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Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
N is a natural number
Quantity A: Sum of cubes of first N odd natural numbers
Quantity B: Sum of cubes of first (N - 1) even natural numbers
- a)Quantity A > Quantity B
- b)Quantity A < quantity="" />
- c)Quantity A ≥ Quantity B
- d)Quantity A ≤ Quantity B
- e)Quantity A = Quantity B OR relationship cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Directions: Given below are two quantities named A and B. Based on th...
For N = 2, A = 1 + 27 = 28, and B = 8
For N = 3, A = 1 + 27 + 125, and B = 8 + 64
In both cases, A > B
We know that Nth odd natural number will always be lesser than Nth even natural number, but it will be greater than (N - 1)th even natural number.
The same will hold true for their cubes as we are taking cubes of positive numbers.
The same will hold true when we compare cubes of (N - 2)th odd natural number and (N - 3)th even natural number.
When we sum all of them, we find that A > B.
Hence, the correct option is (A).
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Community Answer
Directions: Given below are two quantities named A and B. Based on th...
To determine the relation between Quantity A and Quantity B, let's analyze the given information step by step.
Quantity A: Sum of cubes of first N odd natural numbers
To calculate the sum of the cubes of the first N odd natural numbers, we need to find the cube of each odd number from 1 to N and then add them together.
Quantity B: Sum of cubes of first (N - 1) even natural numbers
To calculate the sum of the cubes of the first (N - 1) even natural numbers, we need to find the cube of each even number from 2 to (N - 1) and then add them together.
Now, let's compare the two quantities:
- When N = 1:
- Quantity A: Sum of cubes of the first 1 odd natural number = (1^3) = 1
- Quantity B: Sum of cubes of the first (1 - 1) even natural numbers = Sum of cubes of the first 0 even natural numbers = 0
- Quantity A > Quantity B
- When N = 2:
- Quantity A: Sum of cubes of the first 2 odd natural numbers = (1^3) + (3^3) = 1 + 27 = 28
- Quantity B: Sum of cubes of the first (2 - 1) even natural numbers = Sum of cubes of the first 1 even natural number = (2^3) = 8
- Quantity A > Quantity B
- When N = 3:
- Quantity A: Sum of cubes of the first 3 odd natural numbers = (1^3) + (3^3) + (5^3) = 1 + 27 + 125 = 153
- Quantity B: Sum of cubes of the first (3 - 1) even natural numbers = Sum of cubes of the first 2 even natural numbers = (2^3) + (4^3) = 8 + 64 = 72
- Quantity A > Quantity B
By analyzing the above cases, we can observe that for any value of N, Quantity A is always greater than Quantity B. Hence, the correct answer is option A: Quantity A > Quantity B.
In mathematical notation, we can represent this relationship as: Quantity A > Quantity B.
Quantity A: Sum of cubes of first N odd natural numbers
To calculate the sum of the cubes of the first N odd natural numbers, we need to find the cube of each odd number from 1 to N and then add them together.
Quantity B: Sum of cubes of first (N - 1) even natural numbers
To calculate the sum of the cubes of the first (N - 1) even natural numbers, we need to find the cube of each even number from 2 to (N - 1) and then add them together.
Now, let's compare the two quantities:
- When N = 1:
- Quantity A: Sum of cubes of the first 1 odd natural number = (1^3) = 1
- Quantity B: Sum of cubes of the first (1 - 1) even natural numbers = Sum of cubes of the first 0 even natural numbers = 0
- Quantity A > Quantity B
- When N = 2:
- Quantity A: Sum of cubes of the first 2 odd natural numbers = (1^3) + (3^3) = 1 + 27 = 28
- Quantity B: Sum of cubes of the first (2 - 1) even natural numbers = Sum of cubes of the first 1 even natural number = (2^3) = 8
- Quantity A > Quantity B
- When N = 3:
- Quantity A: Sum of cubes of the first 3 odd natural numbers = (1^3) + (3^3) + (5^3) = 1 + 27 + 125 = 153
- Quantity B: Sum of cubes of the first (3 - 1) even natural numbers = Sum of cubes of the first 2 even natural numbers = (2^3) + (4^3) = 8 + 64 = 72
- Quantity A > Quantity B
By analyzing the above cases, we can observe that for any value of N, Quantity A is always greater than Quantity B. Hence, the correct answer is option A: Quantity A > Quantity B.
In mathematical notation, we can represent this relationship as: Quantity A > Quantity B.
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Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2024 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2024 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Banking Exams.
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Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.N is a natural numberQuantity A: Sum of cubes of first N odd natural numbersQuantity B: Sum of cubes of first (N - 1) even natural numbersa)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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