Mathematics Iii (KAS-303) - AKTU Question Paper 2021-22
B.Tech · Semester 3 · Free PDF Download
This is the official AKTU Mathematics Iii Previous Year Question Paper for B.Tech Semester 3, 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
Mathematics Iii (KAS-303) — complete question paper
- aFind the Laplace transform of 𝑒ି௧ 𝑐𝑜𝑠𝑡 𝑑𝑡
- cState Modulation theorem. 2
- dFind the Z-transform of 𝑓ሺ𝑘ሻ ൌ
- eProve that the statement ሺ𝑝→𝑞 ሻ →ሺ 𝑝 ∧𝑞 ሻ is a contingency. 3
- fShow that every sub- group H of an abelian group G is normal. 3
- gHow many bit strings of length 8 either start with 1 or end with two bits 00? 4
- hGiven 𝑓ሺ𝑥ሻ ൌ3 𝑥െ2 , find 𝑓ିଵሺ𝑥ሻ. 4 Q1(i) Define Maximal element and Minimal element of Poset. 5 Q1(j) Prove the Boundedness (NULL) law i.e. 𝑎∗0ൌ0 . 5
- aSolve the following simultaneous equations by Laplace transform 3 ௗ௧ െ𝑦ൌ0 with the conditions 𝑥ሺ0ሻ ൌ0 , 𝑦ሺ0ሻ ൌ0
- bi) Find the Fourier transform of 𝐹ሺ𝑥ሻ ൌ൜ 1 , |𝑥| ൏𝑎 0, |𝑥| 𝑎 ൠ. Hence evaluate ii) Using Parseval’s identity, show that Hence find
- cConsider a ring (𝑅, , ∗) defined by 𝑎∗𝑎ൌ𝑎 . Determine whether the ring is commutative or not
- dSolve the difference equation 𝑦 െ𝑦 ିଵ െ6 𝑦ିଶ ൌ െ30. Given that 𝑦 ൌ 20, 𝑦ଵ ൌ െ 5
- eIn a Boolen algebra B if 𝑏𝑎ൌ𝑐𝑎 and 𝑏𝑎 ᇱ ൌ𝑐𝑎 ᇱ then 𝑏ൌ𝑐 . Also if 𝑏𝑎 ൌ 𝑐𝑎 and 𝑏𝑎ᇱ ൌ𝑐 𝑎ᇱ then 𝑏ൌ𝑐
- aDraw the graph and find the Laplace transform of the triangular wave function of period of 2c given by 𝑓ሺ𝑡ሻ ൌቄ 𝑡, 0 ൏ 𝑡 𝑐
- aDetermine the distribution of temperature in the semi- infinite medium 𝑥0 when the end 𝑥ൌ0 is maintained at zero temperature and the initial distribution of temperature is F(x)
- bSolve by Z-transform the difference equation 𝑦ାଶ 6 𝑦ାଵ 9 𝑦 ൌ2
- aConsider the following argument and determine whether it is valid. Either I will get good marks or I will not graduate. If I did not graduate I will go to Canada. I get good marks. Thus, I would not go to Canada
- bTranslate the following into symbolic form and test the validity of the argument. If 6 is even then 2 does not divide 7. Either 5 is not prime or 2 divides 7. But 5 is prime, therefore ,6 is odd
- aAmong the first 1000 positive integers
- aDetermine the integers which are not divisible by 5, nor by 7, nor by 9
- bDetermine the integers divisible by 5, but not by 7, not by 9
- bProve by Mathematical Induction
- aIf L be any Lattice, then for any 𝑎, 𝑏, 𝑐 ∈ 𝐿. Prove the following: (i) 𝑎∨𝑎ൌ𝑎 . (ii) 𝑎∨𝑏ൌ𝑏∨𝑎 (iii) 𝑎∨ ሺ𝑏∨𝑐 ሻ ൌሺ 𝑎∨𝑏 ሻ∨𝑐
- bFor two posets A and B: (i) Show that if 𝑓: 𝐴 →𝐵 is an order preserving, then 𝑓 is one to one. (ii) Show that if 𝑓: 𝐴 →𝐵 is an order isomorphism, then there is an order isomorphism 𝑔∶𝐵→ 𝐴
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 — KAS-303
Questions that appeared in more than one session, found by comparing 2 years of Mathematics Iii papers (2021-22, 2022-23)
Find the Z-transform of 𝑓ሺ𝑘ሻ ൌ
Appeared in: 2021-22 · 2022-23
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