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

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Q: 137 (IAS/1995)
The value of (a - m) (b - m) ... (y - m) (z - m) is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,7,3,2,3,2

keywords: 

{'indeterminate': [0, 1, 0, 0], 'value': [0, 0, 1, 0]}

The expression given in the question consists of 26 factors, each corresponding to an alphabet from a to z, where every alphabet is treated as a different variable. Now, the value of (a - m), (b - m), ..., (z - m) is evaluated where `m` can be a number or another variable.

In the provided options, options 1 and 2 try to predict a polynomial expression based on the power of `m` and variables, which is not correct because the variables are diverse and we cannot aggregate them into a polynomial function.

Option 4 suggests that the expression is indeterminate or its definite value cannot be determined. Although we don`t have the exact values, we can determine a general value for the expression.

The correct answer is option 3 which suggests that the overall value of the expression is 0. This conclusion comes from the understanding that if `m` is equal to any of the alphabets from a to z, then one term of the multiplication will become zero ((x-m) will be 0 if m=x), making the whole expression equal to zero. Because multiplication with zero results in zero, regardless of the other terms.

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