Which of the following functions have the maximum value unity?

The minimum value of $8 \cos^2 x + 18 \sec^2 x$ for all $x \in R$ wherever it is defined,is:

The number of integral values of $k$,for which the equation $7 \cos x + 5 \sin x = 2k + 1$ has a solution,is

For all values of $\theta$,the values of $3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)$ lie in the interval :

Let $a$ be the maximum value of $(3 \cos \theta - 4 \sin \theta)$ and $\theta \neq \frac{n \pi}{2}$. If $\alpha = a \sin^2 \theta \cos^3 \theta$ and $\beta = a \sin^3 \theta \cos^2 \theta$,then $\sqrt{\frac{(\alpha^2 + \beta^2)^5}{(\alpha \beta)^4}} = $

The value of $5 \cos \theta + 3 \cos \left(\theta + \frac{\pi}{3}\right) + 3$ lies between