Given,

OR

Find the inverse of the matrix , by using elementary row transformations.

From a lot of 20 bulbs which include 5 defectives, a sample of 3 bulbs is drawn at random, one by one with replacement. Find the probability distribution of the number of defective bulbs. Also, find the mean of the distribution.

Show that the relation R on the set Z of all integers defined by (x, y) ∈ R ⇔ (x – y) is divisible by 3 is an equivalence relation.

OR

A binary operation on the set A = {0, 1, 2, 3, 4, 5} is defined as

.

Write the operation table for a * b in A.

Show that zero is the identity for this operation * and each element ‘a’ ≠ 0 of the set is invertible with 6 – a, being the inverse of ‘a’.

Using integration, find the area of the region: {(x, y): 0 ≤ 2y ≤ x² , 0 ≤ y ≤ x, 0 < x < 3}.

Evaluate .

OR

Evaluate as the limit of a sum.