B.TechSemester 12021-22Engineering Mathematics IKAS-103T
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Engineering Mathematics I (KAS-103T) - AKTU Question Paper 2021-22

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 2021-22. 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:2021-22
University:AKTU / UPTU

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Questions Asked in 2021-22

Engineering Mathematics I (KAS-103T) — complete question paper

Section AAttempt all q u e s t i o n s i n b r i e f . 2 x 10 = 20
  • a
    Prove that the matrix 1െ𝑖 െ 1 ቃis unitary. 2 1
  • b
    State Rank-Nullity Theorem. 2 1
  • c
    State Rolle’s Theorem. 2 2
  • d
    Discuss all the symmetry of the curve 𝑥ଶ𝑦ଶ ൌ𝑥 ଶ െ𝑎 ଶ 2 2
  • e
    If 𝑢ൌ 𝑓ሺ𝑦െ𝑧 ,𝑧െ𝑥 ,𝑥െ𝑦ሻ , prove that
  • f
    If 𝑥ൌ𝑒 ௩𝑠𝑒𝑐 𝑢, 𝑦 ൌ 𝑒௩𝑡𝑎𝑛 𝑢 , then evaluate
  • h
    Calculate the volume of the solid bounded by the surface x = 0 , y =0, x+y+z=1 and z=0. i. Show that the vector 𝑉ሬ⃑ ൌ ሺ𝑥൅3 𝑦ሻ𝚤̂ ൅ ሺ𝑦െ3 𝑧ሻ𝚥̂ ൅ ሺ𝑥െ2 𝑧ሻ 𝑘෡ i s solenoidal. j. State Green’s theorem. 2 5
Section BAttempt any three o f t h e f o l l o w i n g :
  • b
    If 𝑦ൌ𝑒 ௧௔௡షభ௫, prove that
  • c
    If 𝑢ଷ ൅𝑣൅𝑤ൌ𝑥൅𝑦 ଶ ൅𝑧 ଶ, ,Show that
  • d
    Evaluate by changing the variables, ∬ ሺ𝑥൅𝑦 ሻଶ region bounded by the parallelogram x+y=0, x+y =2, 3x-2y=0 and 3x-2y
  • e
    Use divergence theorem to evaluate the surface integral ∬ ሺ𝑥𝑑𝑦𝑑𝑧 ൅ௌ 𝑦𝑑𝑧𝑑𝑥 ൅ 𝑧𝑑𝑥𝑑𝑦ሻ where S is the portion of the plane x+2y+3z=6 which lies in the first octant. AKTU_ AKTU_
Section CAttempt any one p a r t o f t h e f o l l o w i n g :
  • a
    Find non-singular matrices P and Q such that PAQ is normal form
  • b
    Find the eigen values and the corresponding eigen vectors of t h e following matrix
  • a
    Find the envelope of the family of lines ௕ ൌ1 , where 𝑎 𝑎𝑛𝑑 𝑏 are connected by the relation 𝑎௡ ൅𝑏 ௡ ൌ𝑐 ௡
  • b
    If y = sin (m sin -1x), find the value of yn at x= 0. 10 2
  • a
    Divide 24 into three parts such that continued product of fi rst,square of second and cube of third is a maximum
  • b
    If 𝑢ൌ𝑠 𝑒 𝑐ିଵ ቀ ௫ା௬ ቁ,prove that 𝑥 Also evaluate 𝑥ଶ డమ௨
  • a
    Evaluate the following integ ral by changing the order of int egration
  • b
    A triangular thin plate with vertices (0,0),(2,0) and (2,4) has density 𝜌ൌ 1൅𝑥൅𝑦 . Then find: (i) The mass of the plate. (ii) The position of its centre of gravity G
  • a
    A fluid motion is given by 𝑣⃑ൌ ሺ𝑦𝑠𝑖𝑛 𝑧 െ 𝑠𝑖𝑛𝑥ሻ𝚤̂ ൅ ሺ𝑥 𝑠𝑖𝑛 𝑧 ൅ 2𝑦𝑧ሻ𝚥̂ ൅ ሺ𝑥𝑦𝑐𝑜𝑠 𝑧 ൅ 𝑦ଶሻ𝑘෠.Is the motion irrotational? If so, find the velocity potential
  • b
    Verify Stoke’s theorem for the function 𝐹⃑ ൌ𝑥 ଶ𝚤̂ ൅𝑥 𝑦 𝚥ෝ integrated round the square whose sides are x=0,y=0,x=a,y=a in the plane

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.

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