How are the following compounds related?

If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}+\vec{b}|=\sqrt{29}$ and $\vec{a} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \vec{b}$,then a possible value of $(\vec{a}+\vec{b}) \cdot(-7 \hat{i}+2 \hat{j}+3 \hat{k})$ is

Which of the following pairs of nitrogenous bases in nucleic acids is incorrectly matched with its category?

The acute angle between the lines $6x^2 + 11xy - 10y^2 = 0$ is

The current in an $AC$ circuit is given by $i = i_1 \sin \omega t + i_2 \cos \omega t$. Its $r.m.s.$ value is:

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=|x|$ and $g(x)=[x-3]$ for $x \in R$,then $\{g(f(x)):-\frac{8}{5} < x < \frac{8}{5}\}$ is equal to