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)`

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 (a) (0,0) (b) (sqrt(3),-(sqrt(3))/2) (c) (-2,2/3) (d) (-sqrt(3),(sqrt(3))/2)

If at each point of the curve y=x^3-a x^2+x+1, the tangent is inclined at an acute angle with the positive direction of the x-axis, then (a) a >0 (b) a<-sqrt(3) (c) -sqrt(3)< a< sqrt(3) (d) non eoft h e s e

If at each point of the curve y=x^3-a x^2+x+1, the tangent is inclined at an acute angle with the positive direction of the x-axis, then (a) a >0 (b) a<-sqrt(3) (c) -sqrt(3)<=a<= sqrt(3) (d) non eoft h e s e

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. )a) 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) (b) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) (d) +-1n((sqrt(3)+sqrt(7))/2)

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) +-1n((sqrt(3)+sqrt(7))/2)

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

If tan^(-1)x+2cot^(-1)x=(2pi)/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 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))

If 4\ cos^(-1)x+sin^(-1)x=pi , then the value of x is (a) 3/2 (b) 1/(sqrt(2)) (c) (sqrt(3))/2 (d) 2/(sqrt(3))