Chapter 1: Number System

Solution:-

(D) 0 ÷ 0 = 0

Zero divided by zero is not defined.

Solution:-

(B) 99999

The number which comes immediately before a particular number is called its predecessor.

The predecessor of 1 lakh is = 1,00,000 – 1

= 99,999

Solution:-

(B) 1000001

The successor of a whole number is the number obtained by adding 1 to it.

We know that, 1 million = 10,00,000

Then, successor = 10,00,000 + 1

= 10,00,001

Solution:-

(A) 10

Even numbers between 58 and 80 are 60, 62, 64, 66, 68, 70, 72, 74, 76, 78.

Solution:-

(C) 17

Prime numbers between 16 to 80 = 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73 and 79.

Then, number of primes between 16 to 80 = 16

Prime numbers between 90 to 100 = 97

Then, number of primes between 90 to 100 = 1

Therefore, Sum of the number of primes between 16 to 80 and 90 to 100 is,

= 16 + 1

= 17

Solution:-

(D) The HCF of an even and an odd number is even.

The HCF of an even and an odd number is odd number.

Solution:-

(B) 3

The largest 4 – digit number = 9999

Prime factors of 9999 = 3 × 3 × 11 × 101

So, 9999 = 3² × 11 × 101

Therefore, distinct prime factors are = 3, 11 and 101

Number of distinct prime factors of the largest 4-digit number is = 3

Solution:-

(A) 2

The smallest 5 – digit number = 10000

Prime factors of 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

So, 10000 = 2⁴ × 5⁴

Therefore, distinct prime factors are = 2 and 5

Number of distinct prime factors of the smallest 5-digit number is = 2

Solution:-

(C) 6

Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, then the original number.

7 – 2 + 5 – 4 + * – 9 + 8 = (5 + *)

For the given number 7254 * 98 to be divisible by 11,

(5 + *) must also be divisible by 11

So, 5 + * = 11

Therefore * = 11 – 5

= 6

Solution:-

(B) 4

1 + 3 = 4 = 4/4 = 1

3 + 5 = 8 = 8/4 = 2

The largest number which always divides the sum of any pair of consecutive odd numbers is 4.