Microscope resolution improved by: MCQ with Answer and Explanation

Explanation:
In the SI system of prefixes, 'Peta' stands for 10^15. Other common large prefixes include Kilo (10^3), Mega (10^6), Giga (10^9), Tera (10^12), and Exa (10^18). It's crucial to memorize both positive and negative powers (like nano, pico, femto) for competitive exams.

Explanation:
Emission requires photon energy hν ≥ work function φ ⇒ ν ≥ ν₀. Intensity affects electron count, not emission possibility. Memory aid: 'Photoelectric: frequency threshold (quantum); intensity affects current'. Quantum physics concept frequently tested in competitive exams.

Explanation:
Escape velocity v_e = √(2GM/R). Mass M = density ρ × volume = ρ×(4/3)πR³. Thus v_e = √(2Gρ×4/3πR³ / R) = √(8GρπR²/3) ∝ R√ρ. Given same density and R_planet = 2R_earth, v_e ∝ R, so v_e_planet = 2 × 11.2 = 22.4 km/s. This derivation shows escape velocity scales linearly with radius for constant density. Memory tip: v_e ∝ √(M/R) and M ∝ R³ for constant ρ, so v_e ∝ R. Such proportional reasoning questions test conceptual grasp of gravitation formulas in competitive exams without heavy calculation.