B.TechSemester 12025-26Engineering Mathematics IBAS103

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.

Course:B.Tech
Semester:Semester 1
Session:2025-26
University:AKTU / UPTU

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Questions Asked in 2025-26

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

Section AAttempt all questions in brief. 02 x 7 = 14
  • b
    Find the Rank of the following Matrix A: ,log3 xxy e= prove that
  • d
    If ,)(),( 5yxyxu += then find the degree of the function ),( yxu
  • e
    If  sin,cos ryrx == , find  sin,cos ryrx ==
  • f
    Evaluate the following integral using the Beta-Gamma function: 3/13)8( dxxx
  • g
    Show that gradient field describing a motion is irrotational
Section BAttempt any three of the following: 07 x 3 = 21
  • a
    Determine the values of  and  such that the following system: has (i) no solution (ii) a unique solution (iii) infinitely many solutions
  • b
    Find the thn derivative of
  • c
    Expand 232 −+ yyx in powers of )1( −x and )2( +y up to 3rd degree using Taylor’s series . 232 −+ yyx
  • d
    Change the order of integration and hence evaluate
  • e
    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
Section CAttempt any one part of the following: 07 x 1 = 07
  • a
    Find 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
  • b
    Trace the curve : ).3()( 22 xaxxay −=+
  • a
    Find the minimum distance from the point )0,2,1( to the cone .222 yxz +=
  • b
    Find approximate value of
  • a
    Prove 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 ===
  • b
    Find the volume of the solid bounded by the co -ordinate planes and the surface
  • a
    Apply Green’s theorem to evaluate  ,cos)sin( +− dyxdxxy where C is the triangle formed .2,2,0 xyxy   ,cos)sin( +− dyxdxxy xyxy 
  • b
    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

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)

2x

Find the thn derivative of

Appeared in: 2024-25 · 2025-26

2x

Change the order of integration and hence evaluate

Appeared in: 2024-25 · 2025-26

2x

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

2x

Trace the curve : ).3()( 22 xaxxay −=+

Appeared in: 2024-25 · 2025-26

2x

Find approximate value of

Appeared in: 2024-25 · 2025-26

2x

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

Engineering Mathematics I — Other Year Papers

AKTU Engineering Mathematics I PYQs from other sessions