`f(x, y) = 0` is a circle such that `f(0, lambda) = 0 and f(lambda, 0)=0` have equal roots and `f(1, 1)= -2` then the radius of the circle is : (A) 4 (B) 8 (C) 2 (D) 1

Let f(x,y)=0 be the equation of a circle. If f(0,lamda)=0 has equal roots lamda=2,2 and f(lamda,0)=0 has roots lamda=(4)/(5),5 then the centre of the circle is

f(x , y)=x^2+y^2+2a x+2b y+c=0 represents a circle. If f(x ,0)=0 has equal roots, each being 2, and f(0,y)=0 has 2 and 3 as its roots, then the center of the circle is (a) (2,5/2) (b) Data is not sufficient (c) (-2,-5/2) (d) Data is inconsistent

Suppose f(x,y)=0 is the equation of a circle such that f(x,1)=0 has equal roots (each equal to 2) and f(1,x)=0 also has equal roots (each equal to zero). The equation of circle is

f(x , y)=x^2+y^2+2a x+2b y+c=0 represents a circle. If f(x ,0)=0 has equal roots, each being 2, and f(0,y)=0 has 2 and 3 as its roots, then the center of the circle is

Let f(x) be a quadratic expression such that f(-1)+f(2)=0 . If one root of f(x)=0 is 3 , then the other root of f(x)=0 lies in (A) (-oo,-3) (B) (-3,oo) (C) (0,5) (D) (5,oo)

If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 is 2 (b) 8 (c) 16 (d) 4

If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 is 2 (b) 8 (c) 16 (d) 4

If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 is 2 (b) 8 (c) 16 (d) 4

Let f be a function such that f(x).f\'(-x)=f(-x).f\'(x) for all x and f(0)=3 . Now answer the question:Number of roots of equation f(x)=0 in interval [-2,2] is (A) 0 (B) 2 (C) 4 (D) 1

Statement 1: If f(x) is differentiable in [0,1] such that f(0)=f(1)=0, then for any lambda in R , there exists c such that f^prime (c) =lambda f(c), 0ltclt1. statement 2: if g(x) is differentiable in [0,1], where g(0) =g(1), then there exists c such that g^prime (c)=0,