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?

If $$n \ge 2$$ is a positive integer, then the sum of the series $${}^{n + 1}{C_2} + 2\left( {{}^2{C_2} + {}^3{C_2} + {}^4{C_2} + ... + {}^n{C_2}} \right)$$ is :

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) $$ \ne $$ 0 for all x $$ \in $$ R. If $$\left| {\matrix{ {f(x)} & {f'(x)} \cr {f'(x)} & {f''(x)} \cr } } \right|$$ = 0, for all x$$ \in $$R, then the value of f(1) lies in the interval :