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

Solved Question Paper

Basic Mathematics Dec-2023

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

Basic Mathematics 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 Basic Mathematics, so students can review how questions are typically framed in past exams and get a sense of the exam pattern. Many students search for basic mathematics previous year question paper 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 briefly : a) Find a, b if a + ib = i/(2 - i).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  2. Answer briefly : b) Solve the equation 3x^2 + 8x + 4 = 0.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  3. Answer briefly : c) If the product of three consecutive numbers in GP is 27, find the first term of GP.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  4. Answer briefly : d) Prove \(\sqrt{\frac{1+\cos\theta}{1-\cos\theta}} = \csc\theta + \cos\theta\).
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  5. Answer briefly : e) Find cos 105°.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  6. Answer briefly : f) Check whether the matrix \(\begin{bmatrix}1 & 2\\2 & 4\end{bmatrix}\) is singular or not.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  7. Answer briefly : g) If \(\begin{bmatrix}a & d\\b & c\end{bmatrix}\,=\,\begin{bmatrix}1 & -2\\-1 & 1\end{bmatrix}\), then find a + b − c + d.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  8. Answer briefly : h) Find the equation of a straight line passing through the point (3, −2) and slope −1.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  9. Answer briefly : i) Find the equation of a circle with center at (1, 2) and radius 4 units.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH
  10. Prove that \begin{vmatrix} x^2 & 1 & x \\ 1 & x & x^2 \\ x & x^2 & 1 \end{vmatrix} = (1 - x^3)^2 .
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  11. Use Cramer's rule to solve the following system of linear equations : x + y + z = 1, 2x + y - z = 3, x - 2y - 3z = 4.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  12. b) Find the mean deviation from the median of the data : 3,9,5,3,12,10,18,4,7,19,21.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  13. a) Find the co-ordinates of the foot of the perpendicular from the point A (-1, 3) to the line 3x - 4y = 10 and hence, find the length of perpendicular from point A to the line.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  14. b) The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  15. a) Find the value of k so that the equation 2x^2 - \frac{k}{3}y^2 + kx - 4y + 2 = 0 represents a circle and hence find center and radius of this circle.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  16. b) If 4 numbers a, b, c, d are in AP, such that, a + b + c + d = 32 and 15ad = 7bc, then find the numbers a, b, c, d.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  17. a) If sin \alpha = \frac{15}{17} and cos \beta = \frac{12}{13}, then find the values of sin(\alpha + \beta), cos(\alpha - \beta) and tan(\alpha + \beta).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  18. b) Evaluate 10C3 + 10C4 + 11C5.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  19. a) Prove that cos \theta - sin \theta = \sqrt{2}\, cos\left(\theta + \frac{\pi}{4}\right)
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  20. b) Find x such that sec (90° + A) + x sin A . tan (90° + A) = cos (90° + A).
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  21. a) If sec A = x + \frac{1}{4x}, prove that sec A + tan A = 2x or \frac{1}{2x}.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  22. b) A two digit number is four times the sum and three times the product of its digits. Find the number.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  23. a) Show that (x+y)(y+z)(z+x)>8xyz.
    Long Answer 8 Marks Dec-2023 • PTU B-TECH
  24. Answer briefly : j) If the matrix A = \( [a_{ij}]_{2\times 2}\), were \(a_{i,j} = 2^{i+j}\), then write down the matrix A.
    Very Short Answer 2 Marks Dec-2023 • PTU B-TECH

Explore all data

FAQ

Frequently Asked Questions

Answers about this subject, solved papers, and preparation.

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

This page lists Basic Mathematics 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 Basic Mathematics 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 Basic Mathematics usually cover?

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

05 Does this page include a Basic Mathematics previous year question paper 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.

We use cookies to improve your experience. You can accept or reject cookies. Learn more about our privacy policy.