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May 2022 term · Mathematics for Data Science II · BSMA1003

Maths 2 End Term: 7 August 2022, Set 4 (May 2022 term)

The IIT Madras BS Mathematics for Data Science II (Maths 2) End Term paper sat on 7 Aug 2022, in the May 2022 term, set 4: 36 questions for 58 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
36
Marks
58
Duration
180 min
MCQ
6
Written
23
MSQ
7
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION DIPLOMA ENDTERM QPD2 07 Aug 2022 IBA · No negative marking.

Question 1

+1 markOne correct option
Figure from the original question paper
  1. A

    Yes

  2. B

    No

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Correct answer

  • A

    Yes

Question 1 on its own page

Question 2

+1 markWritten answer
Figure from the original question paper

Find the number of critical points of the function f(a, b).

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Question 3

+1 markOne or more correct options
Figure from the original question paper

Which of the following options is/are true?

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answers

  • B
    Figure from the original question paper
  • C
    Figure from the original question paper
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Question 4

+2 marksOne correct option
Figure from the original question paper
Figure from the original question paper
  1. A

    T is injective.

  2. B

    T is surjective.

  3. C

    T is an isomorphism.

  4. D

    T is neither injective not surjective.

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Correct answer

  • B

    T is surjective.

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Question 5

+2 marksWritten answer
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Figure from the original question paper
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Question 6

+2 marksWritten answer
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Figure from the original question paper
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Question 7

+2 marksWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

Find the nullity of T.

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Question 8

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

Find the rank of T.

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Question 9

+2 marksOne or more correct options

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

Choose the correct option(s).

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answers

  • A
    Figure from the original question paper
  • C
    Figure from the original question paper
Question 9 on its own page

Question 10

+2 marksOne or more correct options
Figure from the original question paper

Select all that apply.

  1. A

    Condition 1 is satisfied.

  2. B

    Condition 2 is satisfied.

  3. C

    Condition 3 is satisfied.

  4. D

    Condition 4 is satisfied.

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Correct answers

  • B

    Condition 2 is satisfied.

  • C

    Condition 3 is satisfied.

  • D

    Condition 4 is satisfied.

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Question 11

+2 marksOne or more correct options

Which of the following options is/are true?

Which of the following options is/are true?

Which of the following options is/are true?

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
  5. E
    Figure from the original question paper
  6. F
    Figure from the original question paper
Show answer

Correct answers

  • D
    Figure from the original question paper
  • E
    Figure from the original question paper
Question 11 on its own page

Question 12

+2 marksOne or more correct options
Figure from the original question paper

Select all that apply.

  1. A

    A is not equivalent to B.

  2. B

    A is equivalent to B.

  3. C

    A is similar to B.

  4. D

    A is not similar to B.

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Correct answers

  • B

    A is equivalent to B.

  • D

    A is not similar to B.

Question 12 on its own page

Question 13

+2 marksWritten answer
Figure from the original question paper
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Question 14

+2 marksWritten answer
Figure from the original question paper

Find the number of local maxima using the Hessian test.

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Question 15

+2 marksWritten answer
Figure from the original question paper

Find the number of local minima using the Hessian test.

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Question 16

+2 marksWritten answer
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Find the number of saddle points using the Hessian test.

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Question 17

+1 markWritten answer
Figure from the original question paper

Find the number of points at which the Hessian test is indeterminate.

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Question 18

+2 marksOne correct option
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What will be the ratio of the price of the raw materials and the price of the transportation (x : y) when y > x, if the rate of change of the price of the product with respect to the price of the raw materials is 0? (In this context x and y both are always positive).

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
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Correct answer

  • C
    Figure from the original question paper
Question 18 on its own page

Question 19

+3 marksOne or more correct options
Figure from the original question paper

Which of the following statements are true?

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
  5. E
    Figure from the original question paper
Show answer

Correct answers

  • B
    Figure from the original question paper
  • C
    Figure from the original question paper
  • D
    Figure from the original question paper
Question 19 on its own page

Question 20

+2 marksWritten answer
Figure from the original question paper
Figure from the original question paper
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Question 21

+2 marksOne correct option

Which of the following is true for the function:

Which of the following is true for the function:

Which of the following is true for the function:
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • B
    Figure from the original question paper
Question 21 on its own page

Question 22

+2 marksOne correct option
Figure from the original question paper
  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • C
    Figure from the original question paper
Question 22 on its own page

Question 23

+2 marksOne correct option

Which of the following option is/are true?

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • A
    Figure from the original question paper
Question 23 on its own page

Question 24

+1 markWritten answer
Figure from the original question paper

Find the dimension of the image space PW.

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Question 25

+2 marksWritten answer
Figure from the original question paper

Find the dimension of the null space of PW.

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Question 26

+1 markWritten answer
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Figure from the original question paper
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Question 27

+1 markWritten answer
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Figure from the original question paper
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Question 28

+2 marksOne or more correct options
Figure from the original question paper

Choose the correct options about the matrix B.

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answers

  • A
    Figure from the original question paper
  • C
    Figure from the original question paper
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Question 29

+2 marksWritten answer
Figure from the original question paper
Figure from the original question paper
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Question 30

+1 markWritten answer
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Question 31

+1 markWritten answer
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Question 32

+1 markWritten answer

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.
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Question 33

+1 markWritten answer
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Question 34

+1 markWritten answer
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Question 35

+1 markWritten answer
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Question 36

+1 markWritten answer
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