Past year questions

Machine Learning Foundations (BSCS2004) PYQs

66 verified past-year questions tagged to real concepts, week by week. A few samples below — the full bank, filterable by type and difficulty, is in the app.

Distribution by week

Week 1

Week 2

Week 3

Week 4

Sample questions

msq·medium·pyq5

Let $P$ be the projection matrix for a vector $a = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$ . Which of the following options is/are true?

$P$ is orthogonally diagonalizable.

$P^4 = P$ .

Projection of $b = \begin{pmatrix} 1 \\ -1 \end{pmatrix}$ on the vector $a$ is $-\frac{1}{5}a$ .

$\text{Rank}(P) = 2$

nat·medium·pyq5

Let $A = \begin{pmatrix} 2 & 1 & 1 \\ a & 3 & 2 \\ 3 & b & c \end{pmatrix}$ be a 3 × 3 matrix. Let $\alpha$ be the eigenvalue corresponding to the eigenvector $v_1 = \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix}$ and $\beta$ is the eigenvalue corresponding to the eigenvector $v_2 = \begin{pmatrix} 0 \\ 1 \\ -1 \end{pmatrix}$ of matrix A. Find the value of $\alpha + 2\beta$ .

mcq·medium·pyq5

Find the best-fit line for the dataset given below using the least squares method.

x	0	2	3	5
y	1	2	4	3

$\hat{y} = 1.34 + 0.46x$

$\hat{y} = 0.46 + 1.34x$

$\hat{y} = 1.34 - 0.46x$

$\hat{y} = 2.16 + 0.74x$

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