Ferromagnetism is the property of materials like iron, cobalt, and nickel to retain permanent magnetic properties due to aligned electron spins.

De Broglie proposed that all matter exhibits wave-particle duality. Both light (photons) and electrons show properties of both waves and particles, confirmed by experiments like double-slit interference and photoelectric effect.

Work done against constant pressure: W = -PΔV. Given W = -500 J and P = 2 atm = 2 × 101325 Pa. ΔV = -W/P = 500/(2 × 101325) ≈ 2.47 × 10⁻³ m³ = 2.47 L.

Linear expansion: ΔL = α × L₀ × ΔT = 1.2 × 10⁻⁵ × 1 × 100 = 1.2 × 10⁻³ m = 1.2 mm.

Using lens formula: 1/f = 1/u + 1/v. Given f = 15 cm, v = 30 cm: 1/15 = 1/u + 1/30, so 1/u = 1/15 - 1/30 = 1/30, therefore u = 30 cm.

The Second Law of Thermodynamics states that for an isolated system, entropy always increases or remains constant, never decreases. This defines the direction of spontaneous processes and the arrow of time.

Each half has resistance R/2. When connected in parallel: 1/R_new = 1/(R/2) + 1/(R/2) = 4/R, so R_new = R/4.

Object at 2f (40 cm = 2 × 20 cm) forms image at 2f. Using mirror equation confirms v = 40 cm, m = -1 (real, inverted, same size as object).

Height = L × sin(60°) = 10 × (√3/2) = 5√3 m ≈ 8.66 m. The vertical component of the ladder's length is found using trigonometry.

After 30 years = 3 half-lives: N = N₀ × (1/2)³ = N₀/8. The sample reduces by half three times successively.