If X,Y and Z are opositive number such that Y and Z have respectively 1 and 0 at their unit's place and
`Delta =|{:(X,4,1),(Y,0,1),(Z,1,0):}|`
If `(Delta+1)` is divisible by 10 then X has at its unit's place

Options

A. 1
B. 0
C. 2
D. none of these

Answer

C

Explanation

Let `X = 10x + lamda, Y = 10 y + 1 and Z = 10z`, where `x,y,z in N`. Then,
`|(X,4,1),(Y,0,1),(Z,1,0)|`
`rArr Delta = |(10x + lamda,4,1),(10y + 1,0,1),(10z + 0,1,0)| = |(10x ,4,1),(10y,0,1),(10z,1,0)| + |(lamda,4,1),(1,0,1),(0,1,0)|`
`rArr Delta = 10 |(x,4,1),(y,0,1),(z,1,0)| + (1 + lamda)`
`rArr Delta + 1 = 10 |(x,4,1),(y,0,1),(z,1,0)| + (2 - lamda)`
`rArr Delta + 1 = 10k + (2- lamda), " where " k = |(x,4,1),(y,0,1),(z,1,0)|`
It is given that `Delta + 1` is divisible by 10. Therefore,
`2 - lamda = 0 " i.e., " lamda = 2`
`:. X = 10x + 2`
`rArr` 2 is at unit's place of X