Discrete Mathematics (BMC104) - AKTU Question Paper 2024-25
MCA · Semester 1 · Free PDF Download
This is the official AKTU Discrete Mathematics Previous Year Question Paper for MCA Semester 1, academic session 2024-25. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.
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Questions Asked in 2024-25
Discrete Mathematics (BMC104) — complete question paper · 70 marks · 3 Hours
- aWhat is multiplicity of an element in a multiset? Find the multiplicities of each element in the multiset ሼ 𝑎 ,𝑎 ,𝑎 ,ሼ𝑎, 𝑎, 𝑎ሽሽ
- bConsider the two functions 𝑓 and 𝑔 defined on set of real numbers as 𝑓ሺ𝑥ሻ ൌ2 𝑥1 and 𝑔ሺ𝑥ሻ ൌ ଷ. Find 𝑓ିଵ𝑜𝑔ିଵ
- cLet 𝑃ሺ𝑆ሻ be the power set of 𝑆ൌሼ 𝑎 , 𝑏 , 𝑐 ሽ. Determine the greatest lower bound and the least upper bound of the set ሼሼ𝑎ሽ,ሼ 𝑐 ሽ ሽ in the poset
- dState the Modus Ponens rule of inference
- eHow many generators are there o f the cyclic group G of order 6
- fDefine Normal subgroup
- gObtain the generating functi on of the numeric function
- aProve that the relation 𝑅 i n NൈN such that ሺ𝑎, 𝑏ሻ𝑅ሺ𝑐, 𝑑ሻ iff 𝑎 𝑑 ൌ 𝑐 𝑏 f o r 𝑎, 𝑏, 𝑐, 𝑑 ∈ 𝑁 is an equivalence relation. Also find equivalence class of (4,6)
- bProve that ሺ𝐷ଶସ,| ሻ is lattice
- cShow that ሼሾሺ𝑝 ∨ 𝑞ሻ ⇒ 𝑟ሿ ∧ሺ ~ 𝑝 ሻሽ ⟹ሺ 𝑞⟹𝑟 ሻ is a tautology without truth table
- dState and prove Lagrange’s theorem of group
- eProve by mathematical induction: 𝑛ସ െ4 𝑛ଶ is divisible by 3 for all 𝑛
- aFor any set A and B (i) Prove that if 𝐴 ⊆𝐵 then 𝑃ሺ𝐴ሻ⊆𝑃 ሺ 𝐵 ሻ. (ii) Is it true 𝑃ሺ𝐴 ∪𝐵 ሻ ൌ𝑃 ሺ𝐴ሻ∪𝑃 ሺ 𝐵 ሻ? Justify your answer
- bLet a function is defined as 𝑓:𝑅െ ሼ5ሽ →𝑅െ ሼ1ሽ, 𝑓ሺ𝑥ሻ ൌ ௫ିହ , where R is the set of real numbers. Show that 𝑓 is bijective function and also compute inverse of 𝑓
- aShow that if ሺ𝐴, ሻ and ሺ𝐵, ሻ are posets, then ሺ𝐴 ൈ𝐵 ,≼ሻ i s a p o s e t , with partial order ≼ defined by ሺ𝑎, 𝑏ሻ ≼ ሺ𝑎ᇱ,𝑏 ᇱሻ 𝑖𝑓 𝑎 𝑎ᇱ and b 𝑏ᇱ, where 𝑎, 𝑎ᇱ ∈ 𝐴 and 𝑏, 𝑏ᇱ ∈𝐵
- b(i) For any Boolean algebra B prove that (ii) Use Karnaugh map representation to find minimal sum of products expression of 𝐹ሺ𝐴,𝐵 ,𝐶 ,𝐷ሻ ൌ ∑ሺ1,9,11,13,15ሻ
- aExpress the following st atements using quantifiers: (i) There is a student who spends more than 5 hours every weekday i n class. (ii) No well behaved person is quarrelsome. (iii) Everyone meets someone. (iv) All graduates are educated
- bCheck the validity of the following arguments: “If there was a ball game, then travelling was difficult. If th ey arrived on time, then travelling was not di fficult. They arrived on time. Therefore there was no ball game
- aWhat do you mean by cosets of a subgroup? Consider the group Z o f integers under addition and subgroup 𝐻ൌ ሼ… … … ,10, െ5,0,5,10 … … .ሽ considering multiple of 5. Find the cosets of H in Z
- bIf R is ring such that 𝑎ଶ ൌ 𝑎 ∀ 𝑎 ∈ 𝑅, prove that
- aSolve the recurrence relation 𝑎 െ4 𝑎ିଵ 4 𝑎ିଶ ൌ0 given that 𝑎 ൌ
- bIn how many ways can a committee of 3 ladies and 4 gentlemen b e appointed from a group consisting of 8 ladies and 7 gentlemen? What will be the number of ways, if Sanjana of this committee refuse s to serve in a committee in which Akhilesh is a member
Question text is extracted from the official AKTU question paper PDF above. Hindi translations are omitted — every question is printed in English in the original paper. Last verified: 2026-08-23.
Repeated Questions — BMC104
Questions that appeared in more than one session, found by comparing 2 years of Discrete Mathematics papers (2024-25, 2025-26)
Obtain the generating functi on of the numeric function
Appeared in: 2024-25 · 2025-26
Solve the recurrence relation 𝑎 െ4 𝑎ିଵ 4 𝑎ିଶ ൌ0 given that 𝑎 ൌ
Appeared in: 2024-25 · 2025-26
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