Assertion (A): 3x² - 8x - 15 is not factorisable.

Reason (R): The trinomial ax² + bx + c is factorisable, if the value of b² - 4ac, where a = coefficient of x², b = coefficient of x, c = constant, is perfect square, otherwise not.

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): A moving boat goes downstream at 50 km per hour and upstream at 30 km per hour. The speed of stream is 40 km per hour.

Reason (R): If the speed of boat in still water is x km per hour and speed of stream is y km per hour, then y - x = 50 and y + x = 30 ⇒ y = 40.

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): 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.