The distance of the point $(1, 1, 9)$ from the point of intersection of the line $\frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2}$ and the plane $x+y+z=17$ is

If in a $\triangle ABC$,$\frac{1}{a+c} + \frac{1}{b+c} = \frac{3}{a+b+c}$,then $\angle C$ is equal to (in $^{\circ}$)

The angle between a pair of tangents drawn from a point $P$ to the circle $x^{2}+y^{2}+4x-6y+9 \sin^{2} \alpha + 13 \cos^{2} \alpha = 0$ is $2 \alpha$. The equation of the locus of the point $P$ is

Identify the reaction for which $\Delta H \neq \Delta E$ :

The displacement equations of sound waves produced by two sources are given by $y_1 = 5 \sin(400 \pi t)$ and $y_2 = 8 \sin(408 \pi t)$, where $t$ is time in seconds. If the waves are produced simultaneously, the number of beats produced per minute is

Which of the following enzymes is not useful for the digestion of proteins?