B.TechSemester 42021-22Maths IiiKAS403

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.

Course:B.Tech
Semester:Semester 4
Session:2021-22
University:AKTU / UPTU

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Questions Asked in 2021-22

Maths Iii (KAS403) — complete question paper

Section AAttempt all q u e s t i o n s i n b r i e f . 2 * 1 0 = 2 0
  • a
    Evaluate 𝐿ሺ𝑒ି௧ 𝑐𝑜𝑠𝑡ሻ. 1
  • b
    State convolution theorem for Laplace transform. 1
  • c
    Find the Z-transform of 𝑓ሺ𝑘ሻ ൌ𝑐 𝑜 𝑠ቀ
  • d
    State change of scale property in Fourier transform. 2
  • e
    Illustrate a relation which is equivalence on a set A, where 𝐴 ൌ ሼ1,2,3,4,5ሽ. 3
  • f
    Show that every cyclic g roup is an abelian group. 3
  • g
    Show by contradiction that √7 is irrational number. 4
  • h
    If 𝑓ሺ𝑥ሻ ൌ5 𝑥൅1 ,𝑓𝑖𝑛𝑑 𝑓ିଵሺ𝑥ሻ. 4 (i) Prove the idempotent law: (j) Describe complemented lattice with an example. 5
Section BAttempt any three o f t h e f o l l o w i n g : 1 0 * 3 = 3 0
  • a
    Determine the Laplace transform of periodic function define d by the triangular wave function with period of 2a
  • b
    Determine the solution of the difference equation by Z-tra nsform
  • c
    State and prove La grange’s theorem. 3
  • d
    Solve the recurrence relation 𝑎௡ = 2𝑎௡ିଵ − 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
Section CAttempt any one p a r t o f t h e f o l l o w i n g : 1 0 * 1 = 1 0
  • a
    Solve the following simultaneous equations using Laplace tr ansform
  • b
    Find inverse Laplace transform of 𝑙𝑜𝑔 ቀ1൅
  • a
    Solve the equation డ௫మ, 𝑥൐0 , 𝑡൐0 subject to the conditions ሺ𝑖ሻ𝑢ൌ0 , when 𝑥 ൌ 0, 𝑡 ൐ 0 (ii) 𝑢ൌ ቄ1, 0 ൏ 𝑥 ൏ 1
  • b
    Using residue’s method, determine 𝑍ିଵ ቀ
  • a
    Test 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”
  • b
    Show by algebra of proposition: ¬(¬p → q) ∨ (p ∧ ¬q) ≡ ൓ q, where ≡ represents logical equivalent
  • a
    Prove the following by mathematical induction for all n∈ ℕ
  • 1
    2.3 ൅ 2.3.4 ൅ ⋯ … . . ൅ 𝑛ሺ𝑛 ൅ 1ሻሺ𝑛 ൅ 2ሻ ൌ 𝑛ሺ𝑛 ൅ 1ሻሺ𝑛 ൅ 2ሻሺ𝑛 ൅ 3ሻ/4
  • b
    A 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
  • a
    Prove 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)

2x

State convolution theorem for Laplace transform. 1

Appeared in: 2021-22 · 2022-23

2x

Solve the following simultaneous equations using Laplace tr ansform

Appeared in: 2021-22 · 2022-23

2x

Prove the following by mathematical induction for all n∈ ℕ

Appeared in: 2021-22 · 2022-23

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