GATE CSE 2005
Q11.
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs (a,b) and (c,d) in the chosen set such that a \equiv c mod 3 and b \equiv d mod 5Q12.
Consider the languages: L_{1}=\{a^{n}b^{n}c^{m}|n,m \gt 0\} and L_{2}=\{a^{n}b^{m}c^{m}|n,m \gt 0\} Which one of the following statements is FALSE?Q13.
Consider the languages: L_{1}=\{ww^{R}|w\in \{0,1\}*\} L_{2}=\{w\#w^{R}|w\in \{0,1\}*\},where # is a special symbol L_{3}=\{ww|w\in \{0,1\}*\} Which one of the following is TRUE?Q14.
Suppose n processes, P_1,..., P_n share m identical resource units, which can be reserved and released one at a time. The maximum resource requirement of process P_i is s_i, where s_i \gt 0. Which one of the following is a sufficient condition for ensuring that deadlock does not occur?Q15.
Let E1 and E2 be two entities in an E/R diagram with simple single-valued attributes. R1 and R2 are two relationships between E1 and E2, where R1 is one-to-many and R2 is many-to-many. R1 and R2 do not have any attributes of their own. What is the minimum number of tables required to represent this situation in the relational model?Q16.
Let f: B \rightarrow C and g: A \rightarrow B be two functions and let h = f\cdotg. Given that h is an onto function which one of the following is TRUE?Q17.
Consider the set H of all 3 x 3 matrices of the type \begin{bmatrix} a & f & e\\ 0 & b & d\\ 0&0 & c \end{bmatrix} where a,b,c,d,e and f are real numbers and abc\neq0. Under the matrix multiplication operation, the set H is:Q18.
The set {1, 2, 4, 7, 8, 11, 13, 14} is a group under multiplication modulo 15. The inverses of 4 and 7 are respectively:Q19.
A Priority-Queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is given below: 10, 8, 5, 3, 2 Two new elements '1' and '7' are inserted in the heap in that order. The level-order traversal of the heap after the insertion of the elements is:Q20.
The following table has two attributes A and C where A is the primary key and C is the foreign key referencing A with on-delete cascade. The set of all tuples that must be additionally deleted to preserve referential integrity when the tuple (2,4) is deleted is: