GATE 1993 CSE & IT

Show that proposition $$C$$ is a logical consequence of the formula $$A \wedge \left( {A \to \left( {B \vee C} \right) \wedge \left( {B \to \sim A} \right)} \right)$$ using truth t...

Let $${\rm A}$$ be a finite set of size $$n$$. The number of elements in the power set of $${\rm A} \times {\rm A}$$ is

A simple two-pass assembler does the following in the first pass:

If $$A = \left[ {\matrix{ 1 & 0 & 0 & 1 \cr 0 & { - 1} & 0 & { - 1} \cr 0 & 0 & i & i \cr 0 & 0 & 0 & { - i} \cr } } \right]$$ the matrix $${A^4},$$ calculated by the use of Cayley...

Let $$S$$ be an infinite set and $${S_1},\,\,{S_2},....\,\,{S_n}$$ be sets such that $${S_1} \cup {S_2} \cup ....... \cup {S_n} = S$$. Then

Consider a system having m resources of the same type. These resources are shared by 3 processes A, B and C, which have peak demands of 3, 4 and 6 respectively. For what value of m...

A part of the system software, which under all circumstances must reside in the main memory is:

$$\sum\limits_{1 \le k \le n} {O(n)} $$ where O(n) stands for order n is:

The following page addresses, in the given sequence, were generated by a program: 1 2 3 4 1 3 5 2 1 5 4 3 2 3 This program is run on a demand paged virtual memory system, with main...

Assume that the following jobs are to be executed on a single processor system. Job Id CPU Burst Time p 4 q 1 r 8 s 1 t 2 The jobs are assumed to have arrived at time $${0^ + }$$ a...

The root directory of a disk should be placed:

What does the following code do? var a, b : integer; begin a:=a+b; b:=a-b; a:=a-b; end;

The eigen vector (s) of the matrix $$\left[ {\matrix{ 0 & 0 & \alpha \cr 0 & 0 & 0 \cr 0 & 0 & 0 \cr } } \right],\alpha \ne 0$$ is (are)

A certain moving arm disk storage, with one head, has the following specifications. Number of track/recording Surface $$=200$$ Disk rotation speed $$=2400$$$$rpm$$ Track storage ca...

The value of the double integral $$\int\limits_0^1 {\int\limits_x^{{1 \over x}} {{x \over {1 + {y^2}}}\,\,dx\,\,dy = \_\_\_\_\_.} } $$