GATE CSE 2022
Q21.
Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?MSQQ22.
Consider two files systems A and B , that use contiguous allocation and linked allocation, respectively. A file of size 100 blocks is already stored in A and also in B. Now, consider inserting a new block in the middle of the file (between 50^{th} \text{ and }51^{st} block), whose data is already available in the memory. Assume that there are enough free blocks at the end of the file and that the file control blocks are already in memory. Let the number of disk accesses required to insert a block in the middle of the file in A and B are n_A and n_B, respectively, then the value of n_A+n_B isQ24.
Suppose we are given n keys, m hash table slots, and two simple uniform hash functions h_1 and h_2. Further suppose our hashing scheme uses h_1 for the odd keys and h_2 for the even keys. What is the expected number of keys in a slot?Q25.
Which one of the following facilitates transfer of bulk data from hard disk to main memory with the highest throughput?Q26.
Consider the problem of reversing a singly linked list. To take an example, given the linked list below,the reversed linked list should look like Which one of the following statements is TRUE about the time complexity of algorithms that solve the above problem in O(1) space?Q27.
Consider the following two statements with respect to the matrices A_{m \times n},B_{n \times m},C_{n \times n} \text{ and }D_{n \times n}, Statement 1: tr(AB) = tr(BA) Statement 2: tr(CD) = tr(DC) wheretr() represents the trace of a matrix. Which one of the following holds?Q28.
Consider solving the following system of simultaneous equations using LU decomposition. \begin{aligned} x_1+x_2-2x_3&=4 \\ x_1+3x_2-x_3&=7 \\ 2x_1+x_2-5x_3&=7 \end{aligned}where L and U are denoted asL= \begin{bmatrix} L_{11} & 0 & 0 \\ L_{21}& L_{22} & 0 \\ L_{31} & L_{32} & L_{33} \end{bmatrix}, U= \begin{bmatrix} U_{11} & U_{12} & U_{13} \\ 0& U_{22} & U_{23} \\ 0 & 0 & U_{33} \end{bmatrix}Which one of the following is the correct combination of values for L32, U33, and x_1?Q29.
Which of the following is/are the eigenvector(s) for the matrix given below? \begin{pmatrix} -9 &-6 &-2 &-4 \\ -8& -6 & -3 & -1 \\ 20 & 15 & 8 & 5 \\ 32& 21& 7&12 \end{pmatrix}MSQQ30.
Consider a demand paging system with four page frames (initially empty) and LRU page replacement policy. For the following page reference string 7, 2, 7, 3, 2, 5, 3, 4, 6, 7, 7,1, 5, 6,1 the page fault rate, defined as the ratio of number of page faults to the number of memory accesses (rounded off to one decimal place) is