Question
What is the maximum value of (a + b) if '5a346b8' is
divisible by 12?Solution
A number is divisible by 12 if it divisible by both 3 and 4.
A number is divisible by 4 when last two digits of the number is divisible by 4.
'b8' is divisible by 4 when 'b' = 0, 2, 4, 6 or 8
Since, we have to find maximum value, so 'b' = 8.
A number is divisible by 3 when sum of its digit is divisible by 3.
So, (5 + a + 3 + 4 + 6 + 8 + 8) = (34 + a) must be divisible by 3.
So, 'a' = 2, 5 or 8
Since, we have to find maximum value, so 'a' = 8.
Therefore, required value = 8 + 8 = 16
I. x2 + 24x + 143 = 0
II. y2 + 12y + 35 = 0
I: 2x² - 8x + 6 = 0
II: 3y² - 12y + 9 = 0
I. 2x2 + 5x + 2 = 0
II. 4y2 = 1
In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y.
I. x
I. 7p + 8q = 80
II. 9p – 5q = 57
I. 2y2 - 15y + 18 = 0
II. 2x2 + 9x - 18 = 0
I. (4x-5)3Â +Â 1/(4x-5)3Â = 2
II. 2[(y+1/y)2- 2]- 9(y+1/y)= -14
If 3x – 2y = 10 and xy = 11, the value of 27x³ – 8y³ is __________.
I. 9x2 + 45x + 26 = 0
II. 7y2 – 59y − 36 = 0
I. 35x² - 24x – 35 = 0
II. 72y² - 145y + 72 = 0
