x : y = 3 : 2 and (x² + y²) : (x² - y²)

Assertion (A) : The value of (x² + y²) : (x² - y²) = 13 : 5

Reason (R) : x : y = 3 : 2

⇒ $\dfrac{x^2 + y^2}{x^2 - y^2} = \dfrac{(3k)^2 + (2k)^2}{(3k)^2 - (2k)^2} = \dfrac{13}{5}$ ; k ≠ 0

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is the correct reason for R.

4. Both A and R are true and R is the incorrect reason for R.

$\dfrac{(x + y)^4}{(x - y)^4} = \dfrac{16}{1}$

Assertion (A) : x : y = 3 : 1

Reason (R) : $\dfrac{x + y}{x - y} = \dfrac{2}{1}$ and $\dfrac{x + y + x - y}{x + y - x + y} = \dfrac{2 + 1}{2 - 1}$

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is the correct reason for R.

4. Both A and R are true and R is the incorrect reason for R.

Numbers a, b and c are in continued proportion.

Statement 1: (a + b + c)(a - b + c) = a² + b² + c².

Statement 2: b² = ac and (a + b + c)(a - b + c) = (a + c)² - b²

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

If a : b = 3 : 5, find :

(10a + 3b) : (5a + 2b)