August 2023

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

Q. Consider the grammar given below: S → Aa A → BD B → b | ϵ D → d | ϵ Let a, b, d, and $ be indexed as follows: a b d $ 3 2 1 0 Compute the FOLLOW set of the non-terminal B and write the index values for the