Engineering Mathematics I (BAS103) - AKTU Question Paper 2025-26
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 2025-26. 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 2025-26
Engineering Mathematics I (BAS103) — complete question paper · 70 marks · 3 Hours
- bFind the Rank of the following Matrix A: ,log3 xxy e= prove that
- dIf ,)(),( 5yxyxu += then find the degree of the function ),( yxu
- eIf sin,cos ryrx == , find sin,cos ryrx ==
- fEvaluate the following integral using the Beta-Gamma function: 3/13)8( dxxx
- gShow that gradient field describing a motion is irrotational
- aDetermine the values of and such that the following system: has (i) no solution (ii) a unique solution (iii) infinitely many solutions
- bFind the thn derivative of
- cExpand 232 −+ yyx in powers of )1( −x and )2( +y up to 3rd degree using Taylor’s series . 232 −+ yyx
- dChange the order of integration and hence evaluate
- eFind the directional derivative of the divergence of kzjxyixyzyxf ˆˆˆ),,( 22 ++= at the point (2, 1, 2) in the direction of the outer normal to the sphere .9222 =++ zyx 9222 =++ zyx
- aFind the eigen values and eigen vectors of the following Matrix A: 321 XXX , then show that the vectors 321 ,, XXX are linearly dependent. 321 ,, XXX
- bTrace the curve : ).3()( 22 xaxxay −=+
- aFind the minimum distance from the point )0,2,1( to the cone .222 yxz +=
- bFind approximate value of
- aProve that the area in the positive quadrant bounded by the curves 222 ,4,4 cxybxyaxy === 2dxy = is .,;log)(3 1 22 abcda bcd .,;log)(3 1 22 abcda bcd 222 ,4,4 cxybxyaxy ===
- bFind the volume of the solid bounded by the co -ordinate planes and the surface
- aApply Green’s theorem to evaluate ,cos)sin( +− dyxdxxy where C is the triangle formed .2,2,0 xyxy ,cos)sin( +− dyxdxxy xyxy
- bApply Gauss’s divergence theorem to evaluate dsnF ,. where kxjxyizxF and S is the Surface bounded by the planes 0,0,0 === zyx and .422 =++ zyx dsnF ,. kxjxyizxF 422 =++ zyx
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)
Find the thn derivative of
Appeared in: 2024-25 · 2025-26
Change the order of integration and hence evaluate
Appeared in: 2024-25 · 2025-26
Find the directional derivative of the divergence of kzjxyixyzyxf ˆˆˆ),,( 22 ++= at the point (2, 1, 2) in the direction of the outer normal to the sphere .9222 =++ zyx 9222 =++ zyx
Appeared in: 2022-23 · 2025-26
Trace the curve : ).3()( 22 xaxxay −=+
Appeared in: 2024-25 · 2025-26
Find approximate value of
Appeared in: 2024-25 · 2025-26
Apply Gauss’s divergence theorem to evaluate dsnF ,. where kxjxyizxF and S is the Surface bounded by the planes 0,0,0 === zyx and .422 =++ zyx dsnF ,. kxjxyizxF 422 =++ zyx
Appeared in: 2022-23 · 2025-26
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