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Statement-1: the highest power of 3 in ....

Statement-1: the highest power of 3 in `.^(50)C_(10)` is 4.
Statement-2: If p is any prime number, then power of p in n! is equal to `[n/p]+[n/p^(2)]+[n/p^(3)]`+ . . ., where `[*]`
denotes the greatest integer function.
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

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

Verified by Experts

The correct Answer is:
D
`because.^(50)C_(10)=(50!)/(10!40!)`
`thereforeE_(3)(50!)=[50/3]+[50/9]+[50/27]+[50/81]+ . . .`
`=16+5+1+0+ . .=22`
`E_(3)(40!)=[40/3]+[40/9]=[40/27]+[40/81]+ . . .`
`=13+4+1+0=18`
and `E_(3)(10!)=[10/3]+[10/9]+[10/27]+ . . =3+1+0=4`
Hence, highest power of 3 in `.^(50)C_(10)=22-(18+4)=0`
`therefore`Statement-1 is false, statement-2 is true.
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