Yes, girls can apply for the Indian Navy after completing gradation, for this you need to appear in the CDS examination, this examination is conducted by the UPSC. Following are the details of this examination:

Nationality:
A candidate must be either be a
A citizen of India , or
A subject of Bhutan, or
A subject of Nepal, or
A Tibetan refugee who came obvert ot India before the 01 January, 1962 with the intention of spermanently settling in India, or
a Person of Indian origin who has migrated from Pakisthan, Burma, Sri Lanka and East African countires of Kenya, Uganda, the United Republic of Tanzania, Zambia, Malawim Zaire and Ethiopia or Vietnam with the intention of permanently setting in India.

Age Limit:
19-22 Years Naval Academy

Required qualification:
Naval Academy
You should hold B.Sc. with Physics & Mathematics or Bachelor of Engg


CDS Exam Syllabus Details:

Paper 1: English

The objective type question paper is designed to examine the understanding of English of the applicants. English question paper of CDS Exam includes passage for answering few questions related to that passage.

Paper 2: General Knowledge

General Knowledge question paper in CDS examination includes knowledge of current topics and of matters which are observing every day. The aspirants must be able to answer scientific aspects without any particular scientific study. They should have knowledge of History of India and Geographical issues without any specific study. The applicants must be able to answer these general knowledge questions to pass this test.

Paper 3: Elementary Mathematics

The objective type question paper includes various topics of elementary mathematics. Candidates should have posses knowledge about these topics. There are lots of topics to cover which are as following:
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Arithmetic: Aspirants need to perform well in arithmetic which includes Number System, Fundamental Operations, Unitary Methods, and Elementary Number Theorems etc.
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Algebra: The applicants should able to solve basic operations, Remainder Theorem, Quadratic Equations, Linear equations and practical problems etc.
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Geometry: The candidates should able to answer geometric questions which contain Lines and angles, plane and plane figures and their related questions.
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Trigonometry: The applicants need to know the values of Sine x, cosine x and tangent x.
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Menstruation: The all candidates applying for the test should have knowledge of calculating areas of squares, rectangles, triangles, circles and parallelograms etc.
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Statistics: Everyone needs to know the collection and tabulation of data, histograms, pie and bar charts etc.