If x = 1 is a root of the equation $\sqrt{x} + kx - 2$ = 0; the value of k is :

1. 1

2. -1

3. 2

4. -2

The equation $\sqrt{15 - 2x} = x$.

Assertion (A): x = 3.

Reason (R): $\sqrt{15 - 2x} = x$

$\Rightarrow 15 - 2x = x^2 \\[1em] \Rightarrow x^2 - 2x - 15 = 0 \\[1em] \Rightarrow x = -5 \text{ or } x = 3$

1. A is true, R is false.

2. A is false, R is true.

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

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

One root of a quadratic equation is 3 + $\sqrt{2}$.

Statement (1): The other root of the given quadratic equation is 3 - $\sqrt{2}$.

Statement (2): If one root of the given quadratic equation is in the form of a surd, the other root is its conjugate.

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.

The quadratic equation 2x² - 9x + 12 = 0.

Statement (1): Sum of the roots of the equation = $4\dfrac{1}{2}$.

Statement (2): In an quadratic equation ax² + bx + c = 0, sum of the roots = $-\dfrac{\text{b}}{\text{a}}$.

Options

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.