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. Answer the following: a) Give geometric interpretation of mean value theorem.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  2. Answer the following: b) Can Rolle's theorem be applied to the function: f(x) = { x, 0 \le x \le 1 in the interval [0, \pi]. 2 - x, 1 \le x \le 2 in the interval [0, \pi]. }
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  3. Answer the following: c) Evaluate lim_{x\to0} [x^n (\ln x)].
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  4. Answer the following: d) Does the limit lim_{(x,y)\to(0,0)} \frac{xy}{x^2+y^2} exists?
    True / False 2 Marks Dec-2023 • PTU B-TECH
  5. Answer the following: e) Give the coordinates of the center of gravity of solid of mass M.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  6. Answer the following: f) Define convergence, divergence and oscillation of a series.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  7. Answer the following: g) Define D'Alembert's ratio test to check the convergence of the positive term series \sum u_n.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  8. Answer the following: h) Find sum and product of Eigen values of the matrix \left[ \begin{matrix} 1 & -1 \\ 2 & -5 \end{matrix} \right].
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  9. Answer the following: i) Find the inverse of the matrix \left[ \begin{matrix} 3 & 1 \\ 1 & 4 \end{matrix} \right].
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  10. Answer the following: j) Find rank of the matrix \left[ \begin{matrix} 0 & 1 & -3 \\ 1 & 0 & 1 \\ 3 & 1 & 0 \end{matrix} \right].
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  11. a) Expand f(x) = e^x in powers of (x − 1) upto four terms.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  12. b) Evaluate the limit lim_{x→0} \frac{e^x e^{-x}−log(1+x)}{x sin x}.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  13. a) Find the volume of the loop generated by the revolving curve y^2(a + x) = x^2(3a − x) about the x axis.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  14. b) Find extremum of the function 2sinx + cos2x, 0 ≤ x ≤ 2π.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  15. a) Discuss the continuity of the function f(x,y) = \begin{cases} (x^2+y^2)/(xy), & (x,y) \ne (0,0) \\ 0, & (x,y) = (0,0) \end{cases} at (0,0).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  16. b) Find extreme values of 2x + 3y + z subject to the conditions x + z = 1 and x^2 + y^2 = 5.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  17. a) Evaluate the integral \iint_R e^{x^2} dxdy, where R is the region given by R: 2y ≤ x ≤ 2 and 0 ≤ y ≤ 1.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  18. b) Evaluate \iiint_T (x + 3y − 2z) dxdydz, over the boundary of T: 0 ≤ y ≤ x^2, 0 ≤ z ≤ x + y, 0 ≤ x ≤ 1.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  19. Examine the convergence of the series \sum \frac{3·6·9·...(3n)}{7·10·13·...(3n+4)} x^n.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  20. a) Examine the convergence of the series \frac{1}{1.2.3} + \frac{1}{2.3.4} + \frac{1}{3.4.5} + ... .
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  21. b) Examine the convergence of the alternating series 1 − \frac{1}{2^k} + \frac{1}{3^k} − \frac{1}{4^k} + ... , for k > 0.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  22. Find the characteristic equation of the matrix \begin{bmatrix}1 & 4\\2 & 3\end{bmatrix} and hence compute A^{-1}. Find the matrix represented by A^5 − 4A^4 − 7A^3 + 11A^2 − A − 10I.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  23. Reduce the matrix \begin{bmatrix}5 & 3 & 7\\3 & 26 & 2\\7 & 2 & 10\end{bmatrix} to the diagonal form.
    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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