The length of the tangent from the point `(4, 5)` to the circle `x^2 + y^2 + 2x - 6y = 6` is : (A) `sqrt(13)` (B) `sqrt(38)` (C) `2sqrt(2)` (D) `2sqrt(13)`

The length of the perpendicular drawn from the point (3,-1,11) to the line x/2=(y-2)/3=(z-3)/4 is (A) sqrt(33) (B) sqrt(53 (C) sqrt(66) (D) sqrt(29)

The shortest distance between the parabola y^2 = 4x and the circle x^2 + y^2 + 6x - 12y + 20 = 0 is : (A) 0 (B) 1 (C) 4sqrt(2) -5 (D) 4sqrt(2) + 5

The image of the centre of the circle x^2 + y^2 = 2a^2 with respect to the line x + y = 1 is : (A) (sqrt(2), sqrt(2) (B) (1/sqrt(2) , sqrt(2) ) (C) (sqrt(2), 1/sqrt(2)) (D) none of these

The distance of the point (2,1,-1) from the plane x-2y+4z=9 is (A) sqrt(13)/21 (B) 13/21 (C) 13/sqrt(21) (D) sqrt(13/21)

The distance of the point (2,1,-1) from the plane x-2y+4z=9 is (A) sqrt(13)/21 (B) 13/21 (C) 13/sqrt(21) (D) sqrt(13/21)

The length of the perpendicular drawn from the point P(3,4,5) on y -axis is a.3sqrt(2) b.5 c.sqrt(113) d.5sqrt(2) e.sqrt(34)

The length of perpendicular from the poit (1,-1,2) on the line (x+1)/2=(2-y)/3=(z+2)/4 is (A) 0 (B) sqrt(6) (C) sqrt(21) (D) none of these

The length of the tangent of the curve y=x^(2)+2 at (1, 3) is (A) sqrt(5) (B) 3sqrt(5) (C) 3/2 (D) (3sqrt(5))/(2)

The length of the tangent of the curve y=x^(2)+2 at (1 3) is (A) sqrt(5) (B) 3sqrt(5) (C) 3/2 (D) (3sqrt(5))/(2)

The line 2x-y+1=0 is tangent to the circle at the point (2,5) and the center of the circle lies on x-2y=4. The radius of the circle is 3sqrt(5)(b)5sqrt(3)(c)2sqrt(5)(d)5sqrt(2)