Sample questions
You've seen the pattern — here are a few of the actual PYQs.
ESE2024
The plane x = 1 intersects the paraboloid z = x² + y² in a parabola. The slope of the tangent line to the parabola at (1, 2, 5) is
- A 2
- B 6
- C 4 ✓
- D 5
✓ Correct answer: (C)
Engineering › Engineering Mathematics & General
ESE2024
What is the absolute minimum value of f(x, y) = 2 + 2x + 4y − x² − y² on the triangular region in the first quadrant bounded by the lines x = 0, y = 0, and y = 9 − x?
- A −11
- B −43
- C −61 ✓
- D −41
✓ Correct answer: (C)
Engineering › Engineering Mathematics & General
Study how UPSC repeats — not just the papers
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