GATE 2017 CS Set 1

17) Consider the following grammar

p → xQRS
Q → yz|z
R → w|∈
S → y

Which is FOLLOW(Q)?

{R}
{w}
{w, y}
{w, ∉}

Answer: C

Explanation:

Given,

p → xQRS
Q → yz|z
R → w|∈
S → y

Now,

FOLLOW(Q) = FIRST(RS)
= { w, ∈ } υ FIRST(S)
= {w, y}

Therefore option (C) is the correct answer.

18) Threads of a process share

global variables but not heap
heap but not global variables
neither global variables nor heap
both heap and global variables

Answer: D

Explanation:

According to the definition, a thread shares all other resources a process's to which it belongs to, i.e. Code section, Data section (static + heap), Address Space, Permissions, Other resources (e.g., files). It does not share register and stack.

Therefore, option (D) is the correct answer.

19) 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 _____.

Answer: A

Explanation:

The median of Y defines as the least value m such that P(Y⩽m)>1/2.

Given, Y = max{0,X},

then: P(Y⩽0) = P(Y=0) = P(X⩽0) = 1/2 because X is symmetrically distributed to 0.

Therefore, median of Y is 0.

Hence, option (A) is the correct answer.

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

Answer: A

Explanation:

Given,
Total vertices (v) = 10
We know, Tree with n vertices have n-1 edges.
∴ Edge (e) = v - 1 = 9
Therefore, sum of the degrees of all the vertices = 2 * e = 18

Hence option (A) is the correct answer.

21) Consider the Karnaugh map given below, where X represents "don't care" and blank represents 0.

Assume for all inputs (a, b, c, d) the respective complements (a', b', c', d') are also available. The above logic is implemented 2-input NOR gates only. The minimum number of gates required is ____________.

Answer: A

Explanation:

Solving the above k- map we get the following min-term,
F(a,b,c,d) = ca' = ((ca')')' = (c' + a)'

Here, we can see that the min-term also contains the complement of variables. Therefore, the above k-map can be implemented by using one NOR gate.

Hence option (A) is the correct answer.

22) Consider the language L given by the regular expression (a + b) *b(a + b) over the alphabet {a, b}. The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting L is ______.

Answer: B

Explanation:

Minimizing NFA to DFA:

Delta	a	b
A	A	AB
AB	*AC	*ABC
*AC	A	AB
*ABC	*AC	*ABC

From the above table we get,

So, final state will be the state which containing C. Hence no. of state will be 4.

Therefore option(B) is the correct answer.

23) 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

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 _______.

Answer: C

Explanation:

Executing the inner SQL Query, the output will be:

DeptName	Number
AA	4
AB	3
AC	3
AD	2
AE	1

Then the AVG(EC.Num) will find average of Number values in above returned query,
= 4 + 3 + 3 + 2 + 1 = 13 / 5 = 2.6

Therefore option (C) is the correct answer.

24) Consider the following CPU processes with arrival times (in milliseconds) and length of CPU bursts (in milliseconds) as given below:

Process	Arrival Time	Burst Time
P1	0	7
P2	3	3
P3	5	5
P4	6	2

If the pre-emptive shortest remaining time first scheduling algorithm is used to schedule the processes, then the average waiting time across all processes is _______ milliseconds.

Answer: C

Explanation: