Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
Mathematics for Data Science II
Quiz 1 · 26 Oct 2025 (Afternoon)
Official Paper
Examination Instructions & Guidelines
- Solve on notebook/paper first before checking solutions.
- MCQ: Exactly 1 option is correct. Negative marking applies.
- MSQ: One or more options correct. Select all to score.
- NAT: Numerical response. No negative marking.
- Scientific calculator allowed for all calculations.
- Official answer key is sealed at the end of this sheet.
- Q1MCQ4 Marks·Choose one option

- A

- B

- C

- D

- A
- Q2MCQ6 Marks·Choose one option

- ABoth S1 and S2 are true.
- BBoth S1 and S2 are false.
- CS1 is true and S2 is false.
- DS1 is false and S2 is true.
- Q3MSQ6 Marks·Choose all correct options
Choose all the correct statements from the following.
- A

- B

- C

- D

- E

- A
- Q4MSQ6 Marks·Choose all correct options
Let A be a square matrix of order n > 1. Select all the statements which imply that det(A) = 0.
- AAll the entries of one of the columns of A are zero.
- BOne of the columns of A is a scalar multiple of another column.
- CThe diagonal entries of A are all zero.
- DThe determinant of the transpose of A is zero.
- EA^2 = 0.
- Q5NAT3 Marks·Write the number
Your answer: - Q6NAT3 Marks·Write the number
Your answer: - Q7NAT4 Marks·Write the number
Your answer: - Q8NAT4 Marks·Write the number
Your answer: - Q9NAT4 Marks·Write the number
Let A be a 5 × 7 matrix. If n_1 and n_2 are the minimum and maximum possible values for the rank of A, respectively, then find the value of n_2 − n_1.
Your answer: - Q10NAT4 Marks·Write the number
Your answer: Read the passage below, then answer Q11–Q12

Based on the above data, answer the given subquestions.
Q11MCQ3 Marks·Choose one option
- ATRUE
- BFALSE
- Q12NAT3 Marks·Write the number
Your answer: