List of top Questions asked in GATE CS- 2026

Consider the transmission of data bits 110001011 over a link that uses Cyclic Redundancy Check (CRC) code for error detection. If the generator bit pattern is given to be 1001, which one of the following options shows the remainder bit pattern appended to the data bits before transmission?

Which one of the following statements is equivalent to the following assertion?
Turing machine \(M\) decides the language \(L \subseteq \{0,1\}^*\)

Consider an array \(A = [10,\ 7,\ 8,\ 19,\ 41,\ 35,\ 25,\ 31]\). Suppose the merge sort algorithm is executed on array \(A\) to sort it in increasing order. The merge sort algorithm will carry out a total of 7 merge operations.

A merge operation on sorted left array \(L\) and sorted right array \(R\) is said to be void if the output of the merge operation is the elements of array \(L\) followed by the elements of array \(R\).

The number of void merge operations among these 7 merge operations is ______.

A lexical analyzer uses the following token definitions:

• \(letter \rightarrow [A-Za-z]\)
• \(digit \rightarrow [0-9]\)
• \(id \rightarrow letter\,(letter\,|\,digit)^{*}\)
• \(number \rightarrow digit^{+}\)
• \(ws \rightarrow (blank\,|\,tab\,|\,newline)^{+}\)

For the string given below,
\[ x1\ \ 23mm\ \ 78\ \ y\ \ 7z\ \ zz5\ \ 14A\ \ 8H\ \ AaYcD \]
the number of tokens (excluding \(ws\)) that will be produced by the lexical analyzer is ______.

Expedite, Hasten, Hurry,
Fill the blank by choosing a word with a meaning similar to that of the words given above.

Consider the following two finite automata \(D_1\) and \(D_2\).

Which of the following statements is/are true?

In a C runtime environment, which one of the following is stored in the heap?

The values of Stock A and Stock B on a particular day are Rs. 50 and Rs. 80, respectively. An investor invests Rs. 100 in Stock A and Rs. 80 in Stock B. He sells all the stocks the next day when the value of Stock A is Rs. 55 and Stock B is Rs. 70. The profit made by the investor is Rs.

In the context of schema normalization in relational DBMS, consider a set F of functional dependencies. The set of all functional dependencies implied by F is called the closure of F. To compute the closure of F, Armstrong's Axioms can be applied. Consider \(X\), \(Y\), and \(Z\) as sets of attributes over a relational schema. The three rules of Armstrong's Axioms are described as follows.

Reflexivity: If \(Y \subseteq X\), then \(X \to Y\)
Augmentation: If \(X \to Y\), then \(XZ \to YZ\) for any Z
Transitivity: If \(X \to Y\) and \(Y \to Z\), then \(X \to Z\)

The additional rule of Union is defined as follows.
Union: If \(X \to Y\) and \(X \to Z\), then \(X \to YZ\)

It can be proved that the additional rule of Union is also implied by the three rules of Armstrong's Axioms. Listed below are four combinations of these three rules. Which one of these combinations is both necessary and sufficient for the proof?

The determinant of a \(4 \times 4\) matrix \(A\) is 3. The value of the determinant of \(2A\) is ____________.

A system has a Translation Lookaside Buffer (TLB) that has a reach of \(1\) MB. TLB reach is defined as the total amount of physical memory that can be accessed through the TLB entries. The paging system uses pages of size \(4\) KB. The virtual address space is \(64\) GB and physical address space is \(1\) GB. If each TLB entry stores a \(4\)-bit process id, page number, frame number, and a \(2\)-bit control field, then the size of the TLB (in bytes) is ______. (answer in integer)

Note: \(1K=2^{10}\), \(1M=2^{20}\), \(1G=2^{30}\)

Consider the canonical \(LR(0)\) parsing of the grammar below using terminals \(\{a,b,c\}\) and non-terminals \(\{A,B,C,S\}\) with \(S\) as the start symbol.
\[ S \to ACB \]
\[ A \to aA \mid \epsilon \]
\[ C \to cC \mid \epsilon \]
\[ B \to bB \mid b \]
Which one of the following options gives the number of shift-reduce conflicts that will occur in the \(LR(0)\) ACTION table?

Which of the following grammars is/are ambiguous?

Let \(\Sigma = \{a, b, c, d\}\) and let \(L = \{a^i b^j c^k d^l \mid i, j, k, l \geq 0\}\). Which of the following constraints ensure(s) that the language \(L\) is context-free?

A non-pipelined instruction execution unit that operates at 1.6 GHz clock takes an average of 5 clock cycles to complete the execution of an instruction. To improve the performance, the system was pipelined with a goal of achieving an average throughput of one instruction per clock cycle. However, it could operate only at 1.2 GHz due to pipeline overheads. While executing a program in the pipelined design, 30% of instructions encountered a stall of 2 cycles due to pipeline hazards. The speed-up obtained by the pipelined design over the non-pipelined one for this program is ______ (rounded off to two decimal places).

Note: \(1\text{G}=10^{9}\)

Which of the following statements is/are true with respect to the interaction of a web browser with a web server using HTTP 1.1?

Consider \(4 \times 4\) matrices with their elements from \(\{0, 1\}\). The number of such matrices with even number of 1s in every row and every column is ______.

An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice in succession and the number on the top face is recorded each time. The probability that the number appearing in the second roll is an integer multiple of the number appearing in the first roll is ______.

Consider a processor P whose instruction set architecture is the load-store architecture. The instruction format is such that the first operand of any instruction is the destination operand.
Which one of the following sequences of instructions corresponds to the high-level language statement \(Z = X + Y\)?
Note: X, Y, and Z are memory operands. R0, R1, and R2 are registers.

With respect to a TCP connection between a client and a server, which one of the following statements is true?

'When the teacher is in the room, all students stand silently.'
If the above statement is true, which one of the following statements is not necessarily true?

Consider the implementation of sliding window protocol over a lossless link, with a window size of \(W\) frames, where each frame is of size 1000 bits (including header). The bandwidth of the link is 100 kbps (\(1\text{k} = 10^3\)) and the one-way propagation delay is 100 milliseconds. Assume that processing times at the sender and receiver are zero and the transmission time of acknowledgements is also zero. Which one of the following options gives the minimum size of \(W\) (in number of frames) required to achieve 100% link utilization?

For \(n > 1\), the maximum multiplicity of any eigenvalue of an \(n \times n\) matrix with elements from \(\mathbb{R}\) is

Consider the function \(f: \mathbb{R} \to \mathbb{R}\) defined as follows:

where \(c_1, c_2 \in \mathbb{R}\).

If \(f\) is continuous at \(x = 0\), then \(c_1 + c_2 = \) __________. (answer in integer)

Let \(f: \mathbb{R} \to \mathbb{R}\) be defined as follows: \[ f(x) = \left(\dfrac{|x|}{2} - x\right)\left(x - \dfrac{|x|}{2}\right) \] Which of the following statements is/are true?