If `x^2+y^2=1,t h e n` (a)`y y^('')-2(y^(prime))^2+1=0` (b)`yy^('')+(y^(prime))^2+1=0` (c)`y y^('')+(y^(prime))^(-2)-1=0` (d)`y y^('')+2(y^(prime))^2+1=0`

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? y^(x-2x y^(prime))=y y y^(prime)=2x(y^(prime))^2+1 x y^(prime)=2y(y^(prime))^2+2 y^(y-4x y^(prime))=(y^(prime))^2

If x^3-2x^2y^2+5x+y-5=0 and y(1)=1 , then (a) y^(prime)(1)=4/3 (b) y'(1)=-4/3 (c) y''(1)=-8(22)/(27) (d) y^(prime)(1)=2/3

If x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n y^(prime)(1)=4/3 (b) y^(1)=-4/3 y^(1)=-8(22)/(27) (d) y^(prime)(1)=2/3

Let y=f(x) be a parabola, having its axis parallel to the y-axis, which is touched by the line y=x at x=1. Then, (a) 2f(0)=1-f^(prime)(0) (b) f(0)+f^(prime)(0)+f^(0)=1 (c) f^(prime)(1)=1 (d) f^(prime)(0)=f^(prime)(1)

The condition that one of the straight lines given by the equation a x^2+2h x y+b y^2=0 may coincide with one of those given by the equation a^(prime)x^2+2h^(prime)x y+b^(prime)y^2=0 is (a b^(prime)-a^(prime)b)^2=4(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (a b^(prime)-a^(prime)b)^2=(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (h a^(prime)-h^(prime)a)^2=4(a b^(prime)-a^(prime)b)(b h^(prime)-b^(prime)h) (b h^(prime)-b^(prime)h)^2=4(a b^(prime)-a^(prime)b)(h a^(prime)-h^(prime)a)

The condition that one of the straight lines given by the equation a x^2+2h x y+b y^2=0 may coincide with one of those given by the equation a^(prime)x^2+2h^(prime)x y+b^(prime)y^2=0 is (a b^(prime)-a^(prime)b)^2=4(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (a b^(prime)-a^(prime)b)^2=(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (h a^(prime)-h^(prime)a)^2=4(a b^(prime)-a^(prime)b)(b h^(prime)-b^(prime)h) (b h^(prime)-b^(prime)h)^2=4(a b^(prime)-a^(prime)b)(h a^(prime)-h^(prime)a)

If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (a) (varphi^(prime)psi^('')-psi'varphi' ')/((varphi^(prime))^2) (b) (varphi^(prime)psi^('')-psi'varphi' ')/((varphi^(prime))^3) (c) varphi^('')/psi^('') (d) psi^('')/varphi^('')

The differential equation obtained on eliminating A and B from y=A cos\ omegat+bsinomegat , is (a) y^(primeprime)+ y^(prime)=0 (b.) y^(primeprime)+omega^2y=0 (c.) y^(primeprime)=omega^2y (d.) y^(primeprime)+y=0

If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (varphi^(prime)psi^-psi'varphi' ')/((varphi^(prime))^2) (b) (varphi^(prime)psi^-psi'varphi' ')/((varphi^(prime))^3) varphi^(/)psi^ (d) psi^(/)varphi^

If [1 4 2 0]=[x y^2z0],y<0t h e nx-y+z=