NIMCET 2027 2014 Previous Year Questions (PYQs) – Page 12 of 12
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The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls
combined is 50. The percentage of boys in the class is
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Solution
Given averages: Boys = 52, Girls = 42, Combined = 50.
Let the proportion of boys be \(p\) (so girls = \(1-p\)). Weighted mean gives: $$52p + 42(1-p) = 50$$ $$52p + 42 - 42p = 50 \Rightarrow 10p = 8 \Rightarrow p = 0.8.$$
Percentage of boys \(= 0.8 \times 100\% = \boxed{80\%}\).
How many even integers between 4000 and 7000 have four different digits?
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Solution
1: Thousands digit
The number is 4-digit and must be between 4000 and 7000.
So the thousands digit can be: 4, 5, or 6.
Step 2: Units digit
The number must be even, so the units digit must be one of {0, 2, 4, 6, 8}.
3: Count cases
- Case 1: Thousands digit = 4
Units digit ≠ 4 → possible units = {0, 2, 6, 8} → 4 choices.
Hundreds digit = 8 choices, Tens digit = 7 choices.
Total = 4 × 8 × 7 = 224. - Case 2: Thousands digit = 5
Units digit can be {0, 2, 4, 6, 8} → 5 choices.
Hundreds digit = 8 choices, Tens digit = 7 choices.
Total = 5 × 8 × 7 = 280. - Case 3: Thousands digit = 6
Units digit ≠ 6 → possible units = {0, 2, 4, 8} → 4 choices.
Hundreds digit = 8 choices, Tens digit = 7 choices.
Total = 4 × 8 × 7 = 224.
4: Add results
Total = 224 + 280 + 224 = 728.
Final Answer:
There are 728 such even integers.
A road network has parallel roads, which are equidistant from each other and running North-South or
East-West only. The road junctions A, B, C, H and X are such that A is East of B and West of C. H is
South-West of C and South-East of B. B is South-East of X. Which of the junctions are the farthest South and the
farthest East?
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Solution
Four players A, B, C, and D have to form into two pairs, however, no pair can play together more than
seven times in a row A and B have played seven games in a row. C and D have three in a row. C does
not to work with A. Who should play with B?
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Solution
If ROSE is coded as 6821, CHAIR is coded as 73456 and PREACH is coded as 961473, then the code
for SEARCH is
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Solution
Cricket clubs in five towns A, B, C, D and E have one team each named P, Q, R, S and T, not
necessarily in the same order.
The team in A has beaten R, P and S, Q has beaten the teams in E, C and A. Team R is in B and the team in C is
not S.
Which team is in A?
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Solution
Cricket clubs in five towns A, B, C, D and E have one team each named P, Q, R, S and T, not
necessarily in the same order.
The team in A has beaten R, P and S, Q has beaten the teams in E, C and A. Team R is in B and the team in C is
not S.
Where is the team P?
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Solution
Cricket clubs in five towns A, B, C, D and E have one team each named P, Q, R, S and T, not
necessarily in the same order.
The team in A has beaten R, P and S, Q has beaten the teams in E, C and A. Team R is in B and the team in C is
not S.
Where is the team Q?
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Solution
Find the number that comes next in the series
120, 99, 80, 63, 48, ...
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Solution
In a certain school, the number of students in each section was 24. After admitting some students, three
new sections have been started and now there are 16 sections with 21 students in each. What is the number of newly admitted students?
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Solution
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