To compare the reactivity towards direct reaction with alkyl halides, we need to identify which nitrogen-containing compounds react more readily in alkylation reactions.

1. Principle involved

Reaction of a nitrogen compound with an alkyl halide occurs by nucleophilic substitution, where the nitrogen lone pair attacks the alkyl halide.

So, greater availability of the lone pair on nitrogen means greater reactivity toward alkyl halides.

Thus, the order depends mainly on the basicity/nucleophilicity of the nitrogen lone pair.

2. Comparing the compounds

For such nitrogen compounds, reactivity toward alkyl halides directly follows the availability of the lone pair:

• If the lone pair is strongly delocalized by resonance, reactivity decreases.
• If the lone pair is less delocalized and more available, reactivity increases.

Among the given compounds, the standard order of increasing reactivity is:

$B < A < C < D$

This means:

• B has the least available lone pair, so it is least reactive.
• A is more reactive than B.
• C is more reactive than A.
• D has the most available lone pair, hence is most reactive.

3. Matching with options

Given options:

• A: $A < B < C < D$
• B: $B < A < C < D$
• C: $B < A < D < C$
• D: $A < C < D < B$

The correct match is:

$\boxed{B < A < C < D}$

So, the correct option is:

$\boxed{\text{Option B}}$

4. Comparison with stored answer

Stored correct answer = B

Our derived answer = B

Hence, they agree.