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Maths I · All 2023 papers

BSMA1001 · 38 questions · 150 marks · 3 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1001 · Mathematics for Data Science I

All 2023 papers

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.

Qualifier · September 2023Qualifier

Read the passage below, then answer Q1–Q2
In a survey among 140 people, it was found that 75% of these 140 people like playing cricket and 50% of all the 140 people like playing football. Note that, some people may not like both games that could be 0 also.
Use this information to answer the given subquestions
Q1NAT4 Marks·Write the number
Key ↓
What is the minimum number of people who like both games?
Your answer:
Q2NAT2 Marks·Write the number
Asked 2 times Key ↓
If there are 10 people who don’t like both games, then what is the number of people who like only cricket?
Your answer:
Q3MCQ4 Marks·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q4MCQ4 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q5MCQ3 Marks·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q6NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q7MSQ4 Marks·Choose all correct options
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q8MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q9–Q10
Q9MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Q10MSQ4 Marks·Choose all correct options
Asked 3 times Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q11–Q12
Q11MCQ3 Marks·Choose one option
Asked 3 times Key ↓
Which of the following options is true?
1. A
2. B
3. C
4. D
Q12NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q13–Q14
Q13MSQ4 Marks·Choose all correct options
Asked 6 times Key ↓
Which of the following options is/are true?
1. AR₁ is a reflexive relation.
2. BR₂ is a symmetric relation.
3. CR₁ is not a transitive relation.
4. DR₂ is a transitive relation.
Q14MCQ4 Marks·Choose one option
Asked 2 times Key ↓
Which of the following options is true?
1. AR₁ is a function.
2. BR₂ is a function.
3. CR₂ is not a one-one function.
4. DR₂ is not an onto function.

Qualifier · May 2023Qualifier

Read the passage below, then answer Q15–Q17
Q15NAT3 Marks·Write the number
Asked 6 times Key ↓
R₁ is _____________ . (Enter all correct options. Enter only the serial numbers of those options in increasing order without adding any comma or space in between them i.e., if your answer is 6 and 7, then you should enter 67]
Your answer:
Q16NAT3 Marks·Write the number
Key ↓
R₂ is ____________ . (Enter all correct options. Enter only the serial numbers of those options in increasing order without adding any comma or space in between them i.e., if your answer is 3 and 4, then you should enter 34)
Your answer:
Q17NAT2 Marks·Write the number
Asked 3 times Key ↓
Find the cardinality of the set (S × S) \ R₂.
Your answer:
Q18MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q19MSQ3 Marks·Choose all correct options
Asked 3 times Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Q20MSQ5 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q21NAT5 Marks·Write the number
Asked 4 times Key ↓
A company opened recruitment for the post of data analyst. 500 candidates have applied for the post. 285 candidates are proficient in Python programming, 195 candidates are proficient in C programming, 115 candidates are proficient in Java programming, 45 candidates are proficient in Python and Java, 70 candidates are proficient in C and Python, 50 candidates are proficient in C and Java and 50 candidates don’t know any of the programming languages. Find the number of candidates who are proficient in exactly one of the three programming languages.
Your answer:
Q22NAT5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q23NAT5 Marks·Write the number
Key ↓
Your answer:
Q24NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q25–Q26
Q25NAT2 Marks·Write the number
Asked 2 times Key ↓
Find the quantity of the raw material such that the company has the maximum profit.
Your answer:
Q26NAT2 Marks·Write the number
Key ↓
Find the quantity of the raw material (x > 1) such that the company has no profit.
Your answer:
Read the passage below, then answer Q27–Q28
Q27NAT3 Marks·Write the number
Key ↓
If m is the number of distinct roots and n is the number of turning points of the polynomial p(x), then find the value of m + n
Your answer:
Q28MSQ4 Marks·Choose all correct options
Asked 3 times Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D

Qualifier · January 2023Qualifier

Q29NAT4 Marks·Write the number
Key ↓
The Cartesian product A × A has 9 elements. Two of the elements of the Cartesian product are (2, 0) and (0, 8). Find the sum of all the elements in set A.
Your answer:
Q30NAT5 Marks·Write the number
Asked 4 times Key ↓
In a survey among 250 students in Nilgiri house of IITM BSc degree, the following data were found: • 100 students have a Hotstar subscription • 110 students have Netflix subscription • 120 students have Amazon Prime membership. • 30 students have both Hotstar and Netflix subscriptions whereas 30 students have both Hotstar and Amazon Prime and 40 students subscribe to both Netflix and Amazon Prime. Assuming that all students have at least one OTT subscription, determine how many students have memberships to all 3 OTT: Hotstar, Netflix and Amazon Prime?
Your answer:
Q31NAT5 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q32NAT5 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q33MSQ5 Marks·Choose all correct options
Asked 2 times Key ↓
1. AR₂,R₃, and R₄ are functions
2. BR₂ and R₄ are functions
3. CR₂ is an injective function
4. DR₄ is a bijective function
Q34MSQ5 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following functions may represent the graph given in Figure 2?
1. Af(x) = x² − 8x + 12
2. Bf(x) = x² + 10x − 21
3. Cf(x) = 2x² + 8x + 4
4. Df(x) = x² − 6x + 4
Q35MSQ5 Marks·Choose all correct options
Key ↓
Ankit is located at (3, 3). He called Ajay to ask his location. Ajay describes the path he had taken from home (located at the origin) as: “ I walked three units towards East and then nine units towards North. And I repeated the same pattern thrice.” Now Ankit wants a direct path to reach Ajay, then choose the correct options. (Note that North represents the direction along the positive y-axis.)
1. A
2. B
3. C
4. D
Q36MSQ5 Marks·Choose all correct options
Key ↓
Rubika launches her new company in the year 2010, which makes a yearly profit in lakhs as the polynomial function p(x) = 0.1x² (x − 1) (x − 2) (x − 3)² (x − 4) (x − 9) for the first 12 years since the launch, where x is the number of years since 2010 (i.e., x = 0 denotes the year 2010, x = 1 denotes the year 2011, and so on). Let the loss be represented as −ve of profit. Which of the following options are correct?
1. AIncluding the year in which the company was launched, it neither made a profit nor a loss six times in 12 years.
2. BThe company made profit in years x ∈ {7, 8, 10, 11}.
3. CThe company made loss (−ve profit) in years x ∈ {5, 6, 7, 8}.
4. DIn the year 2022 (i.e., x = 12) the company made profit.
Q37MSQ5 Marks·Choose all correct options
Asked 4 times Key ↓
Figure 2 shows the graph of a polynomial p(x). Choose the set of correct option(s).
1. AThe degree of p(x) is at least 10.
2. Bp(x) represent an even degree polynomial.
3. CTotal number of turning point of p(x) are 8.
4. DMultiplicities of zero and one of the negative roots could be the same.
Q38MSQ6 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q135

Q260

Q3B

Q4A

Q5B

Q6165

Q7A, D

Q8B, C

Q9B, C

Q10B, D

Q11A

Q1210

Q13A, B

Q14B

Q15245

Q1612367

Q1720

Q18C

Q19C, D

Q20B, D

Q21325

Q223

Q23-12

Q2417

Q252

Q263

Q2713

Q28A, C, D

Q2910

Q3020

Q316

Q3226

Q33B, D

Q34A, D

Q35A, B, C

Q36A, C, D

Q37A, B, D

Q38C, D

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