If `x^2+y^2=1, then`

(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 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

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)

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)

x + y = tan^(-1)y : y^(2)y' + y^(2) + 1 = 0

If x=logp and y=1/p ,then (a) (d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+y=0 (c) (d^2y)/(dx^2)+(dy)/(dx)=0 (d) (d^2y)/(dx^2)-(dy)/(dx)=0

If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0, then (a) f(4)=f(-4) (b) f(2)+f(-2)=0 (c) f^(prime)(4)+f^(prime)(-4)=0 (d) f^(prime)(2)=f^(prime)(-2)

IF x^3-2x^2y^2+5x+y-5=0 and y(1)=1, then -

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the circle x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0 then prove that 2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '

If y=1/(1+x+x^2+x^3) , then value of (d^2y)/(dx^2) at x=0 is