Points on the curve `f(x)=x/(1-x^2)` where the tangent is inclined at an angle of `pi/4` to the x-axis are (0,0) (b) `(sqrt(3),-(sqrt(3))/2)` `(-2,2/3)` (d) `(-sqrt(3),(sqrt(3))/2)`

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

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

If at each point of the curve y=x^(3)-ax^(2)+x+1, the tangent is inclined at an acute angle with the positive direction of the x -axis,then a>0 (b) a<-sqrt(3)-sqrt(3)<=a<=sqrt(3)( d) none of these

2sqrt(3)x^(2)+x-5sqrt(3)=0

The point(s) on the curve y^(3)+3x^(2)=12y where the tangent is vertical,is(are) ??(+-(4)/(sqrt(3)),-2) (b) (+-sqrt((11)/(3)),1)(0,0)(d)(+-(4)/(sqrt(3)),2)

If tan^(-1)x+2cot^(-1)x=(2 pi)/(3), then x, is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3)(d)sqrt(2)

Domain of f(x)=sin^(-1)[2-4x^2], where [.] denotes the greatest integer function, is: (a)[-(sqrt(3))/2,(sqrt(3))/2]-{0} (b) [-(sqrt(3))/2,(sqrt(3))/2] (c)[-(sqrt(3))/2,(sqrt(3))/2)-{0} (d) (-(sqrt(3))/2,(sqrt(3))/2)-0

The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle x^(2)+y^(2)=4 at (1,sqrt(3)) is 3sqrt(3)(b)2sqrt(3) (c) 4sqrt(3)(d)sqrt(3)

sqrt (2x) -sqrt (3y) = 0sqrt (3x) -sqrt (3y) = 0

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)