[ Question Bank ] — Maths STD 12 Science — Question

Coloured balls are distributed in four boxes as shown in the following table: 

Box	Colour
	Black	White	Red	Blue
I	3	4	5	6
II	2	2	2	2
III	1	2	3	1
IV	4	3	1	5

A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III?

Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table (Table 1.2).
Compute (2 * 3) * 4 and 2 * (3 * 4)
(Hint: use the following table)

*	1	2	3	4	5
1	1	1	1	1	1
2	1	2	1	2	1
3	1	1	3	1	1
4	1	2	1	4	1
5	1	1	1	1	5

Integrate the function sin mx w.r.t. x.

Find all points of local maxima and local minima of the function f given by f(x) = x³ – 3x + 3.