If `f(2x+y/8,2x-y/8)=x y` , then `f(m , n)+f(n,m)=0` (a) only when `m=n` (b) only when `m!=n` (c) only when `m=-n` (d) `for all m and n`

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If y^2=a x^2+b x+c ,then y^3(d^2y)/(dx^2) is (a)a constant (b)a function of x only (c)a function of y only (d)a function of xa n dy

If f(x) satisfies the relation f(x+y)=f(x)+f(y) for all x , y in Ra n df(1)=5,t h e n (a) f(x)i sa nod dfu n c t ion (b) f(x) is an even function (c) sum_(n=1)^mf(r)=5^(m+1)C_2 (d) sum_(n=1)^mf(r)=(5m(m+2))/3

If f(x+y)=f(x)+f(y)-x y-1AAx , y in Ra n df(1)=1, then the number of solution of f(n)=n , n in N , is 0 (b) 1 (c) 2 (d) more than 2

If f (x) =x^(m) and g(x) =x^(n) does f^(@) g=g^(@) f?

Let h(x)=x^(m/n) for x in R , where +m and n are odd numbers and 0 less than m less than n Then y=h(x) has a)no local extremums b)one local maximum c)one local minimum d)none of these

Let f(x) = (x^2 - 1)^(n+1) + (x^2 + x + 1) . Then f(x) has local extremum at x = 1 , when n is (A) n = 2 (C) n = 4 (B) n = 3 (D) n = 5

If x-c is a factor of order m of the polynomial f(x) of degree n (1 < m < n) , then find the polynomials for which x=c is a root.