If the curve ` y^2=7x` cuts the line `y= sqrt(21)` at `D` and curve cuts x-axis at `L`, then LD = `(A) sqrt10 (B) sqrt15 (C) sqrt30 (D) sqrt5`

The radius of the circle touching the straight lines x-2y-1=0 and 3x-6y+7=0 is (A) 1/sqrt(2) (B) sqrt(5)/3 (C) sqrt(3) (D) sqrt(5)

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

If angle between the line (x-2)/1=(y-3)/2=(z+5)/(-2) and 2x-y-kz=lambda is cos^-1 ((2sqrt2)/3) then find k (A) sqrt(3/5) (B) 3/sqrt5 (C) sqrt5/3 (D) sqrt(5/3)

The shortest distance between line y-x=1 and curve x=y^2 is (a) (3sqrt2)/8 (b) 8/(3sqrt2) (c) 4/sqrt3 (d) sqrt3/4

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (a) (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. )a) 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) (b) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) (d) +-1n((sqrt(3)+sqrt(7))/2)

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

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

Locus of the middle points of the line segment joining P(0, sqrt(1-t^2) + t) and Q(2t, sqrt(1-t^2) - t) cuts an intercept of length a on the line x+y=1 , then a = (A) 1/sqrt(2) (B) sqrt(2) (C) 2 (D) none of these

The area between the curves y=sqrt(x),y=x^(2) is