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

Solved Question Paper

Mathematics-1 Dec-2023

PTU • B-TECH • Information Technology • 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. Verify Green’s theorem for \(f(x,y)=e^{-x}\sin y\), \(g(x,y)=e^{-x}\cos y\) and \(C\) is the square with vertices at (0,0), (\(\pi/2\),0), (\(\pi/2\),\(\pi/2\)), (0,\(\pi/2\)).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  2. b) Find the work done by the force \(\mathbf{F}=-xy\,\mathbf{i}+y^2\,\mathbf{j}+z\,\mathbf{k}\) in moving a particle over a circular path \(x^2+y^2=4,\, z=0\) from (2,0,0) to (0,2,0).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  3. a) Evaluate \(\int_C (x+y)dx - x^2dy + (y+z)dz\) where \(C\) is \(x^2=4y,\, z=x,\, 0\le x\le 2\).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  4. b) If \(f(x,y)=x^2-xy-y+y^2\), find all points where the directional derivative in the direction \(\mathbf{b}=(\mathbf{i}+\sqrt{3}\mathbf{j})/2\) is zero.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  5. a) Show that the vector field \(\mathbf{v}=(y^2-x^2)\,i+x(2y+1)\,j\) is irrotational and find a scalar function \(f(x,y,z)\) such that \(\mathbf{v}=grad\,f\)
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  6. b) If a is a constant and r = xi + yj + zk, show that \(curl(a \times r)=2a\)
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  7. a) Find directional derivative of the function \(f(x,y)=x^2y^3+xy\) at a point (2,1) in the direction of a unit vector that makes angle \(\pi/3\) with x-axis.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  8. b) Prove that the eigenvectors of a symmetric matrix are real
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  9. a) The eigenvalues of 3 \(\times\) 3 matrix \(A\) corresponding to the eigenvalues 1,2,3 are \([-1,-1,1]^\mathsf{t}, [0,1,0]^\mathsf{t}, [0,-1,1]^\mathsf{t}\) respectively. Find the matrix A
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  10. Find all the eigenvalues and the corresponding eigenvectors of the following matrix.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  11. b) Find the inverse of the matrix by using Gauss-Jordan method.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  12. a) Examine whether the following set of vectors are linearly independent.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  13. b) Solve the following system of equations using Gauss elimination method.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  14. a) If x, y and z are different and \[\begin{array}{c|c|c} x & x^2 & 1+x^3\\ y & y^2 & 1+y^3\\ z & xz^2 & 1+z^3\end{array}\] then show that 1 + xyz = 0
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  15. 1(j) Evaluate (int_C (x^2 - y^2) ds), where C is the curve defined by x = 3cos t, y = 3sin t, 0 ≤ t ≤ 2π.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  16. 1(i) Find the length of the arc given by r(t) = t i + t^2 j, 0 ≤ t ≤ π/2.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  17. 1(h) Let f be a differentiable scalar field. Then calculate the value of ∇ × (∇f).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  18. 1(g) Define divergence of a vector field.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  19. 1(f) Find the unit normal vector to the surface xy^2 + 2yz = 8 at the point (3, −2, 1).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  20. 1(e) Find the length of the Helix traced by r(t) = acos t i + asin t j + ctk, a > 0, 0 ≤ t ≤ 2π
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  21. 1(d) Define eigenvalues of a matrix.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  22. 1(c) If A and B are symmetric matrices, then show that AB − BA is skew-symmetric.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  23. 1(b) If A and B are square matrices. Is AB = BA? Justify.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  24. 1(a) Define a vector space.
    Very Short Answer 2 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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