Home
Class 12
MATHS
Let f(n) denotes the number of different...

Let f(n) denotes the number of different ways, the positive integer n ca be expressed as the sum of the 1's and 2's. for example, f(4)=5.
i.e., `4=1+1+1+1`
`=1+1+2=1+2+1=2+1+1=2+2`
Q. The number of solutions of the equation `f(n)=n`, where `n in N` is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`becausef(1)=.^(1)C_(0)=1,f(2)=.^(2)C_(0)+.^(1)C_(1)=2,f(3)=.^(3)C_(0)+.^(2)C_(1)=3`,
f(4)=5
and `f(5)=.^(5)C_(0)+.^(4)C_(1)+.^(3)C_(2)=8`
thus, we say that `f(x) gt n` for n=4,5,6, . .
Hence, number of solutions for f(n)=5=n is 3.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(n) denotes the number of different ways, the positive integer n ca be expressed as the sum of the 1's and 2's. for example, f(4)=5. i.e., 4=1+1+1+1 =1+1+2=1+2+1=2+1+1=2+2 Q. The value of f{f(6)} is

Let f(n) denotes the number of different ways, the positive integer n ca be expressed as the sum of the 1's and 2's. for example, f(4)=5. i.e., 4=1+1+1+1 =1+1+2=1+2+1=2+1+1=2+2 Q. In a stage show, f(4) superstars and f(3) junior artists participate. each one is going to present one item, then the number of ways the sequence of items can be planned, if no two junior artists present their items consecutively, is

Let S(n) denotes the number of ordered pairs (x,y) satisfying 1/x+1/y=1/n,ngt1 ,x,y,n in N S(10) equals

Let E={1,2,3,4} and F={1,2} If N is the number of onto functions from E to F , then the value of N/2 is

The number of positive integers satisfying the inequality .^(n+1)C(n-2)-.^(n+1)C(n-1)<=100 is

Let S(n) denotes the number of ordered pairs (x,y) satisfying 1/x+1/y=1/n, " where " n gt 1 " and " x,y,n in N . " " (i) Find the value of S(6). " " (ii) Show that, if n is prime, then S(n)=3, always.

If, for a positive integer n, the quadratic equation, x(x + 1) + (x + 1)(x + 2) +.....+ (x +bar( n-1))(x + n) = 10n has two consecutive integral solutions, then n is equal to

Let f be a function from the set of positive integers to the set of real number such that f(1)=1 and sum_(r=1)^(n)rf(r)=n(n+1)f(n), forall n ge 2 the value of 2126 f(1063) is ………….. .

......... is the minimum value of n such that (1+i)^(2n) = (1 - i)^(2n) . Where n in N .

Let g(x) = ln f(x) where f(x) is a twice differentiable positive function on (0, oo) such that f(x+1) = x f(x) . Then for N = 1,2,3 g''(N+1/2)- g''(1/2) =