GATE CS question library

Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ?

On a non-pipelined sequential processor, a program segment, which is the part of the interrupt service routine, is given to transfer $500$ bytes from an I/O device to memory. Initialize the address register Initialize the count to 500 LOOP: Load a byte from device Store in memory at address given by address register Increment the address register Decrement …

Consider two binary operators $\text{‘} \uparrow \text{’}$ and $\text{‘} \downarrow \text{’}$ with the precedence of operator $\downarrow$ being lower than that of the operator $\uparrow$. Operator $\uparrow$ is right associative while operator $\downarrow$ is left associative. Which one of the following represents the parse tree for expression …

Consider the languages $L1, \:L2 \:and \: L3$ as given below. $L1=\{0^p 1^q \mid p, q \in N\}, \\ L2 = \{0^p 1^q \mid p, q \in N \:and \:p=q\} \: and, \\ L3 = \{0^p 1^q 0^r \mid p, q, r \in N\: and \: p=q=r\}.$ Which of the following statements is NOT TRUE?

An algorithm to find the length of the longest monotonically increasing sequence of numbers in an array $A[0:n-1]$ is given below. Let $L_i$, denote the length of the longest monotonically increasing sequence starting at index $i$ in the array. Initialize $L_{n-1} = 1$. For all $i$ such that $0 \leq i \leq n-2$ …

A max-heap is a heap where the value of each parent is greater than or equal to the value of its children. Which of the following is a max-heap?

Consider a hypothetical processor with an instruction of type $\text{LW R1, 20(R2)}$, which during execution reads a $32\text{-bit}$ word from memory and stores it in a $32\text{-bit}$ register $\text{R1}$. The effective address of the memory location is obtained by the addition of a constant $20$ and the contents of register $\text{R2}$. Which …

What does the following fragment of C program print? char c[] = "GATE2011"; char *p = c; printf("%s", p + p[3] - p[1]);

Let the page fault service time be $10$ milliseconds(ms) in a computer with average memory access time being $20$ nanoseconds (ns). If one page fault is generated every $10^6$ memory accesses, what is the effective access time for memory?

The lexical analysis for a modern computer language such as Java needs the power of which one of the following machine models in a necessary and sufficient sense?

K4 and Q3 are graphs with the following structures. Which one of the following statements is TRUE in relation to these graphs?

A thread is usually defined as a "light weight process" because an Operating System (OS) maintains smaller data structure for a thread than for a process. In relation to this, which of the following statement is TRUE?

If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\left(E\left[X\right]\right)^2$ is denoted by $R$, then

The minimum number of $\text{D}$ flip-flops needed to design a mod-258 counter is

The simplified SOP (Sum of Product) from the Boolean expression $$(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$$ is

Consider a relational table with a single record for each registered student with the following attributes: $\text{Registration\_Num:}$ Unique registration number for each registered student $\text{UID:}$ Unique identity number, unique at the national level for each citizen $\text{BankAccount\_Num:}$ Unique account number at the bank. A student can …

A computer handles several interrupt sources of which of the following are relevant for this question. Interrupt from CPU temperature sensor (raises interrupt if CPU temperature is too high) Interrupt from Mouse (raises Interrupt if the mouse is moved or a button is pressed) Interrupt from Keyboard (raises Interrupt if a key is pressed or released) Interrupt …

Which one of the following is NOT desired in a good Software Requirement Specifications (SRS) document?

HTML (HyperText Markup Language) has language element which permit certain actions other than describing the structure of the web document. Which one of the following actions is NOT supported by pure HTML (without any server or client side scripting) pages?

Which of the following pairs have DIFFERENT expressive power?