Assertion (A): If a² - 8a - 1 = 0.

⇒ $\dfrac{a^2}{a} - \dfrac{8a}{a} - \dfrac{1}{a} = 0$

⇒ $a-\dfrac{1}{a}$ = 8 is not true.

Reason (R): The division of each term of the equation a² - 8a - 1 = 0 is defined only when a is not equal to 0 (zero).

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): If x ≥ 5 and $x +\dfrac{1}{x}$ = m, then $x - \dfrac{1}{x}$ = m - 2.

Reason (R): $(x -\dfrac{1}{x})^2 = (x +\dfrac{1}{x})^2 - 4$

⇒ $x - \dfrac{1}{x} = \sqrt{(x+\dfrac{1}{x})^2-4}$

= $\sqrt{m^2-4}= m - 2$

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): If a = 2, b = -6 and c = 4, then $\dfrac{3abc - a^3 - b^3 - c^3}{ab + bc + ca - a^2 - b^2 - c^2}= 0$

Reason (R): If a + b + c = 0 then a³ + b³ + c³ + 3abc = 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.

Assertion (A): 5x⁵ - 20x³ in the form of factors is 5x³(x² - 4).

Reason (R):

5x⁵ - 20x³
= 5x³(x² - 4)
= 5x³(x + 2)(x - 2).

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.