## Questions from Math FLT

**Questions from Math FLT-06 :- **
5.Three pipes are made of different shapes . The cross-sections of the pipes are an equilateral triangle . A hexagon and a circle. The perimeter of each of these cross- sections is equal . Flow through the pipes is proportional to the area of cross-section . If it takes 8 minutes for the triangular pipe to fill up the tank , what will be the difference in the times taken by the hexagonal and circular pipes
28.if a+b+c=0 , where a ≠ b ≠ c then [(a^{2})/(2a^{2}+bc)] +[(b^{2})/(2b^{2}+ac)] + [(c^{2})/(2c^{2}+ab)] is equal to
29. The maximum possible value of y = min(1/2 - 3x^{2/4} , 5x^{2}/4) for the range 0 < x < 1 is

for 1st one (5.) - I got answer = 1 min 12 sec (approx) - but it is not matching with the answer = 30 sec
I look forward to general approach for questions like last one (29.)

**Also any general approach for question like below (form FLT-M001) -**
1. The lines y=3x and x+y=40 and the x axis bound a triangular area . Find the total number of points on or inside this triangle with integral coordinates?
11.Consider a triangle drawn on the X-Y plane with the vertices at (41,0) ,(0,41) and (0,0), each vertex being represented by its (X,Y) coordinates. The number of points with integer coordinates inside the triangle(excluding all the points on the boundary )is

## Q5. Let the Perimeter = 1

Q5. Let the Perimeter = 1 unit
Equilateral triangle: Side = 1/3
Area = √3/4 x 1/9 = √3 /36
Hexagon : Side = 1/6
Area = 6 x √3/4 x 1/36 = √3 /24
Circle : 2 π r = 1
=> r = 1 / 2 π
Area = π / 4 π ^{2} = 1/4 π
Flow is proportional to Area
So Time x Area = Constant
=> √3 /36 x 480 = √3 /24 x H
=> H = (24 x 480 ) /36 = 320 seconds
And
√3 /36 x 8 = 1/4 π x C
=> C = (480 √3 ) / 9π = 480 /3 √3 π = 290 seconds
Difference = 30 seconds