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`

Find the point on the curve y=x^(3)-11x+5 at which the tangent is y=x-11 .

Find the points on the curve y=x^3-2x^2-x at which the tangent lines are parallel to the line y=3x-2

If the equation of the pair of straight lines passing through the point (1,1) , one making an angle theta with the positive direction of the x-axis and the other making the same angle with the positive direction of the y-axis, is x^2-(a+2)x y+y^2+a(x+y-1)=0,a!=2, then the value of sin2theta is (a) a-2 (b) a+2 (c) 2/(a+2) (d) 2/a

The plane 2x - 3y + 6z + 9 =0 makes an angle with positive direciton of X -axis is ........

At what points on the curve x^(2)+y^(2)-2x-4y+1=0 , the tangents are parallel to the Y-axis ?

If a line makes an angle (pi)/(4) with the positive directions of each of X-axis and Y-axis, then the angle that the line makes with the positive direction of the Z-axis is

Find the points on the curve x^(2)+y^(2)-2x-3=0 at which the tangents are parallel to the X-axis.

A line passes through the point (6, -7, -1) and (2, -3, 1). The direction cosines of the line so directed that the angle made by it with the positive direction of x-axis is acute, are