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"^(74)C(37)-2 is divisible by a. 37^(2)...

`"^(74)C_(37)-2` is divisible by a. `37^(2)` b. 38. c. 36 d. none of these

A

`37^(2)`

B

`38`

C

`36`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `'^(74)C_(37)-2`
`=^(37)C_(0)^(2)+^(37)C_(1)^(2)+^(37)C_(2)^(2)+....^(37)C_(37)^(2)-2`
`='^(37)C_(1)^(2)+^(37)C_(2)^(2)+....^(37)C_(36)^(2)`
is divisible by `37^(2)`
(as each `'^(37)C_(1)`, `'^(37)C_(2)`, `'^(37)C_(3)`, ….`'^(37)C_(36)` are divisible by `37`)
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