The branch of botany that deals with the study of algae is known as:

Two bodies $A$ and $B$ of equal surface area have thermal emissivities of $0.01$ and $0.81$ respectively. The two bodies are radiating energy at the same rate. Maximum energy is radiated from the two bodies $A$ and $B$ at wavelengths $\lambda_A$ and $\lambda_B$ respectively. The difference in these two wavelengths is $1 \mu m$. If the temperature of the body $A$ is $5802 \ K$,then the value of $\lambda_B$ is:

The value of $\cot 70^{\circ} + 4\cos 70^{\circ}$ is

The equation of the plane containing the line $\frac{x + 1}{-3} = \frac{y - 3}{2} = \frac{z + 2}{1}$ and the point $(0, 7, -7)$ is

During which of the following reactions will a gaseous product $NOT$ be produced?

$\sum_{k=1}^{2n+1} (-1)^{k-1} k^2$ is equal to