Phrases Previous Year Questions (PYQs) – 2020 – Page 1 of 12
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Angle of elevation of the top of the tower from 3
points (collinear) A, B and C on a road leading to the
foot of the tower are 30°, 45° and 60°, respectively.
The ratio of AB and BC is
1
2
3
4
Solution
According to the given information, the figure should be as follows. 
Let the height of tower = h
The area enclosed between the curves y2 = x and
y = |x| is
1
2
3
4
Solution
Solving y2 = x and y = x, 
we get, y = 0, x = 0, y = 1, x = 1 Therefore,
If A is a subset of B and B is a subset of C, then
cardinality of A ∪ B ∪ C is equal to
1
2
3
4
Solution
If A ⊆ B and B ⊆ C, then find the cardinality of A ∪ B ∪ C.
Explanation
- Since A is a subset of B, everything in A is already in B.
- Since B is a subset of C, everything in B (and hence A) is already in C.
- Therefore, A ∪ B ∪ C = C.
✅ Final Answer
|A ∪ B ∪ C| = |C|
A set of consecutive positive integers beginning with
1 is written on the blackboard. A student came along
and erased one number. The average of the remaining
numbers is
1
2
3
4
Solution
Four friends A, B, C and D need to cross a bridge in
the night. A maximum of 2 people can cross at a
time. They have only one lamp. A takes one minute
to cross the bridge. B takes 2 minutes, C takes 8
minutes and D takes 11 minutes to cross the bridge
respectively. A pair must walk together at the speed
of the person who walks slowly. What is the
minimum time required to cross the bridge by all the four people?
1
2
3
4
Solution
In a city, 40.1% of the adults are illiterate while
85.1% of the children are literate. If the ratio of the
adults to that of the children is 2:3, then what percent
of the population is literate?
1
2
3
4
Solution
Assume total population = 100.
Given, ratio of adults to children = 2:3.
Thus,
Adults =
Children =
Among adults:
Literate adults =
Among children:
Literate children =
Total literate people =
Thus, percentage of literates =
Given, ratio of adults to children = 2:3.
Thus,
Adults =
Children =
Among adults:
Literate adults =
Among children:
Literate children =
Total literate people =
Thus, percentage of literates =
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