GATE CS question library

If $P = 3$, $R = 27$, $T = 243$, then $Q + S =$ ________

The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum $n$ number of circles can be painted, then the unpainted area available in annular space is _____.

Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, then $\alpha + \beta$ is ________.

The total revenue of a company during $2014-2018$ is shown in the bar graph. If the total expenditure of the company in each year is $500$ million rupees, then the aggregate profit or loss (in percentage) on the total expenditure of the company during $2014-2018$ is ___________.

Consider the functions $e^{-x}$ $x^{2}-\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$?

For parameters $a$ and $b$, both of which are $\omega(1)$, $T(n) = T(n^{1/a})+1$, and $T(b)=1$. Then $T(n)$ is

Consider the following statements. Daisy chaining is used to assign priorities in attending interrupts. When a device raises a vectored interrupt, the CPU does polling to identify the source of interrupt. In polling, the CPU periodically checks the status bits to know if any device needs its attention. During DMA, both the CPU and DMA controller can be bus …

Consider the following data path diagram. Consider an instruction: $R0 \leftarrow R1 +R2$. The following steps are used to execute it over the given data path. Assume that PC is incremented appropriately. The subscripts $r$ and $w$ indicate read and write operations, respectively. $R2_{r},\text{ TEMP1}_{r},ALU_{\text{add}}, \text{ TEMP2}_{w}$ …

The preorder traversal of a binary search tree is $15, 10, 12, 11, 20, 18, 16, 19$. Which one of the following is the postorder traversal of the tree?

What is the worst case time complexity of inserting $n^{2}$ elements into an AVL-tree with $n$ elements initially?

Which one of the following regular expressions represents the set of all binary strings with an odd number of $1’$s?

Consider the following statements. If $L_1 \cup L_2$ is regular, then both $L_1$ and $L_2$ must be regular. The class of regular languages is closed under infinite union. Which of the above statements is/are TRUE?

Consider the following statements. Symbol table is accessed only during lexical analysis and syntax analysis. Compilers for programming languages that support recursion necessarily need heap storage for memory allocation in the run-time environment. Errors violating the condition ‘any variable must be declared before its use’ are detected during syntax …

Consider the language $L = \{a^{n}\mid n \geq 0\} \cup \{a^{n}b^{n}\mid n \geq 0\}$ and the following statements. $L$ is deterministic context-free. $L$ is context-free but not deterministic context-free. $L$ is not $LL(k)$ for any $k$. Which of the above statements is/are TRUE?

Consider allocation of memory to a new process. Assume that none of the existing holes in the memory will exactly fit the process’s memory requirement. Hence, a new hole of smaller size will be created if allocation is made in any of the existing holes. Which one of the following statement is TRUE?

Consider the following statements about process state transitions for a system using preemptive scheduling. A running process can move to ready state. A ready process can move to running state. A blocked process can move to running state. A blocked process can move to ready state. Which of the above statements are TRUE?

Consider a relational database containing the following schemas. …

Which one of the following is used to represent the supporting many-one relationships of a weak entity set in an entity-relationship diagram?

What is the worst case time complexity of inserting $n$ elements into an empty linked list, if the linked list needs to be maintained in sorted order?

Let $\mathcal{R}$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $\mathcal{R}$ at random. The probability that the chosen relation is reflexive (round off to $3$ decimal places) is ______.