If `a+b+c=6` then the maximum value of `sqrt(4a+1)+sqrt(4b+1)+sqrt(4c+1)=`

If a/sqrt(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the family of lines sqrt(a)x+sqrt(b)y+sqrt(c)=0 passes though the fixed point given by (a) (1,1) (b) (1,-2) (c) (-1,2) (d) (-1,1)

If a/sqrt(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the family of lines sqrt(a)x+sqrt(b)y+sqrt(c)=0 passes though the fixed point given by (a) (1,1) (b) (1,-2) (c) (-1,2) (d) (-1,1)

If a/sqrt(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the family of lines sqrt(a)x+sqrt(b)y+sqrt(c)=0 passes though the fixed point given by (a) (1,1) (b) (1,-2) (c) (-1,2) (d) (-1,1)

If the point (a,b) on the curve y= sqrt(x) is close to the point (1,0) , then the value of ab is a) 1/2 b) (sqrt2)/(2) c) 1/4 d) (sqrt2)/(4)

If |z-4/z|=2 then the greatest value of |z| is (A) sqrt(5)-1 (B) sqrt(5)+1 (C) sqrt(5) (D) 2

The value of (sqrt(8))^(1/3) a.2 b.8 c.4 d.sqrt(2)

If a,b,c, are in A.P then prove that (1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a)),(1)/(sqrt(a)+sqrt(b)) are in A.P.

If int (sqrttanx + sqrtcotx) dx = a tan^-1 ((tan x - 1)/sqrt(b tan x)) + c , then the value of sqrt(a^4 + b^5) must be