## Aptitude | GATE CS 1998 | Question 70

Answer the following: a.  Let G1 = (N, T, P, S1) be a CFG where, N= {S1A, B}, T= {a,b} and P is given by… Read More »

## Aptitude | GATE CS 1998 | Question 69

Let M = ({q0, q1}, {0, 1}, {z0, x}, δ, q0, z0, ∅) be a pushdown automaton where δ is given by δ(q0, 1, z0) = {(q0, xz0)}… Read More »

## Aptitude | GATE CS 1998 | Question 68

Let (A, *) be a semi group. Furthermore, for every a and b in A, if a ≠ b, then a*b ≠ b*a. a. Show that for… Read More »

## Aptitude | GATE CS 1998 | Question 67

Suppose A={ a, b, c, d } and Π1 is the following partition of A Π1= { {a, b, c} {d} } a. List the… Read More »

## Aptitude | GATE CS 1998 | Question 66

a.  Prove by induction that the expression for the number of diagonals in a polygon of n sides is n(n-3) /2. b.  Let R be… Read More »

## Aptitude | GATE CS 1998 | Question 66

Derive the expression for the number of expressions required to solve a system of linear equations in n unknowns using the Gaussian Elimination Method. Assume… Read More »

## Aptitude | GATE CS 1998 | Question 65

a. Find the points of local maxima and minima, if any, of the following function defined in 0≤ x ≤ 6. x3-6x+9x-15   b. Integrate Answer:… Read More »

## Aptitude | GATE CS 1998 | Question 64

In a computer system where the ‘best-fit’ algorithm is used for allocating ‘jobs’ to ‘memory partitions’, the following situation was encountered: When will the 20K… Read More »

## Aptitude | GATE CS 1998 | Question 63

In a computer system where the ‘best-fit’ algorithm is used for allocating ‘jobs’ to ‘memory partitions’, the following situation was encountered: When will the 20K… Read More »

## Aptitude | GATE CS 1998 | Question 62

Suppose we have a database consisting of the following three relations. FREQUENTS(student, parlor) giving the parlors each student visits. SERVES(parlor, ice-cream) indicating what kind of… Read More »

## Aptitude | GATE CS 1998 | Question 61

Consider the grammar S →  Aa | b A → Ac | Sd | ε Construct an equivalent grammar with no left recursion and with minimum number… Read More »

## Aptitude | GATE CS 1998 | Question 60

Solve the following recurrence relation: xn = 2xn-1 -1, n>1 x1 = 2 Answer: Explanation: Quiz of this QuestionPlease comment below if you find anything wrong… Read More »

## Aptitude | GATE CS 1998 | Question 59

a.  The implication gate shown below, has two inputs (x and y), the output is 1 except when x=1 and y=0. Realize f=x’y  + xy’ using… Read More »

## Aptitude | GATE CS 1998 | Question 58

[Subjective type] Design a deterministic finite state automaton (using minimum number of states) that recognizes the following language: L = { w ∈ {0,1}* |… Read More »

## Aptitude | GATE CS 1998 | Question 57

[Subjective type] Given a regular expression for the set of binary strings where every 0 is immediately followed by exactly k 1’s and preceded by… Read More »