List of top Questions asked in GATE CS

In the \(4 \times 4\) array shown below, each cell of the first three rows has either a cross (X) or a number. \[ \begin{array}{|c|c|c|c|} \hline 1 & X & 4 & 3
\hline X & 5 & 5 & 4
\hline 3 & X & 6 & X
\hline ? & ? & ? & ?
\hline \end{array} \] 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 row is:
Consider a computer with a \(4 \, \text{MHz}\) processor. Its DMA controller can transfer \(8 \, \text{bytes}\) 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 DMA controller if \(1\%\) of the processor cycles are used for DMA?
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?
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. \begin{center} \includegraphics[width=10cm]{8.png} \end{center} 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 increase in the share of the renewable sources of electricity generation over this period?
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:
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:
Sequence the following sentences in a coherent passage. 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 km across the contact zone. Q: Thus, the geophysicists tend to think of the Himalayas as an active geological event rather than as a static geological feature. R: The natural process of the cooling of this massive edifice absorbed large quantities of atmospheric carbon dioxide, altering the earth’s atmosphere and making it better suited for life. S: Many millennia ago, a breakaway chunk of bedrock from the Antarctic Plate collided with the massive Eurasian Plate.
For positive non-zero real variables \( x \) and \( y \), if \[ \ln\left(\frac{x + y}{2}\right) = \frac{1}{2}\left[\ln(x) + \ln(y)\right], \] then the value of \( \frac{x}{y} + \frac{y}{x} \) is:
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 \( \frac{1}{4} \) 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 their core branches is:
In the sequence \( 6, 9, 14, x, 30, 41 \), a possible value of \( x \) 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 combinations of elements, they conclude that the spell does not work. How many attempts does each wizard make before coming to this conclusion, independently?
If \( \to \) denotes increasing order of intensity, then the meaning of the words [walk \( \to \) jog \( \to \) sprint] is analogous to [bothered \( \to \) ...........\_ \( \to \) daunted].
Consider the 5-state DFA \( M \) accepting the language \( L(M) \subseteq (0+1)^* \) shown below. For any string \( w \in (0+1)^* \), let \( n_0(w) \) be the number of \( 0 \)'s in \( w \) and \( n_1(w) \) be the number of \( 1 \)'s in \( w \). \begin{center} \includegraphics[width = 6cm]{50.png} \end{center} Which of the following statements is/are FALSE?
Consider the following C function definition: \begin{verbatim} int f(int x, int y) { for (int i = 0; i<y; i++) { x = x + x + y; } return x; } \end{verbatim} Which of the following statements is/are TRUE about the above function?
Let \( A \) be any \( n \times m \) matrix, where \( m>n \). Which of the following statements is/are TRUE about the system of linear equations \( Ax = 0 \)?
The symbol \( \rightarrow \) indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?
Consider a binary min-heap containing 105 distinct elements. Let \( k \) be the index (in the underlying array) of the maximum element stored in the heap. The number of possible values of \( k \) is:
Let \( G \) be a directed graph and \( T \) a depth first search (DFS) spanning tree in \( G \) that is rooted at a vertex \( v \). Suppose \( T \) is also a breadth first search (BFS) tree in \( G \), rooted at \( v \). Which of the following statements is/are TRUE for every such graph \( G \) and tree \( T \)?
Consider a Boolean expression given by \( F(X, Y, Z) = \Sigma(3, 5, 6, 7) \). Which of the following statements is/are CORRECT?
Consider the following recurrence relation: \[ T(n) = \begin{cases} \sqrt{n}T(\sqrt{n}) + n & \text{for } n \geq 1,
1 & \text{for } n = 1. \end{cases} \] Which one of the following options is CORRECT?
An array \( [82, 101, 90, 11, 111, 75, 33, 131, 44, 93] \) is heapified. Which one of the following options represents the first three elements in the heapified array?
Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT? \begin{center} \includegraphics[width=8cm]{28.png} \end{center}
TCP client \( P \) successfully establishes a connection to TCP server \( Q \). Let \( N_P \) denote the sequence number in the SYN sent from \( P \) to \( Q \). Let \( N_Q \) denote the acknowledgement number in the SYN ACK from \( Q \) to \( P \). Which of the following statements is/are CORRECT?
Consider a 5-stage pipelined processor with Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access (MEM), and Register Writeback (WB) stages. Which of the following statements about forwarding is/are CORRECT?
Let \( A \) and \( B \) be two events in a probability space with \( P(A) = 0.3 \), \( P(B) = 0.5 \), and \( P(A \cap B) = 0.1 \). Which of the following statements is/are TRUE?