Let’s analyze each of the assertions and their corresponding reasons:
46.
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ASSERTION: \( \frac{3}{2}x^{-1} + 9 = 1 \) is reducible to a linear equation.
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REASON: In a linear equation, the power of \( x \) will be 1.
Analysis: The assertion is false. The equation has a term with \( x^{-1} \), which indicates a power of \( -1 \), not \( 1 \). Therefore, it cannot be reduced to a linear equation. The reason is correct that linear equations have the highest power of \( x \) as 1, but since the assertion is false, the overall statement is false.
47.
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ASSERTION: One of the rational numbers between \( \frac{1}{5} \) and \( \frac{1}{5} \) is \( \frac{9}{2} \).
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REASON: If \( x \) and \( y \) are any two rational numbers such that \( x < y \), then \( \frac{1}{2}(x + y) \) is a rational number between \( x \) and \( y \) such that \( x < \frac{1}{2}(x + y) < y \).
Analysis: The assertion is false. There cannot be a rational number between \( \frac{1}{5} \) and itself. The reason is true in general but does not apply here since the assertion is false.
48.
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ASSERTION: \( 7xy, 8xy, 4yx, 3xy \) are like terms.
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REASON: When the terms have same literal factors or variables, they are called unlike terms.
Analysis: The assertion is true. All the terms have the same variable factors (namely \( xy \)), so they are like terms. The reason is false, as it should say "like terms" instead of "unlike terms." Therefore, this statement is not correctly paired.
49.
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ASSERTION: \( -8abc + 4bac \) is a binomial.
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REASON: If an expression contains two terms, it is a binomial.
Analysis: The assertion is true; there are two terms in the expression, hence it is a binomial. The reason is also true. Since both the assertion and reason are correct, they are appropriately linked. This statement is a correct reason for the assertion.
50.
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ASSERTION: Rational numbers are not associative for multiplication.
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REASON: The associative property states that the sum or the product of three or more numbers doesn't change if they are grouped in a different way.
Analysis: The assertion is false; rational numbers are associative under multiplication (and addition). The reason is true, as it accurately describes the associative property. However, since the assertion is false, the overall statement is incorrect.
In summary:
- 46: False - False
- 47: False - True
- 48: True - False (Incorrectly paired)
- 49: True - True
- 50: False - True