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Maths I · Polynomials & their graphs

BSMA1001 · 19 questions · 80 marks · 7 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1001 · Mathematics for Data Science I

Polynomials & their graphs

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.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Useful Reference Data for this Paper
Q1MCQ4 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q2MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q3NAT5 Marks·Write the number
Key ↓
Your answer:

End Term · 22 Dec 2024 (FN)End Term

Read the passage below, then answer Q4–Q5
Q4MCQ3 Marks·Choose one option
Asked 2 times Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Q5MCQ3 Marks·Choose one option
Asked 3 times Key ↓
Which of the following option is true?
1. A
2. B
3. C
4. D

Qualifier · May 2024Qualifier

Q6MSQ4 Marks·Choose all correct options
Asked 4 times Key ↓
Consider the following polynomial p(x) whose graph is given below:- Which of the following options is/are correct?
1. A
2. B
3. C
4. D
Q7MSQ4 Marks·Choose all correct options
Key ↓
1. Aq(x) is a cubic polynomial.
2. Bq(x) is a quadratic polynomial.
3. Cq(x) has two distinct zeros.
4. Dq(x) does not have any real zeros.

Qualifier · January 2024Qualifier

Q8MSQ5 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q9MSQ4 Marks·Choose all correct options
Asked 4 times Key ↓
Consider the following polynomial p(x) whose graph is given below:- Which of the following options is/are correct.
1. AMultiplicity of -1 and 1 must be same.
2. Bp(x) is increasing in the interval (3,∞).
3. CThe total number of local minima is 3.
4. DThe number of turning points is 5.

Qualifier · September 2023Qualifier

Q10MSQ4 Marks·Choose all correct options
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q11–Q12
Q11MSQ3 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
Q12MSQ4 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 · May 2023Qualifier

Q13MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q14MSQ5 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q15–Q16
Q15NAT3 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:
Q16MSQ4 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

Q17MSQ5 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.
Q18MSQ5 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.
Q19MSQ6 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

Q1B

Q2A, D

Q3-1

Q4D

Q5A

Q6B, C

Q7B, C

Q8B, C, D

Q9B, C

Q10A, D

Q11B, C

Q12B, D

Q13C

Q14B, D

Q1513

Q16A, C, D

Q17A, C, D

Q18A, B, D

Q19C, D

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