NDA Maths mock test: Paper I in the real UPSC pattern
Ten full-length NDA Mathematics mocks with 120 questions each, the 150-minute timer and +2.5 / -0.83 marking. Questions cover the whole syllabus in the usual weightage, including the statement-type and multi-step questions that decide the cut-off.
Sample NDA Maths questions (with answers)
Q1. If a and b are the roots of x² - 5x + 6 = 0, what is a² + b²? (a) 11 (b) 13 (c) 25 (d) 19. Answer: (b) 13 - since a + b = 5 and ab = 6, a² + b² = 25 - 12 = 13.
Q2. If A is a square matrix of order 3 and |A| = 4, what is |adj A|? (a) 4 (b) 16 (c) 64 (d) 12. Answer: (b) 16 - for order n, |adj A| = |A| to the power n - 1 = 4² = 16.
Q3. What is sin²1° + sin²2° + sin²3° + ... + sin²89°? (a) 44 (b) 44.5 (c) 45 (d) 89. Answer: (b) 44.5 - sin²x + sin²(90° - x) = 1, so the 89 terms make 44 pairs plus sin²45° = 1/2.
Q4. Two fair dice are thrown. What is the probability that the sum is neither 5 nor 7? (a) 11/18 (b) 2/3 (c) 13/18 (d) 5/6. Answer: (c) 13/18 - sum 5 happens 4 ways and sum 7 happens 6 ways, leaving 26 of 36 outcomes.
Q5. What is the coefficient of x³ in (1 + x)⁴(1 + 1/x)⁴? (a) 8 (b) 28 (c) 56 (d) 1. Answer: (a) 8 - the product equals (1 + x)⁸ / x⁴, so we need the coefficient of x⁷ in (1 + x)⁸, which is 8.
How the Maths paper is scored
Each correct answer: +2.5. Each wrong answer: -0.83. Unanswered: 0. With 120 questions the paper is out of 300, and attempting about 80-90 questions accurately is a common target for a safe score.
Frequently asked questions
How many questions are in the NDA Maths paper?
120 questions in 2 hours 30 minutes, for 300 marks, with one-third negative marking (-0.83 per wrong answer).
Which topics carry the most weight?
Algebra and Statistics & Probability are the largest areas, followed by Trigonometry, Coordinate Geometry and the two Calculus areas. Our mocks follow that weightage.
Is NDA Maths Mock 1 free?
Yes - take NDA Maths Mock 1 free with a Paper2Test account; the other 9 Maths mocks come with the NDA mock test series.
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