Let a, b, c be such that b(a + c) ≠ 0 if |a&a+1&a-1 -b &b+1&b-1 c &c-1&c+1| + |a+1&b+1&c-1 a-1 &b-1&c+1 (-1)n+2a &(-1)n+1b&(-1)nc|= 0 then the value of n is :

Question

Let a, b, c be such that b(a + c) ≠ 0 if |a&a+1&a-1 -b &b+1&b-1 c &c-1&c+1| + |a+1&b+1&c-1 a-1 &b-1&c+1 (-1)n+2a &(-1)n+1b&(-1)nc|= 0 then the value of n is : (A) any even integer (B) any odd integer (C) any integer (D) zero

Tardigrade Admin · Accepted Answer

|a&a+1&a-1 -b &b+1&b-1 c &c-1&c+1| +(-1)n |a+1&b+1&c-1 a-1 &b-1&c+1 a &-b&c|=|a&a+1&a-1 -b&b+1&b-1 c&c-1&c+1|+(-1)n|a+1&a-1&a b+1&b-1&-b c-1&c+1&c| =|a&a+1&a-1 -b &b+1&b-1 c &c-1&c+1| +(-1)n+1 |a+1&a&a-1 b-1 &-b&b-1 c-1 &c&c+1|=|a&a+1&a-1 -b&b+1&b-1 c&c-1&c+1|+(-1)n+2|a&a+1&a-1 -b&b+1&b-1 c&c-1&c+1| This is equal to zero only if n + 2 is odd i.e. n is odd integer.

Q. Let a,b,c be such that b(a+c) = 0 if ∣∣​a−bc​a+1b+1c−1​a−1b−1c+1​∣∣​+∣∣​a+1a−1(−1)n+2a​b+1b−1(−1)n+1b​c−1c+1(−1)nc​∣∣​=0 then the value of n is :

any even integer

any odd integer

any integer

zero

Q. Let $a, b, c$ be such that $b (a + c)$ $\neq =$ 0 if $∣ ∣ a - b c a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 ∣ ∣ + ∣ ∣ a + 1 a - 1 (- 1)^{n + 2} a b + 1 b - 1 (- 1)^{n + 1} b c - 1 c + 1 (- 1)^{n} c ∣ ∣ = 0$ then the value of $n$ is :