B.TechSemester 12023-24Engineering Mathematics IBAS103

Engineering Mathematics I (BAS103) - AKTU Question Paper 2023-24

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 2023-24. 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:2023-24

University:AKTU / UPTU

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Questions Asked in 2023-24

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

Section AAttempt all q u e s t i o n s i n b r i e f . 2 x 7 = 14

a
Find the product and sum of the eigen values for 𝐴 ൌቂ 8െ 4
b
Find all symmetry in the curve 𝑦ଶሺ𝑎ଶ ൅𝑥 ଶሻ ൌ𝑥 ଶሺ𝑎ଶ െ𝑥 ଶሻ. 2 2
c
Calculate the error in R if 𝐸ൌ𝑅 𝐼 and possible errors in E and I are 30% and 20% respectively. 2 3
d
Determine the value of Γ
e
Prove that 𝐵ሺ𝑝, 𝑞ሻ ൌ𝐵 ሺ𝑝൅1 ,𝑞ሻ ൅𝐵 ሺ𝑝, 𝑞 ൅ 1ሻ 2 4
f
Prove that 𝐴⃗ ൌ ሺ6𝑥𝑦 ൅ 𝑧ଷሻ𝚤̂ ൅ ሺ3𝑥ଶ െ𝑧 ሻ𝚥̂ ൅ ሺ3𝑥𝑧ଶ െ𝑦 ሻ𝑘෠ is irrotational. 2 5
g
Find a unit normal vector to the surface 𝑥𝑦ଷ𝑧ଶ ൌ4 at the point

Section BAttempt any three o f t h e f o l l o w i n g : 7 x 3 = 21

c
Expand 𝑓ሺ𝑥, 𝑦ሻ ൌ𝑒 ௫ cos 𝑦 about the point ቀ1, ସቁ by Taylor’s sereies. 7 3 Evaluate the integral ∬ ሺ𝑦െ𝑥 ሻ𝑑𝑥𝑑𝑦;஽ by changing the variables, D: Region in xy-plane bounded by the lines Find the directional derivative of 𝑓ሺ𝑥, 𝑦, 𝑧ሻ ൌ𝑒 ଶ௫ cos 𝑦𝑧 at ሺ0, 0, 0ሻ in the direction of the tangent to the curve 𝑥 ൌ 𝑎 sin 𝜃 , 𝑦 ൌ 𝑎 cos 𝜃, 𝑧 ൌ 𝑎𝜃 at 𝜃ൌ 𝜋 4ൗ

Section CAttempt any one p a r t o f t h e f o l l o w i n g : 7 x 1 = 7

a
Determine eigen vectors for the matrix 𝐴 ൌ ൥
b
Determine 𝐴ିଵ, 𝐴ିଶ and 𝐴ିଷ if 𝐴 ൌ ൥ ൩ using Cayley- Hamilton theorem
a
If 𝑦ൌc o sሺ𝑚s i nିଵ 𝑥ሻ then prove that ሺ1െ𝑥 ଶሻ𝑦௡ାଶ െ ሺ2𝑛 ൅ 1ሻ𝑥𝑦௡ାଵ ൅ ሺ𝑚ଶ െ𝑛 ଶሻ𝑦௡ ൌ0 . Also find ሺ𝑦௡ሻ଴. 7 2 If 𝑧ൌ 𝑓ሺ𝑥, 𝑦ሻ,𝑥 ൌ 𝑒௨ ൅𝑒 ି௩,𝑦 ൌ 𝑒ି௨ െ𝑒 ௩ then show that
a
If 𝑢ଷ ൅𝑣 ଷ ൌ𝑥൅𝑦 , 𝑢ଶ ൅𝑣 ଶ ൌ𝑥 ଷ ൅𝑦 ଷ, then show The pressure P at any point ሺ𝑥, 𝑦, 𝑧ሻ in space is 𝑃 ൌ 400 𝑥𝑦𝑧ଶ. Find the highest pressure at the surface of a unit sphere 𝑥ଶ ൅𝑦 ଶ ൅𝑧 ଶ ൌ1 using Lagrange’s method
b
Prove that 𝐵ሺ𝑚, 𝑛ሻ ൌ

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.