GATE CS question library

Which of the following definitions below generate the same language as $L$, where $L=\{x^ny^n \text{ such that } n\geq 1 \}$? $E \rightarrow xEy\mid xy$ $x y \mid (x^+xyy^+$) $x^+y^+$

If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is

The solution of differential equation $y''+3y'+2y=0$ is of the form

Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then

In a virtual memory system the address space specified by the address lines of the CPU must be _____ than the physical memory size and ____ than the secondary storage size.

A bag contains $10$ white balls and $15$ black balls. Two balls are drawn in succession. The probability that one of them is black and the other is white is:

A unit vector perpendicular to both the vectors $a=2i-3j+k$ and $b=i+j-2k$ is:

The number of $1$'s in the binary representation of $(3\ast4096 + 15\ast256 + 5\ast16 + 3)$ are:

A shift reduce parser carries out the actions specified within braces immediately after reducing with the corresponding rule of grammar $S \rightarrow xxW \;\text{{print“1"}}$ $S \rightarrow y \;\text{{print“2"}}$ $W \rightarrow Sz\; \text{{print“3"}}$ What is the translation of $xxxxyzz$ using the syntax directed translation scheme described by the …

If the cube roots of unity are $1, \omega$ and $\omega^2$, then the roots of the following equation are $$(x-1)^3 +8 =0$$

A language with string manipulation facilities uses the following operations head(s): first character of a string tail(s): all but exclude the first character of a string concat(s1, s2): s1s2 For the string "$acbc$" what will be the output of concat(head(s), head(tail(tail(s))))

The address sequence generated by tracing a particular program executing in a pure demand based paging system with $100$ records per page with $1$ free main memory frame is recorded as follows. What is the number of page faults? $0100, 0200, 0430, 0499, 0510, 0530, 0560, 0120, 0220, 0240, 0260, 0320, 0370$

The sequence __________ is an optimal non-preemptive scheduling sequence for the following jobs which leaves the CPU idle for ________ unit(s) of time. …

What values of $A, B, C$ and $D$ satisfy the following simultaneous Boolean equations? $\overline{A} + AB =0, AB=AC, AB+A\overline{C}+CD=\overline{C}D$

What is the value of $X$ printed by the following program? program COMPUTE (input, output); var X:integer; procedure FIND (X:real); begin X:=sqrt(X); end; begin X:=2 FIND(X); writeln(X); end.

Assume that $X$ and $Y$ are non-zero positive integers. What does the following Pascal program segment do? while X <> Y do if X > Y then X := X - Y else Y := Y - X; write(X);

The capacity of a memory unit is defined by the number of words multiplied by the number of bits/word. How many separate address and data lines are needed for a memory of $4K \times 16$?

The minimum number of edges in a connected cyclic graph on $n$ vertices is:

The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ is a real number is …

In the interval $[0, \pi]$ the equation $x=\cos x$ has