If X = LCM of (5abc, 2a2 and 3b3) and Y = HCF of (ab, 3bc and - bca) t

1.	If X = LCM of (5abc, 2a2 and 3b3) and Y = HCF of (ab, 3bc and - bca) then which of the following statement regarding X and Y is correct?Statement 1: Y is linear but X is notStatement 2: X is linear but Y is notStatement 3: The value of XY is 30 a2b4c1. Statement I and II2. Statement I and III3. Statement III and II4. None of these
Answer» Correct Answer - Option 2 : Statement I and III Given: It is given that X = LCM of (5abc, 2a² and 3b³) and Y = HCF of (ab, 3bc and - bca) Concept Used: Basic concept of HCF and LCM Calculation: X = LCM of (5abc, 2a² and 3b³) ∴ LCM of (5abc, 2a² and 3b³) = 30 a²b³c Now, Y = HCF of (ab, 3bc and -bca) ∴ HCF of (ab, 3bc and -bca) = b Consider the first statement, Y is linear but X is not ∴ X is 30 a²b³c and Y is b So, statement 1 is correct and statement 2 is incorrect Now, Consider the third statement, the value of XY is 30 a²b⁴c So, XY = 30 a²b³c × b ⇒ 30 a²b⁴c So, statement 3 is correct Hence, option (2) is correct

If X = LCM of (5abc, 2a2 and 3b3) and Y = HCF of (ab, 3bc and - bca) then which of the following statement regarding X and Y is correct?Statement 1: Y is linear but X is notStatement 2: X is linear but Y is notStatement 3: The value of XY is 30 a2b4c1. Statement I and II2. Statement I and III3. Statement III and II4. None of these

Answer» Correct Answer - Option 2 : Statement I and III

Given:

It is given that X = LCM of (5abc, 2a² and 3b³) and Y = HCF of (ab, 3bc and - bca)

Concept Used:

Basic concept of HCF and LCM

Calculation:

X = LCM of (5abc, 2a² and 3b³)

∴ LCM of (5abc, 2a² and 3b³) = 30 a²b³c

Now, Y = HCF of (ab, 3bc and -bca)

∴ HCF of (ab, 3bc and -bca) = b

Consider the first statement, Y is linear but X is not

∴ X is 30 a²b³c and Y is b

So, statement 1 is correct and statement 2 is incorrect

Now, Consider the third statement, the value of XY is 30 a²b⁴c

So, XY = 30 a²b³c × b

⇒ 30 a²b⁴c

So, statement 3 is correct

Hence, option (2) is correct