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September 2023 term · Mathematics for Data Science II · BSMA1003

Maths 2 Quiz 1: 29 October 2023 (September 2023 term)

The IIT Madras BS Mathematics for Data Science II (Maths 2) Quiz 1 paper sat on 29 Oct 2023, in the September 2023 term: 16 questions for 25 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
16
Marks
25
Duration
120 min
Numerical
11
MSQ
4
MCQ
1
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION AN2 EXAM QPF2 29 Oct 2023 · No negative marking.

Question 1

+1 markNumerical answer

Consider the system of linear equations x + ky = 2, kx + y = 2.
Based on the above data, answer the given subquestions.

Find the values of k for which the system of equations has no solution.

Show answer

Correct answer: -1

Question 1 on its own page

Question 2

+1 markNumerical answer

Consider the system of linear equations x + ky = 2, kx + y = 2.
Based on the above data, answer the given subquestions.

Find the values of k for which the system of equations has infinitely many solutions.

Show answer

Correct answer: 1

Question 2 on its own page

Question 3

+2 marksNumerical answer

Consider the system of linear equations x + ky = 2, kx + y = 2.
Based on the above data, answer the given subquestions.

If the system has a unique solution (a, b), what is a − b?

Show answer

Correct answer: 0

Question 3 on its own page

Question 4

+3 marksOne or more correct options

Based on the above data, answer the given subquestions.

Choose the correct option(s) from the following statements.

Select all that apply.

  1. A
  2. B
  3. C
  4. D
  5. E
Show answer

Correct answers

  • A
  • C
  • E
Question 4 on its own page

Question 5

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Find dim(W1 +W2).

Show answer

Correct answer: 2

Question 5 on its own page

Question 6

+2 marksOne or more correct options

Select all that apply.

  1. A

    The figures (a) and (d) represent systems with unique solution.

  2. B

    The figures (b) and (c) represent systems with no solution.

  3. C

    The figures (b) and (d) represent systems with infinitely many solutions.

  4. D

    The figures (a) and (d) represent consistent systems of linear equations.

Show answer

Correct answers

  • B

    The figures (b) and (c) represent systems with no solution.

  • D

    The figures (a) and (d) represent consistent systems of linear equations.

Question 6 on its own page

Question 7

+1 markNumerical answer

Select the correct answers for the given subquestions.

Let A be a 3 × 3 matrix such that A^(T) = −A. Then det(A) =

Show answer

Correct answer: 0

Question 7 on its own page

Question 8

+1 markNumerical answer

Select the correct answers for the given subquestions.

Let A be a 3 × 3 matrix such that det(A) = 2. If B is a matrix obtained from A by swapping the second and third row, and then multiplying the first row by −3, then det(B) =

Show answer

Correct answer: 6

Question 8 on its own page

Question 9

+1 markNumerical answer

Select the correct answers for the given subquestions.

Show answer

Correct answer: 7

Question 9 on its own page

Question 10

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 2

Question 10 on its own page

Question 11

+1 markNumerical answer

Based on the above data, answer the given subquestions.

What is the dimension of the vector space W?

Show answer

Correct answer: 1

Question 11 on its own page

Question 12

+1 markOne correct option

Based on the above data, answer the given subquestions.

Which of the following sets form a basis for W?

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • C
Question 12 on its own page

Question 13

+1 markNumerical answer

Based on the above data, answer the given subquestions.

What is the rank of A?

Show answer

Correct answer: 3

Question 13 on its own page

Question 14

+1 markNumerical answer

Based on the above data, answer the given subquestions.

What is the determinant of B?

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Correct answer: 0

Question 14 on its own page

Question 15

+3 marksOne or more correct options

Based on the above data, answer the given subquestions.

Let v1, v2 and v3 be the column vectors of A and let u1, u2 and u3 be the column vectors of B. Choose the correct option(s) from the following statements.

Select all that apply.

  1. A
  2. B
  3. C
  4. D
  5. E
  6. F
Show answer

Correct answers

  • B
  • D
  • F
Question 15 on its own page

Question 16

+4 marksOne or more correct options

Unless otherwise stated, assume that we consider the usual vector addition and scalar multiplication. Choose the correct option(s) from the following statements.

Select all that apply.

  1. A
  2. B
  3. C
  4. D
  5. E
  6. F
  7. G
Show answer

Correct answers

  • C
  • D
  • F
  • G
Question 16 on its own page