GATE CS question library

​​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

​​​​​Sequence the following sentences in a coherent passage. $\text{P}$: This fortuitous geological event generated a colossal amount of energy and heat that resulted in the rocks rising to an average height of $4 \mathrm{~km}$ across the contact zone. $\text{Q}$: Thus, the geophysicists tend to think of the Himalayas as an active geological event …

​​​​​​A person sold two different items at the same price. He made $10 \%$ profit in one item, and $10 \%$ loss in the other item. In selling these two items, the person made a total of

​​​​The pie charts depict the shares of various power generation technologies in the total electricity generation of a country for the years $2007$ and $2023$. The renewable sources of electricity generation consist of Hydro, Solar and Wind. Assuming that the total electricity generated remains the same from $2007$ to $2023$, what is the percentage …

​​​​A cube is to be cut into $8$ pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube. The minimum number of such cuts required is

In the $4 \times 4$ array shown below, each cell of the first three rows has either a cross $(X)$ or a number. The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross ( $X$ ). Given that the last row has no crosses $(X)$, the sum of the four numbers to be filled in the last …

​​​Consider a computer with a $4 \mathrm{MHz}$ processor. Its $\text{DMA}$ controller can transfer $8$ bytes in $1$ cycle from a device to main memory through cycle stealing at regular intervals. Which one of the following is the data transfer rate (in bits per second) of the $\text{DMA}$ controller if $1 \%$ of the processor cycles are used for …

​​​​Let $p$ and $q$ be the following propositions: $p$ : Fail grade can be given. $q$ : Student scores more than $50 \%$ marks. Consider the statement: "Fail grade cannot be given when student scores more than $50 \%$ marks." Which one of the following is the CORRECT representation of the above statement in propositional logic?

Consider the following $\text{C}$ program. Assume parameters to a function are evaluated from right to left. #include <stdio.h> int g(int p) { printf("%d", p); return p; } int h(int q) { printf("%d", q); return q; } void f(int x, int y) { g(x); h(y); } int main() { f(g(10), h(20)); } Which one of the following options is the CORRECT output of the …

​​​​​Let $\text{T(n)}$ be the recurrence relation defined as follows: $$\begin{array}{l} T(0)=1, \\ T(1)=2, \text{ and } \\ T(n)=5 T(n-1)-6 T(n-2) \text{ for } n \geq 2 \end{array}$$ Which one of the following statements is TRUE?

​​​​​Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that $$f(x)=1-f(2-x)$$ Which one of the following options is the CORRECT value of $\int_{0}^{2} f(x) d x$ ?

​​​​Let $\text{A}$ be the adjacency matrix of a simple undirected graph $\text{G}$. Suppose $\text{A}$ is its own inverse. Which one of the following statements is always TRUE?