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

Solved Question Paper

Mathematics-1 Dec-2023

PTU • B-TECH • Civil 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. Can Rolle's theorem be applied to the function f(x) = x(x+3)^2, x ∈ [−3,1].
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  2. Define gamma function.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  3. Evaluate lim_{x→0} rac{x-sin x}{sin x(1-cos x)}.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  4. If A + B = egin{bmatrix}1 & -1\ -3 & 0end{bmatrix} and A − B = egin{bmatrix}3 & 1\ 1 & 4end{bmatrix}, then find values of A and B
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  5. Find adjoint of egin{bmatrix}2 & 1\ -2 & 3end{bmatrix}.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  6. Define the dimension of vector spaces.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  7. Give the statement of rank nullity theorem.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  8. Give any two properties of Eigen values.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  9. Define skew symmetric matrix with an example.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  10. Find sum and product of latent roots of the matrix egin{bmatrix}1 & -1\ -2 & 1end{bmatrix}.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  11. a) Expand f(x) = tan^-1 x by Maclaurin's theorem.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  12. b) Evaluate \lim_{x\to 1} \frac{x^\,x- x}{1+x-\log x}.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  13. a) Evaluate the integral \int_{0}^{\pi/2} \sqrt{\tan x}\,dx in terms of beta function.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  14. b) Find minima of f(x,y) = 4x^2 + 9y^2 - 8x - 12y + 4.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  15. a) Prove that \[\begin{vmatrix} (b+c)^2 & a^2 & a^2\\ b^2 & (c+a)^2 & b^2\\ c^2 & c^2 & (a+b)^2\end{vmatrix} = 2abc(a+b+c)^2.\]
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  16. b) Solve the equations 3x + y + 2z = 3, 2x - 3y - z = -3, x + 2y + z = 4 using Cramer's rule.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  17. a) Are the vectors (1,1,1,3), (1,2,3,4), (2,3,4,9) linearly dependent.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  18. b) Find the rank of the matrix: \[\begin{pmatrix} 4 & 2 & 1 & 3\\ 6 & 3 & 4 & 7\\ 2 & 1 & 0 & 1\end{pmatrix}\]
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  19. Show that the matrix \[\begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3\end{pmatrix}\] satisfies the equation \(A^3 - 6A^2 + 5A + 11I = 0\).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  20. Let T: \mathbb{R}^3 \to \mathbb{R}^2 be the linear transformation defined by \[T\begin{pmatrix} x \\ y \\ z\end{pmatrix} = \begin{pmatrix} x \\ y + z\end{pmatrix},\] then find the matrix representation of T w.r.t. the ordered basis \(X = \{(1,0,1),(1,1,0),(0,1,0)\}\) in \(\mathbb{R}^3\) and \(Y = \{(1,0),(0,1)\}\) in \(\mathbb{R}^2\).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  21. a) Is the matrix \[\begin{pmatrix} 5 & 3 & 7\\ 3 & 26 & 2\\ 7 & 2 & 10\end{pmatrix}\] orthogonal?
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  22. b) Write the matrix \[\begin{pmatrix} 2 & 0 & -1\\ 5 & 1 & 0\\ 0 & 1 & 3\end{pmatrix}\] as the sum of symmetric and skew symmetric matrices.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  23. Reduce the matrix \[\begin{pmatrix} 1 & 1 & 3\\ 1 & 5 & 1\\ 3 & 1 & 1\end{pmatrix}\] 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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