For the system of linear equations:

$$x - 2y = 1,x - y + kz = - 2,ky + 4z = 6,k \in R$$,

consider the following statements :

(A) The system has unique solution if $$k \ne 2,k \ne - 2$$.

(B) The system has unique solution if k = $$-$$2

(C) The system has unique solution if k = 2

(D) The system has no solution if k = 2

(E) The system has infinite number of solutions if k $$ \ne $$ $$-$$2.

Which of the following statements are correct?

Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2 $$-$$ x) for all x$$ \in $$ (0, 2), f(0) = 1 and f(2) = e². Then the value of $$\int\limits_0^2 {f(x)} dx$$ is :

The negation of the statement

$$ \sim p \wedge (p \vee q)$$ is :

For the statements p and q, consider the following compound statements :

(a) $$( \sim q \wedge (p \to q)) \to \sim p$$

(b) $$((p \vee q) \wedge \sim p) \to q$$

Then which of the following statements is correct?