NDA Previous Year Question Paper Guide for Maths and GAT

The two booklets in brief

Each session has two booklets written on the same day on an OMR sheet. Maths gives 2.5 marks a question; GAT gives 4. A wrong mark costs 0.83 in maths and 1.33 in GAT. GAT starts with 50 English items, after which 100 GK items follow from the sciences, the humanities and recent news. For every chapter name, see our NDA syllabus page.

Booklets come in series such as A, B, C and D. The questions are the same across series but in a different order, so the series printed on your copy matters only for checking answers.

What each NDA previous year question paper reveals

• Maths is long, not tricky: most questions are direct applications of Class 11 and 12 formulas, but 120 of them in 150 minutes leaves little more than a minute each.
• Every chapter appears: trigonometry, calculus, coordinate geometry, algebra, matrices, vectors, statistics and probability all turn up in every session, so skipping a chapter costs real marks.
• Linked questions: maths often gives a short statement followed by two questions built on it, so one mistake can cost twice.
• GAT rewards breadth: physics questions lean on everyday devices and basic laws, history covers both Indian and world events, and geography mixes physical concepts with Indian resources.
• English stays steady: spotting errors, ordering sentences, synonyms, antonyms and passages recur across sessions.

A practice routine that copies exam day

1. Start with the two most recent sessions. Sit the maths paper at the same morning hour as the real exam, with a 150 minute timer and an OMR style answer sheet.
2. Score yourself with the negative marking applied, then list every wrong answer by chapter.
3. Spend the next two days only on the two weakest chapters, then take another maths paper.
4. Take GAT papers in the afternoon. Mark questions you guessed with a small dot so you can see whether guessing is helping or hurting you.
5. Once you have done six to eight sessions, compare your scores with past lines on the NDA cut off page.

NDA maths previous year paper: how to pace it

Split the 150 minutes into three rounds. In the first round, about 70 minutes, answer every question you can solve in under a minute. In the second, about 50 minutes, return to the ones that need a little more working. Use the final 30 minutes for the hardest leftovers and for filling the OMR sheet carefully. Practising this rhythm on old papers stops you from getting stuck on one calculus problem while easy matrix questions wait unanswered at the end.

Practise with five NDA style items

We framed the five items below ourselves; none is copied from a UPSC booklet. Each shows its choices and then the correct one.

1. If the roots of x squared minus 5x plus k equal 0 differ by 1, what is k? Choices: 4, 5, 6, 7. Correct: 6, since the roots are 2 and 3.
2. Find sin 15 degrees times cos 15 degrees. Choices: 1/2, 1/4, 1/8, 1. Correct: 1/4, because the product is half of sin 30 degrees.
3. A pencil dipped in a glass of water looks bent. Which effect of light explains this? Choices: reflection, refraction, dispersion, diffraction. Correct: refraction.
4. Pick the synonym of METICULOUS. Choices: careless, careful, hurried, noisy. Correct: careful.
5. Through which of these states does the Tropic of Cancer not pass? Choices: Gujarat, Jharkhand, Odisha, Mizoram. Correct: Odisha.

Where to get the official papers

Go to the UPSC website and open the previous question papers area under examinations. Papers are listed by exam name and year, so look for the National Defence Academy and Naval Academy exam. UPSC also publishes answer keys for each session once the final result is out, which you can use to check the older booklets.

Stick to the commission's own files, since copies passed around elsewhere can have missing pages or wrong keys. Before you start, confirm your birth date window and Class 12 subjects on NDA eligibility; graduates should look at the CDS syllabus instead.

Using papers from 2023, 2024 and 2025 well

The newest sessions reflect the current style best, so treat papers from 2023, 2024 and 2025 as full mocks under strict timing. Older booklets are still good for chapter practice, especially for maths, where the topic list has hardly changed. Keep one recent session unseen until the last fortnight and use it as a final check of your speed.