NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 1: Real Numbers - Exercise 1.1 - Multiple Choice Questions
Question 2

Question. 2

For some integer \(q\), every odd integer is of the form

(A)

\(q\)

(B)

\(q + 1\)

(C)

\(2q\)

(D)

\(2q + 1\)

Step 1: Recall that even integers are always multiples of 2.

So we can write any even integer as:

\(2q\), where \(q\) is some integer.

Step 2: Odd integers are always one more than an even integer.

Therefore, if an even number is \(2q\), then the next odd number is:

\(2q + 1\).

Step 3: This shows that every odd integer can be expressed in the form:

\(2q + 1\).

Answer: Option D (\(2q + 1\))