Show that the greatest value of `xyz (d - ax - by - cz)` is `(d^(4))/(4^(4)abc)` . (Given `a b,c,x,v,z gt 0 , ax +by+cz lt d)`

If |z-4+3i|le3, then the least value of |z|= (A) 2 (B) 3 (C) 4 (D) 5

If |z-4+3i|le3, then the least value of |z|= (A) 2 (B) 3 (C) 4 (D) 5

(i) If a + b + c = 5 , (a, b, c gt 0) , find the greatest value of a^(3) b^(2) c^(4) . (ii) Find the greatest value of (5 - x)^(2) (x -2)^(2) , given 2 lt x lt 5 .

distance between the parallel planes ax+by+ cz + d =0 and ax+by + cz + d' =0 is

The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is a. 3abc b. 6abc c. abc d. 4abc

Show that the distance between the parallel lines ax+by+c=0 and k(ax+by)+d=0 is |(c-(d)/(k))/(sqrt(a^(2)+b^(2)))|

Let A denotes the set of values of x for which (x+2)/(x-4) le0 and B denotes the set of values of x for which x^2-ax-4 le 0 . If B is the subset of A then a cannot take integral value (a) 0, (b) 1 (c) 2 (d) 3

Let A denotes the set of values of x for which (x+2)/(x-4) le0 and B denotes the set of values of x for which x^2-ax-4 le 0 . If B is the subset of A then a cannot take integral value (a) 0, (b) 1 (c) 2 (d) 3

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then (a) P(x) gt 0 for all x in R and Q(x) lt 0 for all x in R . (b) P(x) lt 0 for all x in R and Q(x) gt 0 for all x in R . (c) neither P(x) gt 0 for all x in R nor Q(x) gt 0 for all x in R . (d) exactly one of P(x) or Q(x) is positive for all real x.

If the greatest valueof |z| such that |z-3-4i|lea is equal to the least value of x^4+x+ 5/x in (0,oo) then a= (A) 1 (B) 4 (C) 3 (D) 2