The equation of the lines passing through the point `(1,0)` and at a distance `(sqrt(3))/2` from the origin is (a)`sqrt(3)x+y-sqrt(3)` =0 (b) `x+sqrt(3)y-sqrt(3)=0` (c) `sqrt(3)x-y-sqrt(3)=0` (d) `x-sqrt(3)y-sqrt(3)=0`

Solve sqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0

Equation(s) of the straight line(s), inclined at 30^0 to the x-axis such that the length of its (each of their) line segment(s) between the coordinate axes is 10 units, is (are) (a) x+sqrt(3)y+5sqrt(3)=0 (b) x-sqrt(3)y+5sqrt(3)=0 (c) x+sqrt(3)y-5sqrt(3)=0 (d) x-sqrt(3)y-5sqrt(3)=0

Solve (sqrt(3) + sqrt(2))^(x) +(sqrt(3)-sqrt(2))^(x)=10

Solve : (sqrt(3)+sqrt(2))^(x)+(sqrt(3)-sqrt(2))^(x)=10

Find the equation of the straight line which passes through the origin and makes angle 60^0 with the line x+sqrt(3)y+sqrt(3)=0 .

Find the equation of the plane containing the lines 2x-y+z-3=0,3x+y+z=5 and a t a distance of 1/sqrt6 from the point (2,1,-1).

The equation of the common tangent touching the circle (x-3)^2+y^2=9 and the parabola y^2=4x above the x-axis is (a) sqrt(3)y=3x+1 (b) sqrt(3)y=-(x+3) (C) sqrt(3)y=x+3 (d) sqrt(3)y=-(3x-1)

The equation of lines on which the perpendiculars from the origin make 30^0 angle with the x-axis and which form a triangle of area (50)/(sqrt(3)) with the axes are (a) sqrt(3)x+y-10=0 (b) sqrt(3)x+y+10=0 (c) x+sqrt(3)y-10=0 (d) x-sqrt(3)y-10=0

A beam of light is sent along the line x-y=1 , which after refracting from the x-axis enters the opposite side by turning through 30^0 towards the normal at the point of incidence on the x-axis. Then the equation of the refracted ray is (a) (2-sqrt(3))x-y=2+sqrt(3) (b) (2+sqrt(3))x-y=2+sqrt(3) (c) (2-sqrt(3))x+y=(2+sqrt(3)) (d) y=(2-sqrt(3))(x-1)

The values of parameter a for which the point of minimum of the function f(x)=1+a^2x-x^3 satisfies the inequality (x^2+x+2)/(x^2+5x+6)<0a r e (2sqrt(3),3sqrt(3)) (b) -3sqrt(3),-2sqrt(3)) (-2sqrt(3),3sqrt(3)) (d) (-2sqrt(2),2sqrt(3))