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`

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

The equations of the line passing through the point of intersection of the lines x-3y+1=0 and 2x+5y-9=0 , whose distance from the origin is sqrt5 .

tan^(2)x -(1+sqrt(3))tanx + sqrt(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) x+sqrt(3)y+5sqrt(3)=0 x-sqrt(3)y+5sqrt(3)=0 x+sqrt(3)y-5sqrt(3)=0 x-sqrt(3)y-5sqrt(3)=0

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 .

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 sqrt(3)y=3x+1 (b) sqrt(3)y=-(x+3) (C) sqrt(3)y=x+3 (d) sqrt(3)y=-(3x-1)

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 (a) (2sqrt(3),3sqrt(3)) (b) -3sqrt(3),-2sqrt(3)) (c) (-2sqrt(3),3sqrt(3)) (d) (-2sqrt(2),2sqrt(3))

The equation of a straight line on which the length of perpendicular from the origin is four units and the line makes an angle of 120^0 with the x-axis is (a) xsqrt(3)+y+8=0 (b) xsqrt(3)-y=8 (c) xsqrt(3)-y=8 (d) x-sqrt(3)y+8=0

The locus of a point that is equidistant from the lines x+y - 2sqrt2 = 0 and x + y - sqrt2 = 0 is (a) x+y-5sqrt2=0 (b) x+y-3sqrt2=0 (c) 2x+2y-3 sqrt2=0 (d) 2x+2y-5sqrt5=0