B.TechSemester 12022-23Engineering Mathematics IBAS-103
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Engineering Mathematics I (BAS-103) - AKTU Question Paper 2022-23

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 2022-23. 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:2022-23
University:AKTU / UPTU

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Questions Asked in 2022-23

Engineering Mathematics I (BAS-103) — complete question paper

Section AAttempt all questions in brief. 2 x 7 = 14 fuEu lHkh iz”uksa dk la{ksi esa mRrj nhft,A
  • a
    If A is a Hermitian matrix, then show that iA is Skew-Hermitian matrix
  • b
    Find the eigen value of the matrix  24A corresponding to the eigen vector
  • c
    If xy 1cos , prove that .0)1( 12 2  xyyx 2  xyyx 1sin , then show that uy ux tan2 ux tan2
  • e
    Find the percentage error in measuring the volume of a rectangular box when the error of 1% is made in measuring each side
  • f
    Evaluate ydxdy over the part of the plane bounded by the line xy and the parabola 24 xxy 
  • g
    Find curl of a vector field given by jyxyixyxF ˆ)(ˆ)( 2222  jyxyixyxF ˆ)(ˆ)( 2222 
Section BAttempt any three of the following: 7 x 3 = 21
  • b
    If ),1(log1 22  xxxy e prove that 2   nnn ynxynyx . 2   nnn ynxynyx
  • c
    Expand xyyxf ),( about )1,1( up to second degree terms and hence evaluate
  • d
    Evaluate the double integral   
  • a
    a ax dxdyxay )( by changing the order of integration
  • e
    Find the directional derivative of scalar function xyzzyxf ),,( at point )3,1,1(P in the direction of the outward drawn normal to the sphere 11222  zyx through the point P
Section CAttempt any one part of the following: 7 x 1 = 7
  • a
    Test the consistency for the following system of equations and if system is
  • b
    Find the eigen values and corresponding eigen vectors of the matrix A
  • a
    Trace the curve ))(( 222222 yayayx  in xy-plane, where a is constant. vuqjs[k.k djsaA
  • b
    If  cos yx yxu , prove that uyyx uxyx cos yx uyyx uxyx
  • a
    Find the Jacobian of the functions ))(( 32211 xxxxy  , ),)(( 32212 xxxxy  ),( 3123 xxxy  hence show that the functions are not independent. Find the relation between them. Qyu ))(( 32211 xxxxy  , Qyu ),)(( 32212 xxxxy  Qyu
  • b
    A rectangular box, which is open at the top, has a capacity of 32 cubic feet. Determine, using Lagrange’s method of multipliers, the dimensions of the box such that the least material is required for the construction of the box
  • a
    Evaluate  R dxdydzzyx ,)2( where R is the region determined by yxzxyx  0,0,10 2 . yxzxyx  0,0,10 2
  • b
    Use Dirichlet’s integral to evaluate  dzdydxxyz throughout the volume bounded by 0,0,0  zyx and 1 zyx . gq, vk;ru ds fy,  dzdydxxyz dks Kkr dhft,A
  • a
    Apply Gauss divergence theorem to evaluate  dsnF ˆ. , where kzjyixF ˆˆ2ˆ4 22  and S is the surface of the region bounded by the cylinder 0,422  zyx , .3z dsnF ˆ
  • b
    Evaluate  C drF. by Stoke’s theorem, where kzxjxiyF ˆ)(ˆˆ 22  and C is the boundary of the triangle with vertices at )0,0,1(),0,0,0( and )0,1,1(

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 — BAS-103

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 directional derivative of scalar function xyzzyxf ),,( at point )3,1,1(P in the direction of the outward drawn normal to the sphere 11222  zyx through the point P

Appeared in: 2022-23 · 2025-26

2x

Find the eigen values and corresponding eigen vectors of the matrix A

Appeared in: 2022-23 · 2024-25

2x

Apply Gauss divergence theorem to evaluate  dsnF ˆ. , where kzjyixF ˆˆ2ˆ4 22  and S is the surface of the region bounded by the cylinder 0,422  zyx , .3z dsnF ˆ

Appeared in: 2022-23 · 2025-26

Engineering Mathematics I — Other Year Papers

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Syllabus & More PYQs

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📘 Engineering Mathematics-I — Unit-wise SyllabusBAS103AKTU 1st Year SyllabusAKTU 1st Year PYQs — All Branches