# Questions by Rounak Agarwal

1
How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1 ?
2
A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded that if the butler is telling the truth then so is the cook; the cook and the gardener cannot both be telling the truth; the gardener and the ... . For each of the four persons can the detective determine whether that person is telling the truth or lying ? Explain your reasoning.
3
Consider a 4-way set associative cache that has 8-lines, with perfect LRU cache replacement and supports a block size of 16-bytes. For the following memory access pattern (shown as byte addresses), find the hit ratio? 3, 5, 6, 21, 32, 14, 5, 10, 11, 12
1 vote
4
Solve the recurrence relation $a_n = a_{n-1} + 2n + 3, a_0 = 4$
5
Question: Six different airlines fly from New York to Denver and seven fly from Denver to San Francisco. How many different pairs of airlines can you choose on which to book a trip from New York to San Francisco via Denver, when you pick an airline for the flight to Denver and an airline for the continuation flight to San Francisco ? How many of these pairs involve more than one airline ?
6
The decomposition of relation R with FD set F into R1 and R2 has lossless join property iff R1 $\cap$ R2 $\rightarrow$ R1 $\in$ F$^+$ OR R1 $\cap$ R2 $\rightarrow$ R2 $\in$ F$^+$ If R is decomposed into more than 2 relations, can we apply ... join property ? Or is that table drawing thing the only way to check for lossless join property ? Answers with reference(s) will be much appreciated. Thanks.
Alphabet : {a, b} Language : Set of all strings which start and end with same symbol Doubt : Can $\epsilon$ be considered as part of the language ? Edit: I can see several people have answered my question in the comments. Perhaps I should have mentioned that I need an ... to be present at the beginning and end of "ab" or even between a and b. If you disagree with me please give some explanation.