Questions on Number theory

Question 1

Question:   Define an even number.

Answer:    A number which is divisible by 2 is called an even number.

Question 2

Question:   Define an odd number.

Answer:    A number when divided by 2 gives remainder 1 is called an odd number.

Question 3

Question:   What is a prime number?

Answer:    A number which has only two factors, namely 1 and then number itself is called a prime number.

Question 4

Question:   What is a composite number?

Answer:    A number which has more than two factors is called composite number.

Question 5

Question:   When a rational number can be expressed as terminating decimal?

Answer:    A rational number can be expressed as terminating decimal, when the factors of its denominator are in the form 2ⁿ x 5^m

Question 6

Question:  

Answer:   
We know that the (r + 1)^th term of (x + a)ⁿ is given by

Question 7

Question:  

Answer:    Expanding by binomial theorem, we get

Question 8

Question:  

Answer:   

Question 9

Question:  

Answer:   
To find the two middle terms:

Since n = 9, the two middle terms are

Question 10

Question:  

Answer: