Questions (100)
Q1ESE2024
The standard deviation of the exponential distribution of f_X(x) = { λe^(−λx), x ≥ 0; 0, x < 0 } is
- A 1/λ
- B 2/λ² ✓
- C 3/λ³
- D 2/λ³
✓ Correct answer: (B)
Engineering › Engineering Mathematics & General
Q2ESE2024
Suppose that 0·1% of the people in a certain area have a disease D and that a mass screening test is used to detect cases. The test gives either a positive or a negative result for each person. Ideally, the test would always give a positive result for a person who has it, and would never do so for a person who has not D. In practice the test gives a positive result with probability 99·9% for a person who has D, and with probability 0·2% for a person who has not. What is the probability that a person for whom the test is positive actually has the disease?
- A 1/3 ✓
- B 5/3
- C 4/3
- D 2/3
✓ Correct answer: (A)
Engineering › Engineering Mathematics & General
Q3ESE2024
Let the random variables X and Y have joint density function given by f_{X,Y}(x, y) = { c(1−y), 0 ≤ x ≤ y ≤ 1; 0, otherwise }. Then the marginal density function for X is
- A f_X(x) = 6(1/2 − x − x²/2) for 0 ≤ x ≤ 1
- B f_X(x) = 6(1/2 + x + x²/2) for 0 ≤ x ≤ 1
- C f_X(x) = 6(1/2 + x − x²/2) for 0 ≤ x ≤ 1
- D f_X(x) = 6(1/2 − x + x²/2) for 0 ≤ x ≤ 1 ✓
✓ Correct answer: (D)
Engineering › Engineering Mathematics & General
Study how UPSC repeats — not just the papers
₹199 / 1 year · Founding Member
Full access unlocks the three things no PYQ PDF gives you:
① Cross-exam learning — see the same idea recur across CSE, CAPF, CDS and NDA.
② Topic evolution — how each idea is framed, year by year.
③ Question intelligence — every PYQ + answer, linked to related concepts and similar questions.
e.g. Round Table Conference: CDS 2017 → CSE 2017 → … → CAPF 2024
15 days free, no card required — then ₹199 for 1 year.
Start your 15-day free trial →