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Recent questions tagged gate1998

13 votes
4 answers
1
GATE CSE 1998 | Question: 10b
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m < n$ and $R^m = R^n$.
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m <...
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21 votes
3 answers
2
GATE CSE 1998 | Question: 6a
Solve the following recurrence relation $x_n = 2x_{n-1}-1, n>1$ $x_1=2$
Solve the following recurrence relation$x_n = 2x_{n-1}-1, n>1$$x_1=2$
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44 votes
9 answers
4
GATE CSE 1998 | Question: 19b
Compute the post fix equivalent of the following expression $3^*\log(x+1)-\frac{a}{2}$
Compute the post fix equivalent of the following expression $3^*\log(x+1)-\frac{a}{2}$
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29 votes
5 answers
6
GATE CSE 1998 | Question: 3b
Give a regular expression for the set of binary strings where every $0$ is immediately followed by exactly $k$ $1$'s and preceded by at least $k$ $1$’s ($k$ is a fixed integer)
Give a regular expression for the set of binary strings where every $0$ is immediately followed by exactly $k$ $1$'s and preceded by at least $k$ $1$’s ($k$ is a fixed...
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26 votes
3 answers
9
GATE CSE 1998 | Question: 25-a
Free disk space can be used to keep track of using a free list or a bit map. Disk addresses require $d$ bits. For a disk with $B$ blocks, $F$ of which are free, state the condition under which the free list uses less space than the bit map.
Free disk space can be used to keep track of using a free list or a bit map. Disk addresses require $d$ bits. For a disk with $B$ blocks, $F$ of which are free, state the...
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21 votes
1 answer
13
GATE CSE 1998 | Question: 21
Derive a recurrence relation for the size of the smallest AVL tree with height $h$. What is the size of the smallest AVL tree with height $8$?
Derive a recurrence relation for the size of the smallest AVL tree with height $h$.What is the size of the smallest AVL tree with height $8$?
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20 votes
1 answer
14
GATE CSE 1998 | Question: 20
Draw the binary tree with node labels $\text{a, b, c, d, e, f and g}$ for which the inorder and postorder traversals result in the following sequences: Inorder: $\text{a f b c d g e}$ Postorder: $\text{a f c g e d b}$
Draw the binary tree with node labels $\text{a, b, c, d, e, f and g}$ for which the inorder and postorder traversals result in the following sequences:Inorder: $\text{a f...
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33 votes
5 answers
16
GATE CSE 1998 | Question: 18
For a set-associative Cache organization, the parameters are as follows: ... $1 \leq m \leq l$. Give the value of the hit ratio for $l = 1$.
For a set-associative Cache organization, the parameters are as follows:$$\begin{array}{|c|l|} \hline \text {$t _c$} & \text{Cache Access Time }\\\hline \text{$t _m$} &...
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23 votes
3 answers
18
GATE CSE 1998 | Question: 16
Design a synchronous counter to go through the following states:$1, 4, 2, 3, 1, 4, 2, 3, 1, 4 \dots $
Design a synchronous counter to go through the following states:$$1, 4, 2, 3, 1, 4, 2, 3, 1, 4 \dots $$
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12 votes
4 answers
20
GATE CSE 1998 | Question: 14
Let $G_1 = (N, T, P, S_1)$ be a CFG where, $N=\{S_1, A, B\},T=\{a, b\}$ and $P$ ... $5$ production rules. Is $L_2$ inherently ambiguous?
Let $G_1 = (N, T, P, S_1)$ be a CFG where, $N=\{S_1, A, B\},T=\{a, b\}$ and $P$ is given by$$\begin{array}{l|l}S_1 \rightarrow a S_1 b &S_1 \rightarrow a B b \\S_1 \right...
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32 votes
3 answers
22
GATE CSE 1998 | Question: 12
Let $(A, *)$ be a semigroup, Furthermore, for every $a$ and $b$ in $A$, if $a \neq b$, then $a*b \neq b*a$. Show that for every $a$ in $A$, $a*a=a$ Show that for every $a$, $b$ in $A$, $a*b*a=a$ Show that for every $a,b,c$ in $A$, $a*b*c=a*c$
Let $(A, *)$ be a semigroup, Furthermore, for every $a$ and $b$ in $A$, if $a \neq b$, then $a*b \neq b*a$.Show that for every $a$ in $A$, $a*a=a$Show that for every $a$,...
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20 votes
6 answers
24
GATE CSE 1998 | Question: 10a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$
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5 votes
1 answer
25
GATE CSE 1998 | Question: 9
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one operation refers to a multiplication followed by an addition.
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one ...
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13 votes
1 answer
26
GATE CSE 1998 | Question: 8
Find the points of local maxima and minima, if any, of the following function defined in $0\leq x\leq 6$. $x^3-6x^2+9x+15$ Integrate $\int_{-\pi}^{\pi} x \cos x dx$
Find the points of local maxima and minima, if any, of the following function defined in $0\leq x\leq 6$. $$x^3-6x^2+9x+15$$Integrate $$\int_{-\pi}^{\pi} x \cos x dx$$
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26 votes
2 answers
28
GATE CSE 1998 | Question: 6b
Consider the grammar S $\rightarrow Aa \mid b$ A $\rightarrow Ac \mid Sd \mid \epsilon$ Construct an equivalent grammar with no left recursion and with minimum number of production rules.
Consider the grammarS $\rightarrow Aa \mid b$A $\rightarrow Ac \mid Sd \mid \epsilon$Construct an equivalent grammar with no left recursion and with minimum number of pr...
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