GATE AG 2019 • Q44 MCQ • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Drought and its classification

Question Statement:

Hydrology: Hydrological cycle and measurement of its components; meteorological parameters and their measurement; analysis of precipitation data; runoff estimation; hydrograph analysis, unit hydrograph theory and application; stream flow measurement; flood routing, hydrological reservoir and channel routing, Infiltration – indices and equations, drought and its classification. A catchment has 8 raingauge stations. Annual rainfall (cm): 93.8, 106.5, 170.6, 138.7, 87.8, 156.2, 180.9, 110.3. For a 10% error in estimating the mean rainfall, the optimum number of stations is

Options:

  • (A) 4
  • (B) 6
  • (C) 8
  • (D) 10

Official Answer Key:

C

Step-by-Step Solution & Explanation

Mean = (93.8+106.5+170.6+138.7+87.8+156.2+180.9+110.3)/8 = 1044.8/8 = 130.6 cm. Sample standard deviation (n−1 basis): σ ≈ 35.92 cm. Coefficient of variation, Cv = (σ/mean)×100 = (35.92/130.6)×100 ≈ 27.50%. Optimum number of stations for allowable error ε = 10%: N = (Cv/ε)² = (27.50/10)² = 7.56 → round up to the next whole station = 8. Answer: (C) 8.

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