Q75 / 160 · WBJEE 2015 · Mathematics

Let $x_{1}, x_{2}, \ldots, x_{13}$ be 15 distinct numbers chosen from $1,2,3, \ldots, 15 .$ Then, the value of $\left(x_{1}-1\right)\left(x_{2}-1\right)\left(x_{3}-1\right) \ldots\left(x_{15}-1\right)$ is

  • A
    always $\leq 0$
  • Correct answer
    B
    0
  • C
    akays even
  • D
    aways odd

Solution

Since, $x_{1}, x_{2} \ldots, x_{15}$ are among $1,2,3, \ldots, 15$. So, $x_{1}$ 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

Hence, the correct answer is option: 'B'.

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