GATE 2020
Question 1 
Two straight lines are drawn perpendicular to each other in XY plane. If α and β are the acute angles the straight lines make with the Xaxis, then α+β is ______.
60°  
120°  
180°  
90° 
We know a + α + β = 180
α + β = 180  90
α + β = 90
Question 2 
The total revenue of a company during 20142018 is shown in the bar graph. If the total expenditure of the company in each year is 500 million rupees, then the aggregate profit or loss (in percentage) on the total expenditure of the company during 20142018 is ______.
20% profit  
20% loss  
16.67% loss  
16.67% profit 
20142018
Total expenditure = 500 million/year = 500 × 5 = 2500 million
Revenue total (from the graph)
= 400 + 500 + 600 + 700 + 800
= 3000 million
Profit = 3000  2500 = 500
⟹ 500/2500 = 20% profit
Question 3 
The figure below shows an annular ring with outer and inner radii as b and a, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is ______.
π[(b^{2}  a^{2}) + π/4(b  a)^{2}]  
π[(b^{2}  a^{2})  π/4(b  a)^{2}]  
π[(b^{2}  a^{2})  n(b  a)^{2}]  
π[(b^{2}  a^{2}) + n(b  a)^{2}] 
Area of nonpainted between 2 circles area of part 1 = πb^{2}  πa^{2} = π(b^{2}  a^{2})
Radius of painted circles = ba/2
Area of painted circle = π(ba/2)^{2}
For n circles = nπ(ba/2)^{2}
Nonpainted area = π[b^{2}  a^{2} n/4(b  a)^{2}]
Question 4 
Goods and Services Tax (GST) is an indirect tax introduced in India in 2017 that is imposed on the supply of goods and services, and it subsumes all indirect taxes except few. It is a destinationbased tax imposed on goods and services used, and it is not imposed at the point of origin from where goods come. GST also has a few components specific to state governments, central government and Union Territories (UTs).
Which one of the following statements can be inferred from the given passage?
GST includes all indirect taxes.
 
GST is imposed at the point of usage of goods and services.
 
GST does not have a component specific to UT.  
GST is imposed on the production of goods and services.

Question 5 
Select the word that fits the analogy:
Cook : Cook :: Fly : _____
Flyer  
Flying  
Flew  
Flighter 
FlyFlyer
Question 6 
The drawn of the 21st century witnessed the melting glaciers oscillating between giving too much and too little to billions of people who depend on them for fresh water. The UN climate report estimates that without deep cuts to manmade emissions, at least 30% of the northern hemisphere’s surface permafrost could melt by the end of the century. Given this situation of imminent global exodus of billions of people displaced by rising seas, nationstates need to rethink their carbon footprint for political concerns, if not for environmental ones.
Which one of the following statements can be inferred from the given passage?
Nationstates are responsible for providing fresh water to billions of people.  
Billions of people are affected by melting glaciers.
 
Nationstates do not have environmental concerns.  
Billions of people are responsible for manmade emissions. 
Question 7 
There are multiple routes to reach from node 1 to node 2, as shown in the network.
The cost of travel on an edge between two nodes is given in rupees. Nodes ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, and ‘f’ are toll booths. The toll price at toll booths marked ‘a’ and ‘e’ is Rs.200, and is Rs.100 for the other toll booths. Which is the cheapest route from node 1 to node 2?
1fe2
 
1fb2  
1b2  
1ac2

1  f  e  2 ─ 100 + 100 + 200 = 400
1  f  b  2 ─ 100 + 0 + 200 = 300 ⇾ shortest [Answer]
1  b  2 ─ 300 + 200 = 500
1  a  c ─ 2  200 + 100 + 100 = 400
Question 8 
Raman is confident of speaking English _____ six months as he has been practicing regularly_____the last three weeks.
for, in  
during, for
 
for, since
 
within, for

Question 9 
If P = 3, R = 27, T = 243, then Q+S = ______.
80  
110  
40  
90 
P=3^{1}, Q=3^{2}, R=3^{3}, S=3^{4}, T=3^{5}
Q+S = 3^{2} + 3^{4} = 9+81 = 90
Question 10 
His knowledge of the subject was excellent but his classroom performance was ______.
good
 
praiseworthy  
extremely poor  
desirable

Question 11 
Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ______.
7 
If ‘H” is a subgroup of finite group (G,*) then O(H) is the divisor of O(G).
Given that the order of group is 35. Its divisors are 1,5,7,35.
It is asked that the size of largest possible subgroup other than G itself will be 7.
Question 12 
Consider a relational database containing the following schemas.
The primary key of each table is indicated by underlying the constituent fields.
SELECT s.sno, s.sname FROM Suppliers s, Catalogue c WHERE s.sno = c.sno AND Cost > (SELECT AVG (cost) FROM Catalogue WHERE pno = ‘P4’ GROUP BY pno);
The number of rows returned by the above SQL query is
0  
5  
4  
2 
AVG(COST)

225
The outer query “select s.sno, s.sname from suppliers s, catalogue c where s.sno=c.sno” returns:
SNO SNAME

S1 M/s Royal furniture
S1 M/s Royal furniture
S1 M/s Royal furniture
S2 M/s Balaji furniture
S2 M/s Balaji furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
So, the final result of the query is:
SN SNAME

S2 M/s Balaji furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
S3 M/s Premium furniture
Therefore, 4 rows will be returned by the query.
Question 13 
Consider the language L = {a^{n} n≥0} ∪ {a^{n}b^{n} n≥0} and the following statements.
 I. L is deterministic contextfree.
II. L is contextfree but not deterministic contextfree.
III. L is not LL(k) for any k.
Which of the above statements is/are TRUE?
II only  
III only  
I only  
I and III only 
We can make DPDA for this.
L is not LL(k) for any “k” look aheads. The reason is the language is a union of two languages which have common prefixes. For example strings {aa, aabb, aaa, aaabbb,….} present in language. Hence the LL(k) parser cannot parse it by using any lookahead “k” symbols.
Question 14 
For parameters a and b, both of which are ω(1), T(n) = T(n^{1/a})+1, and T(b)=1.
Then T(n) is
θ(log_{a} log_{b} n)  
θ(log_{b} log_{a} n)
 
θ(log_{2} log_{2} n)
 
θ(log_{ab} n)

T(n) = [T(n^{1/a2})+1] + 1
= [T(n^{1/a3})+1] + 2
= [T(n^{1/a3})] + 3
= [T(n^{1/ak})] + b
= log_{b} n = a^{k}
= log log_{b} n = k log a
= k= log_{a} log_{b} n
T(n)=1+log_{a} log_{b} n
T(n)=O(log_{a} log_{b} n)
Question 15 
Consider the following statements.
 I. If L_{1} ∪ L_{2} is regular, then both L_{1} and L_{2} must be regular.
II. The class of regular languages is closed under infinite union.
Which of the above statements is/are TRUE?
Both I and II
 
II only  
Neither I nor II  
I only

Assume L_{1} = {a^{n} b^{n}  n>0} and L_{2} = complement of L_{1}
L_{1} and L_{2} both are DCFL but not regular, but L_{1} U L_{2} = (a+b)* which is regular.
Hence even though L_{1} U L_{2} is regular, L_{1} and L_{2} need not be always regular.
Statement II is wrong.
Assume the following finite (hence regular) languages.
L_{1} = {ab}
L_{2} = {aabb}
L_{3} = {aaabbb}
.
.
.
L_{100} = {a^{100} b^{100}}
.
.
.
If we take infinite union of all above languages i.e,
{L_{1} U L_{2} U ……….L_{100} U ……}
then we will get a new language L = {a^{n} b^{n}  n>0}, which is not regular.
Hence regular languages are not closed under infinite UNION.
Question 16 
Consider the following statements.
 I. Daisy chaining is used to assign priorities in attending interrupts.
II. When a device raises a vectored interrupt, the CPU does polling to identify the source of the interrupt.
III. In polling, the CPU periodically checks the status bits to know if any device needs its attention.
IV. During DMA, both the CPU and DMA controller can be bus masters at the same time.
Which of the above statements is/are TRUE?
I and IV only  
I and II only
 
III only  
I and III only

StatementII is false as vectored interrupt doesn’t involve polling but nonvectored interrupt involves polling.
StatementIII is true as polling means that CPU periodically checks the status bits to know if any device needs attention.
StatementIV is false as during DMA only one of the CPU or DMA can be bus master at a time.