Let's analyze each assertion and reason:
46.
- ASSERTION: \(2x^2 + 9 = 1\) is reducible to a linear equation.
- REASON: In a linear equation, the power of \(x\) will be 1.
- Evaluation: The assertion is incorrect because \(2x^2 + 9 = 1\) is a quadratic equation, not linear. The reason is also flawed as it doesn't explain the reducibility in terms of what makes an equation linear. Hence, both the assertion and reason are false.
47.
- ASSERTION: One of the rational numbers between \(x\) and \(y\) is \(\frac{x+y}{2}\).
- REASON: If \(x\) and \(y\) are any two rational numbers such that \(x < y\), then \(3(x + 3)\) is a rational number between \(x\) and \(y\) such that (x < 3(x+3) < y.
- Evaluation: The assertion is true; the rational number between two rational numbers \(x\) and \(y\) can indeed be \(\frac{x+y}{2}\). The reason is not true as it suggests a specific expression that does not necessarily yield a number between \(x\) and \(y\); it may not be valid depending on \(x\) and \(y\). Therefore, assertion is true, but reason is false.
48.
- ASSERTION: \(7xy, 8xy, 4xy, 3xy\) are like terms.
- REASON: When the terms have the same literal factors or variables, they are called unlike terms.
- Evaluation: The assertion is true because all the terms have the same variables \(xy\), hence they are like terms. However, the reason is incorrect because it misdefines like terms and states that they are called unlike terms, which is wrong. Thus, assertion is true, but reason is false.
49.
- ASSERTION: \(-8abc + 4bac\) is a binomial.
- REASON: If an expression contains two terms, it is a binomial.
- Evaluation: The assertion is true because \(-8abc + 4bac\) does consist of two terms, making it a binomial. The reason is also true as a binomial is defined as an expression with exactly two terms. Thus, both assertion and reason are true.
50.
- ASSERTION: Rational numbers are not associative for multiplication.
- 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.
- Evaluation: The assertion is false because rational numbers do obey the associative property for multiplication. The reason correctly explains the associative property, but because it is false that rational numbers are not associative, the assertion is false. Therefore, assertion is false, but reason is true.
Summary:
- 46: Both Assertion and Reason are false.
- 47: Assertion is true, Reason is false.
- 48: Assertion is true, Reason is false.
- 49: Both Assertion and Reason are true.
- 50: Assertion is false, Reason is true.
1 answer