The GATE Grind

GATE 2022 MN – Question 39

Mineral Economics, Mine Planning, Systems Engineering · Mine Planning · 2 marks · Multiple choice

Match semivariogram shapes P–S with models I pure nugget, II exponential, III spherical, IV Gaussian, and properties E reaches sill at finite range, F reaches sill asymptotically, G reaches sill instantaneously. Retain the printed option combinations.

Diagram for GATE 2022 MN question 39
  1. P–III–E; Q–II–F; R–IV–E; S–I–G
  2. P–II–F; Q–I–G; R–III–E; S–IV–E
  3. P–IV–G; Q–III–F; R–II–E; S–I–E
  4. P–II–E; Q–I–E; R–III–F; S–IV–G

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Show answer and explanation

Correct answer: (A) P–III–E; Q–II–F; R–IV–E; S–I–G

Explanation

P has the spherical shape with a finite-range sill (III, E). Q is exponential and approaches its sill asymptotically (II, F). R has the smooth near-origin Gaussian shape (IV). S is pure nugget, reaching its nonzero sill immediately for positive lag (I, G). These model identities select A. Source caveat: A prints property E for the Gaussian model, although an exact Gaussian variogram approaches its sill asymptotically; only a practical-range approximation treats it as having reached the sill.

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