GATE CSE 2023
Q1.
Suppose in a web browser, you click on the www.gate-2023.in URL. The browser cache is empty. The IP address for this URL is not cached in your local host, so a DNS lookup is triggered (by the local DNS server deployed on your local host) over the 3-tier DNS hierarchy in an iterative mode. No resource records are cached anywhere across all DNS servers. Let RTT denote the round trip time between your local host and DNS servers in the DNS hierarchy. The round trip time between the local host and the web server hosting www.gate-2023.in is also equal to RTT. The HTML file associated with the URL is small enough to have negligible transmission time and negligible rendering time by your web browser, which references 10 equally small objects on the same web server. Which of the following statements is/are CORRECT about the minimum elapsed time between clicking on the URL and your browser fully rendering it?Q2.
Let f and g be functions of natural numbers given by f(n)=n and g(n)=n^2. Which of the following statements is/are TRUE?Q3.
Consider functions Function 1 and Function 2 expressed in pseudocode as follows:Let f_1(n) and f_2(n) denote the number of times the statement "x = x + 1" is executed in Function 1 and Function 2, respectively. Which of the following statements is/are TRUE?Q4.
An 8-way set associative cache of size 64 KB (1 KB = 1024 bytes) is used in a system with 32-bit address. The address is sub-divided into TAG, INDEX, and BLOCK OFFSET. The number of bits in the TAG is ____.Q5.
The value of the definite integral \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1} (4x^2y-z^3)dzdydx is _____. (Rounded off to the nearest integer)Q6.
Let f(x)=x^3+15x^2-33x-36 be a real-valued function. Which of the following statements is/are TRUE?Q7.
Let U = {1, 2,...,n}, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A, B be subsets of U with |A| = |B| = k and A\cap B=\phi . We say that a permutation of U separates A from B if one of the following is true. - All members of A appear in the permutation before any of the members of B. - All members of B appear in the permutation before any of the members of A. How many permutations of U separate A from B?Q8.
Consider the C function foo and the binary tree shown. typedef struct node { int val; struct node *left, *right; } node; int foo(node *p) { int retval; if (p == NULL) return 0; else { retval = p->val + foo(p->left) + foo(p->right); printf("%d ", retval); return retval; } } When foo is called with a pointer to the root node of the given binary tree, what will it print?Q10.
Consider the context-free grammar G below S\rightarrow aSb \;| \;X X\rightarrow aX \;| \;Xb \;|\; a\;|\; b where S and X are non-terminals, and a and b are terminal symbols. The starting non-terminal is S. Which one of the following statements is CORRECT?