NET December 2021 Computer Science Solved Paper 2 Question 1

 Q: 1 Let us assume a person climbing the stairs can take one stair or two stairs at a time. How many ways can this person climb a flight of eight stairs?

(a) 21

(b) 24

(c) 31

(d) 34

Answer : d

Solution:

First Method :

In this case answer would be 9th Fibonacci number as number of stairs are 8 so answer is fib(9) = 34.
If number of stairs = n then total ways will be fib(n+1).

Second Method :

Here, we have to use the concept of combination to find the number of ways in which a person can walk up a stairway which has 8 steps. So, we have to make
pairs of the combination of 1 and 2 steps and then by using the concept of the combination we will get the number of ways a person can walk up a stairway of 8 steps.



It is given that there are 8 steps of the stairway and he can take only 1 or 2 steps up the
stairs at a time.

   No. of Step 1               No. of Step 2               Total Ways

   8                                        0                                    1               

   6                                        1                                  (7!)/(6!)(1!) = 7

   4                                        2                                  (6!)/(4!)(2!) = 15

   2                                        3                                  (5!)/(2!)(3!) = 10

   0                                        4                                     1

Adding all we get 1+7+15+10+1= 34

So, 34 is right answer which is also 9th Fibonacci Number.

C Program to Find nth Fibonacci Number

#NTA #NET #NETDECEMBER2021 Discrete Mathematics Combination