Gate (CS) 2022 Paper with Solution | GATE Computer Science Engineering(CSE) 2025 Mock Test Series - Computer Science Engineering (CSE) PDF Download

 Page 1


 
1. Let r be a root of the equation 
2
x + 2x + 6 = 0
.
Then the value of the expression
? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
 is
(a) 126 (b) –51
(c) 51 (d) –126
Sol: (d)
r be the root of the equation 
2
x + 2x + 6 = 0 so
it will satisfy
2
r + 2r + 6 = 0 ...(i)
Now, ? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
? ? ? ? ?
2 2
r + 5r + 6 r + 9r + 20
? ? ? ? ?
2 2
r + 2r + 6 + 3r r + 2r + 6 +7r +14
? ? ? ? ?
0 + 3r 0 +7r +14
? ? ?
3r 7r +14
? ? ? ? ?
2
21 r + 2r = 21 –6
? –126
Option (d) is correct.
2. Some people believe that “what gets measured,
improves”. Some others believe that “what gets
measured, gets gamed”. One possible reason for
the difference in the beliefs is the work culture
e in organizations. In organizations with good
work culture, metrices help improve outcomes.
However, the same metrices are counterproduc-
tive in organizations with poor work culture.
Which one of the following is the CORRECT
logical inference based on the information in
the above passage ?
(a) Metrices are always counterproductive in
organizations with good work culture
(b) Metrices are useful in organizations with
good work culture.
(c) Metrices are useful in organizations with
poor work culture.
(d) Metrices are never useful in organizations
with good work culture.
Sol: (b)
Metrices are useful in organizations with good
work culture.
3. A palindrome is a word that reads the same
forwards and backwards. In a game of words, a
player has the following two plates painted with
letters.
A D
From the additional plates given in the options,
which one of the combinations of additional
plates would allow the player to construct a
five-letter palindrome. The player should use
all the five plates exactly once. The plates can
be rotated in their plane.
(a)
(b)
(c)
(d)
Sol: (c)
A word, sentence or a number that reads the
same backward or forward.
Ex. RADAR
MADAM
REFER
12321
So, option (c) R A R (after rotating
2nd and 3rd plates) is a palindrome.
Option (c) is correct.
4. The corners and mid-points of the sides of a
triangle are named using the distinct letters,
P, Q, R, S, T and U, but not necessarily in the
same order. Consider the following statements :
• The line joining P and R is parallel to the
line joining Q and S.
• P is placed on the side opposite to the corner
T.
• S and U cannot be placed on the same side.
Which one of the following statements is correct
based on the above information ?
(a) P cannot be placed at a corner
(b) R cannot be placed at a corner
(c) S cannot be placed at a corner
(d) U cannot be placed at a mid-point
Sol: (c)
Page 2


 
1. Let r be a root of the equation 
2
x + 2x + 6 = 0
.
Then the value of the expression
? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
 is
(a) 126 (b) –51
(c) 51 (d) –126
Sol: (d)
r be the root of the equation 
2
x + 2x + 6 = 0 so
it will satisfy
2
r + 2r + 6 = 0 ...(i)
Now, ? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
? ? ? ? ?
2 2
r + 5r + 6 r + 9r + 20
? ? ? ? ?
2 2
r + 2r + 6 + 3r r + 2r + 6 +7r +14
? ? ? ? ?
0 + 3r 0 +7r +14
? ? ?
3r 7r +14
? ? ? ? ?
2
21 r + 2r = 21 –6
? –126
Option (d) is correct.
2. Some people believe that “what gets measured,
improves”. Some others believe that “what gets
measured, gets gamed”. One possible reason for
the difference in the beliefs is the work culture
e in organizations. In organizations with good
work culture, metrices help improve outcomes.
However, the same metrices are counterproduc-
tive in organizations with poor work culture.
Which one of the following is the CORRECT
logical inference based on the information in
the above passage ?
(a) Metrices are always counterproductive in
organizations with good work culture
(b) Metrices are useful in organizations with
good work culture.
(c) Metrices are useful in organizations with
poor work culture.
(d) Metrices are never useful in organizations
with good work culture.
Sol: (b)
Metrices are useful in organizations with good
work culture.
3. A palindrome is a word that reads the same
forwards and backwards. In a game of words, a
player has the following two plates painted with
letters.
A D
From the additional plates given in the options,
which one of the combinations of additional
plates would allow the player to construct a
five-letter palindrome. The player should use
all the five plates exactly once. The plates can
be rotated in their plane.
(a)
(b)
(c)
(d)
Sol: (c)
A word, sentence or a number that reads the
same backward or forward.
Ex. RADAR
MADAM
REFER
12321
So, option (c) R A R (after rotating
2nd and 3rd plates) is a palindrome.
Option (c) is correct.
4. The corners and mid-points of the sides of a
triangle are named using the distinct letters,
P, Q, R, S, T and U, but not necessarily in the
same order. Consider the following statements :
• The line joining P and R is parallel to the
line joining Q and S.
• P is placed on the side opposite to the corner
T.
• S and U cannot be placed on the same side.
Which one of the following statements is correct
based on the above information ?
(a) P cannot be placed at a corner
(b) R cannot be placed at a corner
(c) S cannot be placed at a corner
(d) U cannot be placed at a mid-point
Sol: (c)
 
Using above information we can draw,
P/U
S/Q
Q/S
U/P
R
T
S can’t be place at a corners because PR is
parallel with QS.
Option (c) is correct.
5. A box contains five balls of same size and shape.
Three of them are green coloured balls and two
of them are orange coloured balls. Balls are
drawn from the box one at a time. If a green
ball is drawn, it is not replaced. If an orange
ball is drawn, it is replaced with another orange
ball.
First ball is drawn. What is the probability of
getting an orange ball in the next draw ?
(a)
23
50
(b)
1
2
(c)
19
50
(d)
8
25
Sol: (a)
G ? green
O ? Orange
3G
20
2G
20
3G
2O
Green
Orange
3/5
2/5
Green
Orange
2/4
2/4
Green
Orange
3/5
2/5
P(E) =
3 2 2 2
× + ×
5 4 5 5
=
3 4
+
10 25
=
23
50
Option (a) is correct.
6. A plot of land must be divided between four
families. They want their individual plots to be
similar in shape, not necessarily equal in area.
The land has equally spaced poles, marked as
dots in the below figure. Two ropes, R1 and R2,
are already present and cannot be moved.
What is the least number of additional straight
ropes needed to create the desired plots ? A
single rope can pass through three poles that
are aligned in a straight line.
R
2
R
1
(a) 2 (b) 3
(c) 4 (d) 5
Sol: (b)
R
2
R
5
R
3
R
1
R
4
R
3
 ? First additional Rope
R
4
? Second additional Rope
R
5
? Third additional Rope
So, using 3 additional ropes. We are able to
divide into 4 similar shape plots.
7. A function y(x) is defined in the interval [0, 1]
on the x-axis as
y(x) =
1
2 if 0 x
3
1 3
3 if x
3 4
3
1 if x 1
4
?
? ?
?
?
?
? ? ?
?
?
? ?
?
?
Which one of the following is the area under
the curve for the interval [0, 1] on the x-axis.
(a)
13
6
(b)
6
5
(c)
5
6
(d)
6
13
Page 3


 
1. Let r be a root of the equation 
2
x + 2x + 6 = 0
.
Then the value of the expression
? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
 is
(a) 126 (b) –51
(c) 51 (d) –126
Sol: (d)
r be the root of the equation 
2
x + 2x + 6 = 0 so
it will satisfy
2
r + 2r + 6 = 0 ...(i)
Now, ? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
? ? ? ? ?
2 2
r + 5r + 6 r + 9r + 20
? ? ? ? ?
2 2
r + 2r + 6 + 3r r + 2r + 6 +7r +14
? ? ? ? ?
0 + 3r 0 +7r +14
? ? ?
3r 7r +14
? ? ? ? ?
2
21 r + 2r = 21 –6
? –126
Option (d) is correct.
2. Some people believe that “what gets measured,
improves”. Some others believe that “what gets
measured, gets gamed”. One possible reason for
the difference in the beliefs is the work culture
e in organizations. In organizations with good
work culture, metrices help improve outcomes.
However, the same metrices are counterproduc-
tive in organizations with poor work culture.
Which one of the following is the CORRECT
logical inference based on the information in
the above passage ?
(a) Metrices are always counterproductive in
organizations with good work culture
(b) Metrices are useful in organizations with
good work culture.
(c) Metrices are useful in organizations with
poor work culture.
(d) Metrices are never useful in organizations
with good work culture.
Sol: (b)
Metrices are useful in organizations with good
work culture.
3. A palindrome is a word that reads the same
forwards and backwards. In a game of words, a
player has the following two plates painted with
letters.
A D
From the additional plates given in the options,
which one of the combinations of additional
plates would allow the player to construct a
five-letter palindrome. The player should use
all the five plates exactly once. The plates can
be rotated in their plane.
(a)
(b)
(c)
(d)
Sol: (c)
A word, sentence or a number that reads the
same backward or forward.
Ex. RADAR
MADAM
REFER
12321
So, option (c) R A R (after rotating
2nd and 3rd plates) is a palindrome.
Option (c) is correct.
4. The corners and mid-points of the sides of a
triangle are named using the distinct letters,
P, Q, R, S, T and U, but not necessarily in the
same order. Consider the following statements :
• The line joining P and R is parallel to the
line joining Q and S.
• P is placed on the side opposite to the corner
T.
• S and U cannot be placed on the same side.
Which one of the following statements is correct
based on the above information ?
(a) P cannot be placed at a corner
(b) R cannot be placed at a corner
(c) S cannot be placed at a corner
(d) U cannot be placed at a mid-point
Sol: (c)
 
Using above information we can draw,
P/U
S/Q
Q/S
U/P
R
T
S can’t be place at a corners because PR is
parallel with QS.
Option (c) is correct.
5. A box contains five balls of same size and shape.
Three of them are green coloured balls and two
of them are orange coloured balls. Balls are
drawn from the box one at a time. If a green
ball is drawn, it is not replaced. If an orange
ball is drawn, it is replaced with another orange
ball.
First ball is drawn. What is the probability of
getting an orange ball in the next draw ?
(a)
23
50
(b)
1
2
(c)
19
50
(d)
8
25
Sol: (a)
G ? green
O ? Orange
3G
20
2G
20
3G
2O
Green
Orange
3/5
2/5
Green
Orange
2/4
2/4
Green
Orange
3/5
2/5
P(E) =
3 2 2 2
× + ×
5 4 5 5
=
3 4
+
10 25
=
23
50
Option (a) is correct.
6. A plot of land must be divided between four
families. They want their individual plots to be
similar in shape, not necessarily equal in area.
The land has equally spaced poles, marked as
dots in the below figure. Two ropes, R1 and R2,
are already present and cannot be moved.
What is the least number of additional straight
ropes needed to create the desired plots ? A
single rope can pass through three poles that
are aligned in a straight line.
R
2
R
1
(a) 2 (b) 3
(c) 4 (d) 5
Sol: (b)
R
2
R
5
R
3
R
1
R
4
R
3
 ? First additional Rope
R
4
? Second additional Rope
R
5
? Third additional Rope
So, using 3 additional ropes. We are able to
divide into 4 similar shape plots.
7. A function y(x) is defined in the interval [0, 1]
on the x-axis as
y(x) =
1
2 if 0 x
3
1 3
3 if x
3 4
3
1 if x 1
4
?
? ?
?
?
?
? ? ?
?
?
? ?
?
?
Which one of the following is the area under
the curve for the interval [0, 1] on the x-axis.
(a)
13
6
(b)
6
5
(c)
5
6
(d)
6
13
 
Sol: (a)
3
2
1
0
1/3 3/4 1
x
Area =
1 3 1 3
2 × +3 × – +1× 1 –
3 4 3 4
? ? ? ?
? ? ? ?
? ? ? ?
=
2 5 1
+3 × +1×
3 12 4
=
2 15 1 8 +15 + 3 26 13
+ + = = =
3 12 4 12 12 6
Another Solution :
y(x) =
1
2 if 0 x
2
1 3
3 if x
3 4
3
1 if x 1
4
?
? ?
?
?
?
? ? ?
?
?
? ?
?
?
Area =
? ?
1
0
y x dx
?
? 
1/3 3/4 1
0 1/3 3/4
2dx + 3dx + 1dx
? ? ?
? ? ? ? ? ? ?
1/3 3/4 1
0 1/3 3/4
2 x + 3 x + x
? 
2 3 1 1
+3 – +
3 4 3 4
? ?
? ?
? ?
?
8 +15 +3
12
=
26 13
=
12 6
8. In a recently conducted national entrance test,
boys constituted 65% of those who appeared for
the test. Girls constituted the remaining
candidates and they accounted for 60% of the
qualified candidates.
Which one of the following is the correct logical
inference based on the information provided in
the above passage ?
(a) The number of boys who appeared for the
test is less than the number of girls who
appeared
(b) The number of boys who qualified the test is
less than the number of girls who qualified.
(c) Equal number of boys and girls appeared for
the test
(d) Equal number of boys and girls qualified.
Sol: (b)
Let total candidates appeared = x
Appeared boys = 65%x = 0.65x
Appeared girls = 35%x = 0.35x
Let total qualified = y
qualified boys = 40%y = 0.4y
qualified girls = 0.6%y = 0.6y
Option (b) is correct because 0.6y > 0.4y.
Option (b) is correct.
9. The ______ is too high for it to be considered
_____.
(a) fair/fare (b) fare/fair
(c) fare /fare (d) faer /fair
Sol: (b)
The fare is too high for it to be considered fair.
10. Given below are four statements.
Statement 1 : All students are inquisitive
Statement 2 : Some students are inquisitive
Statement 3 : No student in inquisitive
Statement 4 : Some students are not inquisitive
From the given four statements, find the two
statements that CANNOT BE TRUE
simultaneously, assuming that there is at least
one student in the class.
(a) Statement 1 and Statement 3
(b) Statement 3 and Statement 4
(c) Statement 1 and Statement 2
(d) Statement 2 and Statement 4
Sol: (a)
Students
Inquisitive
1. All students are inquisitive.
Students
Inquisitive
Page 4


 
1. Let r be a root of the equation 
2
x + 2x + 6 = 0
.
Then the value of the expression
? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
 is
(a) 126 (b) –51
(c) 51 (d) –126
Sol: (d)
r be the root of the equation 
2
x + 2x + 6 = 0 so
it will satisfy
2
r + 2r + 6 = 0 ...(i)
Now, ? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
? ? ? ? ?
2 2
r + 5r + 6 r + 9r + 20
? ? ? ? ?
2 2
r + 2r + 6 + 3r r + 2r + 6 +7r +14
? ? ? ? ?
0 + 3r 0 +7r +14
? ? ?
3r 7r +14
? ? ? ? ?
2
21 r + 2r = 21 –6
? –126
Option (d) is correct.
2. Some people believe that “what gets measured,
improves”. Some others believe that “what gets
measured, gets gamed”. One possible reason for
the difference in the beliefs is the work culture
e in organizations. In organizations with good
work culture, metrices help improve outcomes.
However, the same metrices are counterproduc-
tive in organizations with poor work culture.
Which one of the following is the CORRECT
logical inference based on the information in
the above passage ?
(a) Metrices are always counterproductive in
organizations with good work culture
(b) Metrices are useful in organizations with
good work culture.
(c) Metrices are useful in organizations with
poor work culture.
(d) Metrices are never useful in organizations
with good work culture.
Sol: (b)
Metrices are useful in organizations with good
work culture.
3. A palindrome is a word that reads the same
forwards and backwards. In a game of words, a
player has the following two plates painted with
letters.
A D
From the additional plates given in the options,
which one of the combinations of additional
plates would allow the player to construct a
five-letter palindrome. The player should use
all the five plates exactly once. The plates can
be rotated in their plane.
(a)
(b)
(c)
(d)
Sol: (c)
A word, sentence or a number that reads the
same backward or forward.
Ex. RADAR
MADAM
REFER
12321
So, option (c) R A R (after rotating
2nd and 3rd plates) is a palindrome.
Option (c) is correct.
4. The corners and mid-points of the sides of a
triangle are named using the distinct letters,
P, Q, R, S, T and U, but not necessarily in the
same order. Consider the following statements :
• The line joining P and R is parallel to the
line joining Q and S.
• P is placed on the side opposite to the corner
T.
• S and U cannot be placed on the same side.
Which one of the following statements is correct
based on the above information ?
(a) P cannot be placed at a corner
(b) R cannot be placed at a corner
(c) S cannot be placed at a corner
(d) U cannot be placed at a mid-point
Sol: (c)
 
Using above information we can draw,
P/U
S/Q
Q/S
U/P
R
T
S can’t be place at a corners because PR is
parallel with QS.
Option (c) is correct.
5. A box contains five balls of same size and shape.
Three of them are green coloured balls and two
of them are orange coloured balls. Balls are
drawn from the box one at a time. If a green
ball is drawn, it is not replaced. If an orange
ball is drawn, it is replaced with another orange
ball.
First ball is drawn. What is the probability of
getting an orange ball in the next draw ?
(a)
23
50
(b)
1
2
(c)
19
50
(d)
8
25
Sol: (a)
G ? green
O ? Orange
3G
20
2G
20
3G
2O
Green
Orange
3/5
2/5
Green
Orange
2/4
2/4
Green
Orange
3/5
2/5
P(E) =
3 2 2 2
× + ×
5 4 5 5
=
3 4
+
10 25
=
23
50
Option (a) is correct.
6. A plot of land must be divided between four
families. They want their individual plots to be
similar in shape, not necessarily equal in area.
The land has equally spaced poles, marked as
dots in the below figure. Two ropes, R1 and R2,
are already present and cannot be moved.
What is the least number of additional straight
ropes needed to create the desired plots ? A
single rope can pass through three poles that
are aligned in a straight line.
R
2
R
1
(a) 2 (b) 3
(c) 4 (d) 5
Sol: (b)
R
2
R
5
R
3
R
1
R
4
R
3
 ? First additional Rope
R
4
? Second additional Rope
R
5
? Third additional Rope
So, using 3 additional ropes. We are able to
divide into 4 similar shape plots.
7. A function y(x) is defined in the interval [0, 1]
on the x-axis as
y(x) =
1
2 if 0 x
3
1 3
3 if x
3 4
3
1 if x 1
4
?
? ?
?
?
?
? ? ?
?
?
? ?
?
?
Which one of the following is the area under
the curve for the interval [0, 1] on the x-axis.
(a)
13
6
(b)
6
5
(c)
5
6
(d)
6
13
 
Sol: (a)
3
2
1
0
1/3 3/4 1
x
Area =
1 3 1 3
2 × +3 × – +1× 1 –
3 4 3 4
? ? ? ?
? ? ? ?
? ? ? ?
=
2 5 1
+3 × +1×
3 12 4
=
2 15 1 8 +15 + 3 26 13
+ + = = =
3 12 4 12 12 6
Another Solution :
y(x) =
1
2 if 0 x
2
1 3
3 if x
3 4
3
1 if x 1
4
?
? ?
?
?
?
? ? ?
?
?
? ?
?
?
Area =
? ?
1
0
y x dx
?
? 
1/3 3/4 1
0 1/3 3/4
2dx + 3dx + 1dx
? ? ?
? ? ? ? ? ? ?
1/3 3/4 1
0 1/3 3/4
2 x + 3 x + x
? 
2 3 1 1
+3 – +
3 4 3 4
? ?
? ?
? ?
?
8 +15 +3
12
=
26 13
=
12 6
8. In a recently conducted national entrance test,
boys constituted 65% of those who appeared for
the test. Girls constituted the remaining
candidates and they accounted for 60% of the
qualified candidates.
Which one of the following is the correct logical
inference based on the information provided in
the above passage ?
(a) The number of boys who appeared for the
test is less than the number of girls who
appeared
(b) The number of boys who qualified the test is
less than the number of girls who qualified.
(c) Equal number of boys and girls appeared for
the test
(d) Equal number of boys and girls qualified.
Sol: (b)
Let total candidates appeared = x
Appeared boys = 65%x = 0.65x
Appeared girls = 35%x = 0.35x
Let total qualified = y
qualified boys = 40%y = 0.4y
qualified girls = 0.6%y = 0.6y
Option (b) is correct because 0.6y > 0.4y.
Option (b) is correct.
9. The ______ is too high for it to be considered
_____.
(a) fair/fare (b) fare/fair
(c) fare /fare (d) faer /fair
Sol: (b)
The fare is too high for it to be considered fair.
10. Given below are four statements.
Statement 1 : All students are inquisitive
Statement 2 : Some students are inquisitive
Statement 3 : No student in inquisitive
Statement 4 : Some students are not inquisitive
From the given four statements, find the two
statements that CANNOT BE TRUE
simultaneously, assuming that there is at least
one student in the class.
(a) Statement 1 and Statement 3
(b) Statement 3 and Statement 4
(c) Statement 1 and Statement 2
(d) Statement 2 and Statement 4
Sol: (a)
Students
Inquisitive
1. All students are inquisitive.
Students
Inquisitive
 
2. Some students are inquisitive.
If all are true then some also true so first
and second can be true simultaneously.
Students Inquisitive
3. No student is inquisitive.
4. Some students are not acquisitive.
Students
Inquisitive
If some students are in inquisitive true then
some students are not inquisitive is also true.
Second and fourth can be true simultaneously.
So, option (a) is correct.
TECHNICAL
11. Let WB and WT be two sets associate cache
organizations that use LRU algorithm for cache
block replacement. WB is a write back cache
and WT is a write through cache. Which of the
following statements is FALSE ?
(a) A read miss in WB will never lead to eviction
of a dirty block from WB.
(b) Each cache block in WB and WT has a dirty
bit.
(c) Eviction of a block from WT will not lead to
data transfer from cache to main memory.
(d) Every write hit in WB leads to a data
transfer from cache to main memory.
Sol: (a, b, d)
In write through policy, all the write operation
is made in main memory and cache memory
simultaneously, ensure that main memory is
valid.
In write back policy, at the time of block
replacement when dirty bit is set on the line
changes is written back into the memory.
The cache eviction is a strategy in which the
data is removed from the cache.
(i) To make room for more relevant cache
entries.
(ii) To shrink the cache to make available more
RAM for other users.
(a) For read/write misses in write back, a line
needed to be evicted for the newly fetched
block. Hence, option (a) is false.
(b) In write back, dirty bit is set for those lines
which are updated.
In write through, no dirty bit is required.
Hence option (b) is FALSE.
(c) In write through, no need to do eviction of
a block from cache. So there is no data
transfer required from cache to main
memory. Hence, option (c) is TRUE.
(d) In write back, data transfer from cache to
memory is required at the time of block
replacement, i.e. when eviction required.
Hence, option (d) is FALSE.
12. In a relational data model, which one of the
following statements is TRUE ?
(a) A relation with only two attributes is always
in BCNF.
(b) BCNF decomposition preserve functional
dependencies.
(c) Every relation has at least one non-prime
attribute.
(d) If all attributes of a relation are prime
attributes, then the relation is in BCNF.
Sol: (a)
At last one of the following holds in BCNF.
(i) ? ? ? is a trivial functional dependency i.e
? ? ? .
(ii) ? is a superkey.
Thus, a relation with only two attribute must
be in BCNF.
BCNF decomposition doesn’t preserve functional
dependencies.
It is not mandatory that every relation has at
least one non-prime attribute.
If all attributes of relation are prime attribute,
then the relation is always in 3NF.
13. Consider the following languages :
? ? ? ?
1
L = ww|w a,b * ?
? ?
n n m
2
L = a b c |m,n 0 ?
? ?
m n n
3
L = a b c |m,n 0 ?
Page 5


 
1. Let r be a root of the equation 
2
x + 2x + 6 = 0
.
Then the value of the expression
? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
 is
(a) 126 (b) –51
(c) 51 (d) –126
Sol: (d)
r be the root of the equation 
2
x + 2x + 6 = 0 so
it will satisfy
2
r + 2r + 6 = 0 ...(i)
Now, ? ? ? ? ? ? ? ?
r + 2 r + 3 r + 4 r + 5
? ? ? ? ?
2 2
r + 5r + 6 r + 9r + 20
? ? ? ? ?
2 2
r + 2r + 6 + 3r r + 2r + 6 +7r +14
? ? ? ? ?
0 + 3r 0 +7r +14
? ? ?
3r 7r +14
? ? ? ? ?
2
21 r + 2r = 21 –6
? –126
Option (d) is correct.
2. Some people believe that “what gets measured,
improves”. Some others believe that “what gets
measured, gets gamed”. One possible reason for
the difference in the beliefs is the work culture
e in organizations. In organizations with good
work culture, metrices help improve outcomes.
However, the same metrices are counterproduc-
tive in organizations with poor work culture.
Which one of the following is the CORRECT
logical inference based on the information in
the above passage ?
(a) Metrices are always counterproductive in
organizations with good work culture
(b) Metrices are useful in organizations with
good work culture.
(c) Metrices are useful in organizations with
poor work culture.
(d) Metrices are never useful in organizations
with good work culture.
Sol: (b)
Metrices are useful in organizations with good
work culture.
3. A palindrome is a word that reads the same
forwards and backwards. In a game of words, a
player has the following two plates painted with
letters.
A D
From the additional plates given in the options,
which one of the combinations of additional
plates would allow the player to construct a
five-letter palindrome. The player should use
all the five plates exactly once. The plates can
be rotated in their plane.
(a)
(b)
(c)
(d)
Sol: (c)
A word, sentence or a number that reads the
same backward or forward.
Ex. RADAR
MADAM
REFER
12321
So, option (c) R A R (after rotating
2nd and 3rd plates) is a palindrome.
Option (c) is correct.
4. The corners and mid-points of the sides of a
triangle are named using the distinct letters,
P, Q, R, S, T and U, but not necessarily in the
same order. Consider the following statements :
• The line joining P and R is parallel to the
line joining Q and S.
• P is placed on the side opposite to the corner
T.
• S and U cannot be placed on the same side.
Which one of the following statements is correct
based on the above information ?
(a) P cannot be placed at a corner
(b) R cannot be placed at a corner
(c) S cannot be placed at a corner
(d) U cannot be placed at a mid-point
Sol: (c)
 
Using above information we can draw,
P/U
S/Q
Q/S
U/P
R
T
S can’t be place at a corners because PR is
parallel with QS.
Option (c) is correct.
5. A box contains five balls of same size and shape.
Three of them are green coloured balls and two
of them are orange coloured balls. Balls are
drawn from the box one at a time. If a green
ball is drawn, it is not replaced. If an orange
ball is drawn, it is replaced with another orange
ball.
First ball is drawn. What is the probability of
getting an orange ball in the next draw ?
(a)
23
50
(b)
1
2
(c)
19
50
(d)
8
25
Sol: (a)
G ? green
O ? Orange
3G
20
2G
20
3G
2O
Green
Orange
3/5
2/5
Green
Orange
2/4
2/4
Green
Orange
3/5
2/5
P(E) =
3 2 2 2
× + ×
5 4 5 5
=
3 4
+
10 25
=
23
50
Option (a) is correct.
6. A plot of land must be divided between four
families. They want their individual plots to be
similar in shape, not necessarily equal in area.
The land has equally spaced poles, marked as
dots in the below figure. Two ropes, R1 and R2,
are already present and cannot be moved.
What is the least number of additional straight
ropes needed to create the desired plots ? A
single rope can pass through three poles that
are aligned in a straight line.
R
2
R
1
(a) 2 (b) 3
(c) 4 (d) 5
Sol: (b)
R
2
R
5
R
3
R
1
R
4
R
3
 ? First additional Rope
R
4
? Second additional Rope
R
5
? Third additional Rope
So, using 3 additional ropes. We are able to
divide into 4 similar shape plots.
7. A function y(x) is defined in the interval [0, 1]
on the x-axis as
y(x) =
1
2 if 0 x
3
1 3
3 if x
3 4
3
1 if x 1
4
?
? ?
?
?
?
? ? ?
?
?
? ?
?
?
Which one of the following is the area under
the curve for the interval [0, 1] on the x-axis.
(a)
13
6
(b)
6
5
(c)
5
6
(d)
6
13
 
Sol: (a)
3
2
1
0
1/3 3/4 1
x
Area =
1 3 1 3
2 × +3 × – +1× 1 –
3 4 3 4
? ? ? ?
? ? ? ?
? ? ? ?
=
2 5 1
+3 × +1×
3 12 4
=
2 15 1 8 +15 + 3 26 13
+ + = = =
3 12 4 12 12 6
Another Solution :
y(x) =
1
2 if 0 x
2
1 3
3 if x
3 4
3
1 if x 1
4
?
? ?
?
?
?
? ? ?
?
?
? ?
?
?
Area =
? ?
1
0
y x dx
?
? 
1/3 3/4 1
0 1/3 3/4
2dx + 3dx + 1dx
? ? ?
? ? ? ? ? ? ?
1/3 3/4 1
0 1/3 3/4
2 x + 3 x + x
? 
2 3 1 1
+3 – +
3 4 3 4
? ?
? ?
? ?
?
8 +15 +3
12
=
26 13
=
12 6
8. In a recently conducted national entrance test,
boys constituted 65% of those who appeared for
the test. Girls constituted the remaining
candidates and they accounted for 60% of the
qualified candidates.
Which one of the following is the correct logical
inference based on the information provided in
the above passage ?
(a) The number of boys who appeared for the
test is less than the number of girls who
appeared
(b) The number of boys who qualified the test is
less than the number of girls who qualified.
(c) Equal number of boys and girls appeared for
the test
(d) Equal number of boys and girls qualified.
Sol: (b)
Let total candidates appeared = x
Appeared boys = 65%x = 0.65x
Appeared girls = 35%x = 0.35x
Let total qualified = y
qualified boys = 40%y = 0.4y
qualified girls = 0.6%y = 0.6y
Option (b) is correct because 0.6y > 0.4y.
Option (b) is correct.
9. The ______ is too high for it to be considered
_____.
(a) fair/fare (b) fare/fair
(c) fare /fare (d) faer /fair
Sol: (b)
The fare is too high for it to be considered fair.
10. Given below are four statements.
Statement 1 : All students are inquisitive
Statement 2 : Some students are inquisitive
Statement 3 : No student in inquisitive
Statement 4 : Some students are not inquisitive
From the given four statements, find the two
statements that CANNOT BE TRUE
simultaneously, assuming that there is at least
one student in the class.
(a) Statement 1 and Statement 3
(b) Statement 3 and Statement 4
(c) Statement 1 and Statement 2
(d) Statement 2 and Statement 4
Sol: (a)
Students
Inquisitive
1. All students are inquisitive.
Students
Inquisitive
 
2. Some students are inquisitive.
If all are true then some also true so first
and second can be true simultaneously.
Students Inquisitive
3. No student is inquisitive.
4. Some students are not acquisitive.
Students
Inquisitive
If some students are in inquisitive true then
some students are not inquisitive is also true.
Second and fourth can be true simultaneously.
So, option (a) is correct.
TECHNICAL
11. Let WB and WT be two sets associate cache
organizations that use LRU algorithm for cache
block replacement. WB is a write back cache
and WT is a write through cache. Which of the
following statements is FALSE ?
(a) A read miss in WB will never lead to eviction
of a dirty block from WB.
(b) Each cache block in WB and WT has a dirty
bit.
(c) Eviction of a block from WT will not lead to
data transfer from cache to main memory.
(d) Every write hit in WB leads to a data
transfer from cache to main memory.
Sol: (a, b, d)
In write through policy, all the write operation
is made in main memory and cache memory
simultaneously, ensure that main memory is
valid.
In write back policy, at the time of block
replacement when dirty bit is set on the line
changes is written back into the memory.
The cache eviction is a strategy in which the
data is removed from the cache.
(i) To make room for more relevant cache
entries.
(ii) To shrink the cache to make available more
RAM for other users.
(a) For read/write misses in write back, a line
needed to be evicted for the newly fetched
block. Hence, option (a) is false.
(b) In write back, dirty bit is set for those lines
which are updated.
In write through, no dirty bit is required.
Hence option (b) is FALSE.
(c) In write through, no need to do eviction of
a block from cache. So there is no data
transfer required from cache to main
memory. Hence, option (c) is TRUE.
(d) In write back, data transfer from cache to
memory is required at the time of block
replacement, i.e. when eviction required.
Hence, option (d) is FALSE.
12. In a relational data model, which one of the
following statements is TRUE ?
(a) A relation with only two attributes is always
in BCNF.
(b) BCNF decomposition preserve functional
dependencies.
(c) Every relation has at least one non-prime
attribute.
(d) If all attributes of a relation are prime
attributes, then the relation is in BCNF.
Sol: (a)
At last one of the following holds in BCNF.
(i) ? ? ? is a trivial functional dependency i.e
? ? ? .
(ii) ? is a superkey.
Thus, a relation with only two attribute must
be in BCNF.
BCNF decomposition doesn’t preserve functional
dependencies.
It is not mandatory that every relation has at
least one non-prime attribute.
If all attributes of relation are prime attribute,
then the relation is always in 3NF.
13. Consider the following languages :
? ? ? ?
1
L = ww|w a,b * ?
? ?
n n m
2
L = a b c |m,n 0 ?
? ?
m n n
3
L = a b c |m,n 0 ?
 
Which of the following statements is/are
FALSE ?
(a) Neither L
1
 nor L
2
 is context-free.
(b) L
2
, L
3
 and 
2 3
L L ? all are context-free
(c) Neither L
1
 nor L
2 
is complement is context-
free
(d) L
1
 is not context-free but L
2
 and L
3
 are
deterministic context-free.
Sol: (a, b, c)
Given languages,
? ? ? ? ?
1
L = ww|w a,b *
? ? ?
n n m
2
L = a b c |m,n 0
? ? ?
m n n
3
L = a b c |m,n 0
Language L
1
 is not accepted by PDA, because
we can’t figure out middle element of string.
Hence it is not context free language.
Language L
2
 is accepted by PDA, because each
element ‘a’ is pushed in the stack and for each
element ‘b’ pop operation is performed, and
finally any number of input symbol ‘c’ is possible.
Hence language L
2
 is context free language.
Language L
3
 is accepted by PDA, because after
any number of input element ‘a’, for element ‘b’
push operation in performed and  for element ‘c’
pop operation is performed & stack becomes empty.
Hence, language L
3
 is context free language.
Thus, L
1
 - Not context free
L
2
 - Context free.
Option (a) is FALSE.
L
2
 - Context free
L
3
 - Context free
? ?
n n n m m m
2 3
L L = a b c or a b c |m,n 0 ? ?
This language is context sensitive language.
Option (b) is FALSE.
L
1
 - Not context free
1
L - Context free
Option (c) is FALSE.
L
1
 - Not context free
L
2
 - Deterministic context free
L
3
 - Deterministic context free
Option (d) is TRUE.
14. The value of the following limit is _____.
2 x
x 0+
x
Lim
1 – e
?
Sol: (–0.5)
+ 2 x
x 0
x
Lim
1 – e
?
? put 0 in equation 
0 0
=
1 –1 0
?
? Apply L' hospital rule, we get (differentiate
numerator and denominator)
?
+
x 0
2 x
1
2 x
Lim
2
0 – e .
2 x
?
?
+
x 0
2 x
1
x
2
Lim
1
–2e .
2 x
?
? 
+ 2 x
x 0
1
Lim
–2e
?
? 
1
– = –0.5
2
15. Which one of the following is the closed form for
the generating function of the sequence ? ?
n
n 0
a
?
defined below ?
n
n +1, n is odd
a =
1, otherwise
?
?
?
(a)
? ?
? ?
2
2
2
x 1 + x
1
+
1 – x
1 – x
(b)
? ?
? ?
2
2
x 3 – x
1
+
1 – x
1 – x
(c)
? ?
2
2
2x 1
+
1 – x
1 – x
(d)
? ?
2
2
x 1
+
1 – x
1 – x
Sol: (a)
a
n
=
n +1 if n is odd
1 otherwise
?
?
?
? ? ? ?
n – 1 n – K +1
2
 = 
2 3
0 1 2 3
4 5
4 5
a + a x + a x + a x
+a x + a x +...
= 
2 3 4 5
1+ 2x + x + 4x + x + 6x +...