GATE CS question library

In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue $1$ are

Consider a machine with a byte addressable main memory of $2^{20}$ bytes, block size of $16$ bytes and a direct mapped cache having $2^{12}$ cache lines. Let the addresses of two consecutive bytes in main memory be $\textsf{(E201F)}_{16}$ and $\textsf{(E2020)}_{16}$. What are the tag and cache line addresses ( in hex) for main memory address …

While inserting the elements $71, 65, 84, 69, 67, 83$ in an empty binary search tree (BST) in the sequence shown, the element in the lowest level is

The result evaluating the postfix expression $10 \ 5 + 60 \ 6 / * 8 -$ is

Consider a software program that is artificially seeded with 100 faults. While testing this program, 159 faults are detected, out of which 75 faults are from those artificially seeded faults. Assuming that both real and seeded faults are of same nature and have same distribution, the estimated number of undetected real faults is _______.

Two processes $X$ and $Y$ need to access a critical section. Consider the following synchronization construct used by both the processes …

The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is

In a web server, ten WebPages are stored with the URLs of the form http://www.yourname.com/var.html; where var is a different number from 1 to 10 for each Webpage. Suppose the client stores the Webpage with var = 1 (say W1) in the local machine, edits and then tests. Rest of the Webpages remains on the web server. W1 contains several relative URLs of the …

Consider the following C program segment. # include <stdio.h> int main() { char s1[7] = "1234", *p; p = s1 + 2; *p = '0'; printf("%s", s1); } What will be printed by the program?

Consider a CSMA/CD network that transmits data at a rate of $100\;\textsf{Mbps}\; (10^8\;\text{bits}$ per second) over a $1\;\textsf{km}$ (kilometre) cable with no repeaters. If the minimum frame size required for this network is $1250\;\text{bytes},$ What is the signal speed $\textsf{(km/sec)}$ in the cable?

The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.

Consider the following relation Cinema($\textit{theater, address, capacity}$) Which of the following options will be needed at the end of the SQL query SELECT P1.address FROM Cinema P1 such that it always finds the addresses of theaters with maximum capacity?

Consider the equality $\displaystyle{\sum_{i=0}^n} i^3 = X$ and the following choices for $X$: $\Theta(n^4)$ $\Theta(n^5)$ $O(n^5)$ $\Omega(n^3)$ The equality above remains correct if $X$ is replaced by

Let $\#$ be the binary operator defined as $X\#Y = X'+Y'$ where $X$ and $Y$ are Boolean variables. Consider the following two statements. $(S_1)$ $(P\#Q)\#R = P\#(Q\#R)$ $(S_2)$ $Q\#R = (R\#Q)$ Which are the following is/are true for the Boolean variables $P, Q$ and $R$?

The maximum number of processes that can be in $\textit{Ready}$ state for a computer system with $n$ CPUs is :

The exports and imports (in crores of $Rs$.) of a country from the year $2000$ to $2007$ are given in the following bar chart. In which year is the combined percentage increase in imports and exports the highest?

Most experts feel that in spite of possessing all the technical skills required to be a batsman of the highest order, he is unlikely to be so due to lack of requisite temperament. He was guilty of throwing away his wicket several time after working hard to lay a strong foundation. His critics pointed out that until he addressed his problem, success at the …

Choose the most appropriate equation for the function drawn as thick line, in the plot below.

The head of newly formed government desires to appoint five of the six selected members $P, Q, R, S, T$ and $U$ to portfolios of Home, Power, Defense, Telecom, and Finance. U does not want any portfolio if $S$ gets one of the five. $R$ wants either Home or Finance or no portfolio. $Q$ says that if $S$ gets Power or Telecom, then she must get the …

Alexander turned his attention towards India, since he had conquered Persia. Which one of the statements below is logically valid and can be inferred from the above sentence?