The system of equations 15y - 10x + 50 = 0, 2x - 3y - 5 = 0

is consistent and has exactly two solutions

Determinants — NDA Previous Year Questions

61 solved PYQs · 2021–2025 · Mathematics

Solved PYQs: 61
Years covered: 2021–2025
Avg / year: ~12
Subject: Mathematics

How many NDA questions come from Determinants?

Determinants has contributed 61 questions to National Defence Academy Examination papers between 2021 and 2025 — an average of about 12 questions a year. That count is measured from EByAi’s bank of 15,695 NDA questions, not estimated from a syllabus. Every one of the 61 questions carries a written, step-by-step solution, and each is tagged to Determinants within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Determinants questions from real NDA papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 61 Determinants questions (with full written solutions) are available in practice.

Question 1 · NDA 2025
The system of equations 15y - 10x + 50 = 0, 2x - 3y - 5 = 0
1. (A) $has a unique solution$
2. (B) $has infinitely many solutions$
3. (C) $is inconsistent$
4. (D) $is consistent and has exactly two solutions$
Show answerAnswer
$Answer: (C) is inconsistent$
Question 2 · NDA 2025
Consider the following in respect of a non-singular matrix M:

I. ∣M^2∣=∣M∣^2

II. ∣M∣=∣M^-1∣

III. ∣M∣=∣M^T∣

How many of the above are correct?
1. (A) $None$
2. (B) $One$
3. (C) $Two$
4. (D) $All three$
Show answerAnswer
$Answer: (C) Two$
Question 3 · NDA 2024
If P is a skew-symmetric matrix of order 3, then what is det(P) equal to?
1. (A) $-1$
2. (B) $0$
3. (C) $1$
4. (D) $3$
Show answerAnswer
$Answer: (B) 0$
Question 4 · NDA 2023
If Δ(7, 4, 2, α) = 0, then α is a root of which one of the following equations ?
1. (A) $7x 2 + 4x + 2 = 0$
2. (B) $7x 2 - 4x + 2 = 0$
3. (C) $7x 2 + 8x + 2 = 0$
4. (D) $7x 2 - 8x + 2 = 0$
Show answerAnswer
$Answer: (C) 7x 2 + 8x + 2 = 0$
Question 5 · NDA 2023
If Δ(a, b, c, α) = 0 for every α > 0, then which one of the following is correct?
1. (A) $a, b, c are in AP$
2. (B) $a, b, c are in GP$
3. (C) $a, 2b, c are in AP$
4. (D) $a, 2b, c are in GP$
Show answerAnswer
$Answer: (B) a, b, c are in GP$

Determinants questions by year

Year	Questions	Share of chapter questions
2025	15
2024	8
2023	16
2022	10
2021	12

Practise these 61 questions with solutions

Free to start — 25 past-year questions a day with full written solutions, no card needed.

Start Determinants practice free

FAQs

How many NDA questions have been asked from Determinants?

EByAi's bank holds 61 real NDA questions from Determinants, asked between 2021 and 2025 — about 12 per year on average. Every count is measured from actual papers, not estimated.

Is Determinants important for NDA?

61 questions over 5 papers make Determinants a steady-weightage chapter in NDA Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Determinants PYQs online for free?

Yes. EByAi lets you solve NDA past-year questions in the browser with written solutions — free daily practice, no card needed.

More NDA Mathematics chapters

All NDA Mathematics chapters →NDA overview →