In which of the following is the gametophytic phase dominant?

The centroid of the triangle formed by the pair of straight lines $12x^2 - 20xy + 7y^2 = 0$ and the line $2x - 3y + 4 = 0$ is:

$A$ long straight wire carrying a current of $30 ~A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} ~T$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 ~cm$ away from the wire is
$\left(\mu_0=4 \pi \times 10^{-7} ~H/m\right)$

The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$ is

The circumcentre of the triangle with vertices at $(-2, 3)$,$(1, -2)$ and $(2, 1)$ is

$\int \frac{x^{49} \tan ^{-1}\left(x^{50}\right)}{1+x^{100}} d x = k\left(\tan ^{-1}\left(x^{50}\right)\right)^2 + c$,then $k$ is equal to