GATE CS question library

The grammar $A \rightarrow AA \mid (A) \mid \epsilon$ is not suitable for predictive-parsing because the grammar is:

The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be:

An undirected graph $G$ has $n$ nodes. its adjacency matrix is given by an $n \times n$ square matrix whose (i) diagonal elements are 0’s and (ii) non-diagonal elements are 1’s. Which one of the following is TRUE?

A program $P$ reads in $500$ integers in the range $[0, 100]$ representing the scores of $500$ students. It then prints the frequency of each score above $50$. What would be the best way for $P$ to store the frequencies?

Which one of the following are essential features of an object-oriented programming language? Abstraction and encapsulation Strictly-typedness Type-safe property coupled with sub-type rule Polymorphism in the presence of inheritance

A common property of logic programming languages and functional languages is:

An Abstract Data Type (ADT) is:

What does the following C-statement declare? int (*f) (int * );

A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is:

Box $P$ has $2$ red balls and $3$ blue balls and box $Q$ has $3$ red balls and $1$ blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes $P$ and $Q$ are $\dfrac{1}{3}$ and $\dfrac{2}{3}$ …

Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$?

What are the eigenvalues of the following $2\times 2$ matrix? $$\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$$

Consider the following system of linear equations : $$2x_1 - x_2 + 3x_3 = 1$$ $$3x_1 + 2x_2 + 5x_3 = 2$$ $$-x_1+4x_2+x_3 = 3$$ The system of equations has

Which one of the following graphs is NOT planar?

Consider the set $H$ of all $3 * 3$ matrices of the type $$\left( \begin{array}{ccc} a & f & e \\ 0 & b & d \\ 0 & 0 & c \end{array} \right)$$ where $a,b,c,d,e$ and $f$ are real numbers and $abc ≠ 0.$ Under the matrix multiplication operation, the set $H$ is:

What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$

Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE?

Let $R$ and $S$ be any two equivalence relations on a non-empty set $A$. Which one of the following statements is TRUE?

Let $P, Q,$ and $R$ be three atomic propositional assertions. Let $X$ denote $( P ∨ Q ) → R$ and $Y$ denote $(P → R) ∨ (Q → R).$ Which one of the following is a tautology?

What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student"