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Maths I · Qualifier · January 2023

BSMA1001 · 10 questions · 50 marks · 60 min

Answer key Take as mock

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1001 · Mathematics for Data Science I

Qualifier · January 2023

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
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.

Q1NAT4 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:
Q2NAT5 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:
Q3NAT5 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q4NAT5 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q5MSQ5 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
Q6MSQ5 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
Q7MSQ5 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
Q8MSQ5 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.
Q9MSQ5 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.
Q10MSQ6 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

Q110

Q220

Q36

Q426

Q5B, D

Q6A, D

Q7A, B, C

Q8A, C, D

Q9A, B, D

Q10C, D

Questions and answer keys are reproduced from the official IIT Madras BS papers. BTechi is not affiliated with IIT Madras.