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May 2023 term · Mathematics for Data Science I · BSMA1001

Mathematics for Data Science I Quiz 2: 6 August 2023 (May 2023 term)

The IIT Madras BS Mathematics for Data Science I (Maths 1) Quiz 2 paper sat on 6 Aug 2023, in the May 2023 term: 14 questions for 50 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
14
Marks
50
Duration
120 min
Numerical
6
MSQ
8
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION AN2 EXAM QPF2 06 Aug 2023 · No negative marking.

Question 1

+5 marksNumerical answer
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Correct answer: 8

Question 1 on its own page

Question 2

+5 marksNumerical answer
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Correct answer: 8

Question 2 on its own page

Question 3

+3 marksOne or more correct options

Consider the following functions f1:D1→Rf_1 : D_1 \to \mathbb{R}, f2:D2→Rf_2 : D_2 \to \mathbb{R}, f3:D3→Rf_3 : D_3 \to \mathbb{R} and g:D→Rg : D \to \mathbb{R}, defined as:

  • f1(x)=sin⁡2xf_1(x) = \sin 2x.
  • f2(x)=ln⁡(x2−6x+8)f_2(x) = \ln(x^2 - 6x + 8).
  • f3(x)=e3x+5f_3(x) = e^{3x} + 5.
  • g(x)=f1(x)+f2(x)+f3(x)g(x) = f_1(x) + f_2(x) + f_3(x).

Let D1,D2,D3D_1, D_2, D_3 and DD be the (largest) domains of the functions f1(x),f2(x),f3(x)f_1(x), f_2(x), f_3(x) and g(x)g(x), respectively. Use this information to answer the subquestions.

Which of the following options is/are true?

Select all that apply.

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

Correct answers

  • A
  • B
  • C
Question 3 on its own page

Question 4

+5 marksOne or more correct options

Consider the following functions f1:D1→Rf_1 : D_1 \to \mathbb{R}, f2:D2→Rf_2 : D_2 \to \mathbb{R}, f3:D3→Rf_3 : D_3 \to \mathbb{R} and g:D→Rg : D \to \mathbb{R}, defined as:

  • f1(x)=sin⁡2xf_1(x) = \sin 2x.
  • f2(x)=ln⁡(x2−6x+8)f_2(x) = \ln(x^2 - 6x + 8).
  • f3(x)=e3x+5f_3(x) = e^{3x} + 5.
  • g(x)=f1(x)+f2(x)+f3(x)g(x) = f_1(x) + f_2(x) + f_3(x).

Let D1,D2,D3D_1, D_2, D_3 and DD be the (largest) domains of the functions f1(x),f2(x),f3(x)f_1(x), f_2(x), f_3(x) and g(x)g(x), respectively. Use this information to answer the subquestions.

Which of the following options is/are true?

Select all that apply.

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

Correct answers

  • B
  • C
Question 4 on its own page

Question 5

+3 marksOne or more correct options

Which of the following options is/ are true?

Select all that apply.

  1. A

    If a function is continuous at a particular point, then the function is differentiable at that point.

  2. B

    If a function is differentiable at a particular point, then the function must be continuous at that point.

  3. C

    If a function is continuous at a particular point, then the limit of the function exists at that point.

  4. D

    If the limit of a function exists at a particular point, then the function is continuous at that point.

Show answer

Correct answers

  • B

    If a function is differentiable at a particular point, then the function must be continuous at that point.

  • C

    If a function is continuous at a particular point, then the limit of the function exists at that point.

Question 5 on its own page

Question 6

+2 marksNumerical answer
Show answer

Correct answer: 0.5

Question 6 on its own page

Question 7

+2 marksNumerical answer
Show answer

Correct answer: 27

Question 7 on its own page

Question 8

+3 marksOne or more correct options

Which of the following options is/are true?

Select all that apply.

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

Correct answers

  • B
  • C
  • D
Question 8 on its own page

Question 9

+2 marksNumerical answer
Show answer

Correct answer: 9

Question 9 on its own page

Question 10

+2 marksNumerical answer

Consider the function f(x)f(x) given below:

f(x)={2x2sin(1x)+bif x≠0,5if x=0f(x) = \begin{cases} 2x^2 sin\left(\frac{1}{x}\right) + b & \text{if } x \neq 0, \\ 5 & \text{if } x = 0 \end{cases}

Assume that ff is continuous at x=0x = 0. Use this information to answer the subquestions.

Find the value of b.

Show answer

Correct answer: 5

Question 10 on its own page

Question 11

+4 marksOne or more correct options

Consider the function f(x)f(x) given below:

f(x)={2x2sin(1x)+bif x≠0,5if x=0f(x) = \begin{cases} 2x^2 sin\left(\frac{1}{x}\right) + b & \text{if } x \neq 0, \\ 5 & \text{if } x = 0 \end{cases}

Assume that ff is continuous at x=0x = 0. Use this information to answer the subquestions.

Which of the following options is/are true for the function f(x) at x = 1?

Select all that apply.

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

Correct answers

  • A
  • D
Question 11 on its own page

Question 12

+4 marksOne or more correct options

Select all that apply.

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

Correct answers

  • B
  • D
Question 12 on its own page

Question 13

+5 marksOne or more correct options

Select all that apply.

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

Correct answers

  • A
  • D
  • E
Question 13 on its own page

Question 14

+5 marksOne or more correct options

Select all that apply.

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

Correct answers

  • A
  • C
Question 14 on its own page