Sample questions
You've seen the pattern — here are a few of the actual PYQs.
ESE2024
The temperature distribution T(x) at a distance x, measured from one end, along a bar of length L is given by T(x) = Kx(L − x)(0 ≤ x ≤ L), where K = constant. A Fourier series expansion consisting of sine terms only for T(x) is
- A (8KL²/π³) Σ_{n=1}^∞ 1/(2n−1)³ sin (2n−1)πx/L ✓
- B (8KL²/π³) Σ_{n=1}^∞ 1/(2n−1)² sin (2n−1)πx/L
- C (8KL²/π³) Σ_{n=1}^∞ 1/(2n−1)³ sin (2n−1)πx/L
- D (8KL²/π³) Σ_{n=1}^∞ 1/(2n−1)² sin (2n−1)πx/L
✓ Correct answer: (A)
Engineering › Engineering Mathematics & General
ESE2024
Passing a sinusoidal voltage A sin ωt through a half-wave rectifier produces the clipped sine wave shown in the following figure. A Fourier series expansion of the rectified wave is
- A f(t) = (A/π)[1 + (π/2) sin ωt + 2 Σ_{n=1}^∞ cos 2nωt/(4n²−1)]
- B f(t) = (A/π)[1 + (π/2) sin ωt + 2 Σ_{n=1}^∞ cos 2nωt/(4n²−1)] ✓
- C f(t) = (A/π)[1 + (π/2) sin ωt − 2 Σ_{n=1}^∞ cos 2nωt/(4n²−1)]
- D f(t) = (A/π)[1 − (π/2) sin ωt + 2 Σ_{n=1}^∞ cos 2nωt/(4n²−1)]
✓ Correct answer: (B)
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 →