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100+ Free UPSC NDA (I) Practice Questions

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Fill in the blank: 'The commanding officer insisted that every recruit ___ present at the parade.'

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2026 Statistics

Key Facts: UPSC NDA (I) Exam

270

Total MCQs (120 Maths + 150 GAT)

UPSC NDA & NA notification

900

Total Written Marks

UPSC

2.5 hrs

Duration per Paper

UPSC

1/3

Negative Marking per Wrong Answer

UPSC

Rs. 100

Application Fee (General/OBC Male)

UPSC NDA notification

25%

Minimum Qualifying Marks per Paper

UPSC

UPSC's NDA & NA (I) written exam has two objective papers — Mathematics (120 questions, 300 marks) and the General Ability Test (150 questions, 600 marks) — totalling 270 MCQs and 900 marks across 5 hours. The GAT splits into English (200 marks) and General Knowledge (400 marks). Wrong answers lose one-third of the marks; candidates need at least 25% in each paper. Qualifiers proceed to the 900-mark SSB interview.

Sample UPSC NDA (I) Practice Questions

Try these sample questions to test your UPSC NDA (I) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1If A = {1, 2, 3} and B = {3, 4}, what is A ∪ B?
A.{1, 2, 3, 4}
B.{3}
C.{1, 2, 4}
D.{1, 2, 3, 3, 4}
Explanation: The union A ∪ B contains every element that is in A, in B, or in both, listed once each. Combining {1, 2, 3} and {3, 4} gives {1, 2, 3, 4}.
2What is the modulus of the complex number z = 3 + 4i?
A.5
B.7
C.25
D.1
Explanation: For z = a + bi, the modulus |z| = √(a² + b²). Here |z| = √(3² + 4²) = √(9 + 16) = √25 = 5.
3The binary number 1011 is equal to which decimal number?
A.11
B.13
C.9
D.1011
Explanation: Reading place values from the right: 1×8 + 0×4 + 1×2 + 1×1 = 8 + 0 + 2 + 1 = 11. Each binary digit weights a power of 2.
4The sum of the first 20 terms of the arithmetic progression 2, 5, 8, 11, … is:
A.610
B.590
C.600
D.620
Explanation: Here a = 2 and common difference d = 3. Using Sₙ = n/2 × [2a + (n−1)d], S₂₀ = 10 × [4 + 19×3] = 10 × [4 + 57] = 10 × 61 = 610.
5If the roots of the quadratic equation x² − 5x + 6 = 0 are α and β, what is the value of α + β?
A.5
B.6
C.−5
D.1
Explanation: For ax² + bx + c = 0, the sum of roots equals −b/a. Here −(−5)/1 = 5. The product of roots c/a would be 6.
6How many distinct arrangements can be made using all letters of the word 'LEVEL'?
A.30
B.120
C.60
D.20
Explanation: LEVEL has 5 letters with L repeated twice and E repeated twice. The count is 5!/(2!×2!) = 120/4 = 30.
7What is the value of log₁₀ 1000?
A.3
B.10
C.100
D.1
Explanation: log₁₀ 1000 asks for the power to which 10 must be raised to give 1000. Since 10³ = 1000, the logarithm equals 3.
8In the binomial expansion of (1 + x)⁵, what is the coefficient of x²?
A.10
B.5
C.20
D.15
Explanation: The coefficient of xʳ in (1 + x)ⁿ is C(n, r). For x² in (1 + x)⁵, C(5, 2) = 5!/(2!3!) = 10.
9If A is a 2×2 matrix with det(A) = 5, what is det(2A)?
A.20
B.10
C.5
D.40
Explanation: For an n×n matrix, det(kA) = kⁿ × det(A). For a 2×2 matrix, det(2A) = 2² × 5 = 4 × 5 = 20.
10What is the determinant of the identity matrix I of order 3?
A.1
B.0
C.3
D.9
Explanation: The identity matrix has 1s on its main diagonal and 0s elsewhere. Its determinant equals the product of the diagonal entries, 1×1×1 = 1, for any order.

About the UPSC NDA (I) Exam

The National Defence Academy and Naval Academy Examination (NDA & NA) is conducted by the Union Public Service Commission twice a year for admission to the Army, Navy, and Air Force wings of the NDA and the Indian Naval Academy Course. The written examination has two objective papers: Mathematics (120 questions, 300 marks) and the General Ability Test (150 questions, 600 marks), each lasting 2.5 hours, for a total of 270 questions and 900 marks. The GAT comprises Part A (English, 200 marks) and Part B (General Knowledge, 400 marks, covering Physics, Chemistry, General Science, History, Geography, and Current Events). Negative marking deducts one-third of a question's marks for each wrong answer, and candidates must score at least 25% in each paper. Those who clear the written exam are called for the Services Selection Board (SSB) interview, a separate non-MCQ stage also worth 900 marks.

Questions

270 scored questions

Time Limit

2 hours 30 minutes per paper (5 hours total across two papers)

Passing Score

Minimum 25% in each paper; overall written cut-off varies by session (recent cut-offs around 350 of 900)

Exam Fee

Rs. 100 (General/OBC male); free for SC/ST, female, and wards of JCOs/NCOs/ORs (Union Public Service Commission (UPSC), conducted offline at centres across India)

UPSC NDA (I) Exam Content Outline

33%

Mathematics (Paper I)

120 questions of 10+2 standard on algebra, matrices and determinants, trigonometry, analytical geometry, differential and integral calculus, vector algebra, and statistics and probability

22%

GAT Part A — English

About 50 questions (200 marks) on grammar, vocabulary, synonyms/antonyms, comprehension, and sentence cohesion

11%

GAT Part B — Physics

Around 25 questions (25% of GK) on mechanics, heat, light, sound, electricity, magnetism, and modern physics

9%

GAT Part B — History & Polity

Around 20 questions (20% of GK) on the freedom movement, Indian and world history, the Constitution, and polity

9%

GAT Part B — Geography

Around 20 questions (20% of GK) on physical, world, and Indian geography including monsoons, rivers, and the solar system

7%

GAT Part B — Chemistry

Around 15 questions (15% of GK) on physical/chemical changes, atomic structure, acids and bases, and common compounds

5%

GAT Part B — General Science

Around 10 questions (10% of GK) on biology basics, the human body, nutrition, and everyday science

4%

GAT Part B — Current Events

Around 10 questions (10% of GK) on national and international affairs, defence, awards, and key institutions

How to Pass the UPSC NDA (I) Exam

What You Need to Know

  • Passing score: Minimum 25% in each paper; overall written cut-off varies by session (recent cut-offs around 350 of 900)
  • Exam length: 270 questions
  • Time limit: 2 hours 30 minutes per paper (5 hours total across two papers)
  • Exam fee: Rs. 100 (General/OBC male); free for SC/ST, female, and wards of JCOs/NCOs/ORs

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

UPSC NDA (I) Study Tips from Top Performers

1Master 10+2 mathematics thoroughly — algebra, trigonometry, and calculus carry the most weight in the 120-question Maths paper.
2Practice under the one-third negative-marking rule so you learn when to attempt and when to leave a question blank.
3Read an English newspaper daily to build vocabulary, comprehension, and current-affairs awareness at the same time.
4Use NCERT textbooks (Classes 9-12) as the backbone for Physics, Chemistry, General Science, History, and Geography.
5Prioritise high-weight GK sections: Physics (~25%), History/Polity (~20%), and Geography (~20%) within Part B.
6Solve at least the last 5-10 years of previous NDA papers to learn the question style and recurring topics.
7Take full-length timed mock papers for both Maths and GAT and review every error to convert weaknesses into marks.

Frequently Asked Questions

What is the UPSC NDA exam?

The National Defence Academy and Naval Academy Examination (NDA & NA) is a UPSC-conducted entrance exam for admission to the Army, Navy, and Air Force wings of the NDA and the Indian Naval Academy. It has two written papers — Mathematics and the General Ability Test — followed by an SSB interview.

What is the NDA exam pattern and marking scheme?

Paper I (Mathematics) has 120 questions for 300 marks, and Paper II (GAT) has 150 questions for 600 marks, each lasting 2.5 hours — 270 questions and 900 marks in total. Correct answers earn +2.5 (Maths) or +4 (GAT); wrong answers lose one-third of the marks (−0.83 in Maths, −1.33 in GAT).

What subjects are covered in the General Ability Test?

The GAT has Part A — English (200 marks) and Part B — General Knowledge (400 marks). General Knowledge covers Physics (about 25%), History and Polity (about 20%), Geography (about 20%), Chemistry (about 15%), General Science (about 10%), and Current Events (about 10%).

What is the passing or qualifying score for NDA?

Candidates must score at least 25% in each paper to qualify, and UPSC sets an overall written cut-off for each session. Recent written cut-offs have been around 350 out of 900, but the exact figure changes every cycle based on difficulty and vacancies.

Who is eligible to apply for the NDA exam?

Unmarried male and female candidates aged about 16.5 to 19.5 years who have passed or are appearing in Class 12 are eligible. Candidates for the Air Force, Naval wings, and the 10+2 Cadet Entry Scheme at the Indian Naval Academy must have studied Physics, Chemistry, and Mathematics in Class 12.

How much does the NDA application cost?

The application fee is Rs. 100 for General and OBC male candidates. SC/ST candidates, all female candidates, and wards of JCOs/NCOs/ORs are exempt from the fee.

Is there an interview after the written exam?

Yes. Candidates who clear the written examination are called for the Services Selection Board (SSB) interview, a separate non-MCQ stage worth 900 marks. It spans about five days and assesses intelligence, personality, psychology, group tasks, and a personal interview.

How many times is the NDA exam held each year?

UPSC conducts the NDA & NA examination twice a year — NDA I (typically in April) and NDA II (typically in September). There is no fixed limit on attempts other than the prescribed age window.