If `((a^2+1)^2)/(2a-i)=x+i y ,` then `x^2+y^2` is equal to a. `((a^2+1)^4)/(4a^2+1)` b. `((a+1)^2)/(4a^2+1)` c. `((a^2-1)^2)/((4a^2-1)^2)` d. none of these

If x+ iy=(1+ 4i)(1+5i) , then (x^(2)+y^(2)) is equal to :

intx/(4+x^4)\ dx is equal to 1/4tan^(-1)x^2 (b) 1/4tan^(-1)((x^2)/2) (c) 1/2tan^(-1)((x^2)/2) (d) none of these

If (1-i)x+(1+i)y=1-3i , then (x,y) is equal to (a) (2,-1) (b) (-2,1) (c) (-2,-1) (d) (2,1)

If y=(1+1/(x^2))/(1-1/(x^2)) , then (dy)/(dx) = a. -(4x)/((x^2-1)^2) b. -(4x)/(x^2-1) c. (1-x^2)/(4x) d. (4x)/(x^2-1)

The equation of the hyperbola whose foci are (6,4) and (-4,4) and eccentricity 2 is a. ((x-1)^2)/(25//4)-((y-4)^2)/(75//4)=1 b. ((x+1)^2)/(25//4)-((y+4)^2)/(75//4)=1 c. ((x-1)^2)/(75//4)-((y-4)^2)/(25//4)=1 d. none of these

Let A=[(1, 2), (3,-5)] and B=[(1, 0), (0, 2)] and X be a matrix such that A=B X , then X is equal to (a) 1/2[(2, 4), (3, -5)] (b) 1/2[(-2, 4), (3, 5)] (c) [(2, 4), (3,-5)] (d) none of these

If the polar with respect to y^2 = 4ax touches the ellipse x^2/alpha^2 + y^2/beta^2=1 , the locus of its pole is (a) (x^2)/(alpha^2)-(y^2)/(4a^2 alpha^2"/"beta^2)=1 (b) (x^2)/(alpha^2)+(beta^2 y^2)/(4a^2)=1 (c) a^2x^2+b^2y^2=1 (d) None of these

d/(dx)[log{e^x((x-2)/(x+2))^(3//4)}] equals (a) (x^2-1)/(x^2-4) (b) 1 (c) (x^2+1)/(x^2-4) (d) e^x(x^2-1)/(x^2-4)

Locus of all such points from where the tangents drawn to the ellipse x^2/a^2 + y^2/b^2 = 1 are always inclined at 45^0 is: (A) (x^2 + y^2 - a^2 - b^2)^2 = (b^2 x^2 + a^2 y^2 - 1) (B) (x^2 + y^2 - a^2 - b^2)^2 = 4(b^2 x^2 + a^2 y^2 - 1) (C) (x^2 + y^2 - a^2 - b^2)^2 = 4(a^2 x^2 + b^2 y^2 - 1) (D) none of these

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(dx) is equal to 4 (b) 3 (c) 1 (d) 0