Mathematics
a, b and c are in continued proportion.
Assertion (A): a is first proportion.
Reason (R): The first proportion is always the smallest of the three numbers.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Ratio Proportion
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Answer
Three numbers a, b, c are in continued proportion if:
⇒ b2 = ac
Here, a is called the first proportion, b is the mean (or geometric mean), c is the third proportion.
So, assertion (A) is true.
Lets take an example, a = 9, b = 6 and c = 4.
When three numbers a, b, c are in continued proportion if:
Here, a = 9 is first proportion but it is not the smallest number among three.
So, reason (R) is false.
Thus, Assertion (A) is true, but Reason (R) is false.
Hence, option 1 is the correct option.
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Related Questions
A mixture of paint is prepared by mixing 2 parts of red pigments with 5 parts of the base. Using the given information in the following table, find the values of a, b and c to get the required mixture of paint.
Parts of red pigment Parts of base 2 5 4 a b 12.5 6 c a = 10, b = 10, c = 10
a = 5, b = 2, c = 5
a = 10, b = 5, c = 10
a = 10, b = 5, c = 15
Assertion (A): Mean proportion between is 5.
Reason (R): Mean proportion between two numbers is the positive square root of their product.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
a, b, c and d are in proportion.
Assertion (A): a + b, a - b, c + d and c - d are in proportion.
Reason (R): .
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
a, b, c and d are in proportion.
Assertion (A): a - c, c, b - d, d are in proportion.
Reason (R): a, c, b and d are in proportion.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).