GATE CS question library

Let $L \subseteq \Sigma^*$ where $\Sigma = \left\{a,b \right\}$. Which of the following is true?

Which of the following is false?

Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false?

Which two of the following four regular expressions are equivalent? ($\varepsilon$ is the empty string). $(00)^ * (\varepsilon +0)$ $(00)^*$ $0^*$ $0(00)^*$

The formula used to compute an approximation for the second derivative of a function $f$ at a point $x_0$ is

Two dice are thrown simultaneously. The probability that at least one of them will have $6$ facing up is

Which of the following statements is FALSE?

Suppose $X$ and $Y$ are sets and $|X| \text{ and } |Y|$ are their respective cardinality. It is given that there are exactly $97$ functions from $X$ to $Y$. From this one can conclude that

Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is

Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to

Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$

Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$

Find the minimum value of $3-4x+2x^2$.

How many minimum spanning trees does the following graph have? Draw them. (Weights are assigned to edges).

Determine the number of divisors of $600.$

A computer system has a $4 \ K$ word cache organized in block-set-associative manner with $4$ blocks per set, $64$ words per block. The number of bits in the SET and WORD fields of the main memory address format is:

Let $\Sigma=\left\{0,1\right\}, L = \Sigma^*$ and $R=\left\{0^n1^n \mid n > 0\right\}$ then the languages $L \cup R$ and $R$ are respectively

A finite state machine with the following state table has a single input $x$ and a single out $z$. …

Which of the following statements is true? As the number of entries in a hash table increases, the number of collisions increases. Recursive programs are efficient The worst case complexity for Quicksort is $O(n^2)$ Binary search using a linear linked list is efficient

The postfix expression for the infix expression $A+B*(C+D)/F+D*E$ is: