In which one of the following do male and female gametophytes not have a free-living independent existence?

Consider two statements $S_1$ and $S_2$. $S_1$: If $f(x)$ is a differentiable function with $f^{\prime}(x) = 0$ in $(a, b)$ and $f(x)$ is increasing in $(a, b)$,then $\frac{f(x)}{f^{\prime}(x)}$ is also increasing in $(a, b)$. $S_2$: Both $\sin x$ and $\tan x$ are increasing functions in $\left(0, \frac{\pi}{2}\right)$. Which of the following is true?

If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$,then $\alpha$ is equal to:

The more commonly used baking powder contains about $30 \% NaHCO_3, 20 \% NaAl(SO_4)_2, 10 \% Ca(H_2PO_4)_2$ and $40 \% $ starch. Which of the following statements is/are correct?

In a two-slit experiment with monochromatic light,fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by $5 \times 10^{-2} \ m$ towards the slits,the change in fringe width is $3 \times 10^{-5} \ m$. If the separation between the slits is $10^{-3} \ m$,the wavelength of light used is ......... $\mathring{A}$.

$A$ bag contains $5$ black balls,$4$ white balls,and $3$ red balls. If a ball is selected at random,the probability that it is a black or red ball is