The following symptoms correspond to which of the following disorder :
1. Deaf-mutism
2. Abnormal skin
3. Mental retardation in children
(a) Myxoedema
(b) Cretinism
(c) Down's syndrome
(d) Grave's disease

Options

A. Myxoedema
B. Cretinism
C. Down's syndrome
D. Grave's disease

Answer

To solve the question regarding the symptoms of deaf-mutism, abnormal skin, and mental retardation in children, we will analyze each option provided and see which one corresponds to these symptoms.

### Step-by-Step Solution:

1. **Identify the Symptoms**:
- The symptoms given are:
1. Deaf-mutism
2. Abnormal skin
3. Mental retardation in children

2. **Analyze Each Option**:
- **(a) Myxoedema**: This condition is related to hypothyroidism in adults and does not typically present with the symptoms listed. It is characterized by swelling and does not include deaf-mutism or mental retardation.

- **(b) Cretinism**: This is a condition caused by severe hypothyroidism during childhood. It is associated with physical and mental developmental delays, which can include mental retardation, deaf-mutism, and abnormal skin (such as dry skin). This option matches all the symptoms provided.

- **(c) Down's syndrome**: This genetic disorder is caused by an extra chromosome (trisomy 21) and is associated with intellectual disability and certain physical features, but it does not typically include deaf-mutism or abnormal skin as primary symptoms.

- **(d) Grave's disease**: This is an autoimmune disorder that leads to hyperthyroidism, which is characterized by symptoms such as weight loss and increased heart rate. It does not correlate with the symptoms listed in the question.

3. **Conclusion**:
- Based on the analysis, the only option that corresponds to all the symptoms of deaf-mutism, abnormal skin, and mental retardation in children is **(b) Cretinism**.

### Final Answer:
**(b) Cretinism**