1.Gate previous questions.


1..     In the matrix equation Px = q, which of the following is a necessary condition for the existence of at least           one solution for the unknown vector x:

(a)     Augmented matrix [P q] must have the same rank as matrix P

(b)     Vector q must have only non-zero elements

(c)     Matrix P must be singular

(d)     Matrix P must be square 

2.           If P and Q are two random events, then the following is TRUE:

(a)     Independence of P and Q implies that probability (P ∩ Q) = 0

(b)     Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)

(c)     If P and Q are mutually exclusive, then they must be independent

(d) Probability (P ∩ Q) ≤  Probability (P)

3.       If S = _∫ x ⁻³dx, then S has the value

1
(a)	−1		(b)	1	(c)	1	(d) 1
3			4		2