GATE CS question library

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.

​​A rectangular paper sheet of dimensions $54 \mathrm{~cm} \times 4 \mathrm{~cm}$ is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

The pie chart presents the percentage contribution of different macronutrients to a typical $2,000\; \mathrm{kcal}$ diet of a person. The typical energy density $(\mathrm{kcal} / \mathrm{g})$ of these macronutrients is given in the table. …

A rectangular paper of $20 \mathrm{~cm} \times 8 \mathrm{~cm}$ is folded $3$ times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in $\mathrm{cm}$ ) is

​​The least number of squares to be added in the figure to make $\text{A B}$ a line of symmetry is

​​Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combination of elements, they conclude that the spell does not work. How many attempts does each wizard make before coming to …

​​​​​If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [walk $\rightarrow$ jog $\rightarrow$ sprint] is analogous to [bothered $\rightarrow$ ________$\rightarrow$ daunted]. Which one of the given options is appropriate to fill the blank?

​​​​In an engineering college of $10,000$ students, $1,500$ like neither their core branches nor other branches. The number of students who like their core branches is $1 / 4^{\text{th }}$ of the number of students who like other branches. The number of students who like both their core and other branches is $500$. The number of students who like …

For positive non-zero real variables $x$ and $y$, if $$\ln \left(\frac{x+y}{2}\right)=\frac{1}{2}[\ln (x)+\ln (y)]$$ then, the value of $\frac{x}{y}+\frac{y}{x}$ is

​​​​​In the sequence $6,9,14, x, 30,41$, a possible value of $x$ is