The correct order of increasing basic nature for the bases `NH_(3) CH_(3)NH_(2) and (CH_(3))_(2)NH` is :

Options

A. `CH_(3)NH_2 lt NH_3 lt (CH_3)_2 NH`
B. `(CH_3 )_2NH lt NH_3 lt CH_3 NH_2`
C. `NH_3 lt CH_3NH_2 lt (CH_3)_2 NH`
D. `NH_(3) lt (CH_3)_2 NH lt CH_3 NH_2`

Answer

To determine the correct order of increasing basic nature for the bases NH₃ (ammonia), CH₃NH₂ (methylamine), and (CH₃)₂NH (dimethylamine), we need to analyze the basicity of each compound based on their structure and the inductive effects of the alkyl groups attached to the nitrogen atom.

### Step-by-Step Solution:

1. **Understanding Basicity**:
- Basicity refers to the ability of a compound to donate a lone pair of electrons. The easier it is for a compound to donate its lone pair, the stronger the base it is.

2. **Analyzing NH₃ (Ammonia)**:
- Ammonia has a lone pair of electrons on the nitrogen atom. However, it has no alkyl groups to provide any electron-donating inductive effect. Therefore, it has the least basic character among the three compounds.

3. **Analyzing CH₃NH₂ (Methylamine)**:
- Methylamine has one methyl group attached to the nitrogen. The methyl group exhibits a +I (inductive) effect, which increases the electron density on the nitrogen atom. This makes it easier for the nitrogen to donate its lone pair compared to ammonia. Thus, methylamine is more basic than ammonia.

4. **Analyzing (CH₃)₂NH (Dimethylamine)**:
- Dimethylamine has two methyl groups attached to the nitrogen. Each methyl group contributes to the +I effect, which significantly increases the electron density on the nitrogen atom. This makes it even easier for dimethylamine to donate its lone pair compared to both ammonia and methylamine. Therefore, dimethylamine is the most basic among the three.

5. **Establishing the Order**:
- Based on the analysis, we can establish the order of increasing basicity as follows:
- NH₃ < CH₃NH₂ < (CH₃)₂NH

### Final Answer:
The correct order of increasing basic nature is:
**NH₃ < CH₃NH₂ < (CH₃)₂NH**