If $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \infty}}}$,then which of the following is true?

The number of values of $b$ for which there is an isosceles triangle with sides of lengths $b+5$,$3b-2$,and $6-b$ is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4-8x^3+11x^2+32x-60=0$ and $\alpha < \beta < \gamma < \delta$, then $4\alpha+3\beta+2\gamma+\delta=$

If the roots of the equation $x^2 - 8x + (a^2 - 6a) = 0$ are real,then:

$A$ building construction work can be completed by two masons $A$ and $B$ together in $22.5$ days. Mason $A$ alone can complete the work in $24$ days less than mason $B$ alone. Then mason $A$ alone will complete the work in: (in $days$)

The smallest value of the constant $m > 0$ for which $f(x) = 9mx - 1 + \frac{1}{x} \geq 0$ for all $x > 0$ is: