यदि `a+b+c+d=4` है तो `1/((1-a)(a-b)(a-c))+1/((a-b)(a-c)(a-d))+1/((a-c)(1-d)(1-a))+1/((1-d)(1-a)(1-b))` का मान ज्ञात करें।

Options

A. 0
B. 5
C. 1
D. 4

Answer

A

Explanation

`a+b+c+d=4`
`1/((1-a)(a-b)(1-c))+1/((1-b)(1-c)(1-d))`
`+1/((1-c)(1-d)(1-a))+1/((1-d)(1-a)(1-b))`
Put `a=0,b=0` and `c=2` and `d=2`
`a+b+c+d=0+0+2+2=4=4` (satisfy)
`1/((1-0)(1-0)(1-2))+1/((1-0)(1-2)(1-2))`
`+1/((1-2)(1-2)(1-0))+1/((1-2)(1-0)(1-0))`
`implies 1/(-1)+(1/(+1))+1/(-1xx-1)+1/(-1)`
`implies -1+1+1-1=0`