Maths Iii (KAS403) - AKTU Question Paper 2021-22
B.Tech · Semester 4 · Free PDF Download
This is the official AKTU Maths Iii Previous Year Question Paper for B.Tech Semester 4, academic session 2021-22. 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 2021-22
Maths Iii (KAS403) — complete question paper
- aEvaluate 𝐿ሺ𝑒ି௧ 𝑐𝑜𝑠𝑡ሻ. 1
- bState convolution theorem for Laplace transform. 1
- cFind the Z-transform of 𝑓ሺ𝑘ሻ ൌ𝑐 𝑜 𝑠ቀ
- dState change of scale property in Fourier transform. 2
- eIllustrate a relation which is equivalence on a set A, where 𝐴 ൌ ሼ1,2,3,4,5ሽ. 3
- fShow that every cyclic g roup is an abelian group. 3
- gShow by contradiction that √7 is irrational number. 4
- hIf 𝑓ሺ𝑥ሻ ൌ5 𝑥1 ,𝑓𝑖𝑛𝑑 𝑓ିଵሺ𝑥ሻ. 4 (i) Prove the idempotent law: (j) Describe complemented lattice with an example. 5
- aDetermine the Laplace transform of periodic function define d by the triangular wave function with period of 2a
- bDetermine the solution of the difference equation by Z-tra nsform
- cState and prove La grange’s theorem. 3
- dSolve the recurrence relation 𝑎 = 2𝑎ିଵ − 3 for n > 0, with the initial condition 𝑎 = 4
- e(i) Minimize the following Boolean expression using k-map: (ii) Explain AND Gate, OR Gate, NOT Gate, and also construct t heir logic circuits
- aSolve the following simultaneous equations using Laplace tr ansform
- bFind inverse Laplace transform of 𝑙𝑜𝑔 ቀ1
- aSolve the equation డ௫మ, 𝑥0 , 𝑡0 subject to the conditions ሺ𝑖ሻ𝑢ൌ0 , when 𝑥 ൌ 0, 𝑡 0 (ii) 𝑢ൌ ቄ1, 0 ൏ 𝑥 ൏ 1
- bUsing residue’s method, determine 𝑍ିଵ ቀ
- aTest the validity of the following argument. “It is not sunny and it is cold.” “We will swim only if it is sunny.” “If we do not swim, then we will canoe.” “If we canoe, then we will be home early.” Therefore “We will be home early”
- bShow by algebra of proposition: ¬(¬p → q) ∨ (p ∧ ¬q) ≡ q, where ≡ represents logical equivalent
- aProve the following by mathematical induction for all n∈ ℕ
- 12.3 2.3.4 ⋯ … . . 𝑛ሺ𝑛 1ሻሺ𝑛 2ሻ ൌ 𝑛ሺ𝑛 1ሻሺ𝑛 2ሻሺ𝑛 3ሻ/4
- bA large software development company employs 100 computer programmers. Of them, 45 are proficient in Java, 30 in C#, 20 in Python, six in C# and Java, one in Java and Python, five in C# and Python, and just one programmer is proficient in all three languages above. Determine the number of computer programmers that are not proficient in any of these three languages
- aProve that a poset has at most one greatest element and one least element. 5
- b(i) Define Least and Greatest element of a Poset. (ii) Describe the power set of S = {a, b, c}. Draw the Hasse di agram of (P(S), ⊆) and write the greatest, least, maximal and least element of ( P(S), ⊆). P(S) is denoting power set of S
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 — KAS403
Questions that appeared in more than one session, found by comparing 2 years of Maths Iii papers (2021-22, 2022-23)
State convolution theorem for Laplace transform. 1
Appeared in: 2021-22 · 2022-23
Solve the following simultaneous equations using Laplace tr ansform
Appeared in: 2021-22 · 2022-23
Prove the following by mathematical induction for all n∈ ℕ
Appeared in: 2021-22 · 2022-23
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