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Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.
Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Direction : In the following questions, a statement of assertion (A) i...
if a,b,c are in AP, then b − a = c − b
a + c = 2b
For 1/bc, 1/ac, 1/ab
= 1/ac - 1/bc = b - a / abc
1/ac - 1/ac = c - a/abc
From above two equations,
1/bc, 1/ac, 1/ab are also in AP.
And their common difference is divided by abc since numbers are also divided by abc.
So, if a,b,c are in AP and you divide the numbers by their product abc they will remain in AP.
Most Upvoted Answer
Direction : In the following questions, a statement of assertion (A) i...
Assertion : Let the positive numbers a, b, c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.
Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.
To understand and prove the given assertion and reason, let's break it down into different parts.
**Definition of an Arithmetic Progression (A.P.)**
An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant.
**Proof of Assertion**
Let's assume that a, b, and c are positive numbers in A.P. with a common difference of d.
The terms in the A.P. are:
a, a + d, a + 2d, ...
To prove that 1/bc, 1/ac, and 1/ab are also in A.P., we need to show that the difference between consecutive terms is constant.
The terms when each term is divided by abc are:
1/bc, 1/(a+d)c, 1/(a+2d)c, ...
We need to find the difference between consecutive terms:
(1/(a+d)c) - (1/bc) = (bc - ac - d*c) / (bc(a+d)c)
= (b - a - d) / (a+d)bc
(1/(a+2d)c) - (1/(a+d)c) = [(a+d)c - (a+2d)c] / [(a+d)c(a+2d)c]
= -d / (a+d)(a+2d)c
As we can see, the difference between consecutive terms is constant and equal to -d / (a+d)(a+2d)c.
Therefore, the terms 1/bc, 1/(a+d)c, 1/(a+2d)c, ... are also in A.P.
**Explanation of Reason**
The reason states that if each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.
To understand this reason, let's consider an example:
Consider the A.P. 2, 5, 8, 11, ...
If we divide each term of this A.P. by 2*5*8 (abc), we get the sequence:
(2*5*8)/2 = 20, (5*8*11)/(5*8) = 11, ...
As we can see, the resulting sequence 20, 11, ... is also in A.P. with a common difference of 11-20 = -9.
Therefore, the reason is correct and supports the assertion.
**Conclusion**
Both the assertion and reason are true, and the reason correctly explains the assertion.
Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.
To understand and prove the given assertion and reason, let's break it down into different parts.
**Definition of an Arithmetic Progression (A.P.)**
An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant.
**Proof of Assertion**
Let's assume that a, b, and c are positive numbers in A.P. with a common difference of d.
The terms in the A.P. are:
a, a + d, a + 2d, ...
To prove that 1/bc, 1/ac, and 1/ab are also in A.P., we need to show that the difference between consecutive terms is constant.
The terms when each term is divided by abc are:
1/bc, 1/(a+d)c, 1/(a+2d)c, ...
We need to find the difference between consecutive terms:
(1/(a+d)c) - (1/bc) = (bc - ac - d*c) / (bc(a+d)c)
= (b - a - d) / (a+d)bc
(1/(a+2d)c) - (1/(a+d)c) = [(a+d)c - (a+2d)c] / [(a+d)c(a+2d)c]
= -d / (a+d)(a+2d)c
As we can see, the difference between consecutive terms is constant and equal to -d / (a+d)(a+2d)c.
Therefore, the terms 1/bc, 1/(a+d)c, 1/(a+2d)c, ... are also in A.P.
**Explanation of Reason**
The reason states that if each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.
To understand this reason, let's consider an example:
Consider the A.P. 2, 5, 8, 11, ...
If we divide each term of this A.P. by 2*5*8 (abc), we get the sequence:
(2*5*8)/2 = 20, (5*8*11)/(5*8) = 11, ...
As we can see, the resulting sequence 20, 11, ... is also in A.P. with a common difference of 11-20 = -9.
Therefore, the reason is correct and supports the assertion.
**Conclusion**
Both the assertion and reason are true, and the reason correctly explains the assertion.
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Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer?
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Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer?.
Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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Here you can find the meaning of Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Let the positive numbers a,b,c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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