Which of the following statements is not correct?1. Difference of squa

1.	Which of the following statements is not correct?1. Difference of squares of two odd numbers is odd.2. We can express 30 as n × (n + 1) × (n + 3), where n is a natural number.3. 3/4 < 219/2921. Statement 1 and Statement 2 are not correct2. Statement 2 and Statement 3 are not correct3. Statement 1 and Statement 3 are not correct4. All are correct
Answer» Correct Answer - Option 3 : Statement 1 and Statement 3 are not correct Concept used: Product of two odd natural numbers is always odd. Difference and sum of two odd numbers is always even. Calculation: Statement 1: Let x and y be two odd numbers As, product of two odd numbers is always odd ⇒ x² is odd ⇒ y² is odd \|x² – y²\| is even, because difference of two odd numbers is always even. Hence, Statement 1 is not correct Statement 2 We can express 30 as 2 × 3 × 5 ⇒ 30 = 2 × (2 + 1) × (2 + 3) For n = 2, 30 can be expressed as n × (n + 1) × (n + 3) Hence, Statement 2 is correct Statement 3 3/4 = (3 × 73/(4 × 73) = 219/292 Hence, Statement 3 is not correct ∴ Statement 1 and Statement 3 are not correct

Which of the following statements is not correct?1. Difference of squares of two odd numbers is odd.2. We can express 30 as n × (n + 1) × (n + 3), where n is a natural number.3. 3/4 < 219/2921. Statement 1 and Statement 2 are not correct2. Statement 2 and Statement 3 are not correct3. Statement 1 and Statement 3 are not correct4. All are correct

Answer» Correct Answer - Option 3 : Statement 1 and Statement 3 are not correct

Concept used:

Product of two odd natural numbers is always odd.

Difference and sum of two odd numbers is always even.

Calculation:

Statement 1:

Let x and y be two odd numbers

As, product of two odd numbers is always odd

⇒ x² is odd

⇒ y² is odd

|x² – y²| is even, because difference of two odd numbers is always even.

Hence, Statement 1 is not correct

Statement 2

We can express 30 as 2 × 3 × 5

⇒ 30 = 2 × (2 + 1) × (2 + 3)

For n = 2, 30 can be expressed as n × (n + 1) × (n + 3)

Hence, Statement 2 is correct

Statement 3

3/4 = (3 × 73/(4 × 73) = 219/292

Hence, Statement 3 is not correct

∴ Statement 1 and Statement 3 are not correct