Question 1 |
The Lucas sequence L_n is defined by the recurrence relation:
L_n=L_{n-1}+L_{n+2}, \; for \; n\geq 3,
with L_1=1 \; and \; L_2=3
Which one of the options given is TRUE?
L_n=L_{n-1}+L_{n+2}, \; for \; n\geq 3,
with L_1=1 \; and \; L_2=3
Which one of the options given is TRUE?
L_n=\left ( \frac{1+\sqrt{5}}{2} \right )^n+\left ( \frac{1-\sqrt{5}}{2} \right )^n | |
L_n=\left ( \frac{1+\sqrt{5}}{2} \right )^n - \left ( \frac{1-\sqrt{5}}{3} \right )^n | |
L_n=\left ( \frac{1+\sqrt{5}}{2} \right )^n+\left ( \frac{1-\sqrt{5}}{3} \right )^n | |
L_n=\left ( \frac{1+\sqrt{5}}{2} \right )^n- \left ( \frac{1-\sqrt{5}}{2} \right )^n |
Question 1 Explanation:
Question 2 |
Consider the following recurrence:
\begin{aligned} f(1)&=1; \\ f(2n)&=2f(n)-1, & \text{for }n \geq 1; \\ f(2n+1)&=2f(n)+1, & \text{for }n \geq 1. \end{aligned}
Then, which of the following statements is/are TRUE?
MSQ
\begin{aligned} f(1)&=1; \\ f(2n)&=2f(n)-1, & \text{for }n \geq 1; \\ f(2n+1)&=2f(n)+1, & \text{for }n \geq 1. \end{aligned}
Then, which of the following statements is/are TRUE?
MSQ
f(2^n-1)=2^n-1 | |
f(2^n)=1 | |
f(5 \dot 2^n)=2^{n+1}+1 | |
f(2^n+1)=2^n+1 |
Question 2 Explanation:
Question 3 |
Consider the recurrence relation a_{1}=8, a_{n}=6n^{2}+2n+a_{n-1}. Let a_{99}= K \times 10^{4}. The value of K is .
198 | |
148 | |
226 | |
312 |
Question 3 Explanation:
Question 4 |
Let a_{n} be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for a_{n}?
a_{n}=a_{n-1}+2a_{n-2} | |
a_{n}=a_{n-1}+a_{n-2} | |
a_{n}=2a_{n-1}+a_{n-2} | |
a_{n}=2a_{n-1}+2a_{n-2} |
Question 4 Explanation:
Question 5 |
Let a_{n} represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for a_{n}?
a_{n-2}+a_{n-1}+2^{n-2} | |
a_{n-2}+2a_{n-1}+2^{n-2} | |
2a_{n-2}+a_{n-1}+2^{n-2} | |
2a_{n-2}+2a_{n-1}+2^{n-2} |
Question 5 Explanation:
There are 5 questions to complete.
Question 5 all the options are wrongly typed please correct it.
Question 5 all the options are wrongly typed please correct it.
Can you please share more details.
Options Updated.