If `a+b+3c=1 and a gt 0, b gt 0, c gt 0`, then the greratest value of `a^(2)b^(2)c^(2)` is

If 2a+b+3c=1 and a gt 0, b gt 0, c gt 0 , then the greatest value of a^(4)b^(2)c^(2)"_____" .

If ab=2a+3b, agt0, b gt0 , then the minimum value of ab is

If a,b,c are in H.P, where a gt c gt 0, then :

If a+c , a+b , b+c are in G.P and a,c,b are in H.P. where a , b , c gt 0 , then the value of (a+b)/(c ) is

If a lt 0 and b lt 0 , then (a +b)^(2) gt 0 .

If a gt 0,bgt 0,cgt0 and 2a +b+3c=1 , then

Let a gt 0, b gt 0 and c lt0. Then, both the roots of the equation ax^(2) +bx+c=0

Statement -1 : If a gt b gt c , then the lines represented by (a-b)x^(2)+(b-c)xy+(c-a)y^(2)=0 are real and distinct. Statement-2 : Pair of lines represented by ax^(2)+2hxy+by^(2)=0 are real and distinct if h^(2) gt ab .

If a + b =1, a gt 0,b gt 0, prove that (a + (1)/(a))^(2) + (b + (1)/(b))^(2) ge (25)/(2)

Statement I If a gt 0 and b^(2)- 4ac lt 0 , then the value of the integral int(dx)/(ax^(2)+bx+c) will be of the type mu tan^(-1) . (x+A)/(B)+C , where A, B, C, mu are constants. Statement II If a gt 0, b^(2)- 4ac lt 0 , then ax^(2)+bx +C can be written as sum of two squares .