Question

200!/100! is divisible by (A)2^99 (B)2^100 (C)2^101 (D)none

Answer 1

200! / 100!
= 200 * 199 * 198 *.... * 101
= 200 * 198 * 196 * ..... * 102  -----> 50 multiples of '2'
= 2^50 * 100 * 99 * 98 * 97 * 96 * ... * 1
= 2^50 * 100 * 98 * 96 * ... * 2 ----> 50 multiples of '2'
= 2^(50 + 50) * 50 * 49 * 48 * 47 * ... * 1
= 2^100 * 50 * 48 * ... * 2
= 2^(100 + 25) * 25 * ... * 1
= 2^125 * 24 * ... * 2
=  2^137 * 12 * 11 * ... * 1
= 2^143 * 6 * 5 * 4 * ... * 1
= 2^143 * 6 * 4 * ... * 2
= 2^146 * 3 * 2 * 1
= 2^147

.'. We can see .... $2 ^ {147}$ divides 200! / 100!

Answer 2

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the process by which green plants and some other organisms use sunlight to synthesize nutrients from carbon dioxide and water. Photosynthesis in plants generally involves the green pigment chlorophyll and generates oxygen as a by-product.