The nature of roots of quadratic equation 3x² − 6x − 3 = 0 are :

1. real and equal

2. real, distinct and rational

3. real, distinct and irrational

4. no real roots

Assertion (A): If a die is rolled, the probability of getting a number greater than 6 is $\dfrac{1}{6}$.

Reason (R): There are six possible outcomes when rolling a die, {1, 2, 3, 4, 5, 6}.

1. (A) is true and (R) is false.

2. (A) is false and (R) is true.

3. Both (A) and (R) are true and (R) is the correct explanation of (A).

4. Both (A) and (R) are true but (R) is not the correct explanation of (A).

What must be added to x³ + 7x² + 3x + 2 so that the result is completely divisible by (x + 2)?

1. −40

2. −16

3. 16

4. 40

In the given diagram, ΔAOB is a right-angled triangle and C is the mid-point of AB. The coordinates of the point which is equidistant from the three vertices of ΔAOB is :

1. (x, y)

2. (y, x)

3. $\Big(\dfrac{x}{2}, \dfrac{y}{2}\Big)$

4. $\Big(\dfrac{2x}{3}, \dfrac{2y}{3}\Big)$