UPSC Prelims 2026 · CSAT Paper 2 · Set DMathematicsQ 10 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 10

Question

Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x² and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?

(a)1/7
(b)1/5
(c)5/7
(d)1

UnlockIAS answer: (b)1/5

Solution

y = kx² with 50 = k·25 → k = 2; xz = constant = 5 · 7/25 = 7/5. y = 98 → x² = 49 → x = 7, so z = (7/5)/7 = 1/5.

UnlockIAS expert key, prepared 24 May 2026 and cross-verified by re-deriving the answer — this is our key, not the official UPSC provisional key (awaited).

Section

Mathematics

Topic Reference

Algebra — Variation (proportion)

Official UPSC key still awaited

UPSC has announced (PIB Release 2262441, 18 May 2026) that the provisional answer key for CSE Prelims 2026 will be released “soon after Exam”. Until then, use the CSAT score calculator for your qualifying-status estimate, and join the per-question discussion below.

CSAT Score Calculator

Check your 33% qualifying status

Official Notification

PIB Release 2262441

Back to all 80 CSAT questions