GATE CS question library

The threshold level for logic 1 in the TTL family is

A multiplexer with a $4-bit$ data select input is a

What happens when a bit-string is XORed with itself $n$-times as shown: $\left[B \oplus (B \oplus ( B \oplus (B \dots n \text{ times}\right]$

The string $1101$ does not belong to the set represented by

Regarding the power of recognition of languages, which of the following statements is false?

Which of the following set can be recognized by a Deterministic Finite state Automaton?

If the regular set $A$ is represented by $A = (01 + 1)^*$ and the regular set $B$ is represented by $B = \left(\left(01\right)^*1^*\right)^*$, which of the following is true?

The number of functions from an $m$ element set to an $n$ element set is

Let $R_1$ and $R_2$ be two equivalence relations on a set. Consider the following assertions: $R_1 \cup R_2$ is an equivalence relation $R_1 \cap R_2$ is an equivalence relation Which of the following is correct?

Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is

What is the converse of the following assertion? I stay only if you go

Consider the function $y=|x|$ in the interval $[-1, 1]$. In this interval, the function is

Which of the following statements applies to the bisection method used for finding roots of functions:

Consider the following set of equations $x+2y=5$ $4x+8y=12$ $3x+6y+3z=15$ This set

A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is

A program $P$ reads and processes $1000$ consecutive records from a sequential file $F$ stored on device $D$ without using any file system facilities. Given the following Size of each record $= 3200$ bytes Access time of $D = 10$ msecs Data transfer rate of $D = 800 \times 10^3$ bytes/second CPU time to process each record $= 3$ msecs What is …

Let $f=(\bar{w} + y)(\bar{x} +y)(w+\bar{x}+z)(\bar{w}+z)(\bar{x}+z)$ Express $f$ as the minimal sum of products. Write only the answer. If the output line is stuck at $0$, for how many input combinations will the value of $f$ be correct?

Let $R (a, b, c)$ and $S(d, e, f)$ be two relations in which $d$ is the foreign key of $S$ that refers to the primary key of $R$. Consider the following four operations $R$ and $S$ Insert into $R$ Insert into $S$ Delete from $R$ Delete from $S$ Which of the following can cause violation of the referential integrity constraint above?

For a database relation $R(a, b, c, d)$, where the domains $a, b, c, d$ include only atomic values, only the following functional dependencies and those that can be inferred from them hold $a \rightarrow c$ $b \rightarrow d$ This relation is

Each Process $P_i, i = 1\ldots 9$ is coded as follows repeat P(mutex) {Critical section} V(mutex) forever The code for $P_{10}$ is identical except it uses V(mutex) in place of P(mutex). What is the largest number of processes that can be inside the critical section at any moment?