[" (2) "4x^(2)-4a^(2)y=(a^(4)+4)=0],[" (b) "(1)/(p+8)+x=(1)/(p)-(1)/(2)+(1)/(x)]

The solution of (dy)/(dx)=(1)/(2x-y^(2)) is given by , (A) y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," 4"(1)/(2)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)," (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)

2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(4z)=4

[" The solution of "(dy)/(dx)=(1)/(2x-y^(2))" is given by "],[[" (A) "y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)],[" (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)]]

The mirror image of the parabola y^(2)=4x in the tangent to the parabola at the point (1,2) is (a)(x-1)^(2)=4(y+1)(b)(x+1)^(2)=4(y+1)(c)(x+1)^(2)=4(y-1) (d) (x-1)^(2)=4(y-1)

If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4)) then show that (i) x_(1)+x_(2)+x_(3)+x_(4)=0 (ii) y_(1)+y_(2)+y_(3)+y_(4)=0 (iii) x_(1)x_(2)x_(3)x_(4)=c^(4) (iv) y_(1)y_(2)y_(3)y_(4)=c^(4)

If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4)) then show that (i) x_(1)+x_(2)+x_(3)+x_(4)=0 (ii) y_(1)+y_(2)+y_(3)+y_(4)=0 (iii) x_(1)x_(2)x_(3)x_(4)=c^(4) (iv) y_(1)y_(2)y_(3)y_(4)=c^(4)

lim_(x->a){[(a^(1/2)+x^(1/2))/(a^(1/4)-x^(1/4)))^(- 1)-(2(a x)^(1/4))/(x^(3/4)-a^(1/4)x^(1/2)+a^(1/2)x^(1/4)-a^(3/4))]^(- 1)-sqrt2^(log_4 a)}^8

The mirror image of the parabola y^2=4x in the tangent to the parabola at the point (1, 2) is (a) (x-1)^2=4(y+1) (b) (x+1)^2=4(y+1) (c) (x+1)^2=4(y-1) (d) (x-1)^2=4(y-1)

Orthogonal trajectories of the family of curves represented by x^(2)+2y^(2)-y+c=0 is (A) y^(2)=a(4x-1)(B)y^(2)=a(4x^(2)-1)(C)x^(2)=a(4y-1)(D)x^(2)=a(4y^(2)-1)

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