Question

If ‘P’ is a negative odd number and ‘Q’ is a Prime number other than 2, then which of the following options is INCORRECT. Indicate all possible answers.

• A. PQ is negative odd integer
• B. PQ is negative prime number
• C. PQ square root is real
• D. PQ is negative even number

Hint:

Remember: Odd × Odd = Odd, Odd × Even = Even. Always apply sign rules carefully with negative numbers.

Answer 1

The Correct Option is B

Step 1: Identify properties of P and Q.
- \( P \) is a negative odd number. - \( Q \) is a prime other than 2, so \( Q \) is an odd positive integer.
Step 2: Multiply P and Q.
- Odd × Odd = Odd. - Negative × Positive = Negative. So \( PQ \) must be a negative odd integer.
Step 3: Check each option.
- (A) True, because PQ is negative odd integer. - (B) False, because product of two numbers greater than 1 cannot be prime. - (C) True, every integer (including negative) has a real square root if we consider absolute value (but not in natural numbers). In real numbers, \(\sqrt{|PQ|}\) exists. - (D) False, PQ cannot be even since both P and Q are odd. Thus, incorrect options are (B) and (D).
Final Answer: \[ \boxed{B, D} \]