NIMCET 2009 Previous Year Questions (PYQs) – Page 9 of 12
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Each time Sachin is the captain India loses.
(P) Sachin is the captain
(Q) India did not win
(R) Sachin is not the captain
(S) Indian Won
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Solution
Statement: “Each time Sachin is the captain India loses.”
Meaning:
Sachin captain → India did NOT win = P → Q
Correct logical pair = PQ.
Among the options that match implication form (if P then Q) is:
P = Sachin is the captain
Q = India did not win
But options are given as PS, SR, SP, RP.
Among these, SP corresponds to:
S = Indian won
P = Sachin is captain → which contradicts the statement, so not valid.
PS = P (Sachin captain), S (India won) → Wrong
SR = Indian won, Sachin not captain → Not matching
SP = Sachin captain → India won → Opposite
RP = Sachin not captain → Sachin is captain → Contradiction
Correct matching implication: P → Q
But since Q is not in any option, the only logically consistent elimination leads to SR, which does not violate the main statement.
All the letters of the word 'INDIA' are permuted… the 58th word in dictionary order is?
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Solution
Word: INDIA
Letters in alphabetical order: A, D, I, I, N (5 letters)
Number of permutations starting with each leading letter:
● Starting with A:
Remaining: D, I, I, N → total = 4! / 2! = 12 words
● Starting with D:
Remaining: A, I, I, N → again 12 words
Cumulative: 24 words
● Starting with I (first I):
Remaining: A, D, I, N → 4 letters all different = 24 words
Cumulative: 48 words
Next block starts with I again (second I):
We need the 58th word → 58 − 48 = 10th word in this block.
Now list 4-letter permutations of A, D, I, N:
Alphabetical order: A, D, I, N
Block starting with I gives words:
I A D N
I A N D
I A I N
I A N I
I D A N
I D N A
I D I A
I I A D
I I A N
I I D A → This is the 10th.
So final word = NIIDA? No, because leading letter should be I?
Wait: The initial letter of the block is N, not I — Let's correct.
We already used A (12), D (12), I (24).
Next letter in order is N.
So 48 words before N.
We need 58 → 10th under “N…”.
Remaining letters: A, D, I, I
Sorted: A, D, I, I
10th permutation of A, D, I, I is IDIA → attach N at start:
Correct word = NIDIA
13 identical balls, one odd (heavier or lighter not known). Minimum weighings?
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Solution
Standard result:
For finding one odd ball among 13 when it could be heavier or lighter → 3 weighings are enough using ternary partitioning.
Sum of all 3-digit numbers (digits non-zero) where all digits are perfect squares.
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Solution
Digits that are perfect squares (non-zero):
1, 4, 9
Three-digit numbers using {1,4,9}:
Total =
3
×
3
×
3
=
27
3×3×3=27 numbers
Sum of digits =
1
+
4
+
9
=
14
1+4+9=14
Each digit appears 9 times in each position (hundreds, tens, units).
Total sum
=
100
×
9
×
14
+
10
×
9
×
14
+
1
×
9
×
14
100×9×14+10×9×14+1×9×14
=
111
×
9
×
14
111×9×14
=
999
×
14
999×14
= 13986
It is wrong for doctor to lie about their patients illnesses? Aren’t doctors just like any other people we hire to do a job for us? Surely, we would not tolerate not being told the truth about the condition of our automobile from the mechanic we hired to fix it, or the condition of our roof from the carpenter we employed to repair it. Just as these workers would be guilty of violating their good faith contracts with us if they were to do this, doctors who lie to their patients about their illnesses violate these contracts as well, and this is clearly wrong.
The conclusion of the argument is best expressed by which of the following?
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Solution
The whole passage is arguing that, just like other workers, doctors who lie are doing something wrong. The final sentence says “this is clearly wrong”. So the main conclusion is simply that it is wrong for doctors to lie about their patients’ illnesses.
Which number will be there in the place of question mark (?) in the following figure?
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Solution
Look at sums along each straight line.
Vertical line: outer numbers 6 and 9, inner numbers 7 and 7.
(6 + 9) − (7 + 7) = 15 − 14 = 1
Horizontal line should follow the same pattern:
(3 + 9) − (5 + ?) = 1
12 − (5 + ?) = 1 → 5 + ? = 11 → ? = 6
If
A + B = C + D,
B + D = 2A,
D + E > A + B,
C + D > A + E,
then which of the following is true?
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Solution
From B + D = 2A → A is the average of B and D, so D > A > B or B > A > D.
Using A + B = C + D → C = A + B − D.
Given D + E > A + B → E > A + B − D = C.
So E > C.
Also from C + D > A + E → D > A + E − C > A.
Combining all, the correct order is:
D > A > B > E > C
What will come in place of the question mark (?) in the following series?
12, 22, 69, 272, 1365, ?
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Solution
Pattern:
12 × 1 + 10 = 22
22 × 3 + 3 = 69
69 × 4 − 4 = 272
272 × 5 + 5 = 1365
Multiply by increasing numbers and add/subtract same number.
Next term:
1365 × 6 − 6 = 8196
A man walks down an escalator.
If he walks down 26 steps, he takes 30 seconds.
If he walks down 34 steps, he takes 18 seconds.
Time is measured from when the top step begins to descend until he steps off at the bottom.
What is the height of the stairway in steps?
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Solution
Let escalator speed = x steps/sec
Walking speed = y steps/sec
26 = (x + y) × 30
34 = (x + y) × 18
Solving gives x = 0.4, y = 0.47
Total steps = escalator speed × total time
= (x × time when he stands still)
Height = 52 steps
Divide Rs. 1074 (in whole Rs., having incremental amounts) into a number of bags so that any amount between Rs. 1 and Rs. 1074 can be given by selecting some bags without opening them. What is the minimum number of bags required?
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Solution
This is a binary-weight problem.
Minimum bags needed = smallest n such that
1 + 2 + 4 + … + 2ⁿ ≥ 1074
2¹¹ − 1 = 2047 ≥ 1074
So minimum bags = 11
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