If a random variable X follows the Binomial distribution B(33, p) such that

$$3P(X = 0) = P(X = 1)$$, then the value of $${{P(X = 15)} \over {P(X = 18)}} - {{P(X = 16)} \over {P(X = 17)}}$$ is equal to :

The domain of the function

$$f(x) = {{{{\cos }^{ - 1}}\left( {{{{x^2} - 5x + 6} \over {{x^2} - 9}}} \right)} \over {{{\log }_e}({x^2} - 3x + 2)}}$$ is :

Let $$S = \left\{ {\theta \in [ - \pi ,\pi ] - \left\{ { \pm \,\,{\pi \over 2}} \right\}:\sin \theta \tan \theta + \tan \theta = \sin 2\theta } \right\}$$.

If $$T = \sum\limits_{\theta \, \in \,S}^{} {\cos 2\theta } $$, then T + n(S) is equal to :

The number of choices for $$\Delta \in \{ \wedge , \vee , \Rightarrow , \Leftrightarrow \} $$, such that

$$(p\Delta q) \Rightarrow ((p\Delta \sim q) \vee (( \sim p)\Delta q))$$ is a tautology, is :