UGC NET CSE | January 2017 | Part 3 | Question: 24

Question

A recursive function $h$, is defined as follows:

$\begin{array} {} h(m) & =k, \text{if  } m=0 \\  &=1, \text{if } m=1 \\  &=  2 h(m-1)+4h(m-2), \text{if } m \geq 2 \end{array}$

If the value of $h(4)$ is $88$ then the value of $k$ is:

• A. $0$  
• B. $1$  
• C. $2$  
• D. $-1$

Comments

https://gateoverflow.in/113801/ugcnet-dec2016-iii-24

Answer 1

given that 

h(m)=k, if m=0 
= 1, if m=1 
= 2h(m-1) + 4h(m-2), if m≥2 
If the value of h(4) is 88 then the value of k is

h(4)=2h(3)+4h(2)=2(2h(2)+4h(1))+4h(2) =8h(2)+8h(1)=8(2h(1)+4h(0))+8h(1)=24h(1)+32h(0)=24+32k=88=>k=2

hence ans is option 3

Answer 2

h(2)=2h(1)+4h(0) =2+4k
h(3)= 2h(2)+4h(1) = 4+8k+4 = 8+8k
h(4)= 2h(3)+4h(2) = 16+16k+8+16k= 32k+24 =88
32k=64
k=2

Answer 3

h(0)=k

h(1)=1

h(2)=2h(1)+4h(0)

     =2+4k

h(3) =2h(2)+4h(1)

      =4+8k+4 = 8+8k

Therefore, h(4)=32k+24 =88

k=2 (Answer)

Answer 4

Upon solving the recurrence we get 

32k + 24 = 88
k = 64/32
k=2 (Answer)