Page 1
PAGE
1
..Q.1 to Q.5 Carry One Mark Each..
Question 1
“I have not yet decided, what will I do this evening; I_______ visit a friend”.
(A) Mite (B) Would
(C) Might (D) Didn’t
Ans. (C)
Sol. Given :
“I have not yet decided, what will I do this evening; I might visit a friend”.
Hence, the correct option is (C).
Question 2
Eject : Insert :: Advance : _______. (By word meaning)
(A) Advent (B) Progress
(C) Retreat (D) Loan
Ans. (C)
Sol. Given :
Eject is related to insert in a special manner as they are opposite in meaning for each other. In the same
way of relationship advance will be related to retreat, as advance means forward and retreat means
backward.
Hence, the correct option is (C).
Question 3
In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with
its centre at V such that it passes through P. What is the area (in cm
2
) of the shaded region? (The
diagram is representative)
(A)
25
3
?
(B)
20
3
?
(C) 6 ? (D) 7 ?
Ans. (A)
Sol. Sum of interior angles =
0
( 2)180 n ?
Each angle of regular hexagon,
0
0
( 2)180
120
n
n
?
?
P
R S
T
V
Q
Page 2
PAGE
1
..Q.1 to Q.5 Carry One Mark Each..
Question 1
“I have not yet decided, what will I do this evening; I_______ visit a friend”.
(A) Mite (B) Would
(C) Might (D) Didn’t
Ans. (C)
Sol. Given :
“I have not yet decided, what will I do this evening; I might visit a friend”.
Hence, the correct option is (C).
Question 2
Eject : Insert :: Advance : _______. (By word meaning)
(A) Advent (B) Progress
(C) Retreat (D) Loan
Ans. (C)
Sol. Given :
Eject is related to insert in a special manner as they are opposite in meaning for each other. In the same
way of relationship advance will be related to retreat, as advance means forward and retreat means
backward.
Hence, the correct option is (C).
Question 3
In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with
its centre at V such that it passes through P. What is the area (in cm
2
) of the shaded region? (The
diagram is representative)
(A)
25
3
?
(B)
20
3
?
(C) 6 ? (D) 7 ?
Ans. (A)
Sol. Sum of interior angles =
0
( 2)180 n ?
Each angle of regular hexagon,
0
0
( 2)180
120
n
n
?
?
P
R S
T
V
Q
PAGE
2
2
0
Required Area
360
R
?
??
0
2
0
120
5
360
??
25
3
?
?
Hence, the correct option is (A).
Question 4
A duck named Donald Duck says “All ducks always lie.”
Based only on the information above, which one of the following statements can be logically inferred
with certainty?
(A) Donald Duck always lies. (B) Donald Duck always tells the truth.
(C) Donald Duck’s statement is true. (D) Donald Duck’s statement is false.
Ans. (D)
Sol. Given :
A duck named Donald Duck says “All ducks always lie.”
According to the given information Donald Duck’s statement is false.
Hence, the correct option is (D).
Question 5
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is
a mirror image of the other part about that line.
The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares,
upto 5 more may be coloured black. Which one among the following options depicts the minimum
number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is
representative)
(A) d (B) c, d, i
(C) c, i (D) c, d, i, f, g
Ans. (B)
Sol. Given :
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is
a mirror image of the other part about that line.
The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares,
upto 5 more may be coloured black.
a
c d
e f
g
h
i
j k
b
Page 3
PAGE
1
..Q.1 to Q.5 Carry One Mark Each..
Question 1
“I have not yet decided, what will I do this evening; I_______ visit a friend”.
(A) Mite (B) Would
(C) Might (D) Didn’t
Ans. (C)
Sol. Given :
“I have not yet decided, what will I do this evening; I might visit a friend”.
Hence, the correct option is (C).
Question 2
Eject : Insert :: Advance : _______. (By word meaning)
(A) Advent (B) Progress
(C) Retreat (D) Loan
Ans. (C)
Sol. Given :
Eject is related to insert in a special manner as they are opposite in meaning for each other. In the same
way of relationship advance will be related to retreat, as advance means forward and retreat means
backward.
Hence, the correct option is (C).
Question 3
In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with
its centre at V such that it passes through P. What is the area (in cm
2
) of the shaded region? (The
diagram is representative)
(A)
25
3
?
(B)
20
3
?
(C) 6 ? (D) 7 ?
Ans. (A)
Sol. Sum of interior angles =
0
( 2)180 n ?
Each angle of regular hexagon,
0
0
( 2)180
120
n
n
?
?
P
R S
T
V
Q
PAGE
2
2
0
Required Area
360
R
?
??
0
2
0
120
5
360
??
25
3
?
?
Hence, the correct option is (A).
Question 4
A duck named Donald Duck says “All ducks always lie.”
Based only on the information above, which one of the following statements can be logically inferred
with certainty?
(A) Donald Duck always lies. (B) Donald Duck always tells the truth.
(C) Donald Duck’s statement is true. (D) Donald Duck’s statement is false.
Ans. (D)
Sol. Given :
A duck named Donald Duck says “All ducks always lie.”
According to the given information Donald Duck’s statement is false.
Hence, the correct option is (D).
Question 5
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is
a mirror image of the other part about that line.
The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares,
upto 5 more may be coloured black. Which one among the following options depicts the minimum
number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is
representative)
(A) d (B) c, d, i
(C) c, i (D) c, d, i, f, g
Ans. (B)
Sol. Given :
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is
a mirror image of the other part about that line.
The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares,
upto 5 more may be coloured black.
a
c d
e f
g
h
i
j k
b
PAGE
3
In the figure given below, MN is the vertical line of symmetry for the figure, for which we have to
colour the box ‘i’.
In the figure given below, PQ is the horizontal line of symmetry for the figure, for which we have to
colour box ‘c’ and ‘d’.
Therefore, we have to colour 3 boxes c, d, i to achieve two line of symmetry MN and PQ.
Hence, the correct option is (B).
..Q.6 to Q.10 Carry Two Marks Each..
Question 6
Based only on the truth of the statement 'Some humans are intelligent', which one of the following
options can be logically inferred with certainty?
(A) No human is intelligent (B) All humans are intelligent
(C) Some non-humans are intelligent (D) Some intelligent beings are humans
Ans. (D)
Sol. Given :
Statement ‘Some humans are intelligent’.
a
c d
e f
g
h
i
j k
b
a
c
d
e
f
g
h
j
k
b
M
N
i
a
e
f
g
h
j k
b
P
i
c
d
Q
Page 4
PAGE
1
..Q.1 to Q.5 Carry One Mark Each..
Question 1
“I have not yet decided, what will I do this evening; I_______ visit a friend”.
(A) Mite (B) Would
(C) Might (D) Didn’t
Ans. (C)
Sol. Given :
“I have not yet decided, what will I do this evening; I might visit a friend”.
Hence, the correct option is (C).
Question 2
Eject : Insert :: Advance : _______. (By word meaning)
(A) Advent (B) Progress
(C) Retreat (D) Loan
Ans. (C)
Sol. Given :
Eject is related to insert in a special manner as they are opposite in meaning for each other. In the same
way of relationship advance will be related to retreat, as advance means forward and retreat means
backward.
Hence, the correct option is (C).
Question 3
In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with
its centre at V such that it passes through P. What is the area (in cm
2
) of the shaded region? (The
diagram is representative)
(A)
25
3
?
(B)
20
3
?
(C) 6 ? (D) 7 ?
Ans. (A)
Sol. Sum of interior angles =
0
( 2)180 n ?
Each angle of regular hexagon,
0
0
( 2)180
120
n
n
?
?
P
R S
T
V
Q
PAGE
2
2
0
Required Area
360
R
?
??
0
2
0
120
5
360
??
25
3
?
?
Hence, the correct option is (A).
Question 4
A duck named Donald Duck says “All ducks always lie.”
Based only on the information above, which one of the following statements can be logically inferred
with certainty?
(A) Donald Duck always lies. (B) Donald Duck always tells the truth.
(C) Donald Duck’s statement is true. (D) Donald Duck’s statement is false.
Ans. (D)
Sol. Given :
A duck named Donald Duck says “All ducks always lie.”
According to the given information Donald Duck’s statement is false.
Hence, the correct option is (D).
Question 5
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is
a mirror image of the other part about that line.
The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares,
upto 5 more may be coloured black. Which one among the following options depicts the minimum
number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is
representative)
(A) d (B) c, d, i
(C) c, i (D) c, d, i, f, g
Ans. (B)
Sol. Given :
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is
a mirror image of the other part about that line.
The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares,
upto 5 more may be coloured black.
a
c d
e f
g
h
i
j k
b
PAGE
3
In the figure given below, MN is the vertical line of symmetry for the figure, for which we have to
colour the box ‘i’.
In the figure given below, PQ is the horizontal line of symmetry for the figure, for which we have to
colour box ‘c’ and ‘d’.
Therefore, we have to colour 3 boxes c, d, i to achieve two line of symmetry MN and PQ.
Hence, the correct option is (B).
..Q.6 to Q.10 Carry Two Marks Each..
Question 6
Based only on the truth of the statement 'Some humans are intelligent', which one of the following
options can be logically inferred with certainty?
(A) No human is intelligent (B) All humans are intelligent
(C) Some non-humans are intelligent (D) Some intelligent beings are humans
Ans. (D)
Sol. Given :
Statement ‘Some humans are intelligent’.
a
c d
e f
g
h
i
j k
b
a
c
d
e
f
g
h
j
k
b
M
N
i
a
e
f
g
h
j k
b
P
i
c
d
Q
PAGE
4
Can be represented by given venn diagram as shown below,
Option (A) No human is intelligent, is wrong as some human are intelligent.
Option (B) All humans are intelligent, is wrong as we have no information about remaining part of
human.
Option (C) Some non-humans are intelligent, is wrong as we have no information about non-humans.
Option (D) Some intelligent beings are humans, can be inferred as some intelligent being are human can
be seen in the diagram.
Hence, the correct option is (D).
Question 7
Which one of the options can be inferred about the mean, median, and mode for the given probability
distribution (i.e. probability mass function), P( ?? ), of a variable x?
(A) mean = median ? mode (B) mean = median = mode
(C) mean ? median = mode (D) mean ? mode = median
Ans. (A)
Sol.
Humans Intelligent
17 ? 13 ? 9 ? 5 ? 1 ? 1 5 9 13 17
( ) P x
x
17 ? 13 ? 9 ? 5 ? 1 ? 1 5 9 13 17
Mode
Modian
Mode
Page 5
PAGE
1
..Q.1 to Q.5 Carry One Mark Each..
Question 1
“I have not yet decided, what will I do this evening; I_______ visit a friend”.
(A) Mite (B) Would
(C) Might (D) Didn’t
Ans. (C)
Sol. Given :
“I have not yet decided, what will I do this evening; I might visit a friend”.
Hence, the correct option is (C).
Question 2
Eject : Insert :: Advance : _______. (By word meaning)
(A) Advent (B) Progress
(C) Retreat (D) Loan
Ans. (C)
Sol. Given :
Eject is related to insert in a special manner as they are opposite in meaning for each other. In the same
way of relationship advance will be related to retreat, as advance means forward and retreat means
backward.
Hence, the correct option is (C).
Question 3
In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with
its centre at V such that it passes through P. What is the area (in cm
2
) of the shaded region? (The
diagram is representative)
(A)
25
3
?
(B)
20
3
?
(C) 6 ? (D) 7 ?
Ans. (A)
Sol. Sum of interior angles =
0
( 2)180 n ?
Each angle of regular hexagon,
0
0
( 2)180
120
n
n
?
?
P
R S
T
V
Q
PAGE
2
2
0
Required Area
360
R
?
??
0
2
0
120
5
360
??
25
3
?
?
Hence, the correct option is (A).
Question 4
A duck named Donald Duck says “All ducks always lie.”
Based only on the information above, which one of the following statements can be logically inferred
with certainty?
(A) Donald Duck always lies. (B) Donald Duck always tells the truth.
(C) Donald Duck’s statement is true. (D) Donald Duck’s statement is false.
Ans. (D)
Sol. Given :
A duck named Donald Duck says “All ducks always lie.”
According to the given information Donald Duck’s statement is false.
Hence, the correct option is (D).
Question 5
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is
a mirror image of the other part about that line.
The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares,
upto 5 more may be coloured black. Which one among the following options depicts the minimum
number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is
representative)
(A) d (B) c, d, i
(C) c, i (D) c, d, i, f, g
Ans. (B)
Sol. Given :
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is
a mirror image of the other part about that line.
The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares,
upto 5 more may be coloured black.
a
c d
e f
g
h
i
j k
b
PAGE
3
In the figure given below, MN is the vertical line of symmetry for the figure, for which we have to
colour the box ‘i’.
In the figure given below, PQ is the horizontal line of symmetry for the figure, for which we have to
colour box ‘c’ and ‘d’.
Therefore, we have to colour 3 boxes c, d, i to achieve two line of symmetry MN and PQ.
Hence, the correct option is (B).
..Q.6 to Q.10 Carry Two Marks Each..
Question 6
Based only on the truth of the statement 'Some humans are intelligent', which one of the following
options can be logically inferred with certainty?
(A) No human is intelligent (B) All humans are intelligent
(C) Some non-humans are intelligent (D) Some intelligent beings are humans
Ans. (D)
Sol. Given :
Statement ‘Some humans are intelligent’.
a
c d
e f
g
h
i
j k
b
a
c
d
e
f
g
h
j
k
b
M
N
i
a
e
f
g
h
j k
b
P
i
c
d
Q
PAGE
4
Can be represented by given venn diagram as shown below,
Option (A) No human is intelligent, is wrong as some human are intelligent.
Option (B) All humans are intelligent, is wrong as we have no information about remaining part of
human.
Option (C) Some non-humans are intelligent, is wrong as we have no information about non-humans.
Option (D) Some intelligent beings are humans, can be inferred as some intelligent being are human can
be seen in the diagram.
Hence, the correct option is (D).
Question 7
Which one of the options can be inferred about the mean, median, and mode for the given probability
distribution (i.e. probability mass function), P( ?? ), of a variable x?
(A) mean = median ? mode (B) mean = median = mode
(C) mean ? median = mode (D) mean ? mode = median
Ans. (A)
Sol.
Humans Intelligent
17 ? 13 ? 9 ? 5 ? 1 ? 1 5 9 13 17
( ) P x
x
17 ? 13 ? 9 ? 5 ? 1 ? 1 5 9 13 17
Mode
Modian
Mode
PAGE
5
Median
11
0
2
??
??
Mode = –13, 13
So, Median ? Mode
Hence, the correct option is (A).
Question 8
The James Webb telescope, recently launched in space, is giving humankind unprecedented access to
the depths of time by imaging very old stars formed almost 13 billion years ago. Astrophysicists and
cosmologists believe that this odyssey in space may even shed light on the existence of dark matter.
Dark matter is supposed to interact only via the gravitational interaction and not through the
electromagnetic-, the weak- or the strong-interaction. This may justify the epithet “dark” in dark matter.
Based on the above paragraph, which one of the following statements is FALSE?
(A) No other telescope has captured images of stars older than those captured by the James Webb
telescope.
(B) People other than astrophysicists and cosmologists may also believe in the existence of dark
matter.
(C) The James Webb telescope could be of use in the research on dark matter.
(D) If dark matter was known to interact via the strong-interaction, then the epithet “dark” would
be justified.
Ans. (D)
Sol. Given :
The James Webb telescope, recently launched in space, is giving humankind unprecedented access to
the depths of time by imaging very old stars formed almost 13 billion years ago. Astrophysicists and
cosmologists believe that this odyssey in space may even shed light on the existence of dark matter.
Dark matter is supposed to interact only via the gravitational interaction and not through the
electromagnetic-, the weak- or the strong-interaction. This may justify the epithet “dark” in dark matter.
According to the given paragraph statement in option (D) is FALSE.
As, “Dark matter is supposed to interact only via the gravitational interaction and not through the
electromagnetic-, the weak- or the strong-interaction.”
Hence, the correct option is (D).
Question 9
Let a = 30!, b = 50! &c = 100! Consider the following numbers :
log , log , log , log
a c b a
c a a b
Which one of the following inequalities is CORRECT?
(A) log a log log log
c b a a
abc ? ? ? (B) log a log log log
c a b b
bac ? ? ?
(C) log a log log c log
c b a a
ab ? ? ? (D) log a log log log
b c a a
abc ? ? ?
Ans. (A)
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