Class 6 Exam > Class 6 Questions > Which of the following statements is incorrec...
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Which of the following statements is incorrect?
- a)The square of any positive integer is always positive.
- b)A parallelogram with four right angles is a rectangle.
- c)The sum of any two even numbers is always even.
- d)The cube of an even number is always odd.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which of the following statements is incorrect?a)The square of any pos...
The square of any positive integer is always positive, so Option A is correct.
A parallelogram with four right angles is indeed a rectangle, making Option B correct.
The sum of any two even numbers is always even, so Option C is correct.
The cube of an even number is not always odd; it is always even, making Option D incorrect.
A parallelogram with four right angles is indeed a rectangle, making Option B correct.
The sum of any two even numbers is always even, so Option C is correct.
The cube of an even number is not always odd; it is always even, making Option D incorrect.
Most Upvoted Answer
Which of the following statements is incorrect?a)The square of any pos...
Understanding the Incorrect Statement
The statement in question is:
“The cube of an even number is always odd.”
This statement is incorrect. Let's break down why.
Definition of Even Numbers
- Even numbers are integers that can be divided by 2 without a remainder.
- Examples include: 0, 2, 4, 6, 8, etc.
Calculating the Cube of an Even Number
- When you cube an even number (multiply it by itself three times), the result is also even.
- Example:
- If we take 2 (an even number), its cube is 2 x 2 x 2 = 8, which is even.
- If we take 4, its cube is 4 x 4 x 4 = 64, which is also even.
General Rule for Even Numbers
- The cube of any even number can be represented as (2n)³, where n is an integer.
- This simplifies to 8n³, which is still even since it can be divided by 2.
Conclusion
- Thus, the cube of an even number is never odd; it is always even.
- Therefore, option D is indeed the incorrect statement among the choices provided.
This distinction between even and odd numbers is fundamental in mathematics, and understanding it helps clarify many concepts in number theory.
The statement in question is:
“The cube of an even number is always odd.”
This statement is incorrect. Let's break down why.
Definition of Even Numbers
- Even numbers are integers that can be divided by 2 without a remainder.
- Examples include: 0, 2, 4, 6, 8, etc.
Calculating the Cube of an Even Number
- When you cube an even number (multiply it by itself three times), the result is also even.
- Example:
- If we take 2 (an even number), its cube is 2 x 2 x 2 = 8, which is even.
- If we take 4, its cube is 4 x 4 x 4 = 64, which is also even.
General Rule for Even Numbers
- The cube of any even number can be represented as (2n)³, where n is an integer.
- This simplifies to 8n³, which is still even since it can be divided by 2.
Conclusion
- Thus, the cube of an even number is never odd; it is always even.
- Therefore, option D is indeed the incorrect statement among the choices provided.
This distinction between even and odd numbers is fundamental in mathematics, and understanding it helps clarify many concepts in number theory.
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Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer?.
Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 6.
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Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Which of the following statements is incorrect?a)The square of any positive integer is always positive.b)A parallelogram with four right angles is a rectangle.c)The sum of any two even numbers is always even.d)The cube of an even number is always odd.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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