Chapter 1: Number System

Solution:-

(D) 60

The LCM of 6 and 5 is 30.

So, 30 is divisible by 10, 15 and 30 in the given options.

But, 30 is not divisible by 60.

Solution:-

(D) 39

The prime factors of 1729 = 7 × 13 × 19

Therefore, the sum of prime numbers = 7 + 13 + 19

= 39

Solution:-

(B) 4

Let us assume an odd natural number be 5.

Then, predecessor of 5 = 5 -1 = 4

Successor of 5 = 5 + 1 = 6

Then, the product of predecessor and successor = 4 × 6

= 24

24 is divided by 4 = 24/4 = 6

Therefore, the greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1, is 4.

Solution:-

(A) 2

Prime factors of,

75 = 3 × 5 × 5

60 = 2 × 2 × 3 × 5

105 = 3 × 5 × 7

So, common prime factors in the given three numbers are 3 and 5.

Therefore, the number of common prime factors of 75, 60, 105 is 2.

Solution:-

(A) 8, 10

First of all, both the numbers are even.

Then, common factor of both numbers is 2 other than 1.

Therefore, 8 and 10 are not coprime.

Solution:-

(C) 22222222

To check the divisibility of a number by 11, the rule is to find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.

So, 2 – 2 + 2 – 2 + 2 – 2 + 2 – 2 = 0

Therefore, 22222222 is divisible by 11.

Solution:-

(B) 60

Factors of 10, 15 and 30 is,

Then, LCM of 10, 15 and 30 is 2 × 2 × 3 × 5 × 1 = 60

Solution:-

(C) 75

Factors of 180.

Then, factors of 180 = 2 × 2 × 3 × 3 × 5

180 is not divided by 180.

Therefore, 75 is not the HCF of the number 180.

In questions 39 to 98, state whether the given statements are true (T) or false (F).

Solution:-

True.

As per the rule of the Roman numerals, a symbol is not repeated more than three times.

Solution:-

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.