Let x1, x2, ............ ,x15 be 15 distinct numbers chosen from 1, 2, 3,........... , 15. Then the value of (x1-1),(x3-1) .......... (x15-1) is

Question

Let x1, x2, ............ ,x15 be 15 distinct numbers chosen from 1, 2, 3,........... , 15. Then the value of (x1-1),(x3-1) .......... (x15-1) is (A) always le 0 (B) 0 (zero) (C) always even (D) always odd

Tardigrade Admin · Accepted Answer

Since, x1, x2, ldots, x15 are among 1,2,3, ldots, 15 . So, x1 can take any value from 1,2,3, ldots, 15. Among these values, one of the number must be 1 , hence product will be 0 .

Q. Let $x_{1}, x_{2}, ............, x_{15}$ be 15 distinct numbers chosen from $1, 2, 3, ..........., 15.$ Then the value of $(x_{1} - 1), (x_{3} - 1) .......... (x_{15} - 1)$ is

always $\leq 0$

$0$ (zero)

always even

always odd

Since, $x_{1}, x_{2}, \dots, x_{15}$ are among $1, 2, 3, \dots, 15.$ So, $x_{1}$ can take any value from $1, 2, 3, \dots$ , 15. Among these values, one of the number must be 1 , hence product will be 0 .

Q. Let x1​,x2​,............,x15​ be 15 distinct numbers chosen from 1,2,3,...........,15. Then the value of (x1​−1),(x3​−1)..........(x15​−1) is

always ≤0

0 (zero)