Mathematics

National Defence Academy (NDA)

Overview

• The National Defence Academy (NDA) is the Joint Services academy of the Indian Armed Forces.
• Located in Khadakwasla, Pune, Maharashtra.

History

• Established in 1954.
• First tri-service academy in the world.

Academy Structure

• Divided into three divisions:
  • Army Division
  • Navy Division
  • Air Force Division
• Each division has its own squadron.

Curriculum

• Three-year course:
  • First year: Basic training and academics
  • Second year: Specialized training in respective services
  • Third year: Advanced training and commissioning
• Curriculum includes:
  • Humanities
  • Science
  • Languages
  • Physical education
  • Military training

Entrance Examination

• Conducted by the Union Public Service Commission (UPSC)
• Held twice a year
• Exam pattern:
  • Written exam (Mathematics and General Ability Test)
  • Service Selection Board (SSB) interview
  • Medical examination

Eligibility Criteria

• Age: 16.5 to 19.5 years
• Nationality: Indian
• Marital status: Unmarried
• Educational qualification: 10+2 or equivalent with Physics and Mathematics

Career Prospects

• Commissioned as officers in the Indian Armed Forces
• Opportunities for further education and training
• Leadership roles in various fields

National Defence Academy (NDA)

Overview

• Joint Services academy of the Indian Armed Forces
• Located in Khadakwasla, Pune, Maharashtra

History

• Established in 1954
• First tri-service academy in the world

Academy Structure

• Divided into three divisions: Army, Navy, and Air Force
• Each division has its own squadron

Curriculum

• Three-year course with the following structure:
  • First year: Basic training and academics
  • Second year: Specialized training in respective services
  • Third year: Advanced training and commissioning
• Subjects covered: Humanities, Science, Languages, Physical education, and Military training

Entrance Examination

• Conducted by the Union Public Service Commission (UPSC)
• Held twice a year
• Exam pattern consists of:
  • Written exam (Mathematics and General Ability Test)
  • Service Selection Board (SSB) interview
  • Medical examination

Eligibility Criteria

• Age: 16.5 to 19.5 years
• Nationality: Indian
• Marital status: Unmarried
• Educational qualification: 10+2 or equivalent with Physics and Mathematics

Career Prospects

• Commissioned as officers in the Indian Armed Forces
• Opportunities for further education and training
• Leadership roles in various fields

Inverse Functions

Definition

• A function f has an inverse function f^(-1) if it is both one-to-one and onto.

Properties

• A one-to-one function f has a one-to-one inverse function f^(-1).
• An onto function f has an onto inverse function f^(-1).
• The inverse of the inverse function f^(-1) is the original function f, i.e., (f^(-1))^(-1) = f.

Finding Inverse Functions

• To find the inverse function f^(-1), switch x and y in the original function f(x) = y.
• Solve for y in the modified function to obtain f^(-1)(y) = x.
• The resulting function is the inverse function f^(-1).

Examples

Inverse of Linear Function

• If f(x) = 2x, then f^(-1)(x) = x/2.

Inverse of Quadratic Function

• If f(x) = x^2, then f^(-1)(x) = ±√x.