GATE CSE 2019
Q31.
In an RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also is known that \phi(n)=2880, where \phi() denotes Euler's Totient Function, then the prime factors of n which is greater than 50 is _________ .Q32.
Consider Z = X - Y where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of:Q34.
Let the set of functional dependencies F=\{QR\rightarrow S,R\rightarrow P,S\rightarrow Q\} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z where Y = (PR) and Z = (QRS). Consider the two statements given below: I. Both Y and Z are in BCNF II. Decomposition of X into Y and Z is dependency preserving and lossless. Which of the above statements is/are correct?Q35.
Consider the augmented grammar given below: S'\rightarrow S S \rightarrow \lt L \gt |id L \rightarrow L,S|S Let I_0=CLOSURE(\{[S'\rightarrow \cdot S]\}) . The number of items in the set GOTO(I_0,\lt) is __________.Q36.
Consider the following given grammar: S \rightarrow Aa A \rightarrow BD B \rightarrow b|\epsilon D \rightarrow d|\epsilon Let a, b, d and $ be indexed as follows: Compute the FOLLOW set of the non-terminal B and write the index values for the symbols in the FOLLOW set in the descending order. (For example, if the FOLLOW set is {a, b, d, $}, then the answer should be 3210). Answer:_____Q38.
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 ___________Q39.
Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x^2+6xY+3Y+6 has only real roots is (rounded off to 1 decimal place) _________.Q40.
Consider three concurrent processes P1, P2 and P3 as shown below, which access a shared variable D that has been initialized to 100. The process are executed on a uniprocessor system running a time-shared operating system. If the minimum and maximum possible values of D after the three processes have completed execution are X and Y respectively, then the value of Y-X is __________.