Let's analyze each assertion and its corresponding reason.
### Question 6:
- Assertion: 0.189 is a terminating decimal.
- Reason: A decimal in which a digit or set of digits is repeated periodically is called a repeating or recurring decimal.
Analysis:
- The assertion states that 0.189 is a terminating decimal. A terminating decimal is a decimal that ends after a finite number of digits.
- The reason provided describes a repeating or recurring decimal, which is a decimal where a digit or group of digits repeat infinitely. Examples include 0.333... and 0.142857142857...
Conclusion for Question 6:
- The assertion is true because 0.189 is indeed a terminating decimal.
- The reason is also true; it correctly defines a repeating or recurring decimal.
- However, the reason does not provide an explanation for the assertion.
Correct Answer for Question 6: (b) Both assertion and reason are true but reason is not the correct explanation of assertion.
### Question 7:
- Assertion: The zeroes of the polynomial [tex]\( f(x) = x^2 - 5x + 6 \)[/tex] are 3 and 2.
- Reason: A linear polynomial has exactly one zero.
Analysis:
- The assertion states that the zeroes of the quadratic polynomial [tex]\( x^2 - 5x + 6 \)[/tex] are 3 and 2. We can verify this by factoring the polynomial: [tex]\( x^2 - 5x + 6 = (x - 3)(x - 2) \)[/tex]. Setting each factor to zero, we get the solutions [tex]\( x = 3 \)[/tex] and [tex]\( x = 2 \)[/tex].
- The reason states that a linear polynomial has exactly one zero, which is indeed true. A linear polynomial of the form [tex]\( ax + b = 0 \)[/tex] will have exactly one solution, [tex]\( x = -\frac{b}{a} \)[/tex].
Conclusion for Question 7:
- The assertion is true as the solutions to the polynomial are indeed 3 and 2.
- The reason is true; a linear polynomial does have exactly one zero.
- However, the reason is unrelated to the assertion, making the reason false in the context of explaining the assertion.
Correct Answer for Question 7: (c) Assertion is true, but reason is false.
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### Summary:
Assertions and reasons evaluated in each question match the conclusions derived above.
- For question 6, the correct answer is (b).
- For question 7, the correct answer is (c).
