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UGC NET Computer Science Previous Year Questions (PYQs)
UGC NET Computer Science Discrete Mathematics PYQ
UGC NET Computer Science PYQ
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Let P denote “She is intelligent” and Q denote “She is happy.”
Given statements:
(a) If she is intelligent, then she is unhappy.
(b) She is neither intelligent nor happy.
(c) It is necessary to be not intelligent in order to be happy.
(d) To be not intelligent is to be unhappy.
Which option gives the correct propositional expressions?
- (a) P→¬Q; (b) P ∧ ¬Q; (c) Q→¬P; (d) P→¬Q
- (a) P→Q; (b) ¬P ∧ ¬Q; (c) ¬Q→P; (d) ¬P→¬Q
- (a) P→¬Q; (b) ¬P ∧ ¬Q; (c) Q→¬P; (d) ¬P→¬Q
- (a) P→¬Q; (b) P ∧ ¬Q; (c) Q↔P; (d) ¬P→¬Q
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Solution
Translate each statement:
(a) “If intelligent then unhappy” ⇒ P → ¬Q.
(b) “Neither intelligent nor happy” ⇒ ¬P ∧ ¬Q.
(c) “Being not intelligent is necessary for being happy” ⇒ Q → ¬P.
(d) “Not intelligent implies unhappy” ⇒ ¬P → ¬Q.
Only Option 3 matches all four translations.
Answer: 3
UGC NET Computer Science PYQ
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
In a group of 120 people:
65 eat Rice, 45 eat Bread, 42 eat Curd,
20 eat both Rice and Bread, 25 eat both Rice and Curd, 15 eat both Bread and Curd,
and 8 eat all three items.
Which of the following is the number of people who eat at least one of the three items?
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Solution
Using the formula for union of three sets:
n(R ∪ B ∪ C) = n(R) + n(B) + n(C) − n(R ∩ B) − n(R ∩ C) − n(B ∩ C) + n(R ∩ B ∩ C)
Substitute:
= 65 + 45 + 42 − 20 − 25 − 15 + 8
= 152 − 60 + 8
= 100
Hence, 100 people eat at least one of the three items.
UGC NET Computer Science PYQ
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
| List I (Statements) | List II (Logic Type) |
|---|---|
| A. If the Indian team wins, then it is raining | IV. Conditional |
| B. If the Indian team does not win, then it is not raining | I. Inverse |
| C. If it is raining, then the Indian team wins | II. Converse |
| D. If it is not raining, then the Indian team does not win | III. Contrapositive |
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Solution
A → IV → Conditional statement
B → I → Inverse (negating both sides)
C → II → Converse (reversing condition and result)
D → III → Contrapositive (negating and reversing)
UGC NET Computer Science PYQ
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
The tight asymptotic bound for the recurrence:
$T(n) = 2T(n/4) + \sqrt{n}$
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Solution
We use the Master Theorem for $T(n) = aT(n/b) + f(n)$ Here, $a = 2$, $b = 4$, so $n^{\log_b a} = n^{\log_4 2} = n^{1/2} = \sqrt{n}$ Thus, $f(n) = \sqrt{n}$ is of the same order as $n^{\log_b a}$. Therefore, by Case 2 of Master Theorem, $T(n) = \Theta(n^{\log_b a} \log n) = \Theta(\sqrt{n} \log n)$ ✅ But wait! Let’s check growth dominance carefully: Actually, when $f(n) = \Theta(n^{\log_b a})$, we multiply by $\log n$, hence the correct bound is $\boxed{T(n) = \Theta(\sqrt{n} \log n)}$
UGC NET Computer Science PYQ
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
A positive integer is selected at random from the set of positive integers not exceeding 200.
What is the probability that the selected number is divisible by either 2 or 5?
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Solution
Let total numbers = 200 Divisible by 2 → 200/2 = 100 Divisible by 5 → 200/5 = 40 Divisible by both (LCM 10) → 200/10 = 20 Using inclusion–exclusion: n(2 ∪ 5) = 100 + 40 − 20 = 120 Probability = 120 / 200 = 3/5
UGC NET Computer Science PYQ
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Let m and n be positive integers.
(A) If n ≠ 1, then m < mn.
(B) If k is composite, then k = mn where 1 < m, n > k.
(C) If mn = 1, then m = 1 and n = 1.
(D) If k is composite, then k = mn where 1 < m, n < k.
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Solution
(B) is false (for composite k, both factors are < k). (A), (C), (D) are true for positive integers.
UGC NET Computer Science PYQ
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Choose the correct statement for a group G:
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UGC NET Computer Science UGC NET PYQ UGC NET Computer Science UGC NET Computer Science 26 June 2025 (Paper II) PYQ
Solution
Reason: From (xy)² = xyxy = x²y² = xxyy. Left-multiply by x⁻¹ and right-multiply by y⁻¹ to get yx = xy, hence G is abelian. (2) and (3) are false (there exist non-abelian groups where every element has order 3 or 5, e.g., unitriangular 3×3 matrices over ℤ₃/ℤ₅). (4) is false because every subgroup of an abelian (commutative) group is abelian.UGC NET Computer Science
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