Prove that the greatest value of xy is
`c^(3)//sqrt(ab)`, if `a^(2) x^(4) + b^(2) y^(4) = c^(6)`.

Prove that the greatest value of x y is c^3//sqrt(2a b)dot if a^2x^4+b^4y^4=c^6dot

If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (a) (c^2)/(sqrt(a b)) (b) (c^3)/(a b) (c) (c^3)/(sqrt(2a b)) (d) (c^3)/(2a b)

If (alpha,beta) is a point on the circle whose center is on the x-axis and which touches the line x+y=0 at (2,-2), then the greatest value of alpha is (a) 4-sqrt(2) (b) 6 (c) 4+2sqrt(2) (d) +sqrt(2)

The greatest value of sin^4theta+cos^4thetai s 1/2 (b) 1 (c) 2 (d) 3

The greatest integral value of a such that sqrt( 9 - a^2 + 2x - x^2) >= sqrt(16 - x^2) for at least one positive value of x is (a) 3 (b) 4 (c) 6 (d) 7

Prove that {:[( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) ]:} =4a^(2) b^(2) c^(2)

The value of lim_(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is 4 (b) 1/2 (c) 2 (d) 1/4

If a variable tangent to the curve x^2y=c^3 makes intercepts a , bonx-a n dy-a x e s , respectively, then the value of a^2b is 27c^3 (b) 4/(27)c^3 (c) (27)/4c^3 (d) 4/9c^3

Prove that the minimum value of ((a+x)(b+x))/((c+x))a ,b > c ,x >-c is (sqrt(a-c)+sqrt(b-c))^2

The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x ,y ,z is (a) sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) 8sqrt(2)