Enzymes are sensitive to

If $\tan \theta + \tan \left(\theta + \frac{\pi}{3}\right) + \tan \left(\theta + \frac{2\pi}{3}\right) = 3$,then which of the following is equal to $1$?

The line $2x + \sqrt{6}y = 2$ is a tangent to the curve $x^2 - 2y^2 = 4$. The point of contact is

For an ellipse with eccentricity $e = \frac{1}{2}$,the centre is at the origin. If one directrix is $x = 4$,then the equation of the ellipse is:

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. Fresnel's diffraction pattern occurs when the source of light or the screen on which the diffraction pattern is seen,or when both,are at a finite distance from the aperture.
$B$. Diffracted light can be used to estimate the helical structure of nucleic acids.

The angle between the line $\frac{x + 1}{3} = \frac{y - 1}{2} = \frac{z - 2}{4}$ and the plane $2x + y - 3z + 4 = 0$ is: