If `xy=a^2 and S = b^2x + c^2y` where `a, b and c` are constants then the minimum value of S is

If xy=a^(2) and S=b^(2)x+c^(2)y where a,b and c are constants then the minimum value of S is

Find the order of the differential equation corresponding to (i) y = c(x-c)^(2) where c is an arbitrary constant. (ii) y = Ae^(x) + Be^(3x) + Ce^(5x) where A, B, C are arbitrary constant. (iii) xy = c e^(x) + b e^(-x) + x^(2) where b, c are arbitrary constants. (iv) The family of all circles in the xy-plane with centre at the origin.

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If a , ba n dc are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If a , ba n dc are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

Consider the points O(0,0), A(0,1) , and B(1,1) in the x-y plane. Suppose that points C(x,1) and D(1,y) are chosen such that 0ltxlt1 . And such that O,C, and D are collinear. Let the sum of the area of triangles OAC and BCD be denoted by S. Then which of the following is/are correct?. (a) Minimum value of S is irrational lying in ( 1 / 3 , 1 / 2 ) (b) Minimum value of S is irrational in ( 2 / 3 , 1 ) . (c) The value of x for the minimum value of S lies in ( 2 / 3 , 1 ) . (d) The value of x for the minimum values of S lies in ( 1 / 3 , 1 / 2 ) .

lfequations (a + 2)x^2 + bx + c = 0& 2x^2 + 3x + 4=0 have a common root where a, b, c in N, then- (A) b^2 -4ac lt 0 (B) minimum value of a +b+ c is 16 (C) b^2 gt 4ac+8c (D) minimum value of a + b + c = 7 lf one ofthe roots of x^2-bx + c = 0; b, c in Q

If y=((ax+b))/((x^2+c)), and (2xy'+y)y''=k(xy''+y'')y'' , where a,b,c are constants and y'denote differentiation w.r.t.x then the value of k is