B.TechSemester 12024-25Engineering Mathematics IBAS103

Engineering Mathematics I (BAS103) - AKTU Question Paper 2024-25

B.Tech · Semester 1 · Free PDF Download

This is the official AKTU Engineering Mathematics I Previous Year Question Paper for B.Tech 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.

Course:B.Tech

Semester:Semester 1

Session:2024-25

University:AKTU / UPTU

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Questions Asked in 2024-25

Engineering Mathematics I (BAS103) — complete question paper · 70 marks · 3 Hours

Section AAttempt all questions in brief. 2 x 07 = 14

a
Find the eigen values of the matrix ቂ 𝑐𝑜𝑠𝜃 െ𝑠𝑖𝑛𝜃
b
If 𝑢ൌ ௫ା௬ , find the value of 𝑥
c
What is the difference between total derivatives and partial d erivatives?
d
What are the applications of Jacobians
e
Write the statement of Liouville’s Theorem
g
Prove that 𝑐𝑢𝑟𝑙 𝑟⃗ ൌ0

Section BAttempt any three of the following: 07 x 3 = 07

a
Find two non-singular matrices P and Q such that PAQ is in n ormal form, Where 𝐴 ൌ ൥
b
Find the 𝑛௧௛ derivative of 𝑡𝑎𝑛ିଵ ቀ
c
Find the volume of the largest rectangular parallelepiped th at can be inscribed in the ellipsoid
d
Apply Dirichlet’s theorem to evaluate ∭ 𝑥𝑦𝑧𝑑𝑥𝑑𝑥𝑑𝑧 taken throughout the ellipsoid
e
Show that the vector 𝑓ሺ𝑟ሻ𝑟⃗ is irrotational. Where 𝑟⃗ ൌ𝑥 𝚤̂ ൅𝑦 𝚥̂ ൅𝑧 𝑘෠

Section CAttempt any one part of the following: 07 x 1 = 07

a
Find the eigen values and eigen vectors of the following matrices: 𝐴 ൌ
b
Discuss for all values of K f or the system of equations 1 K 2 𝑥൅𝑦൅4 𝑧ൌ6 , 𝑥൅2 𝑦െ2 𝑧ൌ6 , 𝐾 𝑥൅𝑦൅𝑧ൌ6 as regards existence and nature of solution
a
Trace the curve 𝑦ଶሺ𝑎൅𝑥 ሻ ൌ𝑥 ଶሺ3𝑎 െ 𝑥ሻ
b
If 𝑢ൌ 𝑓ሺ𝑟ሻ,𝑤 ℎ 𝑒 𝑟 𝑒 𝑟ଶ ൌ𝑥 ଶ ൅𝑦 ଶ,prove that
a
If 𝑢ൌ𝑥 𝑦 𝑧 , 𝑣ൌ𝑥ଶ ൅𝑦 ଶ ൅𝑧 ଶ𝑎𝑛𝑑
b
Find the maxima and minima of the function 𝑠𝑖𝑛𝑥 ൅ 𝑠𝑖𝑛𝑦 ൅ sinሺ𝑥 ൅ 𝑦ሻ
a
Find the area inside the circle 𝑟ൌ2 𝑎 𝑐 𝑜 𝑠 𝜃 and outside the circle 𝑟ൌ𝑎
b
Change the order of integration and then evaluate
a
Show that div (grad𝑟௡ሻൌ𝑛 ሺ 𝑛൅1 ሻ 𝑟௡ିଶ. Where 𝑟⃗ ൌ𝑥 𝚤̂ ൅𝑦 𝚥̂ ൅𝑧 𝑘෠
b
Verify Stokes theorem for 𝐹⃗ ൌ ሺ𝑥ଶ ൅𝑦 ଶሻî െ2 𝑥 𝑦ĵ taken round the rectangle bounded by the lines𝑥ൌ0 , 𝑥ൌ𝑎 , 𝑦ൌ0 , 𝑦ൌ𝑏

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 — BAS103

Questions that appeared in more than one session, found by comparing 4 years of Engineering Mathematics I papers (2022-23, 2023-24, 2024-25, 2025-26)

If 𝑢ൌ ௫ା௬ , find the value of 𝑥

Appeared in: 2023-24 · 2024-25 · 2025-26

Find the eigen values of the matrix ቂ 𝑐𝑜𝑠𝜃 െ𝑠𝑖𝑛𝜃

Appeared in: 2023-24 · 2024-25

Prove that 𝑐𝑢𝑟𝑙 𝑟⃗ ൌ0

Appeared in: 2023-24 · 2024-25

Find the 𝑛௧௛ derivative of 𝑡𝑎𝑛ିଵ ቀ

Appeared in: 2024-25 · 2025-26

Find the eigen values and eigen vectors of the following matrices: 𝐴 ൌ

Appeared in: 2022-23 · 2024-25

Trace the curve 𝑦ଶሺ𝑎൅𝑥 ሻ ൌ𝑥 ଶሺ3𝑎 െ 𝑥ሻ

Appeared in: 2024-25 · 2025-26

If 𝑢ൌ 𝑓ሺ𝑟ሻ,𝑤 ℎ 𝑒 𝑟 𝑒 𝑟ଶ ൌ𝑥 ଶ ൅𝑦 ଶ,prove that

Appeared in: 2023-24 · 2024-25

Change the order of integration and then evaluate

Appeared in: 2024-25 · 2025-26

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