Editorial review: 9 October 2026
Prepare NDA mathematics and GAT with checked practice
NDA preparation needs more than a large daily timetable. Connect the applicable syllabus with a question you can solve, an error you can explain and a separate check on a changed input. Keep written-paper practice distinct from the other selection requirements and from personal eligibility or medical judgments.
This guide uses the dated official NDA II 2026 scheme and original worked exercises in arithmetic progressions, reading comprehension and basic physics. The examples are author-created, not actual previous-year questions or an official answer key. The older year in the retained URL does not determine the scheme or eligibility conditions that apply to a reader.
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Appendix I of the official NDA II 2026 notice gives the following written papers:
| Paper | Marks | Duration |
|---|---|---|
| Mathematics | 300 | 2½ hours |
| General Ability Test | 600 | 2½ hours |
Written total: 900. SSB carries a separate 900. Written papers are objective; mathematics and GAT Part B are Hindi–English. Calculators and mathematical/logarithmic tables are not permitted for these written papers.
GAT comprises English, 200 marks, and general knowledge, 400. Its GK headings cover physics, chemistry, general science, history, geography and current events. Mathematics includes algebra, matrices/determinants, trigonometry, analytical geometry, differential calculus, integral calculus/differential equations, vector algebra and statistics/probability. The GK list is non-exhaustive; approximate weights are not guaranteed future question counts.
Use the full applicable notice and later instructions for detailed rules. This is a dated preparation reference, not confirmation of current applications, your appointment or eligibility. No application deadline or universal age, vision or physical-training prescription is inferred here.
Map coverage without claiming it is complete
Create a record of the actual branch practised, question, worked method and checked result. One arithmetic-progression exercise belongs within algebra; it does not complete every algebra topic. One speed calculation does not cover physics, let alone all six GK groups.
For written preparation, keep mathematics and GAT records visible separately. Reading comprehension and source interpretation can be practised with short original passages, while factual GK preparation needs appropriate subject sources and dates. The separate SSB requirement is not satisfied by a correct mathematical answer.
The NDA mock test and current-affairs hub provide available practice and reading routes. Check the displayed settings of a particular mock before treating its timing and scoring as an exact reproduction of an official paper. Use official sources for recruitment instructions.
Original mathematics exercise: the fifth term
Question: A sequence begins at 6 and increases by 4 each step. What is its fifth term, and what is the sum of its first five terms?
The first five terms are 6, 10, 14, 18, 22. The fifth term is 22. There are four increases between the first and fifth terms, not five.
Using the arithmetic-progression notation, first term a = 6, common difference d = 4 and n = 5:
nth term = a + (n − 1)d
fifth term = 6 + (5 − 1) × 4
= 6 + 16
= 22
sum of first n terms = n/2 × [2a + (n − 1)d]
sum of first five = 5/2 × [12 + 16]
= 5/2 × 28
= 70
The direct addition check is 6 + 10 + 14 + 18 + 22 = 70, which agrees with the formula. These checks establish results for this supplied sequence only. They do not prove that a learner can solve every progression problem under examination conditions.
Diagnose the supplied mistake
In this fictional practice record, Devika's first answer for the fifth term is 26, obtained from 6 + 5 × 4. The error is using five differences after the first term. That expression reaches the sixth term of this sequence, not the fifth.
The targeted correction is to identify the starting term and count the number of intervals before substituting into a formula. Simply writing “revise algebra” would not identify the specific mistake. The source record also contains no timing measurement or reason to claim that this correction improves an actual exam score.
Devika's note can read: “Fifth term needs four increments from the first term. My earlier expression used five. For the supplied sequence, the corrected result is 22, checked by listing five terms.” That note describes a finite correction rather than a claim of mastery.
A separate new-input check
New question: A different sequence begins at 3 and increases by 5. Find its seventh term and the sum of its first seven terms.
Here a = 3, d = 5 and n = 7. The seventh term is 3 + 6 × 5 = 33. The sum is 7/2 × [6 + 30] = 7/2 × 36 = 126.
Listing the terms gives 3, 8, 13, 18, 23, 28, 33, with direct sum 126. This is a separate worked example with changed inputs. It is not an actual later test result for Devika unless her attempt and its result are separately supplied.
Use a new question to check the corrected reasoning rather than copying the earlier answer. Keep a worked answer key distinct from what you personally produced in a timed attempt.
Original English comprehension exercise
Read this author-created passage:
The committee recorded the final count after a recount. The earlier draft was replaced. The passage does not state either numerical count.
Question 1: Was the final count recorded before or after the recount? The passage expressly says after. An answer of “before” conflicts with the stated sequence.
Question 2: What was the final numerical count? It is not stated. The presence of a final record does not supply its numerical contents. Inventing a number would change the passage rather than interpret it.
These questions check sequence and the limit of supplied information. They do not cover all English vocabulary, grammar or comprehension requirements. The critical-thinking guide offers related original exercises in checking what a statement supports.
Original physics exercise: average speed
Question: An invented motion record gives a total distance travelled of 120 metres over 40 seconds. What is the average speed over that interval?
Average speed is total distance divided by elapsed time: 120 ÷ 40 = 3 metres per second. The distance is explicitly total distance travelled, not displacement. The answer therefore concerns average speed, not a directional velocity.
The record does not say the object moved at a constant speed throughout. An average of 3 metres per second cannot establish that its instantaneous speed was always 3. Keep the calculated quantity and the missing motion details separate.
For a distinct variation, total distance 180 metres over 60 seconds also gives 180 ÷ 60 = 3 metres per second. Matching averages does not establish identical motion at every instant. This exercise is basic subject practice, not a forecast that the exact question will appear in NDA.
Turn checked answers into the next practice task
The original cycle identifies a progression interval error, two comprehension checks and an average-speed calculation. A useful next task is specific: solve another progression with a different requested term, explain which passage facts are stated and check the units in a different distance/time question.
To broaden preparation, return to the official headings and choose branches not yet practised. Keep a question wrong because of missing knowledge separate from a transcription error or an unfinished timed attempt. Record the cause only where you have evidence.
Avoid interpreting these few correct worked examples as full-paper readiness, SSB preparation or a selection prediction. Actual recruitment and assessment requirements need their own applicable instructions; generic promises about guaranteed fitness, salary or admission do not follow from written practice.
Frequently asked questions
Are these actual NDA previous-year questions? No. They are original exercises with complete worked answers.
Why is the fifth term not 6 + 5 × 4? There are four increments from the first term to the fifth. Five increments reach the sixth term.
Does a 3 m/s average prove constant speed? No. It is a distance/time average over the supplied interval.
Does this guide determine my eligibility or selection? No. Use the actual notice and appropriate official processes; these exercises establish only their stated written-practice results.