During ice age between _____ modern Homo sapiens arose.

The correct answer is Option (2) → 75,000 - 10,000 years ago

Option (1) 100,000 - 40,000 years ago — Incorrect. This is the time of the Neanderthal man, not of modern humans. The Neanderthals were a separate group of humans that later died out.

Option (2) 75,000 - 10,000 years ago — Correct. Modern Homo sapiens arose during the last ice age, inside this window. Later events of the human story fit after it: pre-historic cave art about 18,000 years ago, and agriculture and settled life about 10,000 years ago.

Option (3) 2000000 - 1500000 years ago — Incorrect. These are the dates of the early hominids. About 2 million years ago the first human-like being, Homo habilis, appeared, and about 1.5 million years ago Homo erectus. Modern humans came much later.

Option (4) 4000000 - 3000000 years ago — Incorrect. This is older than even Homo habilis. No member of the genus Homo had appeared yet, so it cannot be the time of modern humans.

NCERT Extract:
Origin and Evolution of Man – “… The Neanderthal man with a brain size of 1400cc lived in near east and central Asia between 1,00,000-40,000 years back. They used hides to protect their body and buried their dead. Homo sapiens arose in Africa and moved across continents and developed into distinct races. During ice age between 75,000-10,000 years ago modern Homo sapiens arose.”