Final answer:
Options A (11) and C (-2) are rational numbers and thus, when multiplied by a rational number, would yield a rational number. Option B (-1.41421356...) refers to an irrational number and would not produce a rational number when multiplied by itself. Without more information, option D cannot be evaluated.
Step-by-step explanation:
The question asks which number produces a rational number when multiplied by another number, which seems to be missing from the question. However, considering the options provided, we can understand that we need to find a number that, when multiplied by another number, results in a rational number (a number that can be expressed as the quotient of two integers).
Option A (11) is already a rational number, and any rational number multiplied by another rational number will produce a rational number. Option B (-1.41421356...) must be referring to the irrational number that is the square root of 2. This number would not produce a rational number when multiplied by itself since the product would still be irrational. Option C (-2) is a rational number, and like option A, multiplying it by another rational number would yield a rational number. Option D (T) is unclear since 'T' has not been defined, but typically if 'T' were a variable representing a rational number, then it would satisfy the condition.
Without more context, it's hard to provide a fully definitive answer, but based on the choices given, both A (11) and C (-2) would produce a rational number when multiplied by a rational number, while B would not unless it's multiplied by 0, which is a special rational number. Option D cannot be evaluated without additional information about 'T'.