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 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 length of the chord of the parabola y^(2)=x which is bisected at the point (2,1) is (a) 2sqrt(3)( b) 4sqrt(3)(c)3sqrt(2) (d) 2sqrt(5)

The radius of the circle passing through the points (1, 2), (5, 2) and (5, -2) is : (A) 5sqrt(2) (B) 2sqrt(5) (C) 3sqrt(2) (D) 2sqrt(2)

The length of the straight line x-3y=1 intercepted by the hyperbola x^(2)-4y^(2)=1 is (6)/(sqrt(5)) b.3sqrt((2)/(5))c*6sqrt((2)/(5))d .none of these

The eccentricity of the ellipse 4x^(2)+9y^(2)=36 is (1)/(2sqrt(3)) b.(1)/(sqrt(3)) c.(sqrt(5))/(3) d.(sqrt(5))/(6)

The distance between the parallel lnes y=2x+4 and 6x-3y-5 is (A) 1 (B) 17/sqrt(3) (C) 7sqrt(5)/15 (D) 3sqrt(5)/15

The equation of tangent to the curve y=int_(x^(2))^(x^(3))(dt)/(sqrt(1+t^(2))) at x=1 is sqrt(3)x+1=y (b) sqrt(2)y+1=x sqrt(3)x+y=1(d)sqrt(2)y=x

Length of the chord of contact of (2,5) with respect to y^(2)=8x is (3sqrt(41))/(2) (2sqrt(17))/(3) (7sqrt(3))/(5) (5sqrt(3))/(7)

Minimum distance of a point ((3)/(2),0) from the curve y=sqrt(x) is (a) (sqrt(5))/(2) (b) (5)/(4) (c) sqrt(5)(d)(5)/(2)

The square root of (7+3sqrt5) (7-3sqrt5) is (A) 4 (B) sqrt5 (C) 3sqrt5 (D) 2