Domain of the explicit from of the function `y` represented implicity by the equation `(1+x)cos y-x^2=0` is- a.`(-1,\ 1]` b. `(-1,(1-sqrt(5))/2]` c.`[(1-sqrt(5))/2,(1+sqrt(5))/2]` d. `[0,(1+sqrt(5))/2]`

The sum of all the solution(s) of the equation sin^(-1)2x=cos^(-1)x is 0 (2) 2/(sqrt(5)) (3) 1/(sqrt(5)) (4) (-1)/(sqrt(5))

The eccentricity of the ellipse 4x^2+9y^2=36 is a. 1/(2sqrt(3)) b. 1/(sqrt(3)) c. (sqrt(5))/3 d. (sqrt(5))/6

The eccentricity of the ellipse 4x^2+9y^2=36 is a. 1/(2sqrt(3)) b. 1/(sqrt(3)) c. (sqrt(5))/3 d. (sqrt(5))/6

The eccentricity of the hyperbola x^2-4y^2=1 is a. (sqrt(3))/2 b. (sqrt(5))/2 c. 2/(sqrt(3)) d. 2/(sqrt(5))

If sin^(-1)x+cot^(-1)(1/2)=pi/2,\ t h e n\ x is 0 b. 1/(sqrt(5)) c. 2/(sqrt(5)) d. (sqrt(3))/2

The length of the tangent of the curve y=x^(2)+1 at (1 ,3) is (A) sqrt(5) (B) 3sqrt(5) (C) 1/2 (D) 3(sqrt(5))/(2)

The point P(1,1) is translated parallel to 2x=y in the first quadrant through a unit distance. The coordinates of the point P in the new position are (1+-2/(sqrt(5)),1+-1/(sqrt(5))) (1+-1/(sqrt(5)),1+-2/(sqrt(5))) (1/(sqrt(5)),2/(sqrt(5))) (4) (2/(sqrt(5)),1/(sqrt(5)))

Show that 4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)

"tan"(cos^(-1)x) is equal to x/(1+x^2) b. (sqrt(1+x^2))/x c. (sqrt(1-x^2))/x d. sqrt(1-2x)

Let S be the set of all non-zero real numbers such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1a n dx_2 satisfying the inequality |x_1-x_2|<1. Which of the following intervals is (are) a subset (s) of S ? (1/2,1/(sqrt(5))) b. (1/(sqrt(5)),0) c. (0,1/(sqrt(5))) d. (1/(sqrt(5)),1/2)