Solved question paper for MATHS-1 Dec-2023 (B-TECH 1st-2nd)

Solved Question Paper

Engineering mathematics-1 Dec-2023

PTU • B-TECH • Mechanical Engineering • 1st-2nd • Dec-2023

engineering mathematics-1 previous year question papers on BRpaper are organized for students of Punjab Technical University’s Bachelor of Technology program, 1st-2nd semester. This section makes it easier to browse subject-wise old question papers for engineering mathematics-1, so students can review how questions are typically framed in past exams and get a sense of the exam pattern. Many students search for engineering mathematics-1 syllabus while preparing for exams, and this page is built to support exactly that kind of subject-wise browsing and revision. BRpaper is not the official website of Punjab Technical University or any institution, and it does not publish official notices or academic updates.

Solved Questions

Solved
  1. a) Define Exact differential equation and write necessary condition for the differential equation Mdx + Ndy = 0 to be exact.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  2. b) Find the Integrating factor of ydx − xdy + 3x^2y^2e^{x}dx = 0
    Short Answer 2 Marks Dec-2023 • PTU B-TECH
  3. c) Solve the differential equation \(\frac{d^4y}{dx^4} + 8\frac{d^2y}{dx^2} + 16y = 0\)
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  4. d) Define Legendre's linear differential equation.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  5. e) Find the rank of the matrix \(\begin{bmatrix}1&3&4&5\\1&2&6&7\\1&5&0&10\end{bmatrix}\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  6. f) If A and B are hermitian, show that AB − BA is a skew hermitian.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  7. g) Test the convergence of \(\frac{1}{5}+\frac{\sqrt{2}}{7}+\frac{\sqrt{3}}{9}+\frac{\sqrt{4}}{11}+\ldots\ldots\ldots\infty\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  8. h) Define absolute convergence of a series.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  9. i) Find the cube roots of unity.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  10. j) Separate in real and Imaginary part of tan (x + iy).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  11. Sum the series cosθ - 1/2 cos2θ + 1/3 cos3θ - ....... ..... ... ∞
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  12. For what value of K, the equations x + y + z = 1, 2x + y + 4z = k, 4x + y + 10z = k^2 have a solution and solve them completely in each case.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  13. Discuss the convergence of the series: 1 + (α.β/1. v) x + (α(α+1)β(β+1)/(1.2. v.(v+1)) ) x^2 + (α(α+1)(α+2)β(β+1)(β+2)/(1.2.3. v(v+1)(v+2)) ) x^3 + ....
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  14. a) Express log (Log i) in the form A + iB.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  15. b) Discuss the convergence of series Σ_{n=2}^{∞} 1/(n (log n)^b) (p > 0)
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  16. Solve (2x^2 y^2 + y)dx + (3x - x^3 y)dy = 0
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  17. a) Solve : x y (1 + x y^2) (dy/dx) = 1
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  18. b) Find the general solution of the equation y'' + 16y = 32e^{2x} using method of variation of parameters.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  19. Solve x^2 (d^2 y/dx^2) + 3x (dy/dx) + y = 1/(1 - x)^2.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  20. A constant electromotive force E volts is applied to a circuit containing a constant resistance R ohms in series and a constant inductance L henries. If the initial current is zero, show that the current builds up to half its theoretical maximum in (Log 2)/R seconds.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH

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01 Where can I find engineering mathematics-1 previous year question papers for Bachelor of Technology, 1st-2nd semester?

This page lists engineering mathematics-1 question papers uploaded for Punjab Technical University Bachelor of Technology, 1st-2nd semester, organized for subject-wise browsing where available.

02 Are these official Punjab Technical University question papers?

BRpaper is not the official website of Punjab Technical University. These papers are shared for reference and revision purposes only and are not official university material.

03 How can previous year engineering mathematics-1 papers help in exam preparation?

Reviewing past papers can help you understand how questions are typically framed, notice commonly repeated topics, and get a sense of the exam pattern before your own exam.

04 What kind of topics does engineering mathematics-1 usually cover?

The question papers here relate to the official engineering mathematics-1 syllabus set by the university for this course and semester.

05 Does this page include a engineering mathematics-1 syllabus or solved answers?

This page focuses on providing access to the previous year question papers themselves. A separate question bank or solved answers may not be available for every paper.

06 Can I find papers for other subjects in the same Bachelor of Technology?

Yes, BRpaper organizes papers by university, course, stream, and semester, so you can browse other subjects within the same Punjab Technical University Bachelor of Technology.

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