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September 2021 term · Mathematics for Data Science II · BSMA1003

Maths 2 Quiz 1: 10 October 2021, Set POD21TE3QZ1QPA (September 2021 term)

The IIT Madras BS Mathematics for Data Science II (Maths 2) Quiz 1 paper sat on 10 Oct 2021, in the September 2021 term, set POD21TE3QZ1QPA: 9 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
9
Marks
50
Duration
120 min
Numerical
8
MSQ
1
Take as mock testPractise with answers

Updated

No negative marking.

Question 1

+6 marksNumerical answer

NOTE: Enter your answer to the nearest integer.

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Correct answer: 73

Question 1 on its own page

Question 2

+6 marksNumerical answer

Estimate the area of the region bounded by the graph of function f, above the interval [0,10] using the Riemann sum obtained by taking 5 subintervals of equal length and the mid points of the subintervals for the height of the rectangles.
NOTE: Enter your answer to the nearest integer.

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Correct answer: 78

Question 2 on its own page

Question 3

+6 marksNumerical answer

Find out the number of critical points in the interval (-2, 10).
NOTE: Enter your answer to the nearest integer.

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Correct answer: 3

Question 3 on its own page

Question 4

+6 marksNumerical answer

Find out the number of points where f is not differentiable in the interval (-2, 10).
NOTE: Enter your answer to the nearest integer.

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Correct answer: 2

Question 4 on its own page

Question 5

+4 marksOne or more correct options

Find out the correct statements from the following:

Select all that apply.

  1. A
  2. B
  3. C
  4. D
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Correct answers

  • A
  • B
Question 5 on its own page

Question 6

+4 marksNumerical answer

NOTE: Enter your answer to the nearest integer.

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Correct answer: 10

Question 6 on its own page

Question 7

+6 marksNumerical answer

NOTE: Enter your answer to the nearest integer.

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Correct answer: 10

Question 7 on its own page

Question 8

+6 marksNumerical answer

The profit of Company A with respect to time (in months) is given by the function f(t)f(t) (in lakhs) as follows:

f(t)={(t−2)n+1−1t−3if 0≤t<3,⌊t+1⌋+tif t≥3f(t) = \begin{cases} \frac{(t-2)^{n+1} - 1}{t - 3} & \text{if } 0 \leq t < 3, \\ \lfloor t + 1 \rfloor + t & \text{if } t \geq 3 \end{cases}

for some integer n>0n > 0.

The profit of Company B with respect to time (in months) is given by the function g(t)g(t) (in lakhs) as follows:

g(t)={t2if 0≤t<2,2tmif t≥2g(t) = \begin{cases} t^2 & \text{if } 0 \leq t < 2, \\ 2t^m & \text{if } t \geq 2 \end{cases}

for some integer m>0m > 0.

Use the information given above to answer the given subquestions.

NOTE: Enter your answer to the nearest integer.

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Correct answer: 7

Question 8 on its own page

Question 9

+6 marksNumerical answer

The profit of Company A with respect to time (in months) is given by the function f(t)f(t) (in lakhs) as follows:

f(t)={(t−2)n+1−1t−3if 0≤t<3,⌊t+1⌋+tif t≥3f(t) = \begin{cases} \frac{(t-2)^{n+1} - 1}{t - 3} & \text{if } 0 \leq t < 3, \\ \lfloor t + 1 \rfloor + t & \text{if } t \geq 3 \end{cases}

for some integer n>0n > 0.

The profit of Company B with respect to time (in months) is given by the function g(t)g(t) (in lakhs) as follows:

g(t)={t2if 0≤t<2,2tmif t≥2g(t) = \begin{cases} t^2 & \text{if } 0 \leq t < 2, \\ 2t^m & \text{if } t \geq 2 \end{cases}

for some integer m>0m > 0.

Use the information given above to answer the given subquestions.

NOTE: Enter your answer to the nearest integer.

Show answer

Correct answer: 2

Question 9 on its own page