NIMCET 2020 Previous Year Questions (PYQs) – Page 1 of 12
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The expression $\frac{tanA}{1-cotA}+\frac{cotA}{1-tanA}$ can be written as
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Solution
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
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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
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Solution
Solving y2 = x and y = x, 
we get, y = 0, x = 0, y = 1, x = 1 Therefore,
Test the continuity of the function at x = 2
$f(x)= \begin{cases} \frac{5}{2}-x & \text{ if } x<2 \\ 1 & \text{ if } x=2 \\ x-\frac{3}{2}& \text{ if } x>2 \end{cases}$
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Solution
LHL ≠ f(2)
If $3 sin x + 4 cos x = 5$, then $6tan\frac{x}{2}-9tan^2\frac{x}{2}$
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Solution
If A is a subset of B and B is a subset of C, then
cardinality of A ∪ B ∪ C is equal to
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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 $35\frac{7}{15}$. What was the number erased?
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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?
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Solution
Given: A = 1 min, B = 2 min, C = 8 min, D = 11 min. Only 2 can cross at a time with 1 lamp. Pair walks at slower person’s speed.
Best (exam) strategy:
1) A + B cross → 2 min
2) A returns → 1 min
3) C + D cross → 11 min
4) B returns → 2 min
5) A + B cross → 2 min
Total time = 2 + 1 + 11 + 2 + 2 = 18 minutes
Answer: 18 minutes
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?
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Solution
Let total population be $100$ (as given).
Ratio of adults : children $= 2 : 3$
So, total parts $= 2 + 3 = 5$
Adults $= \dfrac{2}{5} \times 100 = 40$
Children $= \dfrac{3}{5} \times 100 = 60$
Now use literacy data:
For adults:
Illiterate adults $= 40.1%$
So, literate adults $= 100% - 40.1% = 59.9%$
Literate adults $= 59.9%$ of $40$
$= \dfrac{59.9}{100} \times 40 = 23.96$
For children:
Literate children $= 85.1%$ of $60$
$= \dfrac{85.1}{100} \times 60 = 51.06$
Total literate population
$= 23.96 + 51.06 = 75.02$
Since total population is $100$,
Literate percentage $= 75.02% \approx 75%$.
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