BTechibtechi.in
Loading Loading
Free IIT Madras BS notes, PYQs and mock tests at btechi.in

Maths II · Basis, dimension & rank

18 questions · 40 marks · 8 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Mathematics for Data Science II

Basis, dimension & rank

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.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Q1NAT4 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q2NAT4 Marks·Write the number
Key ↓
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:
Q3NAT4 Marks·Write the number
Key ↓
Your answer:

End Term · 31 Aug 2025 (FN)End Term

Q4MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options are correct? Let A and B be square matrices of the same order.
1. AThe rows of AB are linear combinations of the rows of A.
2. BThe rows of AB are linear combinations of the rows of B.
3. CThe columns of AB are linear combinations of the columns of A.
4. DThe columns of AB are linear combinations of the columns of B.
Q5NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 31 Aug 2025 (AN)End Term

Q6MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options are correct?
1. A
2. B
3. C
4. D
Q7NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Q8MCQ2 Marks·Choose one option
Key ↓
1. AThe nullity of A is independent of the value of k.
2. BThe nullity of A depends on the value of k, and the set of all possible values for the nullity of A is {1, 2}.
3. CThe nullity of A depends on the value of k, and the set of all possible values for the nullity of A is {0, 1, 2, 3, 4, 5}.
4. DThe nullity of A depends on the value of k, and the set of all possible values for the nullity of A is {2, 3}.

End Term · 13 Apr 2025 (FN)End Term

Read the passage below, then answer Q9–Q12
Based on the above data, answer the given subquestions.
Q9NAT1 Mark·Write the number
Asked 2 times Key ↓
Find the dimension of W.
Your answer:
Q10MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q11MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q12MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following vector spaces is/are isomorphic to W?
1. A
2. B
3. C
4. D

End Term · 13 Apr 2025 (AN)End Term

Read the passage below, then answer Q13–Q16
Based on the above data, answer the given subquestions.
Q13NAT1 Mark·Write the number
Asked 2 times Key ↓
Find the dimension of W.
Your answer:
Q14MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q15MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q16MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following vector spaces is/are isomorphic to W?
1. A
2. B
3. C
4. D

End Term · 22 Dec 2024 (FN)End Term

Q17MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. Adim(W) = 1
2. Bdim(W) = 2
3. Cdim(W) = 3
4. Ddim(W) = 4

End Term · 22 Dec 2024 (AN)End Term

Q18MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q18

Q25

Q32

Q4B, C

Q51

Q6B, C

Q72

Q8D

Q92

Q10C

Q11B

Q12A, D

Q132

Q14C

Q15B

Q16A, D

Q17B

Q18B

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.