What are the respective oxidation states of the underlined atoms in...

In $\mathrm{OF_2}$, fluorine is more electronegative than oxygen and has an oxidation state of $-1$. Let the oxidation state of oxygen be $x$.

$x + 2(-1) = 0 \Rightarrow x = +2$

In $\mathrm{LiH}$, lithium is an alkali metal with an oxidation state of $+1$. Let the oxidation state of hydrogen be $y$.

$+1 + y = 0 \Rightarrow y = -1$

In $\mathrm{K_2Cr_2O_7}$, potassium has an oxidation state of $+1$ and oxygen has an oxidation state of $-2$. Let the oxidation state of chromium be $z$.

$2(+1) + 2z + 7(-2) = 0$

$2 + 2z - 14 = 0$

$2z = 12 \Rightarrow z = +6$

The respective oxidation states are $+2$, $-1$, and $+6$.

Answer: $+2, -1, \text{ and } +6$