If `a , b >0` , then minimum value of `y=(b^2)/(a-x)+(a^2)/x` in `(0,a)` is (a)`(a+b)/a` (b) `(a b)/(a+b)` (c)`1/a+1/b` (d) `((a+b)^2)/a`

If a b c=0 , then find the value of {(x^a)^b}^c (a)1 (b) a (c)b (d) c

If a x+b y+c z=p , then minimum value of x^2+y^2+z^2 is (p/(a+b+c))^2 (b) (p^2)/(a^2+b^2+c^2) (a^2+b^2+c^2)/(p^2) (d) ((a+b+c)/p)^2

If agt0, bgt0, cgt0 and the minimum value of a^2(b+c)+b^2(c+a)+c^2(a+b) is kabc, then k is (A) 1 (B) 3 (C) 6 (D) 4

Minimum value of (b+c)//a+(c+a)//b+(a+b)//c (for real positive numbers a ,b ,c) is (a) 1 (b) 2 (c) 4 (d) 6

If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.

If a+b+c=0 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) 1 (c) -1 (d) 3

The value of c for which the equation a x^2+2b x+c=0 has equal roots is (a) (b^2)/a (b) (b^2)/(4a) (c) (a^2)/b (d) (a^2)/(4b)

Find the minimum value of (a+1/a)^(2) +(b+1/b)^(2) where a gt 0, b gt 0 and a+b = sqrt(15)

If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x is equal to [a , b , in (0,1)] (a) (a-b)/(1+a b) (b) b/(1+a b) (c) b/(1+a b) (d) (a+b)/(1-a b)

Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b varies, the range of m(b) is (A) [0,1] (B) (0,1/2] (C) [1/2,1] (D) (0,1]