If `3^(49)(x+i y)=(3/2+(sqrt(3))/2i)^(100)` and `x=k y` then `k` is: a.`-1//3` b. `sqrt(3)` c. `-sqrt(3)` d.`-1/(sqrt(3))`

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2

The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4 is a. sqrt(30) b. 2sqrt(30) c. 5sqrt(30) d. 3sqrt(30)

The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4 is a. sqrt(30) b. 2sqrt(30) c. 5sqrt(30) d. 3sqrt(30)

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))

(i) If x = (6ab)/(a + b) , find the value of : (x + 3a)/(x - 3a) + (x + 3b)/(x - 3b) . (ii) a = (4sqrt(6))/(sqrt(2) + sqrt(3)) , find the value of : (a + 2sqrt(2))/(a - 2sqrt(2)) + (a + 2sqrt(3))/(a - 2sqrt(3)) .

The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/2 from the origin is (a). sqrt(3)+y-sqrt(3) =0 (b). x+sqrt(3)y-sqrt(3)=0 (c). sqrt(3)x-y-sqrt(3)=0 (d). x-sqrt(3)y-sqrt(3)=0

The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/2 from the origin is (a) sqrt(3)x+y-sqrt(3) =0 (b) x+sqrt(3)y-sqrt(3)=0 (c) sqrt(3)x-y-sqrt(3)=0 (d) x-sqrt(3)y-sqrt(3)=0

The equations of lines passing through the point (1,0) and at distance of (sqrt(3))/(2) units from the origin are (i) sqrt(3)x+y-sqrt(3)=0,sqrt(3)x-ysqrt(3)=0 (ii) sqrt(3)x+y+sqrt(3)=0,sqrt(3)x-y+sqrt(3)=0 (iii) x+sqrt(3)y-sqrt(3)=0,x-sqrt(3)y-sqrt(3)=0 (iv) none of these

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