Step 1: Recall the factor affecting basic strength.
Basic strength depends on the availability of the lone pair of electrons on nitrogen atom for donation.
Greater the availability of the lone pair,
greater is the basic strength
Step 2: Compare \(NH_3\) and \(NH_2OH\).
In
\[
NH_2OH
\]
the oxygen atom is highly electronegative and exerts a strong
\[
-I
\]
(inductive withdrawing) effect.
This decreases the electron density on nitrogen and reduces the availability of the lone pair.
Therefore,
\[
NH_2OH
\]
is less basic than
\[
NH_3
\]
Step 3: Compare \(NH_3\) and \(N_2H_4\).
In hydrazine,
\[
N_2H_4
\]
the adjacent nitrogen atom also exerts an electron withdrawing effect on the other nitrogen atom.
Thus, the lone pair on nitrogen becomes slightly less available compared to ammonia.
Hence,
\[
NH_3
\]
is more basic than
\[
N_2H_4
\]
However, the electron withdrawing effect of nitrogen is weaker than that of oxygen, so
\[
N_2H_4
\]
is more basic than
\[
NH_2OH
\]
Step 4: Arrange the compounds in decreasing basic strength.
Therefore,
\[
NH_3\gt N_2H_4\gt NH_2OH
\]
Step 5: Final conclusion.
Hence, the correct order of relative basic strength is
\[
\boxed{NH_3\gt N_2H_4\gt NH_2OH}
\]