If the direction ratios of a line are `1+lamda, 1-lamda, 2` and the line the makes an angle `60^0` with the y-axis, then `lamda` is (A) `1+sqrt(3)` (B) `2+sqrt(5)` (C) `1-sqrt(3)` (D) `2-sqrt(5)`

(1)/(2+sqrt(3))+(2)/(sqrt(5)-sqrt(3))+(1)/(2-sqrt(5))=0

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 A(1,-1,2),B(2,1,-1)C(3,-1,2) are the vertices of a triangle then the area of triangle ABC is (A) sqrt(12) (B) sqrt(3) (C) sqrt(5) (D) sqrt(13)

Equation of a line which passes through A(2,3) and makes an angle 45^@ with x-axis. If this line meets the line x+y+1=0 at the points P, then distance AP is (A) 2sqrt3 (B) 3 sqrt 2 (C) 5sqrt 2 (D) 2sqrt5

The direction ratio o the lien OP are euqla and the length OP=sqrt(3) . Then the cooredinates of the point P are (A) (-1,-1,-1) (B) (sqrt(3),sqrt(3),sqrt(3)) (C) (sqrt(2),sqrt(2),sqrt(2)) (D) (2,2,2)

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)

A line makes 30^(@) angle with positive direction of y axis in clockwise direction, then slope of line is : ( 1 ) sqrt(3) ( 2 ) - sqrt(3) ( 3 ) 1/(sqrt3) ( 4 ) - 1/(sqrt3)

A straight line L passes through (3,-2) also inclined at an angle 60^@ to the line sqrt(3x)+y=1.If L also intersects the x-axis, then the equation of L is: (A) y+sqrt(3x)+2-3sqrt3=0 (B) y-sqrt(3x)+2+3sqrt3=0 (C) sqrt(3y)-x+3+2sqrt3=0 (D) sqrt(3y)+x-3+2sqrt3=0

If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30^0 , 45^0 and 60^0 respectively, then the ratio, AB : BC, is : (1) sqrt(3):1 (2) sqrt(3):sqrt(2) (3) 1:sqrt(3) (4) 2"":""3

If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=2-t with parameters s and t respectively, are coplanar, then lamda equals (A) -1/2 (B) -1 (C) -2 (D) 0