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MCA NIMCET Binary Logic Puzzle PYQ

MCA NIMCET PYQ
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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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2009 PYQ

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.
MCA NIMCET PYQ
You are on an island with two tribes. One tribe always tells the truth, and the other tribe always lies. You meet three individuals from the island A, B and C. Each individual belongs to one of the tribes. You ask each of them the same question “Is B a truthteller?” “Is B a truthteller?” 
 A says, “Yes B is a truth-teller.” 
 B says, “No, I am not a truth-teller” 
 C. Says, “B is a liar” 

 Given that each individual is either a truth-teller or a liar, who is telling the truth?





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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2024 PYQ

Solution

Given:

  • A says: "Yes, B is a truth-teller."
  • B says: "No, I am not a truth-teller."
  • C says: "B is a liar."

We need to determine: Who is telling the truth?

Step 1: Assume B is a truth-teller:

If **B is a truth-teller**, then B's statement "No, I am not a truth-teller" would be false, which is a contradiction because a truth-teller cannot lie.

So, **B cannot be a truth-teller**.

Step 2: Assume B is a liar:

If **B is a liar**, then B's statement "No, I am not a truth-teller" must be false, meaning B is indeed a truth-teller. But this is a contradiction because B can't be both a liar and a truth-teller.

Thus, **B must be a liar**.

Step 3: A’s statement analysis:

A says, "Yes, B is a truth-teller." Since we concluded that **B is a liar**, A's statement is false.

This means **A is a liar**.

Step 4: C’s statement analysis:

C says, "B is a liar." Since **B is indeed a liar**, C’s statement is true.

Therefore, **C is a truth-teller**.

✅ Final Answer: C is the truth-teller.

MCA NIMCET PYQ
There are three switches A, B and C which can be in ON/OFF position. Their settings change as per the following rules: 
  • If A is the only switch as ON, change B to ON. 
  • If A and B are only switches as ON, change C to ON. 
  • If all three switches are ON, change C to OFF. 
  • For all other situations, all switches in ON are changed to OFF and all switches in OFF are changed to ON
If switches A and B are ON and C is OFF, their changed settings will be:





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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2013 PYQ

Solution

MCA NIMCET PYQ
There are three switches A, B and C which can be in ON/OFF position. Their settings change as per the following rules: 
  • If A is the only switch as ON, change B to ON. 
  • If A and B are only switches as ON, change C to ON. 
  • If all three switches are ON, change C to OFF. 
  • For all other situations, all switches in ON are changed to OFF and all switches in OFF are changed to ON
If only B is ON, the changed setting will be:





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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2013 PYQ

Solution

MCA NIMCET PYQ
There are three switches A, B and C which can be in ON/OFF position. Their settings change as per the following rules: 
  • If A is the only switch as ON, change B to ON. 
  • If A and B are only switches as ON, change C to ON. 
  • If all three switches are ON, change C to OFF. 
  • For all other situations, all switches in ON are changed to OFF and all switches in OFF are changed to ON
If only B is ON in the changed setting, which of the following could have been the original setting?





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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2013 PYQ

Solution

MCA NIMCET PYQ
If $x$ and $y$ are the two digits of the number $565xy$ such that the number is divisible by $80$, then $x+y$ equals





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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2008 PYQ

Solution

For divisibility by $80$, the last two digits must be divisible by $80$. Possible ending is $80$. So $x=8,\ y=0 \Rightarrow x+y=8$. But $y$ must be a digit, so $x+y=8+0=8$,
MCA NIMCET PYQ
There are 6561 balls out of which 1 is heavy. Find the minimum number of weighings required to find the heavy ball.





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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2010 PYQ

Solution

6561 = 3⁸, meaning 8 ternary divisions. Minimum weighings = log₃(6561) = 8 Correct answer: 8
MCA NIMCET PYQ
A remote island has a unique social structure. Individuals are either 'Truth-tellers' (who always speak the truth) or 'Tricksters' (who always lie). You encounter three inhabitants: X, Y, and Z.

X says: "Y is a Trickster."
Y says: "Exactly one of us is a Truth-teller."
What can you definitively conclude about Z?





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MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2025 PYQ

Solution

Let me quickly re-check the logic:

  1. Let T = Truth-teller, L = Trickster (liar).

X says: “Y is a Trickster.”
Y says: “Exactly one of us (X, Y, Z) is a Truth-teller.”

Case 1: Assume X is T.
Then Y must be L.
Y’s statement must be false: “Exactly one of us is a Truth-teller” is false.

  • Truth-tellers so far: X (1).
    If Z were L, then exactly one (X) would be T → Y’s statement would be true, contradiction.
    So Z must be T.
    Configuration: (X T, Y L, Z T) works.

Case 2: Assume X is L.
Then “Y is a Trickster” is false → Y is T.
Now Y’s statement must be true: exactly one of X, Y, Z is T.

  • We already have Y as T, so X and Z must both be L.
    Configuration: (X L, Y T, Z L) works.

Both configurations are consistent:

  • In one, Z is T.

  • In the other, Z is L.

So Z can be either a Truth-teller or a Trickster


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