(x² + 3x) men can do a piece of work in (x² - 2x) days, then one day work of 1 man is :

1. $\dfrac{x + 3}{x - 2}$

2. (x² + 3x)(x² - 2x)

3. $\dfrac{x - 2}{x + 3}$

4. none of these

Statement 1: ₹ (x³ - x) is spent in buying some identical articles at ₹ (x - 1) each. Number of articles bought = $\dfrac{x^3 - x}{x - 1}$

Statement 2: Number of articles bought = $\dfrac{x^3 - x}{x - 1} = \dfrac{x(x - 1)(x + 1)}{x - 1} = x^2 + x$

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.

Assertion (A): Distance of (x² - 7x + 12) km is covered in (x² - 16) hrs.

Speed = $\dfrac{x^2 - 7x + 12}{x^2 - 16}$ km/hr

Reason (R): Speed = Distance x Time

= (x² - 7x + 12)(x² - 16) km/hr

1. A is true, but R is false.

2. A is false, but R is true.

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

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

Factorise :

$a^2 + \dfrac{1}{a^2} - 2 - 3a + \dfrac{3}{a}$