Government & Defence Entrance Exam

Hello Yashyeshwini,
Your parents are correct you need to take a degree course before appearing for any of the government exam like Combined Defense Services or for research exams like CSIR NET for Junior Research Fellowship (JRF) .
You can pursue engineering degree in the the field of your interest as it will help you in both of the fields, defense and research field.
For the CDS exam you need to have
i) For Indian Military Academy/Officers Training Academy: Degree from a recognized university or equivalent
ii) For Indian Naval Academy: Bachelor of Engineering
iii) For Air Force Academy: Degree of a recognized University with Physics and Mathematics at 10+2 level or Bachelor of Engineering.
For the CSIR NET Exam for Junior Research Fellowship (JRF) the Qualification Eligibility are:
M.Sc.
Integrated BS-MS
BS-4 Years
BE/B-Tech
B-Pharma
MBBS
Or an Equivalent Degree.

There are two ways to become IAS officer i.e, by appearing in Civil Service Examination and by appearing in PCS examination conducted by various state Public Sector Commission. PCS officers become IAS after gaining experience and performance. In order to help you few datils on Civil Service Examinations and PCS are givem below:
The Civil Services Examination is a nationwide competitive examination in India conducted by the Union Public Service Commission (UPSC) for recruitment to various Civil Services of the Government of India, including the Indian Administrative Service (IAS), Indian Foreign Service (IFS), Indian Police Service (IPS) and others services. Eligibility condition for appearing in civil services examination is as follow:
(a)The candidate must hold a PASS BACHELOR'S degree from any of the Universities incorporated by an Act of the Central or State Legislature in India or other educational institutions established by an Act of Parliament or declared to be deemed as a University, under Section-3 of the University Grants Commission Act, 1956, or possess an equivalent qualification.
(b) Candidates who have appeared or intend to appear for the final examination and are awaiting results are also eligible to apply for the Preliminary Examination.
(c)A candidate must have attained the age of 21 years and must not have attained the age of 32 years.
(d)You may refer to UPSC website for other eligibility criterion.
It is conducted in two phases - a preliminary examination consisting of two objective-type papers (general studies and aptitude test), and a main examination consisting of nine papers of conventional (essay) type, followed by a personality test (interview). Out of "NINE" there are two qualifying papers; i) any modern Indian language (300 marks) ii) English (300 marks). The marks of these two papers will not be counted in the merit list of the main examination however, qualifying in these two papers is compulsory. Out of "Seven" Papers there are "Five" compulsory papers and Two Optional papers from the subject of your choice.
Provincial Civil Services, abbreviated as PCS, are actually the civil based administrative services of the State Government. These officers relate to the policy making of the state to which they belong. These officers are also selected through an entrance test conducted by the state based Public Service Commission.
You are advised to look at eligibility criteria of PCS os state in which you are planning to appear.

Hi Sangita,
Taking coaching is a very subjective call.
Coaching is your personal call. The deal is how good are you in reasoning, aptitude and English. These are major sections on which IBPS exam is based, though other sections such as general awareness and computer. If your fundamentals regarding these three major subjects are clear and have the required speed, the exam is easy to crack. General awareness and computer is comparatively easy and can be prepared in 3-4 months. But you will need to be disciplined in practicing mock papers and old question papers.
But the above approach will also depend on how disciplined you are. In case you need guidance, some of the popular coaching institutes are: KD campus, Paramount, Career power, etc.
A lot of exam material for the exam is also available free of cost on the internet. That can also be utilised.
All the best.