N2113111 · 60 marks · 2 hrs
Mathematics for Computer Engineering
Exam: 17 Nov 2026 · 14:30-16:30 · Mumbai University, B.E. AI & DS Sem III (NEP-2020).
Units & topics
| Unit | Title & topics |
|---|---|
| Unit 1 | Linear Algebra Eigenvalues & eigenvectors, Diagonalisation, Cayley–Hamilton theorem |
| Unit 2 | LPP & NLPP Lagrange multipliers (NLPP), Solving an LPP (Simplex method), LPP standard form & dual |
| Unit 3 | Modular Arithmetic Chinese Remainder Theorem (CRT), RSA algorithm, Remainder by modular arithmetic |
| Unit 4 | Fourier Series Full Fourier expansion, Finding an in a Fourier expansion |
| Unit 5 | Statistics Spearman rank correlation, Karl Pearson correlation coefficient, Regression lines, Fitting a straight line y = a + bx |
| Unit 6 | Probability Moments (raw moments, moments about origin / mean), Moment generating function (MGF), Poisson distribution, Normal distribution |
Question papers
Scanned originals as printed. Open a paper for preview, or download the PDF.
Dec 2025 · QP 00720
60 marks · 2 hrs · verified — scanned original
May 2026 · QP 14664
60 marks · 2 hrs · verified — scanned original
Most-asked topics
How many questions each topic got in Dec 2025 and May 2026. History, not a prediction — nothing here is guaranteed to appear next.
| Topic | Dec 2025 | May 2026 | Total | Marks |
|---|---|---|---|---|
| Eigenvalues & eigenvectors | 2 | 2 | 4 | 18 |
| Full Fourier expansion | 2 | 2 | 4 | 21 |
| Diagonalisation | 1 | 1 | 2 | 11 |
| Cayley–Hamilton theorem | 1 | 1 | 2 | 8 |
| Lagrange multipliers (NLPP) | 1 | 1 | 2 | 12 |
| Solving an LPP (Simplex method) | 1 | 1 | 2 | 11 |
| LPP standard form & dual | 1 | 1 | 2 | 6 |
| Chinese Remainder Theorem (CRT) | 1 | 1 | 2 | 10 |
Question sets
Topic-wise question sets from the two papers — questions only.
Maths — Topic-wise Question Sets (Dec 2025 + May 2026)
5 pages · Scanned university question papers, grouped by topic · Questions only — no answers
All questions — Dec 2025 + May 2026
42 questions, quoted as printed. No answers are published on this site.
| Q | Topic | Question | Marks | Paper |
|---|---|---|---|---|
| Q1a | Eigenvalues & eigenvectors | If A = [[3, 2, 1], [0, −1, 4], [0, 0, −2]], find eigenvalues of A⁻¹ + 6I. | 3 | maths-dec2025 |
| Q1b | LPP standard form & dual | Transform the LPP to standard form: Maximise Z = 2x₁ + x₂ + 4x₃ Subject to: x₁ − x₂ + 2x₃ ≤ 5 3x₁ + x₂ + 5x₃ ≥ 14 x₁, x₂ ≥ 0 | 3 | maths-dec2025 |
| Q1c | Finding an in a Fourier expansion | Find the value of a_n in the expansion of Fourier series for f(x) = 4 − x² in (0, 2π). | 3 | maths-dec2025 |
| Q1d | Moment generating function (MGF) | A random variable x defines the possible outcomes of tossing a fair die, find moment generating function of x about origin | 3 | maths-dec2025 |
| Q1e | Remainder by modular arithmetic | What is the remainder when 13⁷⁰ is divided by 21? | 3 | maths-dec2025 |
| Q1f | Spearman rank correlation | Obtain Spearman's rank correlation coefficient for following data X2424245525 Y2431514038 | 3 | maths-dec2025 |
| Q2a | Poisson distribution | It is known that the probability of an item produced by a certain machine will be defective is 0.001. If the produced items are sent to the market in packets of 100, find the number of packets containing at least 2 are defective in the consignment of 2000 Packets. | 4 | maths-dec2025 |
| Q2b | Karl Pearson correlation coefficient | Five students got the following percentage of marks in mathematics and statistics Calculate the coefficient of correlation. Maths28341825752324333743 Stats24311134652423535342 | 5 | maths-dec2025 |
| Q2c | Full Fourier expansion | Expand Fourier series for f(x) = x² in (0, 2). | 6 | maths-dec2025 |
| Q3a | Regression lines | Obtain equations of line of regression of x on y for following data. X3144654941 Y4832216643 | 4 | maths-dec2025 |
| Q3b | Chinese Remainder Theorem (CRT) | By using Chinese Remainder theorem, solve x ≡ 1 (mod 3), x ≡ 2 (mod 4), x ≡ 3 (mod 5). | 5 | maths-dec2025 |
| Q3c | Eigenvalues & eigenvectors | Find eigenvalues and eigenvectors of A = [[3, −1, 1], [−1, 5, −1], [1, −1, 3]]. | 6 | maths-dec2025 |
| Q4a | Moments (raw moments, moments about origin / mean) | A random variable X has probability density function f(x) = x²e^−x x ≥ 0 Find 2 moments about origin and mean. | 4 | maths-dec2025 |
| Q4b | Diagonalisation | Show that A = [[2, 2, 1], [1, 3, 1], [1, 2, 2]] is diagonalisable, hence find its diagonalisable matrix. | 5 | maths-dec2025 |
| Q4c | RSA algorithm | In RSA system the public key (E, N) of user A is (7, 187). Calculate φ(N) and private key D. What is the cipher text for M = 10 using the public key? | 6 | maths-dec2025 |
| Q5a | Cayley–Hamilton theorem | Verify Cayley–Hamilton theorem for A = [[2, −1, 1], [−1, 2, −1], [1, −1, 2]]. | 4 | maths-dec2025 |
| Q5b | Normal distribution | The height of school children of one school is normally distributed with mean of 54 inches and standard deviation 12 inches. What proportion of students have height between i. 46 and 56 inches ii. More than 56 | 5 | maths-dec2025 |
| Q5c | Solving an LPP (Simplex method) | Applying Simplex method, solve the following LPP: Maximise Z = 3x₁ + 2x₂ Subject to: x₁ + x₂ ≤ 4 x₁ − x₂ ≤ 2 x₁, x₂ ≥ 0 | 6 | maths-dec2025 |
| Q6a | Fitting a straight line y = a + bx | Fit a straight line of the form y = a + bx to the following data X1479810 Y181419271828 | 4 | maths-dec2025 |
| Q6b | Full Fourier expansion | Find Fourier series for f(x) = x, 0 < x < 2π. | 5 | maths-dec2025 |
| Q6c | Lagrange multipliers (NLPP) | Using Lagrange's multipliers, solve the following NLPP: Optimise z = −x₁² − x₂² + 4x₁ + 8x₂ Subject to: x₁ + x₂ = 4 x₁, x₂ ≥ 0 | 6 | maths-dec2025 |
| Q1a | Eigenvalues & eigenvectors | Find the sum and product of the eigenvalues of A = [[−2, −9, 5], [−5, −10, 7], [−9, −21, 14]]. | 3 | maths-may2026 |
| Q1b | LPP standard form & dual | Construct the dual of the following LPP: Maximise Z = 5x₁ + 4x₂ Subject to: 2x₁ + 6x₂ ≤ 5 7x₁ + 3x₂ ≤ 2 x₁, x₂ ≥ 0 | 3 | maths-may2026 |
| Q1c | Finding an in a Fourier expansion | Find value of a_n in the expansion of Fourier series for f(x) = x² in (−π, π). | 3 | maths-may2026 |
| Q1d | Moments (raw moments, moments about origin / mean) | Calculate first 2 raw moments for probability density function f(x) = { xe^−xx ≥ 0 0Otherwise | 3 | maths-may2026 |
| Q1e | Remainder by modular arithmetic | What is the remainder when 5¹¹ is divided by 7? | 3 | maths-may2026 |
| Q1f | Spearman rank correlation | Obtain Spearman's rank correlation coefficient for following data X181713171921 Y212214171813 | 3 | maths-may2026 |
| Q2a | Poisson distribution | The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7. Find the probability of observing exactly three accidents on this stretch of road next month. | 4 | maths-may2026 |
| Q2b | Karl Pearson correlation coefficient | Calculate the correlation coefficient for the following heights of fathers (X) and their sons (Y) X6566676768697072 Y6768656872726971 | 5 | maths-may2026 |
| Q2c | Full Fourier expansion | Expand Fourier series for f(x) = x² in (0, 2). — the exact repeat. | 6 | maths-may2026 |
| Q3a | Fitting a straight line y = a + bx | Fit a straight line of the form y = a + bx to the following data X1357810 Y845784 | 4 | maths-may2026 |
| Q3b | Chinese Remainder Theorem (CRT) | By using Chinese Remainder theorem, solve x ≡ 3 (mod 4), x ≡ 5 (mod 7). | 5 | maths-may2026 |
| Q3c | Eigenvalues & eigenvectors | Find eigenvalues and eigenvectors of A = [[−9, 4, 4], [−8, 3, 4], [−16, 8, 7]]. | 6 | maths-may2026 |
| Q4a | Moment generating function (MGF) | A random variable X has the following probability distribution X1234 P(X = x)0.20.30.30.2 Find moment generating function about origin of x, hence find first two raw moments. | 4 | maths-may2026 |
| Q4b | Normal distribution | The distribution of wait times at a drive-through restaurant is approximately normal with mean 185 seconds and standard deviation 15 seconds. Find the percentage of wait times that are i. between 155 and 215 seconds. ii. more than 170 seconds. | 5 | maths-may2026 |
| Q4c | Diagonalisation | Check whether A = [[8, −8, −2], [4, −3, −2], [3, −4, 1]] is diagonalisable; if yes, find the diagonalising matrix P and the diagonal matrix D. | 6 | maths-may2026 |
| Q5a | Cayley–Hamilton theorem | Verify Cayley–Hamilton theorem for A = [[3, 2, 1], [1, 2, 2], [3, 2, 1]]. | 4 | maths-may2026 |
| Q5b | Solving an LPP (Simplex method) | Maximise Z = 7x₁ + 5x₂ Subject to: −x₁ − 2x₂ ≥ −6 4x₁ + 3x₂ ≤ 12 x₁, x₂ ≥ 0 | 5 | maths-may2026 |
| Q5c | RSA algorithm | Perform key generation, encryption and decryption for RSA algorithm with primes p = 3, q = 11, message M = 5. | 6 | maths-may2026 |
| Q6a | Full Fourier expansion | Expand Fourier series for f(x) = x in (−π, π). | 4 | maths-may2026 |
| Q6b | Regression lines | Obtain the equation of line of regression of X on Y X212325272820 Y81215171820 | 5 | maths-may2026 |
| Q6c | Lagrange multipliers (NLPP) | Using Lagrange's multipliers, solve the following NLPP: Maximise Z = x₁² + x₂² + x₃² − 10x₁ − 6x₂ − 4x₃ Subject to: x₁ + x₂ + x₃ = 7 x₁, x₂, x₃ ≥ 0 | 6 | maths-may2026 |