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Maths II · Quiz 2 · 3 Aug 2025 (Afternoon)

14 questions · 50 marks · 60 min

Answer key Take as mock

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Mathematics for Data Science II

Quiz 2 · 3 Aug 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.

Q1MCQ2 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}.
Q2MCQ4 Marks·Choose one option
Key ↓
1. Aa) → iii), b) → i), c) → ii)
2. Ba) → ii), b) → i), c) → iii)
3. Ca) → iii), b) → ii), c) → i)
4. Da) → ii), b) → iii), c) → i)
Q3MSQ6 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q4NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q5NAT4 Marks·Write the number
Key ↓
Your answer:
Q6NAT5 Marks·Write the number
Key ↓
Your answer:
Q7NAT5 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q8–Q9
Q8MSQ4 Marks·Choose all correct options
Key ↓
Choose all the correct statements from the following.
1. AThe rank of the linear transformation T is 2.
2. BThe nullity of the linear transformation T is 2.
3. CThe transformation T is invertible.
4. DT cannot be an isomorphism.
Q9NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q10–Q12
Based on the above data, answer the given subquestions.
Q10NAT2 Marks·Write the number
Key ↓
Find the number of columns in the matrix (with respect to any bases) of the linear transformation T.
Your answer:
Q11MCQ2 Marks·Choose one option
Key ↓
Let A denote the matrix of the linear transformation T with respect to standard bases for both the domain and the codomain. Choose the correct statement from the following. (In the options below, REF is used for row echelon form, and RREF is used for reduced row echelon form.)
1. AA is in REF and RREF.
2. BA is neither in RREF nor in REF.
3. CA is in RREF, but not in REF.
4. DA is in REF, but not in RREF.
Q12NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q13–Q14
Based on the above data, answer the given subquestions.
Q13MCQ2 Marks·Choose one option
Asked 3 times Key ↓
Which of the following is the matrix of the linear transformation T with respect to standard bases for both the domain and the codomain.
1. A
2. B
3. C
4. D
Q14MSQ5 Marks·Choose all correct options
Key ↓
Which of the following spaces are isomorphic to the kernel of T?
1. A
2. B
3. C
4. D
5. E
6. F

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1D

Q2A

Q3A, C, D

Q46

Q52

Q6-1

Q75

Q8A, D

Q9-2

Q104

Q11D

Q121

Q13B

Q14D, F

Questions and answer keys are reproduced from the official IIT Madras BS papers. BTechi is not affiliated with IIT Madras.