Which of the following are sets? Justify your answer.
The collection of all the months of a year beginning with the letter J.

3

(a)

Draw the Venn diagram of the following:
A' \(\cap\) (B \(\cup\) C)

3

(a)

\(f: R-\{3\} \rightarrow R\) be defined by \(f(x)=\frac{x^{2}-9}{x-3}\) and \(g: R \rightarrow R\) be defined by \(g(x)=x+3\). Find whether f = g or not.

3

(a)

Find the domain and range of f (x) =\(\sqrt{x-2}\) 

3

(a)

Determine the range and domain of the relation: R = {(x, y): y = I x + 1|, x \(\in\) Z, IxI \(\le\)3}.

3

(a)

Let P(n) be the statement "3ⁿ">n". If p(n) is true, prove that p(n+1) is true.

3

(a)

Solve the quadratic equation 2x² - 4x +3 =0.

3

(a)

The fourth term of a C.P. is 4. Find the product of its first seven terms.

3

(a)

Find the transformed equation of the parabola y²=4ax if the origin is shifted to (-3, 2).

3

(a)

Evaluate:\(\underset { x\rightarrow \frac { p }{ 2 } }{ Lim } \frac { { a }^{ cotx }-{ a }^{ cosx } }{ cotx-cosx } \) 

3

(a)

Write the inverse of the following statements.
If you get a job, then your credentials are good.

3

(a)

Find the standard deviation and the variance of first n natural numbers.

3

(a)

An experiment consists of recording boy-girl composition of families with 2 children
What is the sample space, if we are interested in knowing whether it is a boy or girl in the order of their births?

3

(a)

A card is selected from a pack of 52 cards.
How many points are there in the sample space?

3

(a)

The letters of word 'SOCIETY' are placed at random in a row. What is the probability that three vowels come together?

3

(a)