The outer Himalayas lie between the lesser Himalayas and the Indo-Gangetic plain. Let's break down the options and understand why option A is the correct answer.

a) The outer Himalayas lie between the lesser Himalayas and the Indo-Gangetic plain.
b) The outer Himalayas lie between the foothills and the Indo-Gangetic plain.
c) The outer Himalayas lie between the greater Himalayas and the lesser Himalayas.
d) The outer Himalayas lie between the Indo-Gangetic plains and the peninsula.

The outer Himalayas, also known as the Shivalik Range, are the southernmost range of the Himalayas. They run parallel to the foothills and are located between the lesser Himalayas and the Indo-Gangetic plain. Let's delve deeper into each option to understand why the correct answer is option A.

a) The outer Himalayas lie between the lesser Himalayas and the Indo-Gangetic plain.
The lesser Himalayas, also known as the middle Himalayas or the Himachal Range, are located to the north of the outer Himalayas. They are higher and more rugged than the outer Himalayas. On the other hand, the Indo-Gangetic plain lies to the south of the outer Himalayas. This vast plain is formed by the alluvial deposits of the rivers originating from the Himalayas. Therefore, option A accurately describes the location of the outer Himalayas.

b) The outer Himalayas lie between the foothills and the Indo-Gangetic plain.
While the foothills are indeed located to the north of the outer Himalayas, they are not the correct boundary for the outer Himalayas. The foothills gradually merge into the outer Himalayas, and the boundary between them is not well-defined. Therefore, option B is incorrect.

c) The outer Himalayas lie between the greater Himalayas and the lesser Himalayas.
The greater Himalayas, also known as the high Himalayas or the Himadri Range, are the highest and most continuous range of the Himalayas. They are located to the north of the lesser Himalayas. The outer Himalayas lie to the south of the lesser Himalayas, not between the greater and lesser Himalayas. Therefore, option C is incorrect.

d) The outer Himalayas lie between the Indo-Gangetic plains and the peninsula.
The peninsula refers to the southern part of India, which is separated from the Indo-Gangetic plain by the Vindhya Range. The outer Himalayas are not located between the Indo-Gangetic plain and the peninsula. Therefore, option D is incorrect.

In conclusion, the correct answer is option A - the outer Himalayas lie between the lesser Himalayas and the Indo-Gangetic plain.