Step 1: Decode the term.
No bond resonance is the older name for hyperconjugation, the delocalisation of $\sigma$ electrons of a $\mathrm{C-H}$ bond into an adjacent empty p-orbital or $\pi$ system.
Step 2: State the requirement.
It needs at least one $\alpha$-hydrogen on an $sp^3$ carbon sitting next to an electron-deficient or unsaturated $sp^2$ centre such as a carbocation, radical or alkene.
Step 3: Test $\mathrm{CH_3CH_2Br}$.
This is fully saturated with no vacant p-orbital or adjacent $\pi$ system, so no hyperconjugation.
Step 4: Test the ethyl carbocation.
$\mathrm{\overset{(+)}{C}H_2CH_3}$ has an $sp^2$ cationic carbon with an empty p-orbital, and the neighbouring $\mathrm{CH_3}$ supplies three $\alpha$ C-H bonds that delocalise into it. This is exactly no bond resonance.
Step 5: Test the remaining options.
$\mathrm{CH_3CH_2NO_2}$ is saturated with no such acceptor orbital, and benzene shows ordinary $\pi$-$\pi$ resonance, not hyperconjugation.
Step 6: Conclude.
The species showing no bond resonance is the ethyl carbocation, option (B).
\[ \boxed{\mathrm{\overset{(+)}{C}H_2CH_3}} \]