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GATE CS Engineering Mathematics Previous Year Questions

23 solved GATE CS questions on Engineering Mathematics, drawn from 1 exam year and grouped by year. Every question shows the official answer and a step-by-step solution.

GATE CS 202423 questions

Set 1 Q11Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x) = \max\{x, x^3\}, x \in \mathbb{R}$ , where $\mathbb{R}$ is the set of all real…MCQ · +1 marks · Medium
Set 1 Q12The product of all eigenvalues of the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$ isMCQ · +1 marks · Easy
Set 1 Q14Consider a permutation sampled uniformly at random from the set of all permutations of $\{1, 2, 3, \dots, n\}$ for some $n \geq 4$ . Let $X$ be the event that 1…MCQ · +1 marks · Medium
Set 1 Q27Let $A$ 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?MSQ · +1 marks · Medium
Set 1 Q32Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$ . The…NAT · +1 marks · Medium
Set 1 Q34The number of spanning trees in a complete graph of 4 vertices labelled A, B, C, and D is _________NAT · +1 marks · Easy
Set 1 Q49Let $A$ be any $n \times m$ matrix, where $m > n$ . Which of the following statements is/are TRUE about the system of linear equations $Ax = \mathbf{0}$ ?MSQ · +2 marks · Hard
Set 1 Q51The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and…MSQ · +2 marks · Medium
Set 1 Q52Consider the operators $\diamond$ and $\Box$ defined by $a \diamond b = a + 2b$ , $a \Box b = ab$ , for positive integers. Which of the following statements…MSQ · +2 marks · Medium
Set 1 Q63A 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…NAT · +2 marks · Easy
Set 2 Q3In 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…MCQ · +1 marks · Easy
Set 2 Q12Let $p$ and $q$ be the following propositions: $p$ : Fail grade can be given. $q$ : Student scores more than 50% marks. Consider the statement: "Fail grade…MCQ · +1 marks · Easy
Set 2 Q15Let $T(n)$ be the recurrence relation defined as follows: $T(0) = 1$ , $T(1) = 2$ , and $T(n) = 5T(n - 1) - 6T(n - 2)$ for $n \geq 2$ . Which one of the following…MCQ · +1 marks · Medium
Set 2 Q16Let $f(x)$ 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…MCQ · +1 marks · Medium
Set 2 Q17Let $A$ be the adjacency matrix of a simple undirected graph $G$ . Suppose $A$ is its own inverse. Which one of the following statements is always TRUE?MCQ · +1 marks · Medium
Set 2 Q18When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) isMCQ · +1 marks · Easy
Set 2 Q34Let $P$ be the partial order defined on the set $\{1,2,3,4\}$ as follows $P = \{(x,x) \mid x \in \{1,2,3,4\}\} \cup \{(1,2), (3,2), (3,4)\}$ The number of…NAT · +1 marks · Medium
Set 2 Q44Let $x$ and $y$ be random variables, not necessarily independent, that take real values in the interval $[0,1]$ . Let $z = xy$ and let the mean values of…MCQ · +2 marks · Medium
Set 2 Q47Let $A$ be an $n \times n$ matrix over the set of all real numbers $\mathbb{R}$ . Let $B$ be a matrix obtained from $A$ by swapping two rows. Which of the…MSQ · +2 marks · Medium
Set 2 Q51Let $G$ be an undirected connected graph in which every edge has a positive integer weight. Suppose that every spanning tree in $G$ has even weight. Which of…MSQ · +2 marks · Hard
Set 2 Q59The number of distinct minimum-weight spanning trees of the following graph is _________ [figure]NAT · +2 marks · Hard
Set 2 Q60The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is…NAT · +2 marks · Medium
Set 2 Q63Let $Z_n$ be the group of integers $\{0, 1, 2, \dots, n - 1\}$ with addition modulo $n$ as the group operation. The number of elements in the group…NAT · +2 marks · Medium

Other GATE CS topics

General Aptitude(20)Programming & Data Structures(17)Databases(12)Computer Networks(12)Computer Organization & Architecture(12)Operating System(10)Compiler Design(9)Theory of Computation(8)Digital Logic(8)Algorithms(5)

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