NDA (II) 2019 · Mathematics
A full Mathematics paper in the UPSC NDA pattern. 120 questions in 150 minutes, with a third of the marks deducted for every wrong answer.
120questions
300marks
+2.5 / −0.83per question
39/62/19easy / medium / hard
Sections and topics
One 120-question Mathematics paper covering algebra, trigonometry, calculus, geometry, vectors, statistics and probability.
Mathematics · 120 questions
- Vectors7
- Trigonometric ratios6
- Complex numbers5
- Three-dimensional geometry5
- Applications of derivatives5
- Statistics5
- Probability5
- Quadratic equations4
- Determinants4
- Matrices4
- Trigonometric identities4
- Circles4
- Conic sections4
- Differential equations4
Sample question from this paper
Sets · medium
The number of subsets of that contain the element but do not contain the element is
- A.
- B.
- C.
- D.
Show answer and solution
Answer: A
Fix the two special elements: must be present and must be absent, so only the remaining four elements are free. Each of them can either be included or left out, giving subsets. The answer counts subsets containing with no condition on , and wrongly fixes one more element.
Fix the two special elements: must be present and must be absent, so only the remaining four elements are free. Each of them can either be included or left out, giving subsets. The answer counts subsets containing with no condition on , and wrongly fixes one more element.