Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
BSMA1001 · Mathematics for Data Science I
Qualifier · May 2024
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.
Read the passage below, then answer Q1–Q3
Q1NAT3 Marks·Write the number
Your answer:- Q2NAT2 Marks·Write the number
What is the cardinality of R₁?
Your answer: - Q3MSQ3 Marks·Choose all correct options
Which of the following statements are correct?
- AR₁ is transitive.
- BR₂ is transitive.
- CR₂ is not symmetric.
- D(2,18) is an element in R₂.
Read the passage below, then answer Q4–Q5
Suppose that P₁ and P₂ are two different points in a Cartesian coordinate system, with P₁ located at (3,−2) and P₂ at (−1, 5). Let L₁ and L₂ be lines passing through P₁ and P₂ respectively.
Q4MCQ4 Marks·Choose one option
- A
- B
- C
- D
- A
- Q5MCQ4 Marks·Choose one option
If the x−intercept of the line L₁ is 1 and y− intercept of the line L₂ is -1 and If θ is the angle between L₁ and L₂, then tan θ is equal to
- A
- B
- C
- D
- A
- Q6NAT4 Marks·Write the number
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: - Q7NAT4 Marks·Write the number
Your answer: - Q8MSQ4 Marks·Choose all correct options
Consider the following polynomial p(x) whose graph is given below:-
Which of the following options is/are correct?- A
- B
- C
- D
- A
- Q9MSQ4 Marks·Choose all correct options
Consider the parabola y = x² + 4x + 12. Which of the following option(s) are true?
- AThe co-ordinates of vertex is (−8, 2).
- BThe given equation attains it minima at x = −2.
- Cy-intercept of parabola is 12.
- DThe minimum value for the given equation is 8
- Q10MSQ4 Marks·Choose all correct options
- Aq(x) is a cubic polynomial.
- Bq(x) is a quadratic polynomial.
- Cq(x) has two distinct zeros.
- Dq(x) does not have any real zeros.
- Q11MCQ4 Marks·Choose one option
- AIf b² − 4ac > 0 and a perfect square then there exists a rational root of the quadratic equation.
- BIf b² − 4ac > 0 and not a perfect square then there exists a rational root of the quadratic equation.
- CIf b² − 4ac < 0 and a perfect square then there exists a rational root of the quadratic equation.
- DIf b² − 4ac < 0 and not a perfect square then there exists a rational root of the quadratic equation.