27 at x = 0 is 0. If y=tan 1) 1 2) 2 D 22 3) In 2 3102

If y = tan^(-1) ((1)/(1 + x + x^(2))) + tan^(-1) ((1) /(x^(2) + 2x + 3)) + tan^(-1) ((1)/(x^(2) + 5x + 7)) + ….n terms , then y(0) is

The angle between the curves y=sin x and y = cos x, 0 lt x lt (x)/(2) , is a) tan^-1(2sqrt2) b) tan^-1(3sqrt2) c) tan^-1(3sqrt3) d) tan^-1(5sqrt2)

The center(s) of the circle(s) passing through the points (0, 0) and (1, 0) and touching the circle x^2+y^2=9 is (are) (3/2,1/2) (b) (1/2,3/2) (1/2,2^(1/2)) (d) (1/2,-2^(1/2))

If tan y=(2^(x))/(1+2^(2x+1)), then (dy)/(dx) at x=0 is -(3)/(10) (b) -(3)/(10)ln2-(1)/(10)(d)-(1)/(10)ln2

The radical centre of the circles x^(2)+y^(2)=9 , x^(2)+y^(2)-2x-2y-5=0 , x^(2)+y^(2)+4x+6y-19=0 is A) (0,0) (B) (1,1) (C) (2,2) (D) (3,3)

The angle between the curves, y = x^(2) and y^(2) - x = 0 at the point (1, 1) is a) (pi)/(2) a) tan^(-1)""(4)/(3) c) (pi)/(3) d) tan^(-1)""(3)/(4)

Which of following is/are the part of locus of vertex of parabola. y=1-x^2,x in [0,1],y in [0,1] y=1-x^2,x in [-2,2],y in [0,1] y=1-x^2,x in [-2,2],y in [-3,1] y=1-x^2,x in [-1,1],y in [0,1]

If x<0,\ y<0 such that x y=1 , then tan^(-1)x+tan^(-1)y equals pi/2 (b) -pi/2 (c) pi (d) none of these

If x<0,\ y<0 such that x y=1 , then tan^(-1)x+tan^(-1)y equals pi/2 (b) -pi/2 (c) pi (d) none of these