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

Solved Question Paper

Engineering mathematics-1 May-2023

PTU • B-TECH • Mechanical Engineering • 1st-2nd • May-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. Write short notes on :
    a) Evaluate the triple integral \(\int_{0}^{2}\int_{0}^{2}\int_{0}^{1} y z x y d z d x\).
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  2. Write short notes on :
    b) State stoke’s theorem in the plane.
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  3. Write short notes on :
    c) Evaluate \(\int_{0}^{\infty}\int_{x}^{\infty} \frac{e^{-y}}{y}\,dy\,dx\).
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  4. Write short notes on :
    d) Show that the vector field given by \(\vec{F}=(-x^2+yz)\,\hat{i}+(4y-z^2x)\,\hat{j}+(2xz-4z)\,\hat{k}\) is solenoidal.
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  5. Write short notes on :
    e) State homogeneous function.
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  6. Write short notes on :
    f) Find the gradient of the function \(\phi=y^2-4xy\) at \((1,2)\).
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  7. Write short notes on :
    g) Prove that \(curl(grad\,\phi)=0\)
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  8. Write short notes on :
    h) If \(f(x,y)=x^2y+xy^3-3x+4y-6\), find \(\frac{\partial f}{\partial x}\).
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  9. Define Eigen values.
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  10. Explain nature of rank of a MatricE.
    Very Short Answer 2 Marks May-2023 • PTU B-TECH
  11. Use Gauss Jordan Method to find the inverse of a matrix
    Long Answer 8 Marks May-2023 • PTU B-TECH
  12. If \(U=\csc^{-1}\begin{pmatrix}1&1\1/2&1/2\\x^2+y^2&1\\1&1/2\\x^3+y^3\end{pmatrix}\), prove that
    Long Answer 8 Marks May-2023 • PTU B-TECH
  13. Prove that: a) curl (fA) = (grad f) × A + f curl A .
    Long Answer 8 Marks May-2023 • PTU B-TECH
  14. Prove that: b) Evaluate \(\int_c (x^2+xy)dx=(x^2+y^2)dy\), where c is the square formed by the lines \(x=\pm 1\), y=\pm 1.\)
    Long Answer 8 Marks May-2023 • PTU B-TECH
  15. Evaluate \(\int_{0}^{1}\int_{x^{2}}^{2-x} x y\, d x\, d y\) by changing order of integration.
    Long Answer 8 Marks May-2023 • PTU B-TECH
  16. Show that the Matrix \(A=\begin{bmatrix}6&-2&2\\-2&3&-1\\2&-1&3\end{bmatrix}\) is similar to the diagonal Matrix. Also find the transforming Matrix and the diagonal Matrix.
    Long Answer 8 Marks May-2023 • PTU B-TECH
  17. If \(\theta = t^n e^{4t}\), find the value of \(n\) which will make \(\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial \theta}{\partial r}\right)=\frac{\partial \theta}{\partial t}\).
    Long Answer 8 Marks May-2023 • PTU B-TECH
  18. Verify Gauss Divergence theorem for \(\vec{F}=(x+y^2)i-(2xj+2yz)\,k\) taken over tetrahedron bounded by coordinate planes and the plane \(2x+y+2z=6\).
    Long Answer 8 Marks May-2023 • PTU B-TECH
  19. Calculate volume of the solid bounded by the planes
    Long Answer 8 Marks May-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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