For non-negative integers `ma n dn` a function is defined as follows: `f(m ,n)={n+1ifm=0f(m-1,1)ifm!=0,n=0`
`f(m-1,f(m ,n-1))ifm!=0,n!=0` Then the value of `f(1,1)` is a. 1 b. 12 c. 3 d. 4

For non-negative integers m and n a function is defined as follows: f(m,n)={n+1,ifm=0andf(m−1,1)ifm≠0,n=0andf(m−1,f(m,n−1))ifm≠0,n≠0}Then the value of f(1,1) is:

If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 and f(0)=1 is continuous at x=0 then the value of m+n is a. 2 b. 3 c. -3 d. 7

If f(x) = (x^n-a^n)/(x-a) , then f'(a) is a. 1 b. 1/2 c. 0 d. does not exist

A function f is defined such that f(1)=2, f(2)=5, and f(n)=f(n-1)-f(n-2) for all integer values of n greater than 2. What is the value of f(4)?

For each ositive integer n, define a function f _(n) on [0,1] as follows: f _(n((x)={{:(0, if , x =0),(sin ""(pi)/(2n), if , 0 lt x le 1/n),( sin ""(2pi)/(2n) , if , 1/n lt x le 2/n), (sin ""(3pi)/(2pi), if, 2/n lt x le 3/n), (sin "'(npi)/(2pi) , if, (n-1)/(n) lt x le 1):} Then the value of lim _(x to oo)int _(0)^(1) f_(n) (x) dx is:

If f(x) is a polynomial of degree n such that f(0)=0 , f(x)=1/2,....,f(n)=n/(n+1) , ,then the value of f (n+ 1) is

Let f be defined on the natural numbers as follow: f(1)=1 and for n gt 1, f(n)=f[f(n-1)]+f[n-f(n-1)] , the value of 1/(30)sum_(r=1)^(20)f(r) is

Consider the function f defined on the set of all non-negative interger such that f(0) = 1, f(1) =0 and f(n) + f(n-1) = nf(n-1)+(n-1) f(n-2) for n ge 2 , then f(5) is equal to

Let f be real valued function from N to N satisfying. The relation f(m+n)=f(m)+f(n) for all m,n in N . The range of f contains all the even numbers, the value of f(1) is

Let f(x)=x^(2)+ax+b be a quadratic polynomial in which a and b are integers. If for a given integer n, f(n) f(n+1)=f(m) for some integer m, then the value of m is