, because each of the m elements of A has\r\t\tn choices for mapping. Now here m=|Z|=z, and n=|E|=2xy because number of subsets of a set of size n is 2n,\r\t\t and here set W has size of xy.\r\t\t

A relation R is defined on ordered pairs of integers as follows: (x,y) R(u,v) if x < u and y > v. Then R is:

A Partial Order but not a Total Order

A Total Order

An Equivalence Relation

Neither a Partial Order nor an Equivalence Relation

Neither a Partial Order nor an Equivalence Relation

An equivalence relation on a set x is a subset of x*x, i.e., a collection R of ordered pairs of elements of x, satisfying certain properties. Write “x R y\" to mean (x,y) is an element of R, and we say \"x is related to y,\" then the properties are: 1. Reflexive: a R a for all a Є R, 2. Symmetric: a R b implies that b R a for all a,b Є R 3. Transitive: a R b and b R c imply a R c for all a,b,c Є R.

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An partial order relation on a set x is a subset of x*x, i.e., a collection R of ordered pairs of elements of x, satisfying certain properties. Write “x R y\" to mean (x,y) is an element of R, and we say \"x is related to y,\"

\n\n

then the properties are:

\n\n

1. Reflexive: a R a for all a Є R,

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2. Anti-Symmetric: a R b and b R a implies that for all a,b Є R

\n\n

3. Transitive: a R b and b R c imply a R c for all a,b,c Є R. An total order relation a set x is a subset of x*x, i.e., a collection R of ordered pairs of elements of x, satisfying certain properties.

\n\n

Write “x R y\" to mean (x,y) is an element of R, and we say \"x is related to y,\"

\n\n

then the properties are:

\n\n

1. Reflexive: a R a for all a Є R,

\n\n

2. Anti-Symmetric: a R b implies that b R a for all a,b Є R

\n\n

3. Transitive: a R b and b R c imply a R c for all a,b,c Є R.

\n\n

4. Comparability : either a R b or b R a for all a,b Є R.

\n\n

As given in question, a relation R is defined on ordered pairs of integers as follows: (x,y) R(u,v) if x < u and y > v , reflexive property is not satisfied here, because there is > or < relationship between (x ,y) pair set and (u,v) pair set .

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Other way , if there would have been x <= u and y>= v (or x=u and y=v) kind of relation among elements of sets then reflexive property could have been satisfied. Since reflexive property in not satisfied here , so given relation can not be equivalence, partial orderor total order relation.

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So, option (A) is correct.

\n"},"encodingFormat":"text/plain"}},{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","name":"Question on GATE-CS-2006","text":"\n

For which one of the following reasons does Internet Protocol (IP) use the timeto- live (TTL) field in the IP datagram header

Ensure packets reach destination within that time

Discard packets that reach later than that time

Limit the time for which a packet gets queued in intermediate routers.

Prevent packets from looping indefinitely

Prevent packets from looping indefinitely

The TTL field in an IP packet header is decremented by one each time the packet passes through a router. If the TTL field reaches zero, the router discards the packet and sends an ICMP \"Time Exceeded\" message back to the sender. This prevents packets from circulating endlessly in the network due to routing loops or other issues.
So, the reason IP uses the TTL field is to \"Prevent packets from looping indefinitely.\"

\r\nS -> S * E\r\nS -> E\r\nE -> F + E\r\nE -> F\r\nF -> id
\r\nConsider the following LR(0) items corresponding to the grammar above.
\r\n(i) S -> S * .E\r\n(ii) E -> F. + E\r\n(iii) E -> F + .E

You are given a free running clock with a duty cycle of 50% and a digital waveform f which changes only at the negative edge of the clock. Which one of the following circuits (using clocked D flip-flops) will delay the phase of f by 180°?

A

B

D

C

C

We assume the D flip-flop to be negative edge triggered.  In option (A), during the negative edge of the clock, first flip-flop inverts complement of ‘f’(we get f as the output). But, the complement of the output of first flip-flop(i.e. f\\') is given as the input to the second flip-flop. The second flip flop is enabled by \\'clk\\'. The output at the second flip flop is f\\'+90 degrees (as +ve edged clk at output delays it by 90 degrees). Thus f is delayed by 270 degrees. So, A is not the correct option.  Following the above procedures as in (A) we will get:In option (B) and (D), the output is ‘f’. But, we want inverted ‘f’ as the output. So, (B) and (D) can’t be the answer. In option (C), the first flip-flop is activated by ‘clk’. So, the output of first flip-flop has the same phase as ‘f’. But, the second flip-flop is enabled by complement of ‘clk’. Since the clock ‘clk’ has a duty cycle of 50% , we get the output having phase delay of 180 degrees.  Therefore, (C) is the correct answer.

\n"},"encodingFormat":"text/plain"}},{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","name":"Question on GATE-CS-2006","text":"\n

A CPU has 24-bit instructions. A program starts at address 300 (in decimal). Which one of the following is a legal program counter (all values in decimal)?

400

500

700

600

600

Each address is multiple of 3 as the starting address is 300 and is each instruction consists of 24 bit, i.e., 3 byte.
Thus, in the given options the valid counter will be the one which is the multiple of 3. Out of the options we can see that only 600 satisfies the condition.
Therefore, it is 600.

# GATE-CS-2006

Question 1

Consider the polynomial p(x) = a0 + a1x + a2x2 + a3x3 , where ai ≠ 0 ∀i. The minimum number of multiplications needed to evaluate p on an input x is:
• 3
• 4
• 6
• 9

Question 2

Let X, Y, Z be sets of sizes x, y and z respectively. Let W = X x Y. Let E be the set of all subsets of W. The number of functions from Z to E is:
• z2xy
• z x 2 xy
• z2x + y
• 2xyz

Question 3

The set {1, 2, 3, 5, 7, 8, 9} under multiplication modulo 10 is not a group. Given below are four plausible reasons. Which one of them is false?
• It is not closed
• 2 does not have an inverse
• 3 does not have an inverse
• 8 does not have an inverse

Question 4

A relation R is defined on ordered pairs of integers as follows: (x,y) R(u,v) if x < u and y > v. Then R is:

• Neither a Partial Order nor an Equivalence Relation

• A Partial Order but not a Total Order

• A Total Order

• An Equivalence Relation

Question 5

For which one of the following reasons does Internet Protocol (IP) use the timeto- live (TTL) field in the IP datagram header

• Ensure packets reach destination within that time

• Discard packets that reach later than that time

• Prevent packets from looping indefinitely

• Limit the time for which a packet gets queued in intermediate routers.

Question 6

Consider three CPU-intensive processes, which require 10, 20 and 30 time units and arrive at times 0, 2 and 6, respectively. How many context switches are needed if the operating system implements a shortest remaining time first scheduling algorithm? Do not count the context switches at time zero and at the end.
• 1
• 2
• 3
• 4

Question 7

Consider the following grammar.
S -> S * E
S -> E
E -> F + E
E -> F
F -> id
Consider the following LR(0) items corresponding to the grammar above.
(i) S -> S * .E
(ii) E -> F. + E
(iii) E -> F + .E 
Given the items above, which two of them will appear in the same set in the canonical sets-of-items for the grammar?
• (i) and (ii)
• (ii) and (iii)
• (i) and (iii)
• None of the above

Question 8

You are given a free running clock with a duty cycle of 50% and a digital waveform f which changes only at the negative edge of the clock. Which one of the following circuits (using clocked D flip-flops) will delay the phase of f by 180°?

[caption width="800"] [/caption][caption width="800"] [/caption]
• A

• B

• C

• D

Question 9

A CPU has 24-bit instructions. A program starts at address 300 (in decimal). Which one of the following is a legal program counter (all values in decimal)?

• 400

• 500

• 600

• 700

Question 10

In a binary max heap containing n numbers, the smallest element can be found in time
• O(n)
• O(Logn)
• O(LogLogn)
• O(1)

There are 84 questions to complete.

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