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Topic Vector Calculus
Asked 2 times in ESE over 1 years (2024–2025), peaking in 2024.
Key insights
- Most tested in ESE — 2 of 2 PYQs
- Most asked in 2024
- Recurs across 2 years (2024–2025)
Across exams
ESE · 2How the concept evolved
Rising — more than half its appearances (2 of 2) are since 2016.
Related concepts
Ideas UPSC tests alongside this one — keep exploring.
Sample questions
You've seen the pattern — here are a few of the actual PYQs.
ESE2025
If V = (xyz)î + (3x²y)ĵ + (xz² – y²z)k̂, the value of divergence of V at point (2, –1, 1) will be
- A 14
- B 16
- C 18
- D 20
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
ESE2024
Suppose we do not know the path of a hang glider, but only its acceleration vector a(t) = −(3 cos t)i − (3 sin t)j + 2k. We also know that initially (at time t = 0) the glider departed from the point (4, 0, 0) with velocity v(0) = 3j. What is the glider's position as a function of t?
- A r(t) = (1 + 3 cos t)i + 3 sin tj + t²k
- B r(t) = (−1+3 cos t)i + 3 sin tj + t²k
- C r(t) = (1 − 3 cos t)i + 3 sin tj + t²k
- D r(t) = (1 + 3 cos t)i + 3 sin tj + t²k ✓
✓ Correct answer: (D)
Engineering › Engineering Mathematics & General
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