The Phthalein test is a characteristic test for which of the following?

If $A = \begin{bmatrix} 1 & 0 & 1 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix}$,then $\det(A)$ is equal to

The value of $\cot 70^{\circ} + 4\cos 70^{\circ}$ is

The solution of the differential equation $\frac{dy}{dx} = \frac{x-2y+1}{2x-4y}$ is

The maximum value of $\frac{\log x}{x}, 0 < x < \infty$ is

When a sound wave of wavelength $\lambda$ is propagating in a medium,the maximum velocity of the particle is equal to the wave velocity. The amplitude of the wave is: