1. Which of the following statements are true, and which are false? Justify your answers.
The set € R x^2 1 is a null set. Every polynomial of degree over R has roots in R. For any y € x-y The geometrical representation of the set {ix x is a point.

(e) The system of 3 equations

4x 3y 0
6x 2y 0
can be solved.

2.(a) Solve the equation z^5 32 0.

(b) Show that x^n x n € N.

3.(a) Let P be the set of prime numbers and E be the set of even natural numbers. Represent using the property method, and using a Venn diagram.

(b) Can the following linear system be. solved by Cramer's rule? If yes, solve it using the rule. Otherwise, solve it by Gaussian elimination method.

x 2y 3z 11
2x-y 4z 13
3x 4y-5z= 3

4.(a) If B are any two sets, then state the conditions under which A x B B x A. Justify your conditions.

(b) Obtain the resolvent cubic of
x^4 5x^3 -10x 2 according to Ferrari's method.

5.(a) In the context ofIGNOU examinations, give an example for each of the following: An implication
The converse of above

(iii) The contrapositive of above
A shopkeeper sells pens and pencils in two different packs, Pack I and Pack II. Pack I contains 3 pens and 5 pencils, while Pack II comprises 3 pencils and 4 pens. Find the number of each type of pack that should be bought if 18 pens and 19 pencils are needed.