If `m` is the minimum value of `f(x , y)=x^2-4x+y^2+6y` when `xa n dy` are subjected to the restrictions `0lt=xlt=1a n d0lt=ylt=1,` then the value of `|m|` is________

If the area of the region {(x , y):0lt=ylt=x^2+1,0lt=ylt=x+1,0lt=xlt=2} is A , then the value of 3A-17 is____

Let xa n dy be two real variable such that x >0a n dx y=1 . Find the minimum value of x+y .

Suppose xa n dy are real numbers and that x^2+9y^2-4x+6y+4=0 . Then the maximum value of ((4x-9y))/2 is__________

Find the maxima and minima of the function y=x(x-1)^2,0lt=xlt=2.

If |__.__| denotes the greatest integer less than or equal to the real number under consideration and -1lt=xlt0,0lt=ylt1,1lt=zlt2 , then the value of the determinant |(|__x__|+1,|__y__|,|__z__|),(|__x__|,|__y__|+1,|__z__|),(|__x__|,|__y__|,|__z__|+1)| is

If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, ((1)/(2) lt m lt 3) , then the values of m are

Consider a circle x^2+y^2+a x+b y+c=0 lying completely in the first quadrant. If m_1a n dm_2 are the maximum and minimum values of y/x for all ordered pairs (x ,y) on the circumference of the circle, then the value of (m_1+m_2) is

Let the lines (y-2)=m_1(x-5) and (y+4)=m_2(x-3) intersect at right angles at P (where m_1a n dm_2 are parameters). If the locus of P is x^2+y^2gx+fy+7=0 , then the value of |f+g| is__________

The solution of the differential equation e^(-x) (y+1) dy +(cos^(2) x - sin 2x) y (dx) = 0 subjected to the condition that y = 1 when x = 0 is

The area of the region of the plane bounded by max(|x|,|y|)lt=1a n dx ylt=1/2 is