The domain of the function $f(x) = {}^{(10-x)}C_{(x-6)}$ is...

Let $[x]$ denotes the greatest integer less than or equal to x and $f(x) = [\tan^2 x]$, then which of the following is true ?

If $\sqrt{y + x} + \sqrt{y - x} = c$ and $\dfrac{dy}{dx} = K - \sqrt{\dfrac{y^2}{x^2} - 1}$ , then the value of $K$ is

If $y = (x^2 + 1)^{\sin x}$ for $x > 0$ such that $\dfrac{dy}{dx} = y\left[\dfrac{2x \sin x}{g(x)} + \cos x \cdot \log[g(x)]\right]$, then the function $\dfrac{1}{g(x)}$ is...