Solved question paper for Math1 Dec-2023 (B-TECH 1st-2nd)

Solved Question Paper

Mathematics-1 Dec-2023

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

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 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 mathematics-1 question bank 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 briefly : a) Evaluate \(\int_{0}^{\infty} e^{-x^{3}}\,dx\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  2. Write briefly : b) Prove that \(\gamma(n)=(n-1)!\) if \(n\) is an integer.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  3. Write briefly : c) Show that \(|\cos b+\cos a|<|6-a|\) using mean value theorem.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  4. Write briefly : d) Find \(\frac{df}{dt}\) at \(t=1\), where \(f(x,y)=x\cos y-e^{x}\sin y\), \(x=t^{2}+1\), \(y=t^{3}+t\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  5. Write briefly : e) Find the minimum value of the function \(f(x,y)=3x^{2}+y^{2}-x\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  6. Write briefly : f) Find the eigen values of the matrix : \(\begin{bmatrix}1&0&0\\0&2&1\\2&0&3\end{bmatrix}\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  7. Write briefly : g) Show that the matrices A and A\(^T\) have same set of eigen values.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  8. Write briefly : h) Solve the following system of linear equations: \(x+3y=9\), \(6x-y=3\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  9. Write briefly : i) Write the series expansion for \(\cos x\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  10. Write briefly : j) Find the volume of the solid generated by revolving the finite region bounded by the curves \(y=x^{2}+1\) and \(y=5\) about the line \(x=3\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  11. Find the surface area of the solid generated by revolving the circle \(x^{2}+(y-h)^{2}=a^{2},\ b\ge a\) about the x-axis.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  12. a) Evaluate \(\int_{0}^{\infty} 2^{-16x^{2}}\,dx\) using gamma function.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  13. b) Evaluate \(\lim_{x\to 0} x^{x}\)
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  14. Using Taylor's theorem, obtain the value of \(\cos 31^{\circ}\) correct to 4 decimal places.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  15. Discuss the convergence of the series \(\sum_{n=1}^{\infty}\frac{1}{n^{p}}\), for \(p>0\).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  16. Find the shortest distance between the line \(y=10-2x\) and the hyperbola \(\frac{x^{2}}{4}-\frac{y^{2}}{9}=1\).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  17. Discuss the continuity of the function: \[f(x,y)=\begin{cases}\frac{1}{1+e^{1/x}}+y^{2} & \text{if }(x,y)\ne(0,0)\\ 0 & \text{if }(x,y)=(0,0)\end{cases}\]
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  18. State Cayley Hamilton's theorem and verify it for the matrix: \[A=\begin{bmatrix}1&2&2\\0&2&1\\-1&2&2\end{bmatrix}\]
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  19. Examine whether the matrix: \[A=\begin{bmatrix}3&-1\\-2&1\\0&1\end{bmatrix}\] is diagonalizable. If so, then diagonalize it.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH

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

This page lists 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 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 Mathematics-1 usually cover?

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

05 Does this page include a Mathematics-1 question bank 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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