GATE CS question library

Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE?

​​​​Consider two set-associative cache memory architectures: $\text{WBC}$, which uses the write back policy, and $\text{WTC}$, which uses the write through policy. Both of them use the $\text{LRU}$ (Least Recently Used) block replacement policy. The cache memory is connected to the main memory. Which of the following statements is/are TRUE?

Consider a $512$ GB hard disk with $32$ storage surfaces. There are $4096$ sectors per track and each sector holds $1024$ bytes of data. The number of cylinders in the hard disk is _________.

Consider the following code snippet using the fork () and wait () system calls. Assume that the code compiles and runs correctly, and that the system calls run successfully without any errors. int x=3; while (x>0){ fork (); printf("hello"); wait (NULL) ; X-- ; } The total number of times the printf statement is executed is __________.

A given program has $25 \%$ load/store instructions. Suppose the ideal $\text{CPI}$ (cycles per instruction) without any memory stalls is $2$. The program exhibits $2 \%$ miss rate on instruction cache and $8 \%$ miss rate on data cache. The miss penalty is $100$ cycles. The speedup (rounded off to two decimal places) achieved with a perfect …

The baseline execution time of a program on a $2 \mathrm{GHz}$ single core machine is $100$ nanoseconds ( $n s)$. The code corresponding to $90 \%$ of the execution time can be fully parallelized. The overhead for using an additional core is $10 ~ns$ when running on a multicore system. Assume that all cores in the multicore system run their share …

Let $G=(V, \Sigma, S, P)$ be a context-free grammar in Chomsky Normal Form with $\Sigma=\{a, b, c\}$ and $V$ containing $10$ variable symbols including the start symbol $S$. The string $w=a^{30} b^{30} c^{30}$ is derivable from $S$. The number of steps (application of rules) in the derivation $S \rightarrow^* w$ is __________.

Consider the entries shown below in the forwarding table of an $\text{IP}$ router. Each entry consists of an $\text{IP}$ prefix and the corresponding next hop router for packets whose destination $\text{IP}$ address matches the prefix. The notation " /$\mathrm{N}$ " in a prefix indicates a subnet mask with the most significant $\mathrm{N}$ bits set …

The number of edges present in the forest generated by the $\text{DFS}$ traversal of an undirected graph $G$ with $100$ vertices is $40$. The number of connected components in $G$ is __________.

Consider the following two regular expressions over the alphabet $\{0,1\}$ : $r= 0^{*}+1^{*}$ $s = 01^{*} + 10^{*}$ The total number of strings of length less than or equal to $5$, which are neither in $r$ nor in $s$, is ________.

Consider a memory management system that uses a page size of $2 \mathrm{~KB}$. Assume that both the physical and virtual addresses start from $0$. Assume that the pages $0,1,2$, and $3$ are stored in the page frames $1,3,2$, and $0$, respectively. The physical address (in decimal format) corresponding to the virtual address $2500$ (in decimal …

A bag contains $10$ red balls and $15$ blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to $3$ decimal places) that both balls drawn are red is ___________.

Consider a digital logic circuit consisting of three $2$-to-$1$ multiplexers $\text{M1, M2}$, and $\text{M3}$ as shown below. $\mathrm{X} 1$ and $\mathrm{X} 2$ are inputs of $\mathrm{M} 1$. $\text{X3}$ and $\text{X4}$ are inputs of $\text{M2}$. $\text{A, B}$, and $\text{C}$ are select lines of $\text{M1, M2}$, and $\text{M3}$, …

Consider sending an $\text{IP}$ datagram of size $1420$ bytes (including $20$ bytes of $\text{IP}$ header) from a sender to a receiver over a path of two links with a router between them. The first link (sender to router) has an $\text{MTU}$ (Maximum Transmission Unit) size of $542$ bytes, while the second link (router to receiver) has an …

If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [dry $\rightarrow$ arid $\rightarrow$ parched] is analogous to [diet $\rightarrow$ fast $\rightarrow$ ________ ]. Which one of the given options is appropriate to fill the blank?

​​​If two distinct non-zero real variables $x$ and $y$ are such that $(x+y)$ is proportional to $(x-y)$ then the value of $\frac{x}{y}$

Consider the following sample of numbers: $9,18,11,14,15,17,10,69,11,13$ The median of the sample is

​​​​The number of coins of ₹$1$, ₹$5$, and ₹$10$ denominations that a person has are in the ratio $5:3:13$. Of the total amount, the percentage of money in ₹$5$ coins is

For positive non-zero real variables $p$ and $q$, if $\log \left(p^2+q^2\right)=\log p+\log q+2 \log 3,$ then, the value of $\frac{p^4+q^4}{p^2 q^2}$ is

In the given text, the blanks are numbered $\text{(i) - (iv)}$. Select the best match for all the blanks. Steve was advised to keep his head (i) before heading (ii) to bat; for, while he had a head (iii) batting, he could only do so with a cool head iv his shoulders.