Assertion (A): The 9^th term of a Geometric Progression (G.P.) 6, −12, 24, −48, … is a positive term.

Reason (R): The value of (−2)⁸ is always positive.

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).

The fourth and seventh terms of an Arithmetic Progression (A.P.) are 60 and 114 respectively. Find the :

(a) first term and common difference.

(b) sum of its first 10 terms.

In the given diagram, O is the centre of the circle and the tangent DE touches the circle at B. If ∠ADB = 32°. Find the values of x and y.

The polynomial kx³ + 3x² − 11x − 6 when divided by (x + 1), leaves a remainder of 6.

(a) Find the value of k.

(b) Using the value of k factorise completely the polynomial kx³ + 3x² − 11x − 6.