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51.

State whether the given statement are true (T) or false (F).The number LIV is greater than LVI.

Answer»

False.

Where, L = 50

IV = 4

VI = 6

So, LIV = 50 + 4 = 54

LVI = 50 + 6

Therefore, 54 < 56

Hence, LIV < LVI

52.

State whether the given statement are true (T) or false (F).The number 85764 rounded off to nearest hundreds is written as 85700.

Answer»

False.

The number 85764 rounded off to nearest hundreds is written as 85800.

53.

State whether the given statements are true (T) or false (F).The number 85764 rounded off to nearest hundreds is written as 85700. 

Answer»

The number 85764 rounded off to nearest hundreds is written as 85700. 

False

54.

State whether the given statement are true (T) or false (F).Estimated sum of 7826 and 12469 rounded off to hundreds is 20,000.

Answer»

True.

The number 7826 rounded off to nearest hundreds is written as 7800.

The number 12469 rounded off to nearest hundreds is written as 12500

So, sum of numbers after rounded off to hundreds = 7800 + 12500 = 20,300

Therefore, 20,300 is nearest to 20,000.

55.

LXXV is greater than LXXIV.

Answer» True [LXXV = 75, LXXIV = 74]
56.

State whether the given statement are true (T) or false (F).LXXIV = 74

Answer»

True.

Where, L = 50

X = 10

IV = 4

So, LXXIV = 50 + 10 + 10 + 4

= 74

57.

If a number is divisible by 2 and 3, then it is also divisible by 6. So, if a number is divisible by 2 and 4, it must be divisible by 8

Answer»

False [2 and 4 are not co-primes]

58.

The largest 4-digit number, using any one digit twice, from digits 5, 9, 2 and 6 is (A) 9652 (B) 9562 (C) 9659 (D) 9965

Answer»

(D) 9965

Using 9 as twice from 5, 9, 2 and 6, then then number is 9965.

59.

In Indian System of Numeration, the number 58695376 is written as (A) 58,69, 53, 76 (B) 58,695,376 (C) 5,86,95,376 (D) 586,95,376

Answer»

(C) 5,86,95,376

In Indian System of Numeration, the number 58695376 is written as 5 crore, eighty six lakh, ninety five thousand, three hundred and seventy six = 5,86,95,376

60.

State whether the given statements are true or false:If a number is divisible by 2 and 3, then it is also divisible by 6. So, if a number is divisible by 2 and 4, it must be divisible by 8.

Answer»

False [2 and 4 are not coprimes]

61.

State whether the given statement are true (T) or false (F).In Roman numeration, if a symbol is repeated, its value is multiplied as many times as it occurs.

Answer»

False.

If a symbol is repeated, its value is added as many times as it occurs: i.e. II is equal 2, XX is 20 and XXX is 30.

62.

State whether the given statement are true (T) or false (F).5555 = 5 × 1000 + 5 × 100 + 5 × 10 + 5 × 1

Answer»

True.

Left Hand Side = 5555

Right Hand Side = 5 × 1000 + 5 × 100 + 5 × 10 + 5 × 1

= 5000 + 500 + 50 + 5

= 5555

Left Hand Side = Right Hand Side

63.

State whether the given statement are true (T) or false (F).39746 = 3 × 10000 + 9 × 1000 + 7 × 100 + 4 × 10 + 6

Answer»

True.

Left Hand Side = 39746

Right Hand Side = 3 × 10000 + 9 × 1000 + 7 × 100 + 4 × 10 + 6

= 30000 + 9000 + 700 + 40 + 6

= 39746

Left Hand Side = Right Hand Side

64.

The smallest 4 digit number with different digits is __________ .

Answer»

The smallest 4 digit number with different digits is 1023.

1023 is the right answer because in this numeral there are 4 different digits are used and there can be no possible small number using 4 different digits which are smaller than 1023.

65.

State whether the given statement are true (T) or false (F).82546 = 8 × 1000 + 2 × 1000 + 5 × 100 + 4 × 10 + 6

Answer»

False.

Left Hand Side = 82546

Right Hand Side = 8 × 1000 + 2 × 1000 + 5 × 100 + 4 × 10 + 6

= 8000 + 2000 + 500 + 40 + 6

= 10,546

Left Hand Side ≠ Right Hand Side

66.

State whether the given statement are true (T) or false (F).A whole number divided by another whole number greater than 1 never gives the quotient equal to the former.

Answer»

True.

As per the standard rule, a whole number divided by another whole number greater than 1 never gives the quotient equal to the former.

67.

State whether the given statement are true (T) or false (F).Sum of two consecutive odd numbers is always divisible by 4.

Answer»

True.

For example, 1 + 3 = 4 = 4/4 = 1

11 + 13 = 24 = 24/4 = 6

68.

Fill in the blanks to make the statements true.If 0 is subtracted from a whole number, then the result is the _____ itself .

Answer»

Whole number

If zero is subtracted from a whole number, then the result is the whole number itself.

69.

State whether the given statement are true (T) or false (F).There is a whole number which when added to a whole number, gives the number itself.

Answer»

True.

Zero (0) is a whole number which when added to a whole number, gives the number itself.

70.

State whether the given statement are true (T) or false (F).If a whole number is divided by another whole number, which is greater than the first one, the quotient is not equal to zero.

Answer»

True.

As per the standard rule, if a whole number is divided by another whole number, which is greater than the first one, the quotient is not equal to zero.

71.

State whether the given statement are true (T) or false (F).There is a natural number which when added to a natural number, gives the number itself.

Answer»

False.

We know that, ‘0’ is not a natural number.

Therefore, there is no any natural number which when added to a natural number, gives the number itself.

72.

State whether the given statement are true (T) or false (F).The product of two whole numbers need not be a whole number.

Answer»

False.

The product of two whole number is always a whole number.

Because, we know that, whole numbers are closed under multiplication.

73.

Write 10 crores and 100 crores as in the above table.

Answer»

Ten crores = 10 One crores 

= 100 Ten lakhs

= 1000 Lakhs 

= 10,000 Ten thousands 

= 1,00,000 Thousands 

= 10,00,000 Hundreds 

= 1,00,00,000 Tens 

= 10,00,00,000 Units

Hundred crores = 100 One crores 

= 10 Ten crores = 10,000 Lakhs 

= 1.0. 000 Ten thousands 

= 10.0. 000 Thousands 

= 1.0. 00.000 Hundreds 

= 10.0. 00.000 Tens 

= 100.0. 00.000 Units

74.

As per the census of 2001, the population of four states are given below. Arrange the states in ascending and descending order of their population.(a) Maharashtra 96878627(b) Andhra Pradesh 76210007(c) Bihar 82998509(d) Uttar Pradesh 166197921

Answer»

Ascending order ➝ (b), (c), (a), (d)
Descending order ➝ (d), (a), (c), (b)

75.

Of the following numbers which is the greatest? Which is the smallest 38051425, 30040700, 67205602

Answer»

The greatest number is 67205602 and the smallest number is 30040700.

76.

Write in expanded form :(a) 74836(b) 574021(c) 8907010

Answer»

74836 = 7 × 10000 + 4 × 1000 + 8 × 100 + 3 × 10 + 6 × 1

(b) 574021 = 5 × 100000 + 7 × 10000 + 4 x 1000 + 0 × 100 + 2 × 10 + 1 × 1

(c) 8907010 = 8 × 1000000 + 9 × 100000 + 0 × 10000 + 7 × 1000 + 0 × 100 + 1 × 10 + 0 × 1

77.

Insert commas in the correct positions to separate periods and write the following numbers in words. i) 57657560 ii) 70560762 iii) 97256775613

Answer»

i) 5,76,57,560: Five crores seventy six lakhs fifty seven thousands five hundred and sixty. 

ii) 7,05,60,762: Seven crores five lakhs sixty thousands seven hundred and sixty two.

iii) 9725,67,75,613: Nine thousand seven hundred and twenty five crores sixty seven lakhs seventy five thousand six hundred and thirteen.

78.

Determine the difference between the place value and the face value of 6 in 86456792.

Answer»

Given number is 86456792. By putting commas to separate periods the given number can be written as 8,64,56,792. 

i) Place value of ‘6’ in thousand place = 6 x 1000 = 6,000 Face value of 6 = 6 Difference = 6,000 – 6 = 5,994 

ii) Place value of ‘6’ in ten lakhs palce = 6 x 10,00,000 = 60,00,000 

Face value of 6 = 6 

Difference = 60,00,000 – 6 = 59,99,994

79.

Write the following decimal numbers in the expanded form. (i) 30.04 (ii) 3.04 (iii) 300.04

Answer»

(i) 30.04 = 3 x 10 + 0 x 1 + 0 x \(\frac{1}{10}\) + 4 x \(\frac{1}{100}\) 

= 3 x 10 + \(\frac{4}{100}\)

(ii) 3.04 = 3 x 1 + 0 x \(\frac{1}{10}\) + 4 x \(\frac{1}{100}\) 

= 3 x 1 + \(\frac{4}{100}\)

(iii) 300.04 = 3 x 100 + 0 x 10 + 0 x 1 + 0 x \(\frac{1}{10}\) + 4 x \(\frac{1}{100}\) 

= 3 x 100 + \(\frac{4}{100}\) 

= 3 x 100 + \(\frac{4}{100}\)

80.

Express 7 cm in metre and kilometer.

Answer»

7 cm = \(\frac{7}{100}\) m = 0.07 m 

7 cm = \(\frac{7}{10000}\) km = 0.00007 km

81.

State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form . √m where’m’ is a natural number. (iii) Every real number is an irrational number. 

Answer»

(i)  True. Because set of real numbers contain both rational and irrational number. 

(ii) False. Value of √m is not netagive number. 

(iii) False. Because set of real numbers contain both rational and irrational numbers. But 2 is a rational number but not irrational number.

82.

Are the square roots of all positive integers irrational ? If not, give an example of the square root of a number that is a rationed number.

Answer»

Square root of all positive integers is not irrational number. 

E.g. √4 = 2 Rational number. 

√9 = 3 Rational number.

83.

In January the high temperature recorded was 90°F and the low temperature was -2°F. Find the difference between the high and the low temperatures?

Answer»

The high temperature recorded = 90°F 

The low temperature recorded = -2°F 

Difference = 90°F – (-2°F) 

= 90°F + (Additive inverse of -2°F) 

= 90°F + (+2°F) = 92°F

84.

Between two rational numbers, there is/ are:(A) exactly one rational number(B) no rational number(C) infinitely many rational numbers(D) only one rational number and no irrational number

Answer»

Answer is (C) infinitely many rational numbers

85.

Express the following in the form p/q, where p and q are  integers and q ≠ 0.(i) \(0.\bar { 6 }\)(ii) \(0.4\bar { 7 }\)(iii) \(0.\bar { 001 }\)

Answer»

(i) \(0.\bar { 6 }\)

Let x = \(0.\bar { 6 }\) (Pure recurring decimal)

i.e. x = 0.6666 …(1)

Multiplying (1) by 10, because ones digit i.e. 6 is repeating, we get

10x = 6.6666 …(2)

Subtracting (1) from (2), we get

10x – x = (6.6666…) – (0.6666…)

⇒ 9x = 6

⇒ x = \(\frac { 6 }{ 9 }\)

⇒ x = \(\frac { 2 }{ 3 }\)

(ii) Let x = \(0.4\bar { 7 }\) (Mixed recurring decimal)

i.e. x = 0.47777 …(1)

Multiplying (1) by 10, to make it pure recurring decimal, we get

10x = 4.7777 …(2)

Further multiplying (2) by 10, we get

100x = 47.777 ….(3)

Subtracting (2) from (3), we get

100x – 10x = (47.777…) – (4.7777…)

⇒ 90x = 43

⇒ x = \(\frac { 43 }{ 90 }\)

(iii) Let x = \(0.\bar { 001 }\)

i.e. x = 0.001001001 …(1)

Multiplying (1) by 1000, we get

1000x = 1.001001 …(2)

Subtracting (1) from (2), we get

1000x – x = (1.001001…) – (0.001001…)

⇒ 999x = 1

⇒ x = \(\frac { 1 }{ 999 }\)

86.

Express 0.00323232 … in the form p/q, where p and q are integers and q ≠ 0.

Answer»

Let x = 0.00323232…

Then 100x = 0.323232 ……(1)

and 1000x = 32.323232 …(2)

Subtracting (1) from (2), we get

9900x = 32

⇒ x = \(\frac { 32 }{ 9900 }\)

⇒ x = \(\frac { 8 }{ 2475 }\)

87.

Express 3.2 in the form p/q, where p and q are integers and q ≠ 0.

Answer»

Let x = \(3.\bar { 2 }\) (Pure recurring decimal)

i.e. x = 3.2222 ……(1)

Multiplying (1) by 10, we get

10x = 32.2222 ……(2)

Subtracting (1) from (2), we get

10x – x = (32.222…) – (3.222…)

⇒ 9x = 29

⇒ x = \(\frac { 29 }{ 9 }\)

88.

Is π is a rational number?

Answer»

No, is an irrational number.

Reason: π is the ratio of the circumference of a circle to the length of its diameter. 

The value of π is approximately equal to \(\frac { 22 }{ 7 }\) but not exactly, 

i.e. π = 3.14159265…

Here in the value of π, no sign of recurrence of the digits was found.

Hence π is an irrational number.

But if we will take the value of π exactly equal to \(\frac { 22 }{ 7 }\)

i.e. \(\frac { 22 }{ 7 }\) = \(3.\bar { 142857 }\) then it is said to be rational.

89.

Express \(15.\bar { 712 }\) as a fraction in the simplest form.

Answer»

Let x = \(15.\bar { 712 }\)

i.e. x = 15.7121212 …(1)

Multiplying (1) by 10 and 100 successively, we get

10x = 157.121212 …(2)

and 1000x = 15712.1212 …(3)

Subtracting (2) from (3), we get

1000x – 10x = (15712.1212…) – (157.1212…)

⇒ 990x = 15555

⇒ x = \(\frac { 15555 }{ 990 }\)

⇒ x = \(\frac { 1037 }{ 66 }\)

Hence, \(15.\bar { 712 }\) = \(\frac { 1037 }{ 66 }\)

90.

If Sheela bought 2.083 kg of grapes and 3.752 kg of orange. What is the total weight of fruits

Answer»
2.083
(+)2.752
4.835

Weight of grapes = 2.083 Kg 

Weight of orange = 2.752 Kg 

Total weight = (2.083 + 2.752) Kg 

= 4.835 Kg

91.

Find the value and express as a rational number in standard form:(i) 2/5 ÷ 26/15(ii) 10/3 ÷ -35/12(iii) -6 ÷ -8/17(v) -22/27 ÷ -110/18

Answer»

i) (2/5) / (26/15)

= (2/5) × (15/26)

= (2/1) × (3/26) 

= (2×3) / (1×26) 

= 6/26 

= 3/13

ii) (10/3) / (-35/12)

= (10/3) × (12/-35)

= (10/1) × (4/-35) 

= (10×4)/ (1×-35) 

= -40/35 

= -8/7

iii) -6 / (-8/17)

= -6 × (17/-8)

= -3 × (17/-4) 

= (-3×17)/ (1×-4) 

 = 51/4

iv) (-22/27) / (-110/18)

= (-22/27) × (18/-110)

= (-1/9) × (6/-5)

= (-1/3) × (2/-5) 

= (-1×2) / (3×-5) 

= 2/15

92.

Anbu and Mala travelled from A to C in two different routes. Anbu travelled from place A to place B and from there to place C. A is 8.3 km from B and B is 15.6 km from C. Mala travelled from place A to place D and from there to place C. D is 7.5 km from A and C is 16.9 km from D. Who travelled more and by how much distance?

Answer»

Distance travelled by Anbu: 

From place A to place B = 8.3 km 

Distance from place B to place C = 15.6 km

∴ Total distance travelled by Anbu = 8.3 + 15.6 

= 23.9 km 

Distance travlled by Mala: 

Distance travelled place A to D = 7.5 km 

Distance from place D to place C = 16.9 km 

Total distance travelled by mala = (7.5 + 16.9) km 

= 24.4 km 

24.4 > 23.9 

∴ Mala travelled more distance. 

She travelled (24.4 – 23.9) km more i.e. she travelled 0.5 km more

93.

When Malar woke up her temperature was 102°F. Two hours later it was 3° lower, what was her temperature then?

Answer»

Initially Malar’s temperature = 102°F 

After two hours it lowered 3° ⇒ -3°F 

Here present temperature = 102° + (-3°) = 99°F

94.

The number \(1.\overline{27}\) in the form \(\frac{p}q\), where p and q are integers and q ≠ 0, isA.\(\frac{14}9\)B. \(\frac{14}{11}\)C. \(\frac{14}{13}\)D. \(\frac{14}{15}\)

Answer»

Since, after dividing 14 from 11, we get that number.

95.

\(0.3\overline2\) when expressed in the form \(\frac{p}q\) (p, q are integers, q ≠ 0), isA. \(\frac{8}{25}\)B. \(\frac{29}{90}\)C. \(\frac{32}{99}\)D. \(\frac{32}{199}\)

Answer»

Let x = \(0.3\overline2\)

10x = \(3\overline2\) (i)

100x = \(32.\overline2\) (ii)

Now, subtracting (i) from (ii), we get 

100x – 10x = \(32.\overline2\,-3.\overline2\)

90x = 29

\(\times= \frac{29}{90}\)

96.

\(0.\overline{001}\) when expressed in the form \(\frac{p}q\) (p, q are integers, q ≠ 0), isA. \(\frac{1}{1000}\)B. \(\frac{1}{100}\)C. \(\frac{1}{1999}\)D. \(\frac{1}{999}\)

Answer»

x = \(0.\overline{001}\) (i)

\(1000\times = 001.\overline{001} - 0.\overline{001}\)

999x = 1

\(\times = \frac{1}{999}\)

97.

The number \(0.\overline3\) in the form \(\frac{p}q\),where p and q are integers and q ≠ 0, isA. \(\frac{33}{100}\)B. \(\frac{3}{10}\)C. \(\frac{1}{3}\)D. \(\frac{3}{100}\)

Answer»

Since, among the following only the division of 1 by 3 gives that specified number.

98.

The number of consecutive zeroes in 23×34×54× 7, is A. 3 B. 2 C. 4 D. 5

Answer»

3As the expression has 23 × 53 which yields zeroes in expression.as this would make 1000 so 3 zeroes will be there

99.

Find one irrational number between 0.2101 and 0.2222 ….= .\(0.\overline2\).

Answer»

Let a = 0.2101 

And, b = 0.2222…. 

We observe that the second decimal place a has digit 1 and b has digit 2, therefore, a < b. In the third decimal place a has digit 0. So, if we consider irrational number 

x = 0.211011001100011… 

We find that, 

a < x < b 

Hence, x is required irrational number

100.

Find two irrational numbers lying between 0.1 and 0.12.

Answer»

Let, a = 0.1 = 0.10 

And, b = 0.12 

We observe that in the second decimal place a has digit 0 and b has digit 2. Therefore a < b. So, if we consider irrational numbers 

x = 0.11011001100011… 

y = 0.111011110111110… 

We find that, 

a < x < y < b 

Hence, x and y are required irrational numbers.