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(0)=k;

h(1)=1;

h(m)=2h(m−1)+4h(m−2),if m≥2

h(m-1)=2h(m−2)+4h(m−3)

h(m-2)=2h(m−3)+4h(m−4)

now putting the value of h(m-1) &h(m-2) in h(m)

we got

h(m) = 2(2h(m−2)+4h(m−3)) +4(2h(m−3)+4h(m−4))

      =>4h(m−2)+16h(m−3)+16h(m−4)

      =>4(2h(m−3)+4h(m−4))+16h(m−3)+16h(m−4)

           h(m)=24h(m−3)+32h(m−4)
therefore

          h(4)=24h(1)+32(k)

 =>   88=24(1)+32k  (h(4)=88 given)

=>     32k=64

=>    k=2 (answer)