How it travelled across exams
First appearance in each exam — the same idea, reframed.
EPFO 2015 → CAPF 2016 → ESE 2022
Sample questions
You've seen the pattern — here are a few of the actual PYQs.
ESE2026
What is the expectation of the number of failures preceding the first success in an infinite series of independent trials with constant probability p of success in each trial ?
- A q/p²
- B q/p
- C q/(1+p)
- D 1/(1−q)
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
ESE2026
A deck of n numbered cards is thoroughly shuffled and the cards are inserted into n numbered cells one by one. If the card number i falls in the cell i, we count it as a match, otherwise not, then what is the variance of total number of such matches ?
- A 1
- B 0
- C 1/2
- D 3/4
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
ESE2026
Let X1 and X2 be two independent random variables having variances k and 4 respectively. If the variance of Y = 3X2 − X1 is 49, then what is the value of k ?
- A 7
- B 13
- C 9
- D 11
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
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