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What is A 3-year-old child has eczematous dermatitis on extensor surfaces. His mother has a history of Bronchial asthma. Diagnosis should be – and explain in detail?
In this question:-


The child is 3 years old
History of Asthma in mother
Extensor involvement



First two points suggest the diagnosis of atopic dermatitis (childhood pattern).
About third point (extensor involvement) :-

"Though childhood atopic dermatitis mainly involves flexural parts, less commonly extensor surfaces may also be involved".

Further, you can easily rule out other three options:-

Contact dermatitis

The family history of asthma is not important.
No history of contact to an allergen.

Seborrheic dermatitis

Occurs in adults and less frequently in infants but not in children.

Infantile eczematous dermatitis

Occurs in Infant.