Minimum and Maximum value of identity MCQ Quiz - Objective Question with Answer for Minimum and Maximum value of identity - Download Free PDF
Last updated on Jun 17, 2025
Latest Minimum and Maximum value of identity MCQ Objective Questions
Minimum and Maximum value of identity Question 1:
Three positive integers a, b, c, have a sum of 15. Then the minimum value of (a - 2)2 + (b - 2)2 + (c - 2)2 would be
Answer (Detailed Solution Below)
Minimum and Maximum value of identity Question 1 Detailed Solution
Given:
Sum of integers: a + b + c = 15
Expression to minimize: (a - 2)2 + (b - 2)2 + (c - 2)2
Formula Used:
For a fixed sum of integers, the sum of their squares is minimized when the integers are as close to each other as possible.
Calculations:
Since a, b, c are positive integers and their sum is 15, the most balanced distribution would be to divide 15 by 3.
⇒ 15 / 3 = 5
So, we can choose a = 5, b = 5, and c = 5.
a + b + c = 15
Now, substitute these values into the expression:
⇒ Minimum value = (5 - 2)2 + (5 - 2)2 + (5 - 2)2
⇒ Minimum value = (3)2 + (3)2 + (3)2
⇒ Minimum value = 9 + 9 + 9
⇒ Minimum value = 27
∴ The minimum value of (a - 2)2 + (b - 2)2 + (c - 2)2 would be 27.
Top Minimum and Maximum value of identity MCQ Objective Questions
Minimum and Maximum value of identity Question 2:
Three positive integers a, b, c, have a sum of 15. Then the minimum value of (a - 2)2 + (b - 2)2 + (c - 2)2 would be
Answer (Detailed Solution Below)
Minimum and Maximum value of identity Question 2 Detailed Solution
Given:
Sum of integers: a + b + c = 15
Expression to minimize: (a - 2)2 + (b - 2)2 + (c - 2)2
Formula Used:
For a fixed sum of integers, the sum of their squares is minimized when the integers are as close to each other as possible.
Calculations:
Since a, b, c are positive integers and their sum is 15, the most balanced distribution would be to divide 15 by 3.
⇒ 15 / 3 = 5
So, we can choose a = 5, b = 5, and c = 5.
a + b + c = 15
Now, substitute these values into the expression:
⇒ Minimum value = (5 - 2)2 + (5 - 2)2 + (5 - 2)2
⇒ Minimum value = (3)2 + (3)2 + (3)2
⇒ Minimum value = 9 + 9 + 9
⇒ Minimum value = 27
∴ The minimum value of (a - 2)2 + (b - 2)2 + (c - 2)2 would be 27.