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Statement-1: The number 1000C(500) is no...

Statement-1: The number `1000C_(500)` is not divisible by 11.
Statement-2: The exponent of prime p in n! is
`[(n)/(p)]+[(n)/(p^(2))]+[(n)/(p^(3))]+......+[(n)/(p^(x))]" where "p^(k)lenltp^(k+1)`

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

AI Generated Solution

To solve the problem, we need to analyze both statements and determine their validity. ### Step 1: Understanding Statement 1 We need to determine whether \( \binom{1000}{500} \) is divisible by 11. The binomial coefficient \( \binom{1000}{500} \) can be expressed as: \[ \binom{1000}{500} = \frac{1000!}{500! \times 500!} \] ...
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