The shortest distance form the point (1,2,-1) to the surface of the sphere `(x+1)^(2)+(y+2)^(2)+(z-1)^(2)=6` (A) `3sqrt(6)` (B) `2sqrt(6)` (C) `sqrt(6)` (D) 2

The shortest distance from the origin to a variable point on the sphere (x-2)^(2)+(y-3)^(2)+(z-6)^(2)=1 is-

The minimum value of the function f(x)=2tan x+3cot x where x in(0 (pi)/(2)) is (A) sqrt(6) (B) 2sqrt(6) (C) 6sqrt(2) (D) 12

The minimum value of the function f(x)=2tan x+3cot x where x in(0, (pi)/(2)) is (A) sqrt(6) (B) 2sqrt(6) (C) 6sqrt(2) (D) 12

The minimum value of the function f(x)=2tan x+3cot x where x in(0 (pi)/(2)) is (A) sqrt(6) (B) 2sqrt(6) (C) 6sqrt(2) (D) 12

The shortest distance between the line yx=1 and the curve x=y^(2) is (A)(3sqrt(2))/(8) (B) (2sqrt(3))/(8) (C) (3sqrt(2))/(5) (D) (sqrt(3))/(4)

The point,at shortest distance from the line x+y=10 and lying on the ellipse x^(2)+2y^(2)=6, has coordinates (A) (sqrt(2),sqrt(2)) (B) (0,sqrt(3))(C)(2,1)(D)(sqrt(5),(1)/(sqrt(2)))

The shortest distance between the line 1+x=2y=-12z and x=y+2=6z-6 is

The value of sin(sin^-1 (1/2)+ cos ^-1 (1/3)) is equal to (A) (sqrt(3)+sqrt(8)/6 (B) (1+2sqrt(6))/6 (C) - (1+2sqrt(6))/6 (D) 0