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Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?
- a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1
- b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1
- c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1
- d)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m +1
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where...
Taking lowest possible positive value of m i.e. 1 .
Such that a + b + c + d = 5, so atleast one of them must be grater than 1, take a = b = c = 1 and d = 2
we get a2 + b2 + c2 + d2 = 7 which is equal to 4m2 + 2m + 1 for other values it is greater
than 4m2 + 2m +1.
than 4m2 + 2m +1.
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Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where...
Explanation:
Given that a, b, c, d are four integers such that a + b + c + d = 4m + 1, where m is a positive integer, we need to determine which of the given options is necessarily true regarding the minimum and maximum possible values of a^2 + b^2 + c^2 + d^2.
Minimum Possible Value:
To find the minimum possible value of a^2 + b^2 + c^2 + d^2, we need to minimize each of the integers a, b, c, and d. Since the minimum value of a single integer squared is 0, the minimum possible value of a^2 + b^2 + c^2 + d^2 occurs when each integer is 0.
Therefore, the minimum possible value of a^2 + b^2 + c^2 + d^2 is 0.
Maximum Possible Value:
To find the maximum possible value of a^2 + b^2 + c^2 + d^2, we need to maximize each of the integers a, b, c, and d. Since the maximum value of a single integer squared is infinity, there is no upper bound on the maximum possible value of a^2 + b^2 + c^2 + d^2.
Comparing with the Options:
Now let's compare the minimum and maximum possible values of a^2 + b^2 + c^2 + d^2 with the options given:
a) The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 - 2m + 1
b) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
c) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 - 2m + 1
d) The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
Comparing the options with our findings, we can see that option d) aligns with the minimum possible value of 0, which we determined earlier.
Therefore, the correct answer is option d) The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1.
Given that a, b, c, d are four integers such that a + b + c + d = 4m + 1, where m is a positive integer, we need to determine which of the given options is necessarily true regarding the minimum and maximum possible values of a^2 + b^2 + c^2 + d^2.
Minimum Possible Value:
To find the minimum possible value of a^2 + b^2 + c^2 + d^2, we need to minimize each of the integers a, b, c, and d. Since the minimum value of a single integer squared is 0, the minimum possible value of a^2 + b^2 + c^2 + d^2 occurs when each integer is 0.
Therefore, the minimum possible value of a^2 + b^2 + c^2 + d^2 is 0.
Maximum Possible Value:
To find the maximum possible value of a^2 + b^2 + c^2 + d^2, we need to maximize each of the integers a, b, c, and d. Since the maximum value of a single integer squared is infinity, there is no upper bound on the maximum possible value of a^2 + b^2 + c^2 + d^2.
Comparing with the Options:
Now let's compare the minimum and maximum possible values of a^2 + b^2 + c^2 + d^2 with the options given:
a) The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 - 2m + 1
b) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
c) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 - 2m + 1
d) The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
Comparing the options with our findings, we can see that option d) aligns with the minimum possible value of 0, which we determined earlier.
Therefore, the correct answer is option d) The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1.
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Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer?
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Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer? for CLAT 2024 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CLAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer?.
Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer? for CLAT 2024 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CLAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer?.
Solutions for Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CLAT.
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Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?a)The minimum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1b)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 + 2m + 1c)The maximum possible value of a2 + b2 + c2 + d2 is 4m2 - 2m + 1d)The minimum possible value of a2 + b2+ c2 + d2is 4m2 + 2m +1Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CLAT tests.
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