Q. Which one of the following languages over Σ = {𝑎, 𝑏} is NOT context-free? (A) {𝑤𝑤𝑅 |𝑤 ∈ {𝑎, 𝑏}∗} (B) {𝑤𝑎𝑛𝑏𝑛𝑤𝑅 |𝑤 ∈ {𝑎, 𝑏}∗, 𝑛 ≥ 0} (C) {𝑤𝑎𝑛𝑤𝑅𝑏𝑛 |𝑤 ∈ {𝑎, 𝑏}∗, 𝑛 ≥ 0} (D) {𝑎𝑛𝑏𝑖 | 𝑖 ∈ {𝑛, 3𝑛, 5𝑛}, 𝑛 ≥ 0} Ans: {wanwRbn ⏐ w ∈ {a, […]

Q. Suppose that in an IP-over-Ethernet network, a machine X wishes to find the MAC address of another machine Y in its subnet. Which one of the following techniques can be used for this? A. X sends an ARP request packet to the local gateway’s IP address which then finds the MAC address of Y

Q. Consider three machines M, N, and P with IP addresses 100.10.5.2, 100.10.5.5, and 100.10.5.6 respectively. The subnet mask is set to 255.255.255.252 for all the three machines. Which one of the following is true? (A) M, N, and P all belong to the same subnet (B) Only M and N belong to the same

Q. Two numbers are chosen independently and uniformly at random from the set {1, 2 , . . . , 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is Solution: The 4-bit binary representation of numbers (1, 2, 3, 4………13): 0  –

Q. The value of 351 mod 5 is     . Solution: = 351 mod 5 = (33)17 mod 5 = (27)17 mod 5= {(22)8*21} mod 5= {(4)8*(2)} mod 5= {(-1)8*(2)} mod 5= {(1*2)} mod 5= {(2)} mod 5= 2

Q. An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is   Solution: Given an array of 25