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If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] then maximum value of p-q is ? Where[*] represents the greatest integer function.?
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If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] the...
Maximum value of p-q
Explanation
We are given three decimal numbers A, B, and C. We need to find the maximum value of p-q where p=[A B C] and q=[A] [B] [C] and [*] represents the greatest integer function.
The greatest integer function of a decimal number is the largest integer that is less than or equal to that decimal number. For example, [*] 3.14 = 3 and [*] 5 = 5.
Now, let's consider the values of p and q:
p = [A B C] = A + B/10 + C/100
q = [A] [B] [C] = A + [B]/10 + [C]/100
Since the greatest integer function rounds down the decimal number, we can say that [B] <= b="" and="" [c]=""><=>
Therefore, we can write:
p - q = (B - [B])/10 + (C - [C])/100
As we want to maximize p-q, we need to maximize (B - [B])/10 and (C - [C])/100.
Maximizing (B - [B])/10
Let's consider the decimal part of B:
B = [*B + (B - [*B])] = [*B] + (B - [*B])
Where [*B] is the greatest integer less than or equal to B.
Now, we can write:
B - [*B] = (B - [*B])
As B - [*B] is less than 1, we can say:
(B - [*B])/10 <=>
Therefore, the maximum value of (B - [B])/10 is 0.1 when the decimal part of B is as close to 0.9 as possible.
Maximizing (C - [C])/100
We can apply the same approach to C:
C = [*C + (C - [*C])] = [*C] + (C - [*C])
Where [*C] is the greatest integer less than or equal to C.
Now, we can write:
C - [*C] = (C - [*C])
As C - [*C] is less than 1, we can say:
(C - [*C])/100 <=>
Therefore, the maximum value of (C - [C])/100 is 0.01 when the decimal part of C is as close to 0.99 as possible.
Maximum value of p-q
Therefore, the maximum value of p-q is:
(B - [B])/10 + (C - [C])/100 <= 0.1="" +="" 0.01="">
The maximum value of p-q is
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If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] the...
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If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] then maximum value of p-q is ? Where[*] represents the greatest integer function.?
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If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] then maximum value of p-q is ? Where[*] represents the greatest integer function.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] then maximum value of p-q is ? Where[*] represents the greatest integer function.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] then maximum value of p-q is ? Where[*] represents the greatest integer function.?.
If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] then maximum value of p-q is ? Where[*] represents the greatest integer function.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] then maximum value of p-q is ? Where[*] represents the greatest integer function.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A,B,C are three decimal numbers and p=[A+B+C] and q=[A]+[B]+[C] then maximum value of p-q is ? Where[*] represents the greatest integer function.?.
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