rectangle if
(A) PQRS is a rectangle
(B) PQRS is a parallelogram
(C) diagonals of PQRS are perpendicular
(D) diagonals of PQRS is equal

 

Question. If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio 3: 7 : 6 : 4 then PQRS is a
(A) rhombus
(B) parallelogram
(C) trapezium
(D) kite

 

Question. If PQ and RS are two perpendicular diameters of a circle, then PQRS is a
(A) rectangle
(B) trapezium
(C) square
(D) rhombus but not square

 

Question. If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C at Q, of ∠C and ∠D and ∠A at S, then PQRS is a

(A) Rectangle
(B) rhombus
(C) parallelogram
(D) quadrilateral whose opposite angles are supplementary

 

Question. AB and CD are diameters. Then ACBD is 

(A) Square
(B) trapezium
(C) isosceles trapezium
(D) rectangle

 

Question. ABCD is a square E, F, G, H are the mid-mid-points of the four sides. Then the figure EFGH is
(A) square
(B) rectangle
(C) trapezium
(D) parallelogram

 

Question. If a quadrilateral has two adjacent sides equal and the other two sides equal it is called
(A) parallelogram
(B) square
(C) rectangle
(D) kite

 

Question. Choose the correct statement:
(A) The diagonals of a parallelogram are equal
(B) The diagonals of a rectangle are perpendicular to each other
(C) If the diagonals of a quadrilateral intersect at right angles, it is not necessary a rhombus
(D) Every quadrilateral is either a trapezium or a parallelogram or a kite.

 

Question. If two adjacent angles of a parallelogram are in the ratio 3:2, then the measure of the angles are
(A) 108°, 72°
(B) 72°, 36°
(C) 100°, 80°
(D) 144°, 36°

 

Question. ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must be
(A) square
(B) rectangle
(C) parallelogram
(D) The angle

 

Question. ABCD is a parallelogram. The angle bisectors of ∠A and ∠D meet at O. The measure of ∠AOD is
(A) 45°
(B) 90°
(C) dependent on the angles A and D
(D) cannot be determined from given data

 

Question. The diameter of circumcircle of a rectangle is 10 cm and breath of the rectangle is 6 cm. Its length is
(A) 6 cm
(B) 5 cm
(C) 8 cm
(D) none

 

Question. ABCD is a quadrilateral. AB = BC = CD = DA and ∠A = ∠B = ∠C = ∠D = 90°. Then ABCD can be called ABCD can be called
(A) rhombus
(B) square
(C) parallelogram
(D) all of the foregoing

 

Question. The sum of the angles of a quadrilateral is
(A) 180°
(B) 360°
(C) 270°
(D) depends on the quadrilateral

 

Question. RSTU is a parallelogram as shown in the figure below. Then the shown angle x and y are related 

(A) x = y
(B) x < y
(C) x > y
(D) cannot be determined from given data

 

Question. ABCD and MNOP are quadrilaterals as shown in the figure below. Then 

(A) p + q + r + s = w + x + y + z
(B) p + q + r + s < w + x + y + z
(C) p + q + r + s > w + x + y + z
(D) none of the forgoing

 

Question. A parallelogram which has equal diagonals is a
(A) square
(B) rectangle
(C) rhombus
(D) none

 

Question. IF ABCD is a parallelogram, then ∠A – ∠C is
(A) 180°
(B) 0°
(C) 360°
(D) 90°

 

Question. In a square ABCD the diagonals bisect at O. Then triangle AOB is
(A) an equilateral triangle
(B) an isosceles but not a right angled
(C) a right angled but not an isosceles triangle
(D) an isosceles right angled triangle

 

Question. The angle between two altitudes of a parallelogram ABCD through the vertex D which is obtuse angle is 60°. Then ∠ABC is
(A) 60°
(B) 90°
(C) 120°
(D) 140°

 

Question. To construct a parallelogram, the minimum number of measurements required is
(A) 2
(B) 3
(C) 4
(D) 1

 

Question. If angles P, Q, R and S of the quadrilateral PQRS taken in order, are in the ratio 3 : 7 : 6 : 4, then PQRS is a
(A) Rhombus
(B) Parallelogram
(C) Trapezium
(D) Kite

 

Question. ABCD is parallelogram AC ⊥ BD and ∠ACD = 30°, then ∠ABD is
(A) 45°
(B) 60°
(C) 90°
(D) 120°

 

Question. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus if
(A) PQRS is a rhombus
(B) PQRS is a parallelogram
(C) Diagonals of PQRS are perpendicular
(D) PQRS is a rectangle

 

Question. If the lengths of two diagonals of a rhombus is 12 cm and 16 cm, then the length of each side of the rhombus is
(A) 10 cm
(B) 14 cm
(C) cannot be determined
(D) 5 cm

 

Question. Three angles of quadrilateral are in the ratio 3 : 4 : 5. The difference of the least and the greatest of these is 45°. All the four angles of the quadrilateral are
(A) 63°, 84°, 105°, 108°
(B) 60°, 75°, 120°, 105°
(C) 65°, 80°, 100°, 110°
(D) 85°, 95°, 100°, 130°

 

Question. PQRS is a rhombus. The value of perimeter if PR = 10 cm and QS = 24 cm is
(A) 50 cm
(B) 51 cm
(C) 52 cm
(D) 53 cm

 

Question. The given figure HOPE is a parallelogram. The relation between x, y and z is
(A) x = y + z
(B) y + z – x = 180°
(C) x + y – z = 180°
(D) x + y = 180° – z

 

Question. ABCD is a rhombus in which the altitude from D to side AB bisects AB. Then ∠A and ∠B are
(A) 60°, 120°
(B) 120°, 60°
(C) 80°, 100°
(D) 100°, 80°

 

Question. The sum of the measures of the external angles of any polygon is
(A) 180°
(B) 360°
(C) 540°
(D) Depends on the number of sides

 

Question. The number of sides of a regular polygon whose each exterior angle has a measure of 45° is
(A) 4
(B) 6
(C) 8
(D) 10

Question. If ABCD is an isosceles trapezium, ∠C is equal to
(A) ∠B
(B) ∠A
(C) ∠D
(D) 90°

 

Question. If a pair of opposite sides of a quadrilateral are equal and parallel it is
(A) kite
(B) trapezium
(C) parallelogram
(D) none of these

 

Question. In a parallelogram ABCD, if ∠A = 45°, then the other angles are
(A) 45°, 120°, 120°
(B) 45°, 135°, 135°
(C) 60°, 135°, 135°
(D) 60°, 120°, 120°

 

Question. The sum of the angles of quadrilateral is
(A) 180°
(B) 360°
(C) 270°
(D) Depends on the quadrilateral

 

Question. In the given figure, line RT is drawn parallel to SQ. If ∠QPS = 100°, ∠PQS = 40°, ∠PSR = 85° and ∠QRS = 70°, then ∠QRT is 

(A) 45°
(B) 65°
(C) 85°
(D) 90°

 

Question. Match the following:
1. Rectangle         (p) A quadrilateral having its opposite sides parallel.
2. Square             (q) A parallelogram having its opposite sides equal and one angle measuring 90°
3. Parallelogram   (r) a parallelogram having all sides equal and one angle measuring 90°
4. Rhombus          (s) A quadrilateral in which a pair of opposite sides are parallel
5. Trapezium         (t) A parallelogram having all sides equal
(A) 1t 2s 3r 4p 5q
(B) 1p 2q 3r 4s 5t
(C) 1r 2q 3t 4p 5s
(D) 1q 2r 3p 4t 5s

 

Question. Four angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. The greatest angle is
(A) 125°
(B) 75°
(C) 135°
(D) 120°

 

Question. Diagonals of a rhombus bisect each other at
(A) Acute angle
(B) Obtuse angle
(C) Right angle
(D) ½ right angle

 

Question. Which of the following statements is true?
(A) The diagonals of a rectangle are perpendicular
(B) The diagonals of a rhombus are equal
(C) Every square is a rhombus
(D) Every rhombus is a square

 

Question. In rectangle ABCD, AB = 25 cm and BC = 15 cm. In what ratio does the bisector of ∠C divides AB?
(A) 1 : 3
(B) 2 : 3
(C) 3 : 4
(D) 1 : 4

 

Question. In the figure, P is a point in the interior of ∠AOB and ∠AOB = 36°, If PM ⊥ OA and PN ⊥ OB. Then x is 

(A) 144°
(B) 90°
(C) 216°
(D) 45°

 

Question. A trapezium in which non parallel sides are equal is side to be
(A) right trapezium
(B) equilateral trapezium
(C) isosceles trapezium
(D) none of these

 

Question. If ABCD is a parallelogram, then LA – LC is
(A) 180°
(B) 0°
(C) 360°
(D) 90°

 

Question. If one of the angles measures more than 180° in a quadrilateral, then quadrilateral is known as
(A) A parallelogram
(B) A concave quadrilateral
(C) A convex quadrilateral
(D) A trapezium

 

Question. The ratio of sides of a parallelogram is 3 : 5 and the perimeter is 48 cm, then the sides of the parallelogram are
(A) 9 cm, 12 cm
(B) 9 cm, 15 cm
(C) 10 cm, 12 cm
(D) 8 cm, 15 cm

 

Question: The perimeter of a parallelogram is 180 cm. One side exceeds another by 10 cm. The sides of the parallelogram are
a) 40 cm, 50 cm
b) 50 cm each
c) 45 cm each
d) cannot be determined

 

Question: One of the diagonals of a rhombus is equal to a side of the rhombus. The angles of the rhombus are
a) 60° and 120°
b) 100° and 120°
c) 60° and 80°
d) 120° and 240°

 

Question: In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. Then ABCD is a
a) square
b) rhombus
c) parallelogram
d) trapezium

 

Question: In a parallelogram ABCD, if AB = 2x + 5, CD = y + 1, AD = y + 5 and BC = 3x – 4 then ratio of AB : BC

a) 31 : 35
b) 71 : 21
c) 12 : 11
d) 4 : 7

 

Question: The diaphs of a parallelogram ABCD intersect at O. If ∠BOC- 90° and ∠BDC = 50°, then ∠AOB is
a) 40°
b) 90°
c) 10°
d) 50°

Question: A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is
a) 50°
b) 25°
c) 40°
d) 55°

 

Question: ABCD is a rhombus. IF ∠ACB = 40° , then ∠ADB is
a) 50°
b) 40°
c) 45°
d) 60°

 

Question: The quadrilateral formed by joining the mid points of the sides of a quadrilateral PQRS, taken in order, is a rectangle if
a) diagonals of PQRS are perpendicular
b) PQRS is a rectangle
c) PQRS is a parallelogram
d) diagonals of PQRS is equal

 

Question: If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio 3: 7 : 6 : 4 then PQRS is a
a) trapezium
b) rhombus
c) parallelogram
d) kite

 

Question: If PQ and RS are two perpendicular diameters of a circle, then PQRS is a
a) square
b) rectangle
c) trapezium
d) rhombus but not square

 

Question: AB and CD are diameters. Then ACBD is

a) Rectangle
b) trapezium
c) square
d) isosceles trapezium

 

Question: ABCD is a square E, F, G, H are the mid-mid-points of the four sides. Then the figure EFGH is
a) square
b) trapezium
c) rectangle
d) parallelogram

 

Question: If a quadrilateral has two adjacent sides equal and the other two sides equal it is called
a) kite
b) square
c) parallelogram
d) rectangle

 

Question: Choose the correct statement:
a) If the diagonals of a quadrilateral intersect at right angles, it is not necessary a rhombus
b) Every quadrilateral is either a trapezium or a parallelogram or a kite
c) The diagonals of a rectangle are perpendicular to each other
d) The diagonals of a parallelogram are equal

 

Question: If two adjacent angles of a parallelogram are in the ratio 3:2, then the measure of the angles are
a) 108°, 72°
b) 100°, 80°
c) 72°, 36°
d) 144°, 36°

 

Question: ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must be
a) parallelogram
b) square
c) rectangle
d) the angle

 

Question: The diameter of circumcircle of a rectangle is 10 cm and breath of the rectangle is 6 cm. Its length is
a) 8 cm
b) 6 cm
c) 5 cm
d) none

 

Question: The sum of the angles of a quadrilateral is
a) 360°
b) depends on the quadrilateral
c) 180°
d) 270°

 

Question: A parallelogram which has equal diagonals is a
a) rectangle
b) none
c) square
d) rhombus

 

 CHAPTER –3.

UNDERSTANDING QUADRILATERALS

Put a tick mark (√) on the correct answer:

Q1.How many diagonals does a convex quadrilateral has?
(i) One
(ii) two
(iii) three
(iv) four

Q2.What is the sum of all interior angles of a pentagon?
(i) 180°
(ii)360° 
(iii)540° 
(iv)720°

Q3. How many sides a regular polygon has whose each exterior angle is 45°?
(i) Eight
(ii) seven
(iii) six
(iv) five

Q4.What is the minimum interior angle possible for a regular polygon?
(i) 60° 
(ii)80° 
(iii) 120°
(iv)160°

Q5. What is the maximum exterior angle possible for a regular polygon?
(i) 60°
(ii) 80° 
(iii) 120° 
(iv)160°

Q6. What is the perimeter of the parallelogram whose two adjacent sides are 12cm & 7cm?
(i) 28cm
(ii) 38cm
(iii) 84cm
(iv)168cm

Q7. What is the area of the rectangle whose perimeter is 16 cm & length 5 cm?
(i) 3.2cm2 
(ii) 80cm2 
(iii) 15cm2 
(iv)16cm2

Q8.In the given parallelogram, find the value of ‘x’, ‘y’ & ‘z’

Q9.If the two adjacent angles of a parallelogram are equal then each of its angle is?
(i) 70° 
(ii) 80°
(iii) 90°
(iv) 100°

Q10.If the two diagonals of a rhombus are 8cm & 6cm, its area is?
(i) 28cm2 
(ii) 48cm2 
(iii) 14cm2 
(iv) 24cm2 

 

 

 

 

Chapter 4 

Practical Geometry

 

Question. The minimum number of dimensions needed to construct a rectangle is

(A) 1
(B) 2

(C) 3
(D) 4

 

 

Question. The minimum number of measurements needed to construct a square is

(A) 1
(B) 2

(C) 3
(D) 4

 

 

Question. In a quadrilateral PQRS, if ∠P = ∠R = 100° and ∠S = 75° then ∠Q = ____.

(A) 50°
(B) 85°

(C) 120°
(D) 306°

 

 

Question. The sum of the angles in a quadrilateral is equal to _____

(A) 2 right angles
(B) 3 right angles

(C) 4 right angles
(D) 360 right angles

 

 

Question. If the lengths of two diagonals of a rhombus are 12 cm and 16 cm, then the length of each side of the rhombus is

(A) 10 cm
(B) 14 cm

(C) Cannot be determined
(D) none of these

 

 

Question. If one of the angle measures more than 180° in a quadrilateral, then that is known as

(A) A parallelogram
(B) a concave quadrilateral

(C) A convex quadrilateral
(D) a trapezium

 

 

Question. A quadrilateral which has exactly one pair of parallel sides is called

(A) A parallelogram
(B) a rectangle

(C) A trapezium
(D) a kite

 

 

Question. Which of the following statements is true?

(A) The diagonals of a rectangle are perpendicular

(B) The diagonals of a rhombus are equal

(C) Every square is a rhombus

(D) None of these

 

 Question. The number of measurements required to construct a quadrilateral is

(A) 5
(B) 4

(C) 3
(D) 2

Question. To construct a parallelogram, the minimum number of measurements required is

(A) 2
(B) 3

(C) 4
(D) 1

 

 1. The figure formed by four line segments is called a quadrilateral.

2. A quadrilateral has four sides, four angles and two diagonals.

3 A quadrilateral in which the measure of each angle is less than 180° is known as a convex quadrilateral.

4. A quadrilateral in which one of the angles measures more than 180° is known as a concave quadrilateral.

5. The sum of all angles in a quadrilateral is 360°.

6. To construct a quadrilateral, we need five measurements.

 

Question: The minimum number of dimensions needed to construct a rectangle is
a) 2
b) 4
c) 3
d) 1

 

Question: The minimum number of measurements needed to construct a square is
a) 1
b) 3
c) 2
d) 4

 

Question: In a quadrilateral PQRS, if ∠P = ∠R = 100° and ∠S = 75° then ∠Q = __
a) 85°
b) 306°
c) 120°
d) 50°

 

Question: The sum of the angles in a quadrilateral is equal to
a) 4 right angles
b) 360 right angles
c) 2 right angles
d) 3 right angles

 

Question: If the lengths of two diagonals of a rhombus are 12 cm and 16 cm, then the length of each side of the rhombus is
a) 10 cm
b) cannot be determined
c) 14 cm
d) none of these

 

Question: If one of the angle measures more than 180° in a quadrilateral, then that is known as
a) a concave quadrilateral
b) a trapezium
c) a parallelogram
d) None of these

 

Question: A quadrilateral which has exactly one pair of parallel sides is called
a) a trapezium
b) a parallelogram
c) a rectangle
d) a kite

 

Question: Which of the following statements is true?
a) Every square is a rhombus
b) the diagonals of a rhombus are equal
c) The diagonals of a rectangle are perpendicular
d) none of these

 

Question: The number of measurements required to construct a quadrilateral is
a) 5
b) 3
c) 4
d) 2

 

Question: To construct a parallelogram, the minimum number of measurements required is
a) 3
b) 1
c) 2
d) 4

\

Put a tick mark (√) on the correct answer:

Q1.What the point of intersection of the medians of a triangle called?
(i) circum centre
(ii) In centre
(iii) centroid
iv) orthocenter

Q2.What the point of intersection of the altitudes of a triangle called?
(i) circum centre
(ii) In centre
(iii) centroid
(iv) orthocenter

Q3.What the point of intersection of the side bisectors of a triangle called?
(i) circum centre
(ii) In centre
(iii) centroid
(iv) orthocenter

Q4.What the point of intersection of the angle bisectors of a triangle called?
(i) circum centre
(ii) In centre
(iii) centroid
(iv) orthocentre

Q5.Which of the following is a three dimensional figure?
(i) Square
(ii) Trapezium
(iii) Cube
(iv) Parallelogram

Q6. Find the number of edges of a polyhedron having 20 faces & 12 vertices?
(i) 10
(ii) 20
(iii) 25
(iv) 30

Q7. Find the number of faces of a polyhedron having 6 vertices & 12 edges?
(i) 8
(ii) 10
(iii) 12
(iv) 14

Q8. Find the number of vertices of a polyhedron having 5 faces & 9 edges?
(i) 18
(ii) 12
(iii) 6
(iv) 4

Q9.What the name of the polyhedron is whose base & top are congruent polygons & whose lateral faces are parallelograms in shape?
(i) Tetrahedron
(ii) Trapezium
(iii) Prism
(iv) Parallelogram

Q10.How many faces a tetrahedron has?
(i) 14
(ii) 12
(iii) 6
(iv) 4 

 

 

 

Chapter 5 

Data Handling 

 

 

Q.1 adjoining pie chart gives the expenditure (In percentage) on various items & savings of a family during a month. Answer the following Questions on the basis of the information given in the pie chart.

 

(a) On which item, the expenditure is maximum?

(i) House rent
(ii) Food
(iii) others
(iv) Education

 

(b) Expenditure on which item is equal to the total savings of the family?

(i) House rent
(ii) Food
(iii) Clothes
(iv) Education

 

(c) If the monthly savings of the family is Rs.3000, what is the monthly expenditure on clothes?

(i) Rs. 2000
(ii) Rs. 3000
(iii) Rs.1000
(iv) Rs.4000

 

Q2.What are the possible number of outcomes if a coin is tossed twice?

(i) One
(ii) two
(iii) three
(iv) four

 

Q3.What is the possible number of outcomes if a die is tossed once?

(i) Six
(ii) five
(iii) three
(iv) four

 

Q4.What is the possible number of outcomes if a card is drawn from a pack of 52 cards?

(i) 20
(ii) 30
(iii) 42
(iv) 52

 

Q5.What is the probability of getting a king if a card is drawn from a pack of 52 cards?

(i) 1/52
(ii) 2/52
(iii) 3/52
(iv) 4/52

 

Q6.What is the probability of getting a prime number if a die is tossed once?

(i) 1/6
(ii) 2/6
(iii) 3/6
(iv) 4/6

 

 

 

 

Chapter 6 

Squares and Square Roots 

MCQ Questions Class 8 Mathematics with Answers

 

Question: The square root of 441/961 is
a) 21/31
b) 21/39
c) 37/21
d) 11/13

\

Question: If M is a square number, then the next immediate square number are
a) M + 2 √M +1
b) M2 + 2M
c) M + 5
d) none of these

\

Question:

a) 5/12
b) 7/12
c) 25/44
d) none of these

\

Question:

a) 1
b) 14
c) none of these
d) cannot be determined

\

Question: The square root of 71 × 72 × 73 × 74 + 1 is
a) 5255
b) 9625
c) 9375
d) 5625

\

Question: If a square number ends in 6, the preceding figure is
a) an odd number
b) a composite number
c) an even number
d) a prime number

\

Question: The Value of √(-1) √(-1) is
a) – 1
b) ± 2
c) + 1
d) none

 

Question: The value of (501)2 – (500)2 is
a) 1001
b) 1
c) 101
d) none of these

 

Question: Which of the following is a Pythagorean triplet?
a) (6, 8, 10)
b) (5, 12, 18)
c) (3, 4, 7)
d) none of these

 

Question: The value of 1 + 3 + 5 + 7 + 9 +..... + 25 is
a) 169
b) 625
c) 196
d) 225

 

Question: The smaller number by which 396 must be multiplied so that the product becomes a perfect square is
a) 11
b) 2
c) 5
d) 3

 

Question: The value of √99 X √396 is 
a) 198
b) none of these
c) 208
d) 254

 

Question: Square root of 0.081/0.0064 X 0.484/6.25 X 2.5/21.1 is
a) 0.45
b) 0.95
c) 0.75
d) 0.75

 

Question: The value of 1+√0.01 / 1−√0.01 is close to 
a) 1.6
b) 0.6
c) 1.1
d) 1.7

 

Question:

a) lies between 1 and 2
b) equals 1
c) lies between 0 and 1
d) is greater than 2

 

Question:

a) 9

b) 0

c) – 7

d) 2

 

Question:

a) 6
b) 6.4
c) 3
d) 5

 

Question: A number added to its square gives 56. The number is
a) 7
b) 9
c) 12
d) 8

 

Question: The least number which must be subtracted from 6156 to make its perfect square is
a) 72
b) 82
c) 52
d) 62

 

Question: A four digit perfect square number whose first two digits and last two digits taken separately are also perfect square numbers is
a) 1681
b) 3664
c) 1636
d) 6481

 

 

 

 

CHAPTER –6

SQUARES & SQUARE ROOTS.

Put a tick mark (√) on the correct answer:

Q1. If a number has ‘1’ or ‘9’ in the unit’s place, then its square root ends in which of the following numbers.
(i) 1
(ii) 4
(iii) 5
(iv) 6

Q2. There are how many non-perfect squares between 100 & 121?
(i) 10
(ii) 15
(iii) 20
(iv) 25

Q3.What will be the unit’s digit of 526982
(i) zero
(ii) 4
(iii) 5
(iv) 6

Q4.The sum of first ‘n’ odd natural numbers is given by
(i) 2n
(ii) n2 
(iii) (n + 1)
(iv) n2 + 1

Q5.Which of the following numbers is not a perfect square?
(i) 62500
(ii) 57600
(iii) 90000
(iv) 63147

Q6.Which of the following Pythagorean triplet has the smallest member ‘8’
(i) 8,11,14
(ii) 8,10,12
(iii) 8,9,10
(iv) 8,15 ,17

Q7.Which of the following is the square root of 7056?
(i) 86
(ii) 34
(iii) 54
(iv) 84

Q8.Which of the following numbers by which 9408 must be divided so that the quotient is a Perfect square?
(i) 4
(ii) 3
(iii) 5
(iv) 6.

Q9.Which of the following square number is divisible by each of the numbers 6, 9 7 15?
(i) 400
(ii) 500
(iii) 600
(iv) 900

Q10.Which of the following numbers must be subtracted from 5607to get a perfect square?
(i) 121
(ii) 131
(iii) 141
(iv) 151 

 

1. The square of a number is that number raised to the power 2.
2. A natural number is called a perfect square if it is the square of some natural number.
3. Properties of Squares
(a) A number ending in 2, 3, 7 (or) 8 is never a perfect square.
(B) A number ending in an odd number of zeros is never a perfect square.
(C) Squares of even numbers are given
(D) Squares of odd numbers are odd.
(e) For every natural number ‘n’, we have (n + 1)2 – n2 = (n + 1) + n e.g., – 92 – 82 = 9 + 8 = 17.
(f) A triplet (a, b, c) of three natural numbers a, b and c is called a Pythagorean triplet if a2 + b2 = c2.
5. The square root of a number x is that number which when multiplied by itself gives x as the product.
We denote the square root of x by √x.
6. For any positive numbers ‘a’ and ‘b’ we have
(i) √ab = √a × √b
(ii) √a/b = √a/√b.

Question. The square root of 441/961 is
(A) 21/39
(B) 37/21
(C) 21/31
(D) 11/13

 

Question. If M is a square number, then the next immediate square number are
(A) M + 5
(B) M + 2√M + 1
(C) M2 + 2M
(D) none of these

 

Question. √1/16 + 1/9 =
(A) 7/12
(B) 25/144
(C) 5/12
(D) none

 

Question. If √1+27/169 = 1+x/13 then x =
(A) 1
(B) 14
(C) cannot be determined
(D) none of these

 

Question. The square root of 71 × 72 × 73 × 74 + 1 is
(A) 9375
(B) 9625
(C) 5625
(D) 5255

 

Question. If a square number ends in 6, the preceding figure is
(A) an even number
(B) an odd number
(C) a prime number
(D) a composite number

 

Question. The value of √(-1)√(-1) is
(A) – 1
(B) + 1
(C) ± 2
(D) none

 

Question. The value of (501)2 – (500)2 is
(A) 1
(B) 101
(C) 1001
(D) none of these

 

Question. Which of the following is a Pythagorean triplet?
(A) (6, 8, 10)
(B) (3, 4, 7)
(C) (5, 12, 18)
(D) none of these

 

Question. The value of 1 + 3 + 5 + 7 + 9 + ..... + 25 is
(A) 196
(B) 625
(C) 225
(D) 169

 

Question. The smaller number by which 396 must be multiplied so that the product becomes a perfect square is
(A) 5
(B) 11
(C) 3
(D) 2

 

Question. The value of √99 × √396 is
(A) 208
(B) 198
(C) 254
(D) none of these

 

Question. Square root of 0.081/0.0064 x 0.484/6.25 x 2.5/21.1 is
(A) 0.45
(B) 0.75
(C) 0.95
(D) 0.75

 

Question. √1+ √1+ √1+.........
(A) equals 1
(B) lies between 0 and 1
(C) lies between 1 and 2
(D) is greater than 2

 

Question. The value of 1+√0.01/1-√0.1 is close to
(A) 0.6
(B) 1.1
(C) 1.6
(D) 1.7

 

Question. If x * y =√x2 + y2 , the value of (1 * 2√2) (1 * – 2√2) is
(A) – 7
(B) 0
(C) 2
(D) 9

 

Question. Evaluate √41- √21- √19 - √9
(A) 3
(B) 6
(C) 5
(D) 6.4

 

Question. A number added to its square gives 56. The number is
(A) 12
(B) 9
(C) 8
(D) 7

 

Question. The least number which must be subtracted from 6156 to make its perfect square is
(A) 62
(B) 72
(C) 52
(D) 82

 

Question. A four digit perfect square number whose first two digits and last two digits taken separately are also perfect square numbers is
(A) 1681
(B) 1636
(C) 3664
(D) 6481

 

Question. The square of a natural number subtracted from its cube is 48. The number is
(A) 6
(B) 5
(C) 4
(D) 8

 

Question. The smallest natural number which when added to the difference of squares of 17 and 13 gives a perfect square is
(A) 1
(B) 5
(C) 11
(D) 24

 

Question. If √16/49 = x/49 then x =
(A) 4
(B) 7
(C) 16
(D) 28

 

Question. The square root of a perfect square containing ‘n’ digits has ________ digits.
(A) n+1/2
(B) n/2
(C) A or B
(D) none

 

Question. The area of a square field is 80,244/729 sq. m. The length of each side of the field is
(A) 8.96 m
(B) 10.26 m
(C) 13.54 m
(D) none

 

Question. The square root of 1764 is
(A) 32
(B) 42
(C) 48
(D) 38

 

Question. The square root of 53361 is
(A) 231
(B) 211
(C) 261
(D) 249

 

Question. The least perfect square which is divisible by 2, 4 and 6 is
(A) 36
(B) 64
(C) 16
(D) 18

 

Question. The square root of 390625 is
(A) 645
(B) 225
(C) 735
(D) 625

 

Question. The least perfect square exactly divisible by each of the numbers 6, 9, 15 and 20 is
(A) 3600
(B) 900
(C) 400
(D) 225

 

Question. The sides of a rectangular field are 80 m and 18 m respectively. The length of the diagonal is
(A) 84 m
(B) 98 m
(C) 82 m
(D) 86 m

 

Question. The least number of 4 digits which is a perfect square is
(A) 1000
(B) 1004
(C) 1016
(D) 1024

 

Question. The least number which must be subtracted from 2509 to make it a perfect square is
(A) 6
(B) 9
(C) 12
(D) 14

 

Question. The value of √0.9 is (approx)
(A) 0.3
(B) 0.6
(C) 0.9
(D) 0.4

 

Question. 

 

Question. Which of the following numbers, where in some of the digits have been suppressed by symbols, can possibly be the perfect square of a 3 digit odd number?
(A) 65 × × × 1
(B) 9 × × 1
(C) 10 × × × 4
(D) 9 × × × × × 5

 

Question. The least number which must be added to 196201 to make it a perfect square is
(A) 42
(B) 44
(C) 48
(D) 50

 

Question. The least number which must be subtracted from 2509 to make it a perfect square, is
(A) 6
(B) 9
(C) 12
(D) 14

 

Question. The least number of numbers to be deleted from the set {1, 2, 3 ... 13, 14, 15} so that the product of the remaining numbers is a perfect square is
(A) 1
(B) 2
(C) 3
(D) 4

 

Question. A gardener has 1000 plants. The minimum number of plants he needs more to plant these in such a way that the number of rows and the number of columns remain same is
(A) 100
(B) 24
(C) 89
(D) 156

 

Question. If the diagonal of a square is doubled, the area of the square becomes
(A) 2 times
(B) 3 times
(C) 4 times
(D) 6 times

 

Question. The students of class 8 of a school donated Rs. 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. The number of students in the class, is
(A) 47
(B) 48
(C) 49
(D) 50

 

Question. The smallest number by which 252 must be multiplied so that the product is a perfect square is
(A) 7
(B) 6
(C) 5
(D) 12

 

Question. The value of √900 + √0.09 + √0.000009 is
(A) 30.003
(B) 30.330
(C) 30.303
(D) 30.333

 

Question. If √2√2√2√2√2 = x , then x is
(A) 0
(B) 1
(C) 2
(D) 231/32

 

Question. The number must be subtracted from 16161 to get a perfect square is
(A) 31
(B) 32
(C) 33
(D) 34

 

Question. √284 + √52 + √144
(A) 14
(B) 16
(C) 16.6
(D) 18.8

 

Question. The smallest square number which is divisible by each of the number 6, 9 and 15, is
(A) 100
(B) 400
(C) 900
(D) 1024

 

Question. The smallest number by which 180 must be multiplied so that it becomes a perfect square is
(A) 6
(B) 9
(C) 3
(D) 5

 

Question. The lest square number, which is exactly divisible by each one of the numbers 12, 15, 18 is
(A) 3844
(B) 3364
(C) 3721
(D) 3600

 

Question. The square root of 7 correct upto two places of decimal is
(A) 2.64
(B) 2.65
(C) 2.66
(D) 2.67

 

Question. Between which two consecutive whole numbers does √95 lie?
(A) 7 and 8
(B) 8 and 9
(C) 9 and 10
(D) 10 and 11

 

Question. If √(12+√12+√12+......) = x , then the value of x is
(A) 3
(B) 4
(C) 6
(D) greater than 6

 

Question. If √3 = 1.732 and √2 = 1.414, then the value of 1/√3+√2 is
(A) 0.064
(B) 0.308
(C) 0.318
(D) 2.146

 

Question. Largest perfect square number of three digits divisible by 10, 15 and 25 is
(A) 625
(B) 999
(C) 900
(D) 1024

 

Question. The least square number exactly divisible by each one of the numbers 8, 12, 15, 20 is
(A) 3652
(B) 3600
(C) 4900
(D) 1500

 

Question. The greatest six-digit number, which is a perfect square is
(A) 998001
(B) 995001
(C) 997001
(D) 996001

 

Question. A decimal fraction is multiplied by itself. If the product is 176.252176. The fraction is
(A) 13276
(B) 13.267
(C) 13.287
(D) 13278

 

Question. If √2401 = √7x , then the value of x is
(A) 3
(B) 4
(C) 5
(D) 6

 

Question. The smallest number by which 9408 must be divided so that the quotient is a perfect square, is
(A) 2
(B) 3
(C) 5
(D) 7

 

Question. The square root of the quotient which is a perfect square obtained when 9408 is divided by smallest number is
(A) 56
(B) 168
(C) 54
(D) 55

 

Question. If √2 + √x = √3 , then x =
(A) 1
(B) √7
(C) 7
(D) 49

 

Question. If √.05x5x a =.5x.05x √b , then a/b = ?
(A) 0.0025
(B) 0.025
(C) 0.25
(D) 2.5

 

Question. If √0.01+ √0.0064 = x , then the value of x is
(A) 0.3
(B) 0.03
(C) √0.18
(D) none of these

 

Question. The value of x, for which ax2 – c = 0 

 

Question. If value of √15625 =125, then the value of √156.25 + √1.5625 is
(A) 137.5
(B) 1.375
(C) 13.75
(D) 0.1375

 

Question. Consider the following statements
1. √(√5-2)2 = √5-2
2. √(√6-√7)2 = √7-√6. Of these statements
(A) 1 alone is correct
(B) 2 alone is correct
(C) both 1 and 2 are false
(D) both 1 and 2 are correct

 

Question. Square numbers can only have......at the end
(A) Odd number of zeros
(B) Even number of zeros
(C) Both (A) and (B)
(D) none of these

 

Question. The least perfect square number divisible by 3, 4, 5, 6, 8 is
(A) 900
(B) 1200
(C) 2500
(D) 3600

 

Question. The value of √99 x √396 is
(A) 208
(B) 198
(C) 254
(D) 205

 

Question. If x = √3018 +√36 +√169 , the value of x is
(A) 55
(B) 44
(C) 63
(D) 42

 

Question. If √0.9x0.09x x = 0.9x0.09x √z , then the value of
(A) 0.081
(B) 0.810
(C) 081
(D) 8.09

 

Question. If √169/x = 1.30 then the value of x is
(A) 100
(B) 1000
(C) 10
(D) 1000

 

Question. The value of √7+2√10 is
(A) √6 + v1
(B) √4 + √3
(C) √5 + √2
(D) 2 + √5

 

Question. 

 

Question. A number is 64 times the square of its reciprocal. The number is
(A) 10
(B) 4
(C) 2
(D) 16

 

Question. The smallest perfect square number exactly divisible by 4, 5, 6, 15, 18 is
(A) 800
(B) 225
(C) 361
(D) 900

 

Question. A gardener plants 17956 trees in such a way that there are as many rows as there are trees in a row.
The number of trees in a row are
(A) 136
(B) 164
(C) 134
(D) 166

 

 

 

 

Chapter 7 

Cubes and Cube Roots

 

Question: The value of 3√343 X 3√−64 is 
a) –28
b) –18
c) 28
d) 18

 

Question: The length of each side of the cubical box is 2.4 m. Its volume is
a) 13.824 cu m
b) 13.824 cu cm
c) 13.824 cm2
d) None of these

 

Question: The cube of a number is 8 times the cube of another number. If the sum of the cubes of numbers is 243, the difference of the numbers is
a) 3
b) 6
c) 4
d) none

 

Question: The square of a natural number subtracted from its cube is 48. The number is
a) 4
b) 6
c) 5
d) 8

 

Question: Which of the following numbers are perfect cubes?
a) 343
b) 5324
c) 108
d) 243

 

Question: Which of the following are the cubes of even natural numbers?
a) 13824
b) 3375
c) 729
d) 1331

 

Question: Which of the following are the cubes of odd natural numbers?
a) 6859
b) 32768
c) 4096
d) 1728

 

Question: The cube root of 0.001728 is
a) 0.12
b) 12
c) 1.2
d) none

 

Question: Choose the correct statement
a) All the above
b) Cubes of even natural numbers are even
c) Cubes of negative integers are negative
d) Cubes of odd natural numbers are odd

 

Question: If 72K is a perfect cube, then the value of K is
a) 3
b) 1
c) 2
d) 4

 

Question: The cube root of 272 is
a) 9
b) 27
c) 3
d) none

 

Question: The cube of 0.9 is
a) 0.729
b) none
c) 72.9
d) 7.29

 

Question: The number which is not a perfect cube among the following is
a) 243
b) 1331
c) 216
d) 512

 

Question: The smallest number by which 2560 must be multiplied so that the product is a perfect cube is
a) 25
b) 15
c) 5
d) 10

 

Question: The smallest number by which 8788 must be divided so that the quotient is a perfect cube is
a) 4
b) 16
c) 12
d) 32

 

Question: The cube root of 1.331 is
a) 1.1
b) 0.011
c) 0.11
d) 11

 

Question: Two cubes have volume in the ratio 1 : 27. The ratio of the area of the face of one to that of the other is
a) 1 : 9
b) 1 : 3
c) 1 : 6
d) 1 : 18

 

Question: By what least number must 21600 be multiplied to make it a perfect cube?
a) 10
b) 60
c) 6
d) 30

 

Question: The smallest number by which 392 must be multiplied so that the product is a perfect cube is
a) 7
b) 3
c) 9
d) 5

 

Question: How many small cubes with edges of 10 cm can be just accommodated in a cubical box of 1 m edge?
a) 1000
b) 10
c) 100
d) 10000

 

 

 

 CHAPTER –7. 

CUBES & CUBE ROOTS.

 

Put a tick mark (√) on the correct answer:

Q1.Which of the following numbers must be subtracted from 345 to get a perfect cube?
(i) 121
(ii) 131
(iii) 2
(iv) 24

Q2.Which of the following numbers is a perfect cube?
(i) 343
(ii) 443
(iii) 543
(iv) 643

Q3.Which of the following numbers must be multiplied to 392 to get a perfect cube?
(i) 2
(ii) 3
(iii) 4
(iv) 7

Q4. By which of the following numbers 10648 must be divided to get a perfect cube?
(i) 2
(ii) 4
(iii) 5
(iv) 7

Q5.What is the volume of a cube whose each side is 4cm ?
(i) 24cm3 
(ii) 48 cm3
 (iii) 64 cm3 
(iv) 125 cm3 

 

 

 

 

Cubes and Cube Roots

1. The cube of a number is that number raised to the power 3.

2. A natural number is said to be a perfect cube if it is the cube of some natural number

3. Cubes of all even natural numbers are even

4. Cubes of all odd natural numbers are odd

5. Cubes of negative integers are negative

6. The cube root of a number x is that number whose cube gives x. It is denoted by 3√x

7. For any positive integer x, we have 3√-x = -3√x

8. For any integers a and b, we have

(i) -3√ab = 3√a X 3√x

 

1. The value of 3√343 x 3√-64 is
(A) 28
(B) –28
(C) 18
(D) –18

 

2. The length of each side of the cubical box is 2.4 m. Its volume is
(A) 13.824 cu m
(B) 13.824 cu cm
(C) 13.824 m2
(D) 13.824 cm2

 

3. The cube of a number is 8 times the cube of another number. If the sum of the cubes of numbers is 243, the difference of the numbers is
(A) 3
(B) 4
(C) 6
(D) none

 

4. The square of a natural number subtracted from its cube is 48. The number is
(A) 6
(B) 5
(C) 4
(D) 8

 

5. Which of the following numbers are perfect cubes?
(A) 108
(B) 343
(C) 243
(D) 5324

 

6. Which of the following are the cubes of even natural numbers?
(A) 729
(B) 3375
(C) 1331
(D) 13824

 

7. Which of the following are the cubes of odd natural numbers?
(A) 32768
(B) 4096
(C) 6859
(D) 1728

 

8. The cube root of 0.001728 is
(A) 0.12
(B) 1.2
(C) 12
(D) none

 

9.  √2744 ÷ 3√0.008 =________
(A) 70
(B) 1.2
(C) 12.
(D) None

 

10. Choose the correct statement
(A) Cubes of odd natural numbers are odd
(B) Cubes of even natural numbers are even
(C) Cubes of negative integers are negative
(D) All the above

 

11. If 72K is a perfect cube, then the value of K is
(A) 1
(B) 2
(C) 3
(D) 4

 

12. The cube root of 272 is
(A) 27
(B) 9
(C) 3
(D) none

 

13. If a3 = b3 + c3 + d3, the least value of ‘a’ is
(A) 6
(B) 9
(C) 3
(D) none

 

14. The cube of 0.9 is
(A) 72.9
(B) 0.729
(C) 7.29
(D) none

 

15. The number which is not a perfect cube among the following is
(A) 1331
(B) 216
(C) 243
(D) 512

 

16. The smallest number by which 2560 must be multiplied so that the product is a perfect cube is
(A) 5
(B) 25
(C) 10
(D) 15

 

17. The smallest number by which 8788 must be divided so that the quotient is a perfect cube is
(A) 4
(B) 12
(C) 16
(D) 32

 

18. The cube root of 1.331 is
(A) 0.11
(B) 0.011
(C) 11
(D) 1.1

 

19. The close root of -512/729 is
(A) 4/7
(B) 8/9
(C) -8/9
(D) none

 

20. Two cubes have volume in the ratio 1 : 27. The ratio of the area of the face of one to that of the other is
(A) 1 : 3
(B) 1 : 6
(C) 1 : 9
(D) 1 : 18

 

21. By what least number must 21600 be multiplied to make it a perfect cube?
(A) 6
(B) 10
(C) 30
(D) 60

 

22. The volume of a cube whose surface area is 150 m2 is
(A) 25 m3
(B) 75 m3
(C) 125 m3
(D) 27 m3

 

23. The value of (4096)(1/√3)(√2)2 is
(A) 8
(B) 16
(C) 24
(D) 32

 

24. The smallest number by which 392 must be multiplied so that the product is a perfect cube is
(A) 3
(B) 5
(C) 7
(D) 9

 

25. How many small cubes with edges of 10 cm can be just accommodated in a cubical box of 1 m edge?
(A) 10
(B) 100
(C) 1000
(D) 10000

 

26. What is the smallest number by which 3600 can be divided to make it a perfect cube?
(A) 9
(B) 50
(C) 300
(D) 450

 

27. The volume of cubical box is 216 m3. The length of the longest rod that can be placed in the box is
(A) 6 m
(B) 6√2 m
(C) 6√3 m
(D) 12 m

 

28. Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 98784. The greatest number is
(A) 28
(B) 14
(C) 42
(D) 7

 

29. The value of

(A) 1/4
(B) 1/8
(C) 1/2
(D) 1/16

 

30. The volume of a cubical box is 32.768 cubic meters. The length of one side of the box is
(A) 3.1 m
(B) 3.2 m
(C) 3.3 m
(D) 3.4 m

 

31. 3√√0.000064 equals
(A) 0.02
(B) 0.2
(C) 2.0
(D) 3.0

 

32. The value of 453 – 653 – 203 is
(A) 175500
(B) – 175500
(C) 170000
(D) – 170000

 

33. If 3√2744 ÷ 3√0.008 = x , then the value of x
(A) 70
(B) – 70
(C) 14
(D) – 14

 

34. The cube root of 

(A) 4/3
(B) -(4/3)
(C) 2/3
(D) -(3/2)

 

35. The cube of a two-digit number may not have
(A) Four digits
(B) Five digits
(C) Six digits
(D) Seven digits

 

36. The value of

(A) 4.5
(B) 5.5
(C) 6.5
(D) 7.5

 

37. The cube root of (36)24/(24)/36 is
(A) (3/32)
(B) (3/32)2
(C) (3/32)3
(D) (3/32)4

 

38. The value of 3√81 + 3√192 + 3√375 / 3√24 is
(A) 0 
(B) 1
(C) 2
(D) 3

 

39. The cube of an odd natural number, is
(A) Even
(B) Odd
(C) Even or odd
(D) Can’t say

 

40. Which of the following numbers is not a perfect cube?
(A) 46656
(B) 13825
(C) 3375
(D) 74088

 

41. If 36a4 = a6, then a3 is equal to
(A) (1/6)a6
(B) 6a4
(C) (1/6)a2
(D) 6a2

 

42. The value of

(A) 3 
(B) 10/3
(C) 2/3
(D) 11/3

 

 

 

 

Chapter 8 

Comparing Quantities 

 

Cost price (CP)
The price at which an article is purchased is called its cost price.

Selling Price (SP)
The price at which an article is sold is called its selling price.
a) If SP > CP, there is a gain and Gain = SP – CP
b ) If SP < CP, there is a loss and Loss = CP – SP.

Profit and Loss percentage

1. A trader marks his goods 30% above the cost price but makes a reduction of 6(1/4)% on the marked price for ready money. His gain percent is
(A) 23.75%
(B) 23.25%
(C) 21.875%
(D) 40%

 

2. A publisher sells books to a retail dealer of Rs.5 a copy but allows 25 copies to count as 24. If the retailer sells each of hte 25 copies at Rs.6, his profit percent is
(A) 20%
(B) 25%
(C) 24%
(D) 40%

 

3. A trader marks his goods at 25% above his cost price and allows a discount of 12(1/2)% on purchases for cash payment. The profit percent he makes is
(A) 9(3/8)%
(B) 11(2/3)%
(C) 1(1/3)%
(D) 4(1/11)%

 

4. The percentage equivalent to 3/8 is
(A) 37.5
(B) 0.375
(C) 40
(D) 3.75

 

5. If the discount is 10%, an item bought for Rs.9 is priced at
(A) Rs.11
(B) Rs.10
(C) Rs.8.10
(D) Rs.12

 

6. A cask containing 425 litres lost 8% by leakage and evaporation. The number of litres left in the case were
(A) 425x8/100
(B) 425-425x8/100
(C) 425+425x8/100
(D) 425x425x8/100

 

7. 12(1/2)% Rs.50 is equal to
(A) Rs.6.25
(B) Rs.6.15
(C) Rs.6.75
(D) Rs.6.45

 

8. 8% of Rs.625 is equal to
(A) Rs.50
(B) Rs.75
(C) Rs.80
(D) Rs.100

 

9. 0.9 per cent can be expressed as
(A) 0.009
(B) 0.09
(C) 0.0009
(D) 0.09

 

10. A producer blends two qualities of rice. One costing Rs.12.50 per kg and the other costing Rs.14 per kg in the ratio 4 : 5. Find his profit percent if he sells the mixture at the rate of Rs.16 per kg.
(A) 25%
(B) 15%
(C) 20%
(D) 10%

 

11. Ravi sold an article to Sudhir at a profit of 6% who is in turn sold that to Gopal at a loss of 5%. If Gopal paid Rs.2,014 for the article, find the cost price of the article for Ravi.
(A) Rs.2020
(B) Rs.2000
(C) Rs.1900
(D) Rs.2011

 

12. If a merchant estimates his profits as 20% of the selling price, what is his real profit percent.
(A) 25%
(B) 20%
(C) 22%
(D) 30%

 

13. Karuna bought a car for a certain sum of money. She spent 10% of the cost on repairs and sold the car for a profit Rs.11,000. How much did she spent on repairs, if she made a profit of 20%?
(A) Rs.4000
(B) Rs.4400
(C) Rs.5500
(D) Rs.5000

 

14. An article when sold at a gain of 5% yield Rs.15 more than when sold at a loss of 5%. Its cost price would be
(A) Rs.150
(B) Rs.200
(C) Rs.250
(D) Rs.300

 

15. A man bought goods worth Rs.6000 and sold half ot them at a gain of 10%. At what gain percent must he sell the remainder to get a gain of 25% on the whole?
(A) 40%
(B) 25%
(C) 25%
(D) 20%

 

16. A shopkeeper fixes the MP of an item 35% above its CP. The percentage of discount allowed to gain 8% is
(A) 43%
(B) 30%
(C) 20%
(D) 31%

 

17. A shopkeeper marks his goods at 40% above the cost price and allows discount of 40% on the marked price. His loss or gain is
(A) no loss and no gain
(B) 16% loss
(C) 16% gain
(D) 20% gain

 

18. If SP of an article is 4/3 of its CP then the profit in the transaction is
(A) (1/3)%
(B) 20(1/2)%
(C) 33(1/3)%
(D) 25(1/2)%

 

19. If 5% more is gained by selling an article for Rs.350 than by selling it for Rs.340, the cost of the article is
(A) Rs.50
(B) Rs.160
(C) Rs.200
(D) Rs.225

 

20. A cycle is sold for Rs.880 at a loss of 20%. For how much should it be sold to gain 10%?
(A) Rs.1400
(B) Rs.1210
(C) Rs.1100
(D) Rs.1000

 

21. The gain or loss percent when a carriage, which cost Rs.4000, is sold for Rs.5000 is
(A) 10% loss
(B) 25% loss
(C) 25% profit
(D) The angle

 

22. Sugar is bought at Rs.16.20 per kg and sold at Rs.17.28 per kg. The gain percent is
(A) 6(2/3)%
(B) 3(1/3)%
(C) 10%
(D) 10(2/3)%

 

23. Articles are bought at 423 paise a dozen and sold at 85 paise a score. The profit percent is
(A) 21%
(B) 21(3/7)%
(C) 33(1/3)%
(D) 32%

 

24. Ram buys sweets at 4 items for 90 paise and an equal number at 5 items for 90 paise and sells the whole at 9 items for 180 paise. His loss or gain percent is
(A) 8(16/23)%
(B) 1(19/81)%
(C) 3(2/3)%
(D) None of these

 

25. A merchant buys a 50 litre cask of wine for Rs.6250 and sells it at Rs.130 per litre. His loss or gain percent is
(A) 3(11/50)% loss
(B) 4 % profit
(C) 25% profit
(D) 8% gain

 

26. A woman bought two parcels of toffees, the same number in each parcel. She bought the first back at 25 paise per each toffee and the second pack at 3 toffees for 65 paise. She mixed them together and sold at Rs.3.50 a dozen. Her gain percent is
(A) 15%
(B) 25%
(C) 16(2/3)%
(D) 12%

 

27. The selling price of goods which cost Rs.10 and were sold at a gain of 10% is
(A) Rs.12
(B) Rs.18
(C) Rs.11
(D) Rs.11.10

 

28. The selling price when goods which cost Rs.65 are sold at a loss of 10% is
(A) Rs.71.50
(B) Rs.58.50
(C) Rs.59.75
(D) Rs.66.50

 

29. A man bought 5421 kg of sugar for Rs.7560.90 and sold it so as to gain 25. The selling price per kilogram of sugar is
(A) Rs.16.74
(B) Rs.22.92
(C) Rs.31.46
(D) Rs.12.24

 

30. A man sells a mare for Rs.1085 making a profit of 8(1/2)%. The cost of the mare is
(A) Rs.982
(B) Rs.999.50
(C) Rs.927.75
(D) Rs.1000

 

 

Question: The CI on Rs. 16,000 at 15% p.a. for 2"3 years is
a) Rs. 6218
b) Rs. 5000
c) Rs. 6418
d) Rs. 22,218

 

Question: In what time wiil Rs. 1000 amount to Rs. 1331 at 10% p.a. in Cl?
a) 3 years
b) 1 year
c) 4 years
d) 2 years

 

Question: The present population of a town is 25,000. It grows at 4%, 5% and 8% during first year, second year and third year respectively, the population after 3 years is
a) 29,484
b) 24,576
c) 28,696
d) 30,184

 

Question: The value of an article which was purchased 2 years ago, depreciates at 12% per annum. If its present value is Rs. 9680, the price at which it was purchased is
a) Rs. 12,500
b) Rs. 16,250
c) Rs. 10,000
d) Rs. 14,575

 

Question: The cost of a vehicle is Rs. 1,75,000. If its value depreciates at the rate of 20% per annum, then the total depreciation after 3 years was
a) Rs. 85,400
b) Rs. 82,500
c) Rs. 86,400
d) Rs. 84,500

 

Question: The CI on a certain sum for 2 years is Rs. 410 and 81 is Rs. 400. The rate of interest per annum is
a) 5%
b) 10%
c) 8%
d) 4%

 

Question: The CI on a certain sum for 2 years at 10% per annum is Rs. 525. The 81 on the same sum for double the time at half the rate percent per annum is
a) Rs. 500
b) Rs. 800
c) Rs. 400
d) Rs. 600

 

Question: On a sum of money the SI for two years is Rs.660, while CI is Rs.696.30, the rate of interest being the same in both the cases. the rate of interest is
a) 11%
b) 12%
c) 10%
d) 15%

 

Question: A man borrowed Rs.3125 for CI and it amounted to Rs.4500 in 2 years. the rate of CI per annum is
a) 20%
b) 30%
c) 25%
d) 15%

 

Question: A sum of money doubles itself in 3 years at CI, when the interest is compounded annually. In how many years will it amount to 16 times of itself?
a) 12 years
b) 6 years
c) 8 years
d) 16 years

 

Question: The CI on a certain sum at 5% for 2 years is Rs.328. The SI for that sum at the same rate and for the same period will be
a) Rs.320
b) Rs.325
c) Rs.322
d) Rs.326

 

Question: Find the amount of Rs.12500 for 2 years compounded annually, the rate of interest being 15% for the first year and 16% for the second year
a) Rs.16675
b) Rs.16500
c) Rs.16750
d) None

 

Question: A sum of money, at compound interest, yields Rs.200 and Rs.220 at the end of first and second year respectively. The rate % is
a) 10
b) 20
c) 15
d) 5

 

Question: A sum of money at CI amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
a) 6
b) 12
c) 18
d) 9

 

Question: The CI on a certain sum for 2 years is Rs.41 and SI is Rs.40. Then the rate percent per annum is
a) 5%
b) 8%
c) 4%
d) 6%

 

Question: The difference in SI and CI on a certain sum of money in 2 years at 15% p.a. is Rs.144. The sum is
a) Rs.6400
b) Rs.6200
c) Rs.6000
d) Rs.6300

 

Question: In what time will a sum of Rs. 800 at 5% p.a. Cl amounts to Rs. 882?
a) 2 years
b) 5 years
c) 1 year
d) 4 years

 

Question: The CIon Rs. 8000 for 1 year at 5% p.a. payable half-yearly is
a) Rs. 405
b) Rs. 810
c) Rs. 800
d) Rs. 400

 

Question: What sum lent out at Cl will amount to Rs. 968 in 2 years at 10% p.a. interest?
a) Rs. 800
b) Rs. 1200
c) Rs. 1000
d) None

 

Question: If the difference between 81 and Cl on a certain sum of money for 3 years at 10% p.a. is Rs. 15.50. The sum is
a) Rs. 1000
b) Rs. 1500
c) Rs. 500
d) Rs. 2000

 

 

 

 CHAPTER – 8. 

COMPARING QUANTITIES.

 

Put a tick mark (√) on the correct answer :

Q1. Find which of the following represents 3 : 4 ?
(i) 25%
(ii) 40%
(iii) 50%
(iv) 75%

Q2. If 60% of x is 1200, then the value of ‘x’ is
(i) 1000
(ii) 2000
(iii) 3000
(iv) 4000

Q3. The list price of an article is Rs.220. If it is sold at a discount of 20% , what is its selling price
(i) 100
(ii) 44
(iii) 176
(iv) 200

Q4. A table marked at Rs.15000 is available for Rs.14400 .Find the discount percent?
(i) 2%
(ii) 4%
(iii) 5%
(iv) 7%

Q5. The cost price of an article is Rs 500. If it is sold at a profit of 20% , what is its selling price
(i) Rs. 600
(ii) Rs. 700
(iii) Rs. 400
(iv) Rs. 520

Q6. A man got 10% increase in his salary. If his new salary is 154000, find his original salary?
(i) Rs.160000
(ii) Rs. 150000
(iii) Rs.140000
(iv) Rs.130000

Q7. Find the compound interest on Rs.12600 for 2 years at 10% per annum compounded annually?
(i) Rs. 2646
(ii) Rs. 2700
(iii) Rs.3420
(iv) Rs.4526

Q8. Find the rate of sales tax if an article marked at Rs.5000 is sold for Rs.5200?
(i) 3%
(ii) 4%
(iii) 5%
(iv) 7% 

 

Question:

a) 23.75%

b) 21.875%

c) 23.25%

d) 40%

 

 

Question: A publisher sells books to a retail dealer of Rs.5 a copy but allows 25 copies to count as 24. If the retailer sells each of hte 25 copies at Rs.6, his profit percent is

a) 25%

b) 20%

c) 24%

d) 40%

 

 

Question:

a)

b)

c)

d)

Answer:

 

Question: The percentage equivalent to 3/8 is

a) 37.5

b) 40

c) 0.375

d) 3.75

 

 

Question: A cask containing 425 litres lost 8% by leakage and evaporation. The number of litres left in the case were

a)

b)

c)

d)

Answer:

 

Question:

a) 425X8 /100

b) 425 − 425X8 /100

c) 425 + 425X8 /100

d) None of these

 

 

Question: 8% of Rs.625 is equal to

a) Rs.50

b) Rs.80

c) Rs.75

d) Rs.100

 

 

Question: 0.9 per cent can be expressed as

a) 0.009

b) 0.0009

c) 0.09

d) None of these

 

 

Question: A producer blends two qualities of rice. One costing Rs.12.50 per kg and the other costing Rs.14 per kg in the ratio 4 : 5. Find his profit percent if he sells the mixture at the rate of Rs.16 per kg.

a) 20%

b) 25%

c) 15%

d) 10%

 

 

Question: Ravi sold an article to Sudhir at a profit of 6% who is in turn sold that to Gopal at a loss of 5%. If Gopal paid Rs.2,014 for the article, find the cost price of the article for Ravi.

a) Rs.2000

b) Rs.2011

c) Rs.2020

d) Rs.1900

 

 

Question: If a merchant estimates his profits as 20% of the selling price, what is his real profit percent

a) 25%

b) 22%

c) 20%

d) 30%

 

 

Question: Karuna bought a car for a certain sum of money. She spent 10% of the cost on repairs and sold the car for a profit Rs.11,000. How much did she spent on repairs, if she made a profit of 20%?

a) Rs.5000

b) Rs.4400

c) Rs.4000

d) Rs.5500

 

 

Question: An article when sold at a gain of 5% yield Rs.15 more than when sold at a loss of 5%. Its cost price would be

a) Rs.150

b) Rs.250

c) Rs.200

d) Rs.300

 

 

Question: A man bought 5421 kg of sugar for Rs 7560.90 and sold it so as to gain 25. the selling price per kilogram of sugar is

a) Rs.16.74

b) Rs.31.46

c) Rs.22.92

d) Rs.12.24

 

 

Question: A man bought goods worth Rs.6000 and sold half ot them at a gain of 10%. At what gain percent must he sell the remainder to get a gain of 25% on the whole?

a) 40%

b) 25%

c) 35%

d) 20%

 

 

Question: A shopkeeper fixes the MP of an item 35% above its CP. The percentage of discount allowed to gain 8% is

a) 20%

b) 43%

c) 30%

d) 31%

 

 

Question: A shopkeeper marks his goods at 40% above the cost price and allows discount of 40% on the marked price. His loss or gain is

a) 16% loss

b) 20% gain

c) 16% gain

d) no loss and no gain

 

 

Question: If SP of an article is 4/3 of its CP then the profit in the transaction is

a)

b) 1/3 %

c)

d)

Answer:

 

Question: If 5% more is gained by selling an article for Rs.350 than by selling it for Rs.340, the cost of the article is

a) Rs.200

b) Rs.50

c) Rs.160

d) Rs.225

 

 

Question: A cycle is sold for Rs.880 at a loss of 20%. For how much should it be sold to gain 10%?

a) Rs.1210

b) Rs.1000

c) Rs.1400

d) Rs.1100

 

 

Question: The gain or loss percent when a carriage, which cost Rs.4000, is sold for Rs.5000 is

a) 25% profit

b) 10% loss

c) The angle

d) 25% loss

 

 

Question: Sugar is bought at Rs.16.20 per kg and sold at Rs.17.28 per kg. The gain percent is

a)

b)

c)

d) 10%

Answer:

 

Question: Articles are bought at 423 paise a dozen and sold at 85 paise a score. The profit percent is

a) 21%

b) 32%

c)

d)

 

 

Question: Ram buys sweets at 4 items for 90 paise and an equal number at 5 items for 90 paise and sells the whole at 9 items for 180 paise. His loss or gain percent is

a)

b)

c)

d) None of these

Answer:

 

Question: A merchant buys a 50 litre cask of wine for Rs.6250 and sells it at Rs.130 per litre. His loss or gain percent is

a) 4 % profit

b) 8% gain

c) 25% profit

d)

 

 

Question: The selling price of goods which cost Rs.10 and were sold at a gain of 10% is

a) Rs.11

b) Rs.12

c) Rs.11.10

d) None of these

 

 

Question: The selling price when goods which cost Rs.65 are sold at a loss of 10% is

a) Rs.58.50

b) Rs.66.50

c) Rs.71.50

d) Rs.59.75

 

 

Question:

a) Rs.1000

b) Rs.999.50

c) Rs.982

d) Rs.927.75

 

 

 

 

Chapter 9 

Algebraic Expressions and Identities 

 

 

Question:

a) 152

b) 150

c) 148

d) None

 

 

Question:

a) a + b + c

b) None

c) 0

d) 1

 

 

Question: The value of (x + 3)3 – (x – 3)3 is

a) 18x2 + 54

b) 1 – x3

c) 0

d) 3x2 – 5

 

 

Question: The value of 25x2 + 16y2 + 40xy at x = 1 and y = –1 is

a) 1

b) 81

c) – 48

d) none

 

 

Question:

a) – 2xy

b) – 12xy

c) 2 xy

d) 12 xy

 

Question:

a) 9

b) 1.176

c) 6.66

d) none

 

Question:

a) 8

b) 4

c) 2

d) 6

 

Question:

a) 9

b)

c) Both

d) None of these

 

Question: If 3x – 7y = 10 and xy = – 1 then the value of 9x2 + 49y2 is

a) 58

b) 14/2

c) 104

d) – 104

 

Question:

a) 32

b) 136

c) 64

d) 68

 

Question:

a) 316

b) 361

c) – 188

d) none

 

Question:

a)

b)

c)

d) 0

Answer:

 

Put a tick mark(√) on the correct answer :

Q1.What is the sum of 7xy + 5yz – 3xz & 2xy + 4yz + 2xz ?

(i) 8xy + yz -- xz 

(ii) 9xy + 9yz -- xz 

(iii) 9xy + 9yz + xz 

(iv) 9xy + 9yz + 5xz

Q2. What should be subtracted from 2x2 – 5y2 + 7z2 to get x2 – y2 + z2

(i) x2 –4 y2 +6 z2 

(ii) x2 –3y2 +6 z2 

(iii)3 x2 – 2y2 +2 z2 

(iv) x2 – y2 + z2

Q3.What is the product of 3xy, 4xy & 2xz ?

(i) 24xyz 

(ii) 24x2yz 

(iii) 24 x3y2z 

(iv) 24 x3y2z2

Q4.What is the area of the rectangle of length 4xy & breadth 2xy ?

(i) 8xy2 

(ii) 8x2y 

(iii) 4 x3y2z 

(iv) 8 x2y2

Q5.What is the volume of the cuboid of length 8xy , breadth 3xy & height xy ?

(i) 24xy2 

(ii) 24x2y 

(iii)2 4 x3y2 

(iv) 24 x3y3

Q6. What is the value of the expression 2ab + 3bc + 4ac, when a = b = c = 1?

(i) 5 

(ii) 6 

(iii) 7 

(iv) 8

Q7. What is the formulae for ( x - y )2 ?

(i) x2 + 2xy + y2 

(ii) x2 -- 2xy + y2 

(iii) x2 -- 2xy -- y2 

(iv) x2 -- y2

Q8. What is the simplified form of ( a2 – b2 )2 ?

(i) a4 + 2a2b2 + b4 

(ii) a4 -- 2a2b2 + b4 

(iii) a4 -- 2a2b2 -- b4 

(iv) a4 + a2b2 + b4 

 

Question: (3x – 5y)3 – (5x – 2y)3 + (2x + 3y)3

a) – 3 (3x – 5y) (2x – 5y) (2x + 3y)

b) 3(3x – 5y) (5x – 2y) ( 2x + 3y)

c) (3x – 5y) (2y – 5x) (2x + 3y)

d) (3x – 5y) (5x – 2y) (2x + 3y)

 

 

Question: If a + b + c = 9 and ab + bc + ca = 26, then the value of a3 + b3 + c3 – 3abc is

a) 27

b) 29

c) 729

d) 495

 

 

Question: If x3 + y3 + z3 = 3xyz then the relation between x, y and z is

a) either x + y + z = 0 (or) x = y = z

b) x + y + z = 0

c) x = y = z

d) neither x + y + z = 0 nor x = y = z

 

 

Question: The equality b2 + 5 > 9b + 12 us satisfied if

a) b > 9 (or) b < 0

b) b > 8 (or) b < 0

c) b > 9 (or) b < 1

d) b = 10 (or) b = – 1

 

 

Question:

a) Greater than 2

b) Greater than 4

c) Less than 2

d) Less than 4

 

 

Question:

a) 100

b) 1

c) 10

d) none

 

 

Question:

a) 1

b) ½

c) 0

d) none

 

 

Question:

a) 0.1

b) 0.04

c) 0

d) 0.2

 

 

Question: If 2x + y = 5 then 4x + 2y is equal to

a) 10

b) 8

c) 5

d) 9

 

 

Question: If x + y = 6 and 3x – y = 4 then x – y is equal to

a) – 1

b) 2

c) 0

d) 4

 

 

Question: If the product of two numbers is 10 and the sum is 7, then the larger of the two numbers is

a) 5

b) – 2

c) 2

d) None of these

 

Question: The value of (55)3 – (75)3 + (20)3 is

a) – 247500

b) 125320

c) 251750

d) none

 

 

 

 

 

Chapter 11 

Mensuration 

 

Question: The side of a triangle are 16 cm, 30 cm and 34 cm. Its area is
a) 240 cm2
b) 120 cm2
c) 260 cm2
d) 272 cm2

 

Question: The adjacent sides of a parallelogram are 8 cm and 9 cm. The diagonal joining the ends of this side is 13 cm. Its area is
a) 12√35 cm2
b) 24√35 cm2
c) 150 cm2
d) 72 cm2

 

Question: A square is a special case of
a) rhombus
b) parallelogram
c) isosceles trapezium
d) trapezium

 

Question: Opposite angles of a rhombus are
a) equal
b) never equal
c) supplementary
d) complementary

 

Question: The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to largest side is
a)

b) None of these
c)

d) 30 cm

Answer:

Question: The perimeter of a triangular field is 144 m and the ratio of the sides is 3 : 4 : 5. The area of the field is
a) 864 m2
b) 824 m2
c) 468 m2
d) none

 

Question: A rectangular field has its length and breadth in the ratio 5 : 3. Its area is 3.75 hectares. The cost of fencing it at Rs. 5 per meter is
a) Rs. 4000
b) Rs. 500
c) Rs. 400
d) Rs. 1000

 

Question: If the altitude of an Equilateral triangle is √6 cm, its area is
a) 2√3 cm2
b) 2√2 cm2
c) 6√2 cm2
d) None of these

 

Question: The ratio between the length and the perimeter of a rectangular plot is 1 : 3 and the ratio between the breadth and perimeter of that plot is 1 : 6. What is the ratio between the length and area of that plot?
a) Data inadequate
b) 1 : 6
c) 2 : 1
d) 1 : 8

 

Question: What change in percent is made in the area of a rectangle by decreasing its length and increasing its breadth by 5%?
a) 0.25% decrease
b) 2.5% increase
c) 0.25% increase
d) 2.5% decrease

 

Question: The area of a rhombus is 25 cm2 and one of its diagonals is 4 cm. Its perimeter is
a) 4√53 cm
b) 2√53 cm
c) 36 cm
d) none of these

 

Question: The area of a trapezium is 28 cm2 and one of its parallel sides 6 cm. If its altitude is 4 cm then its other parallel side is
a) 8 cm
b) 6 cm
c) 4 cm
d) none

 

Question: The perimeter of a trapezium is 52 cm and its nonparallel sides are each equal to 10 cm and its altitude is 8 cm. Its area is
a) 128 cm2
b) 118 cm2
c) 112 cm2
d) 124 cm2

 

Question: The area of a rhombus is 120 cm2 and its altitude is 10 cm. The length of the rhombus is
a) 12 cm
b) 4 cm
c) 24 cm
d) 8 cm

 

Question: The area of an isosceles triangle having base x cm and one side y cm is
a)

b)

c) Both
d) none of these

Answer:

Question: The length of diagonal of a square whose area is 16900 m2 is
a) 130√2 m
b) 144 m
c) 169 m
d) None of these

 

Question: The sides of a triangle are 3 cm, 5 cm and 4 cm. Its area is
a) 6 cm2
b) 7.5 cm2
c) 17.5 cm2
d) 27.5 cm2

 

Question: The base of an isosceles right triangle is 30 cm. Its are is
a) 225 cm2
b) 225√3 cm2
c) 5√2 cm2
d) None of these

 

Question: One side of an equilateral triangle is 30 cm. Its area is
a) 225√3 cm2
b) 112.5 cm2
c) 225√2 cm2
d) 225 cm2

 

Question: The sides of a triangle are 16 cm, 30 cm and 34 cm. Its area is
a) None of these
b) 120 cm2
c) 260 cm2
d) 272 cm2

 

 

Q1.What is the area of a rhombus whose diagonals are of lengths 10cm & 8.2 cm?
(i) 24cm2 
(ii) 41 cm2 
(iii) 42 cm2 
(iv) 25 cm2

Q2.What is the area of a trapezium whose two parallel sides are 10 cm & 12cm & height 4cm?
(i) 42cm2 
(ii) 44 cm2 
(iii) 46 cm2 
(iv) 48 cm2

Q3.The area of a rhombus is 240 cm2 . If one of its diagonals is 16 cm, what the length of its other diagonal is?
(i) 32cm
(ii) 30 cm
(iii) 45 cm
(iv) 48 cm

Q4.If each side of an equilateral triangle is doubled, then its area becomes how many times?
(i) 2
(ii) 3
(iii) 4
(iv) 8

Q5.What is the total surface area of a cuboid of dimensions 4cm, 5cm & 6cm?
(i) 142cm2
(ii) 144 cm2
(iii) 146 cm2 
(iv) 148 cm2

Q6.What is the lateral surface area of a cube of side 5cm?
(i) 150cm2 
(ii) 100 cm2
(iii) 140 cm2 
(iv) 130 cm2

Q7.What is the volume of a cuboid whose dimensions are 5cm x 3cm x 2cm ?
(i) 24cm3 
(ii) 20 cm3 
(iii) 30 cm3 
(iv) 17 cm3

Q8.What is the volume of a sphere whose radius is 3cm ?
(i) 24πcm3 
(ii) 36π cm3 
(iii) 30π cm3 
(iv) 27π cm3

Q9.What is the curved surface area of a cone of radius 3cm & height 4 cm?
(i) 14πcm2 
(ii) 15π cm2 
(iii) 16π cm2 
(iv) 17π cm2

Q10. If the height of a cylinder is halved, its volume becomes how many times
?(i) 1/ 2
(ii)1/ 3
(iii) 2
(iv) 3 

 

 

 

 

Chapter 12 

Exponents and Powers 

 

Question: The value of log24 – log15 + log40 is equal to

a) 5log2

b) 7log2

c) 6log2

d) 8log2

 

Question: The value of log105 + log32 – log80 –log21 is

a) log2

b) log4

c) log3

d) log5

 

Question: The value of log mn + log mn+1 + log m1+2n is

a) 2 log m

b) n log m

c) log m

d) 3 log m

 

Question:

a) 11/2

b) 9/2

c) 7/2

d) 3

 

Question:

a) 1

b) 3

c) 0

d) 2

 

Question:

a) 1

b) 3

c) 0

d) 2

 

Question:

a) 1

b) 2

c) None of these

d) 0

 

Question:

a) 5

b) 4

c) 6

d) 7

 

Question:

a) 28

b) not

c) 24

d) 27

 

Question:

a) x2

b) not

c) x

d) x3

 

Question:

a) 2√2

b) 2

c) 4

d) 3

 

Question:

a)

b)

c) none of these

d)

Answer:

 

Question: The value of log108 – log54 – log2 is

a) 0

b) 1

c) 3

d) 2

 

Question: The value of log31 + log31/ 2 + log31/ 4 + log31/8 +.... is equal to

a) log9

b) log3

c) log4

d) None of these

 

Question:

a) 1

b) 3

c) 2

d) not

 

Question:

a) 6

b) 4

c) 3

d) 5

 

Question:

a) 2

b) b

c) 1

d) a

 

Question:

a) 4

b) 1

c) 2

d) Not

 

Question: The value of log xm yn zl + log xyz3− log xm+1y − log ynz2− log zl+1 is equal to 

a) None of these

b) –1

c) 1

d) 2

 

Question:

a) 2.7

b) 2.1

c) 3.0

d) 3.1

 

Q1. Which of the following is the multiplicative inverse of (3 x 4)-2

(i) 12
(ii)1/ 144
(iii) 144
(iv) 1 / 12

Q2.What is the value of ‘ m ‘ if (- 2)2 x (- 5)3 = 50 m ?

(i) 10
(ii) -10
(iii) 100
(iv) - 100

Q3.What is the scientific notation of 0.0023 ?
(i) 2.3 X 10-3
(ii) 23 X 10-3
(iii) 2.3 X 103
(iv) 23 X 103

Q4.What is the usual form of 7.54 x 10-3 ?
(i) 0.0754
(ii) 0.00754
(iii) 0.000754
(iv) 0.0000754

Q5.What is the value of (30 + 40 + 50)?
(i) 7
(ii) - 7
(iii) 3
(iv) - 3

 

 

 

CHAPTER – 13. 

DIRECT & INVERSE PROPORTIONS.

 

Q1.An electric pole, 14metres high, casts a shadow of 10metres. What will be the height of a tree that casts a shadow of 15 metres under similar conditions?
(i) 14 m
(ii) 20 m
(iii) 21 m
(iv) 24 m

Q2.A train is running at a speed of 75 km/hr. What distance will it cover in 20 minutes?
(i) 15km
(ii) 20km
(iii) 23 km
(iv) 25 km

Q3.A machine manufactures 840 bottles in six hours. Find the number of bottles it can manufacture in five hours?
(i) 600
(ii) 650
(iii) 700
(iv) 750

Q4.The scale of a map is given as 1:30000000. If two cities are 4 cm apart on the map, what is the actual distance between them?
(i) 600 km
(ii) 1400 km
(iii) 1300 km
(iv) 1200 km

Q5.If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?
(i) 15
(ii) 14
(iii) 24
(iv) 30

Q6.A car takes 2 hours to reach a destination by running at a speed of 60 km/hr. How long will it take when the car runs at a speed of 80 km/hr?
(i) 1.5 Hrs.
(ii) 1.4 Hrs.
(iii) 2.4Hrs.
(iv) 2.5Hrs.

Q7. 6 pipes are required to fill a tank in 1 hr 20 minutes. How long will it take if only 5 pipes of the same type are used?
i) 2 hr36 minutes.
(ii) 1 hr36 minutes.
(iii) 2 hours.
(iv) 1 hr 30 minutes.

Q8 If 5 people can do a piece of work in 20 days, how many people can do the same work in 2 days?
(i) 8
(ii) 50
(iii) 100
(iv) 200  

 

 

 

Chapter 14 

Factorisation 

 

Q1.What is the HCF of 2x2y & 3xy2 ?

(i) 6xy
(ii) 6x2y2
(iii) xy
(iv) x2y2

Q2. Which of the following is a factor of 6xy – 4y + 6 – 9x ?
(i) 2x + y
(ii) x -- y
(iii) 2x -- 3
(iv) 3x -- 2

Q3. Which of the following is a factor of y2 – 7y + 12 ?
(i) 2y + 3
(ii) y + 3
(iii) y -- 3
(iv) 2y – 2

Q 4.Which of the following is a factor of m4 – 256 ?
(i) m + 4
(ii) m2 + 4
(iii) m2 -- 4
(iv) m + 16

Q 5.Which of the following is a factor of z2 – 4z -- 12 ?
(i) z + 6
(ii) z -- 6
(iii) z2 -- 12
(iv) z + 2

Q6.What is the value of 2x – 3y + 4z at x=2, y = 0 & z =1
(i) 4
(ii) 6
(iii) 8
(iv) 10

Question: One of the factors of a3(b – c)3 + b3(c – a)3 + c3 (a – b)3 is
a) all the above
b) b – c
c) a – b
d) c – a

 

Question: One of the factor of a3 + 8b3 – 64c3 + 24 abc is
a) a + 2b – 4c
b) a + 2b + 4c
c) a – 2b + 4c
d) a – 2b – 4c

 

Question: The value of 0.76 X 0.76 X 0.76 + 0.24 X 0.24 X 0.24 / 0.76 X 0.76 − 0.76 X 0.24 + 0.24 + 0.24 is
a) 1
b) 0.1
c) 0.52
d) 0.01

 

Question: The factors of a2 + b – ab – a are
a) (a–1) (a – b)
b) (a + 1) (a – b)
c) (a + b) (a– 1)
d) none

 

Question: One of the factors of x2 + 1/x2 + 2 − 2x − 2/x is 
a) x + 1/x
b) x − 1/x
c) x + 1/x − 1
d) none of these

 

Question: If the factors of a2 + b2 + 2(ab + bc + ca) are (a + b + m) and (a + b + nc), then the value of m + n is
a) 2
b) 6
c) 4
d) 0

 

Question: If ( x2 + 3x + 5) ( x2 − 3x + 5) = m2 − n2, then m =
a) x2 + 5
b) x2 – 3x
c) 3x
d) none

 

Question: One of the factors of (a2 – b2) (c2 – d2) – 4abcd is
a) cannot be determined
b) ac – bd + bc – ad
c) none of these
d) (ac – bd + bc + ad)

 

Question: The factors of √3x2 + 11x + 6√3 are
a) (x −3√3)(√3x + 2)
b) ac − bd + bc − ad
c) (x + 3√3) (√3x + 2)
d) None of these

 

Question: One of the factors of x7 + xy6 is
a) x2 + y2
b) x
c) y
d) None of these

 

Question: The real factors of x2 + 4 are
a) does not exist
b) none of these
c) (x + 2) (x – 2)
d) (x2 + 2) (x2 – 2)

 

Question: One of the factors of x4 + 4 is
a) x2 – 2x +2
b) none of these
c) x2 + 2
d) x2 – 2

 

Question: The factors of x4 + 2x2 + 9 is
a) (x2 – 2x +3) (x2 + 2x +3)
b) (x2 + 3) (x2–3)
c) factorization is not possible
d) none of these

 

Question: The factors of x2 + xy – 2xz – 2yz are
a) (x + y) (x – 2z)
b) (x + y) (x + 2z)
c) (x – y) (x + 2z)
d) (x – y) (x – 2z)

 

Question: x9 – x is having
a) 5 factors
b) 2 factors
c) 4 factors
d) cannot be determined

 

Question: The factors of 1 – p3 are
a) (1– p) (1 + p + p2)
b) (1 + p) (1 + p2)
c) (1 + p) (1 – p – p2)
d) (1 + p) (1– p2)

 

Question: The factors of 15x2 – 26x + 8 are

a) (3x – 4) (5x – 2)
b) (3x + 4) (5x + 2)
c) (2x – 4) (5x + 2)
d) (3x + 4) (5x – 2)

 

Question: If 3x + 3y = 24 and 2x – 3y = 12 then the value of xy is
a) 18
b) 10
c) 12
d) 14

 

Question: One of the factors of (a2 − b2) (c2 − d2) −4abcd is
a) (ac – bd + bc + ad)
b) Cannot be determined
c) ac + bd + bc + ad
d) ab + bd –bc – ad

 

Question: One factor od a2−c2+b2
a) (a – b + c)
b) None of these
c) (a + b – c)
d) (a + b + c)

 

 

 

 

CHAPTER – 14 

INTRODUCTION TO GRAPHS.

 

The following graph shows the temperature forecast & the actual temperature for each day of a week. On the basis of the graph, answer the following Questions.

 

 

Question. On which days was the forecast temperature the same as the actual temperature?
(i) Mon day, Tuesday
(ii) Tuesday, Friday ,Sunday
(iii) Mon day, Tuesday, Wed.day
(iv)Tuesday, Saturday ,Sunday

Question. What was the maximum forecast temperature during the week?
(i) 35°C
(ii) 45°C
(iii) 30°C
(iv) 15°C

Question. What was the minimum forecast temperature during the week?
(i) 35°C
(ii) 25°C
(iii) 30°C
(iv) 15°C

Question. On which days did the actual temperature differ the most from the forecast temperature ?
(i) Mon day
(ii)Tuesday
(iii) Wed.day
(iv) Thursday 

 

 

 

 

Chapter 16 

Playing with Numbers

 

 

Question. Find the value of ‘A’ & ‘B’ from the following? 

(i) 2 & 3
(ii) 7 & 6
(iii) 8 & 6
(iv) 1 & 7

Question. Find the value of ‘A’ & ‘B’ from the following?

(i) 7 & 4
(ii) 7 & 2
(iii) 2 & 6
(iv) 4 & 7

Question. Find the value of ‘A’ & ‘B’ from the following? 

(i) 3 & 4
(ii) 5 & 2
(iii) 8 & 1
(iv) 4 & 8

Question. If the three digit number 24x is divisible by ‘9’ , what is the value of ‘x’
(i) 3
(ii) 5
(iii) 8
(iv) 4

Question. If 21z5 is a multiple of ‘9’ , where ‘z’ is a digit , find the value of ‘z’ ?
(i) 2
(ii) 3
(iii) 8
(iv) 1