UPSC Prelims 1995·GS1·science-and-technology·science and technology

The value of (a - m) (b - m) ... (y - m) (z - m) is

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  1. A26 + am25 + abm24 +... + a.b.c. ...z
  2. Bm26 - am25 + abm24 +... - a.b.c. ...z
  3. C0Correct
  4. DIndeterminate

Explanation

The expression is a product of terms where each term subtracts the letter m from a different letter of the alphabet, starting from a to z. The series of terms is as follows: (a minus m), (b minus m), (c minus m), and so on. Because the sequence includes every letter from a to z, one of the terms in the middle of this product will inevitably be (m minus m). The value of (m minus m) is 0. Since any number or expression multiplied by zero equals zero, the entire product of the series becomes zero. Therefore, the correct answer is C.
science-and-technology: The value of (a - m) (b - m) ... (y - m) (z - m) is

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