If three points $A, B$ and $C$ have position vectors $(1, x, 3), (3, 4, 7)$ and $(y, -2, -5)$ respectively and if they are collinear, then $(x, y)$ is

The $pK_a$ of a weak acid is $4.8$. What should be the ratio of $\frac{[\text{acid}]}{[\text{salt}]}$,if a buffer of $pH=5.8$ is required?

$\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}$ is equal to :

$A$ double slit experiment is performed by using light of wavelength $6000\,\mathring{A}$. If the distance of the screen is $1\,m$ and the slits are $0.1\,cm$ apart,then calculate the angular position of the $10^{th}$ bright fringe.

Which of the following is a heterosporous pteridophyte?

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is