1.

Consider the following statements:1. The HCF of (p + q) and (p2 – q2) is (p + q).2. The HCF of (p – q) and (p2 – q2) is (p + q).3. The HCF of (p + q) and (p3 + q3) is (p + q).4. The HCF of (p – q) and (p3 – q3)  is (p + q).Which of the above statements is/are correct?1. 1 and 2 only2. 1 and 3 only3. 1, 2, and 4 only4. 1, 3, and 4 only

Answer» Correct Answer - Option 2 : 1 and 3 only

Concept:

The HCF of two or more numbers is the greatest factor that divides each of them exactly.

Calculation:

Statement 1

The factor of (p + q) = (p + q)

The factor of (p2 – q2) = (p + q) (p – q)

The HCF of (p + q) and (p2 – q2)

⇒ (p + q)

Statement 2

The factor of (p – q) = (p – q)

The factor of (p2 – q2) = (p + q) (p – q)

The HCF of (p – q) and (p2 – q2)

⇒ (p – q)

Statement 3

The factor of (p + q) = (p + q)

The factor of (p3 + q3) = (p + q) (p2 – p × q + q2)

The HCF of (p + q) and (p3 + q3)

⇒ (p + q)

Statement 4

The factor of (p – q) = (p – q)

The factor of (p3 – q3) = (p – q) (p2 + p × q + q2)

The HCF of (p – q) and (p3 – q3)  

⇒ (p – q)

∴ Only statement 1 and 3 are correct.


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