Assertion (A): Solution of 217x + 131y = 913 and 131x + 217y = 827 is x = 3, y = 2.

Reason (R): To solve equations of the type ax + by = c and bx + ay = d where a ≠ b, we add them to obtain x + y = $\dfrac{c + d}{a + b}$ and subtract them to obtain x - y = $\dfrac{c - d}{a - b}$ .

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A):

$\dfrac{8^{x+2}+8^{x+1}}{8^{x+2}-8^{x+1}} \\[1em] = \dfrac{x + 2 + x + 1}{x + 2 - x - 1} \\[1em] = 2x + 3$

Reason (R):

$\dfrac{8^{x+2}+8^{x+1}}{8^{x+2}-8^{x+1}} \\[1em] = \dfrac{8^{(x+2+x+1)}}{8^{(x+2-x-1)}} \\[1em] = \dfrac{x + 2 + x + 1}{x + 2 - x - 1} \\[1em] = 2x + 3$

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): 25^{2025-2020-2-2-1} = 1.

Reason (R): Any number raised to the power zero (0) is always equals to 1.

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): $\sqrt\dfrac{1}{4}+\dfrac{1}{\sqrt{0.01}}- \sqrt[3]{27^2} = \dfrac{1}{2}$

Reason (R): $\sqrt[n]{a^m}=a^\dfrac{m}{n}$, where a ≠ 0.

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.