GATE CSE format:nat PYQs & Answers — Page 25

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Questions 241–250 of 281. Imported answers require independent review unless marked reviewed.

Topic practice 281 questionsPage 25 of 29

Consider a simple communication system where multiple nodes are connected by a shared broadcast medium (like Ethernet or wireless). The nodes in the system use the following carrier-sense based medium access protocol. A node that receives a packet to transmit will carrier-sense the medium for 5 units of time. If the node does not detect any other transmission in this duration, it starts transmitting its packet in the next time unit. If the node detects another transmission, it waits until this other transmission finishes, and then begins to carrier-sense for 5 time units again. Once the start to transmit, nodes do not perform any collision detection and continue transmission even if a collision occurs. All transmissions last for 20 units of time. Assume that the transmission signal travels at the speed of 10 meters per unit time in the medium.

Assume that the system has two nodes P and Q, located at a distance d meters from each other. P starts transmitting a packet at time t=0 after successfully completing its carrier-sense phase. Node Q has a packet to transmit at time t=0 and begins to carrier-sense the medium.

The maximum distance d (in meters, rounded to the closest integer) that allows Q to successfully avoid a collision between its proposed transmission and P’s ongoing transmission is _____.

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Let X be a Gaussian random variable with mean 0 and variance σ². Let Y = max(X, 0) where max(a, b) is the maximum of a and b. The median of Y is __________.

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Consider the following tables T1 and T2.

T1:

P	Q
2	2
3	8
7	3
5	8
6	9
8	5
9	8

T2:

R	S
2	2
8	3
3	2
9	7
5	7
7	2

In table T1, P is the primary key and Q is the foreign key referencing R in table T2 with on-delete cascade and on-update cascade. In table T2, R is the primary key and S is the foreign key referencing P in table T1 with on-delete set NULL and on-update cascade. In order to delete record (3, 8) from table T1, the number of additional records that need to be deleted from table T1 is __________.

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Let T be a tree with 10 vertices. The sum of the degrees of all the vertices in T is __________.

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The maximum number of IPv4 router addresses that can be listed in the record route (RR) option field of an IPv4 header is __________.

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Consider the Karnaugh map given below, where X represents “don’t care” and blank represents 0.

Karnaugh map columns labelled

: 00, 01, 11, 10; rows labelled

: 00, 01, 11, 10. Cell values: row 00: blank, X, X, blank; row 01: 1, blank, blank, X; row 11: 1, blank, blank, 1; row 10: blank, X, X, blank.

Diagram for Computer Science and Information Technology question 21

Assume for all inputs

, the respective complements

are also available. The above logic is implemented using 2-input NOR gates only. The minimum number of gates required is ____________.

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Consider the set

under the partial ordering

. The Hasse diagram of the partial order

is shown below.

The minimum number of ordered pairs that need to be added to

to make

a lattice is __________.

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Consider the language

given by the regular expression

over the alphabet

. The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting

is ____________.

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Let

and

be two matrices. Then the rank of

is __________.

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Consider a database that has the relation schema EMP (EmpId, EmpName, and DeptName). An instance of the schema EMP and a SQL query on it are given below.

EMP:

EmpId	EmpName	DeptName
1	XYA	AA
2	XYB	AA
3	XYC	AA
4	XYD	AA
5	XYE	AB
6	XYF	AB
7	XYG	AB
8	XYH	AC
9	XYI	AC
10	XYJ	AC
11	XYK	AD
12	XYL	AD
13	XYM	AE

SQL:

SELECT AVG(EC.Num)

FROM EC

WHERE (DeptName, Num) IN

(SELECT DeptName, COUNT(EmpId) AS

EC(DeptName, Num)

FROM EMP

GROUP BY DeptName)

The output of executing the SQL query is ____________.

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GATE CSE format:nat PYQs

Question 55

Question 19

Question 19

Question 20

Question 20

Question 21

Question 21

Question 22

Question 22

Question 23

EmpId	EmpName	DeptName
1	XYA	AA
2	XYB	AA
3	XYC	AA
4	XYD	AA
5	XYE	AB
6	XYF	AB
7	XYG	AB
8	XYH	AC
9	XYI	AC
10	XYJ	AC
11	XYK	AD
12	XYL	AD
13	XYM	AE

EmpId	EmpName	DeptName
1	XYA	AA
2	XYB	AA
3	XYC	AA
4	XYD	AA
5	XYE	AB
6	XYF	AB
7	XYG	AB
8	XYH	AC
9	XYI	AC
10	XYJ	AC
11	XYK	AD
12	XYL	AD
13	XYM	AE

EmpId	EmpName	DeptName
1	XYA	AA
2	XYB	AA
3	XYC	AA
4	XYD	AA
5	XYE	AB
6	XYF	AB
7	XYG	AB
8	XYH	AC
9	XYI	AC
10	XYJ	AC
11	XYK	AD
12	XYL	AD
13	XYM	AE