`P(1,0,-1),Q(2,0,-3),R(-1,2,0) and S(3,-2,-1)` are four points and d is the projection of `vec(PQ) on vec(RS)` then which of the following is (are) true? (A) `d=6/sqrt(165)` (B) `d= 6/sqrt(33)` (C) `8/sqrt(33)` (D) `d=6/sqrt(5)`

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)

If vec a\ a n d\ vec b are unit vectors, then which of the following values vec adot vec b is not possible? a. sqrt(3) b. sqrt(3)//2 c. 1//sqrt(2) d. -1//2

If the vertices of the parabola be at (-2,0) and (2,0) and one of the foci be at (-3,0) then which one of the following points does not lie on the hyperbola? (a) (-6, 2sqrt(10)) (b) (2sqrt6,5) (c) (4, sqrt(15)) (d) (6, 5sqrt2)

If both a\ a n d\ b are rational numbers, find the values of a\ a n d\ b in each of the following equalities: (sqrt(2)+\ sqrt(3))/(3sqrt(2\ )-\ 2sqrt(3))=a-b\ sqrt(6)

A solution of sin^-1 (1) -sin^-1 (sqrt(3)/x^2)- pi/6 =0 is (A) x=-sqrt(2) (B) x=sqrt(2) (C) x=2 (D) x= 1/sqrt(2)

The value of sin(1/4sin^(-1)((sqrt(63))/8)) is (a) 1/(sqrt(2)) (b) 1/(sqrt(3)) (c) 1/(2sqrt(2)) (d) 1/(3sqrt(3))

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

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

A hyperbola is given with its vertices at (-2,0) and (2,0) one of the foci of hyperbola is (3,0) . Then which of the following points does not lie on hyperbola (A) (sqrt24,5) (B) (sqrt44, 5sqrt2) (C) (sqrt44, -5sqrt2) (D) (-6, 5sqrt2)

If A(1,p^2),B(0,1) and C(p ,0) are the coordinates of three points, then the value of p for which the area of triangle A B C is the minimum is (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) 1/(sqrt(2)) (d) none of these