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Maths I · Most repeated questions

BSMA1001 · 112 questions · 377 marks · 11 papers · 36 question types

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1001 · Mathematics for Data Science I

Most repeated questions

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.

Type 1 · asked 6 times · Relations & functions basics

Check reflexive, symmetric, transitive or equivalence for relations

Read the passage below, then answer Q1
Q1NAT3 Marks·Write the number
Qualifier · May 2023Key ↓
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:
Read the passage below, then answer Q2
Q2MSQ4 Marks·Choose all correct options
Qualifier · September 2023Key ↓
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.
Q3MSQ5 Marks·Choose all correct options
Qualifier · January 2024Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q4
Q4MSQ3 Marks·Choose all correct options
Qualifier · May 2024Key ↓
Which of the following statements are correct?
1. AR₁ is transitive.
2. BR₂ is transitive.
3. CR₂ is not symmetric.
4. D(2,18) is an element in R₂.
Q5MSQ4 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D
Useful Reference Data for this Paper
Q6MSQ4 Marks·Choose all correct options
Quiz 1 · 26 Oct 2025 (AN)Key ↓
1. AR is an equivalence relation.
2. BS is an equivalence relation.
3. CR is not transitive.
4. DS is not symmetric.

Type 2 · asked 6 times · Derivatives, tangents & extrema

Find critical points and local maxima/minima of a function

Read the passage below, then answer Q7–Q8
Q7NAT2 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Your answer:
Q8MSQ2 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
Which of the following option(s) is(are) correct?
1. A
2. B
3. C
4. D
Q9MSQ3 Marks·Choose all correct options
End Term · 13 Apr 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q10–Q11
Q10MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
1. ATRUE
2. BFALSE
Q11MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
1. ATRUE
2. BFALSE
Read the passage below, then answer Q12
Q12NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:

Type 3 · asked 5 times · Sequences & limits

Limit of a rational expression as n or x goes to infinity

Read the passage below, then answer Q13
Q13NAT2 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Your answer:
Read the passage below, then answer Q14
Q14NAT3 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
Your answer:
Read the passage below, then answer Q15
Based on the above data, answer the subquestions.
Q15NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:
Useful Reference Data for this Paper
Q16NAT2 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Your answer:
Q17NAT3 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Your answer:

Type 4 · asked 5 times · Sequences & limits

Evaluate a limit at a point using standard trig/exp limits

Q18NAT2 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
Your answer:
Q19NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:
Useful Reference Data for this Paper
Q20MCQ3 Marks·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Q21NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:
Q22NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 5 · asked 5 times · Continuity & differentiability

Check continuity/differentiability of a piecewise function at points

Read the passage below, then answer Q23–Q24
Q23MCQ1 Mark·Choose one option
End Term · 13 Apr 2025 (FN)Key ↓
1. ATRUE
2. BFALSE
Q24MCQ1 Mark·Choose one option
End Term · 13 Apr 2025 (FN)Key ↓
1. ATRUE
2. BFALSE
Useful Reference Data for this Paper
Q25MSQ4 Marks·Choose all correct options
Quiz 2 · 3 Aug 2025 (AN)Key ↓
1. Af is not continuous.
2. Bf is continuous.
3. Cg is not continuous.
4. Dg is continuous.
Read the passage below, then answer Q26
Q26MSQ3 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
Choose the set of correct options.
1. A
2. B
3. C
4. D
Read the passage below, then answer Q27
Consider the function,
Answer the given subquestions.
Q27MSQ4 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
Which of the following options is (are) correct?
1. A
2. B
3. C
4. D

Type 6 · asked 4 times · Sets & Venn diagram counting

Use inclusion-exclusion on three sets to find a count

Q28NAT5 Marks·Write the number
Qualifier · January 2023Key ↓
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:
Q29NAT5 Marks·Write the number
Qualifier · May 2023Key ↓
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:
Read the passage below, then answer Q30
In a grocery store, 60 customers made a purchase on a specific day. 28 people bought bread, 37 people bought milk and 30 people bought fruits. All the customers bought at least one of the three items. 16 of them bought bread and fruits, 17 of them bought bread and milk and 9 of them bought all the three items.
Q30NAT2 Marks·Write the number
Qualifier · January 2024Key ↓
Find the number of customers who bought milk and fruits.
Your answer:
Q31NAT4 Marks·Write the number
Qualifier · May 2024Key ↓
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:

Type 7 · asked 4 times · Best-fit lines & SSE

Compute SSE of data with respect to a given best-fit line

Q32NAT5 Marks·Write the number
Qualifier · January 2023Key ↓
Your answer:
Read the passage below, then answer Q33
Q33NAT3 Marks·Write the number
Qualifier · September 2023Key ↓
Your answer:
Q34NAT4 Marks·Write the number
Qualifier · May 2024Key ↓
Your answer:
Q35NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 8 · asked 4 times · Polynomials & their graphs

Read a polynomial graph: roots, multiplicity, turning points

Q36MSQ5 Marks·Choose all correct options
Qualifier · January 2023Key ↓
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.
Q37MSQ4 Marks·Choose all correct options
Qualifier · September 2023Key ↓
1. A
2. B
3. C
4. D
Q38MSQ4 Marks·Choose all correct options
Qualifier · January 2024Key ↓
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.
Q39MSQ4 Marks·Choose all correct options
Qualifier · May 2024Key ↓
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

Type 9 · asked 4 times · Quadratic functions

Find a quadratic from its vertex, intercept or other conditions

Q40NAT5 Marks·Write the number
Qualifier · January 2023Key ↓
Your answer:
Q41NAT3 Marks·Write the number
Qualifier · May 2023Key ↓
Your answer:
Useful Reference Data for this Paper
Q42MCQ4 Marks·Choose one option
Quiz 1 · 26 Oct 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Q43NAT4 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 10 · asked 4 times · Functions, exponentials & logarithms

Find the domain of a log or composite function

Q44NAT3 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
Your answer:
Useful Reference Data for this Paper
Read the passage below, then answer Q45
Q45MCQ3 Marks·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q46
Q46MCQ3 Marks·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Choose the correct options.
1. A
2. B
3. C
4. D
Q47MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 11 · asked 4 times · Derivatives, tangents & extrema

Find the tangent line or linear approximation at a point

Read the passage below, then answer Q48
Q48MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
1. ATRUE
2. BFALSE
Read the passage below, then answer Q49
Based on the above data, answer the given subquestions.
Q49NAT3 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:
Read the passage below, then answer Q50
Q50MSQ4 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)Key ↓
Which of the following options is/are true ?
1. A
2. B
3. C
4. D
Useful Reference Data for this Paper
Read the passage below, then answer Q51
Q51MSQ3 Marks·Choose all correct options
Quiz 2 · 3 Aug 2025 (AN)Key ↓
If y = mx + c is the equation of the tangent of f at x = 3 then choose the correct options.
1. A
2. B
3. C
4. D

Type 12 · asked 4 times · Integration & area

Evaluate a definite integral or area under/between curves

Q52NAT4 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Your answer:
Read the passage below, then answer Q53
Q53NAT3 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
Your answer:
Q54MCQ4 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q55
Consider the function,
Answer the given subquestions.
Q55NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 13 · asked 4 times · Graphs: BFS, DFS, colouring & covers

Chromatic number: least colours/compartments for a graph

Q56NAT5 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Your answer:
Read the passage below, then answer Q57
Based on the above data, answer the given subquestions.
Q57NAT3 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
What is the minimum number of colors required to properly color the vertices of the given graph such that no two adjacent vertices share the same color?
Your answer:
Read the passage below, then answer Q58
Suppose Nitya wishes to find the minimum cost spanning tree of the graph given below. While finding the minimum cost spanning tree she finds that a few edge weights are missing (x and y) but she is sure that the weight of the minimum cost spanning tree is 15 in the graph.
Based on the above data, answer the given subquestions.
Q58NAT3 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
What is the minimum number of colors required to properly color the vertices of the given graph such that no two adjacent vertices share the same color?
Your answer:
Q59NAT4 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 14 · asked 3 times · Coordinate geometry & straight lines

True/false: parabola vertex, polynomial degree, perpendicular/parallel lines

Q60MSQ3 Marks·Choose all correct options
End Term · 13 Apr 2025 (AN)Key ↓
Which of the following statements is (are) correct?
1. A
2. B
3. C
4. D
Q61MSQ3 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)Key ↓
Which of the following statements is (are) correct?
1. A
2. B
3. C
4. D
Useful Reference Data for this Paper
Q62MSQ4 Marks·Choose all correct options
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Which of the following statements is(are) true?
1. A
2. B
3. C
4. D

Type 15 · asked 3 times · Polynomials & their graphs

Statements on roots, turning points and end behaviour of a polynomial

Read the passage below, then answer Q63
Q63MSQ4 Marks·Choose all correct options
Qualifier · May 2023Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q64
Q64MSQ4 Marks·Choose all correct options
Qualifier · September 2023Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q65
Q65MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
Which of the following option is true?
1. A
2. B
3. C
4. D

Type 16 · asked 3 times · Relations & functions basics

Find the cardinality of a set built from relations

Read the passage below, then answer Q66
Q66NAT2 Marks·Write the number
Qualifier · May 2023Key ↓
Find the cardinality of the set (S × S) \ R₂.
Your answer:
Read the passage below, then answer Q67
Q67NAT3 Marks·Write the number
Qualifier · May 2024Key ↓
Your answer:
Useful Reference Data for this Paper
Q68NAT4 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 17 · asked 3 times · Coordinate geometry & straight lines

Slopes, intercepts, parallel/perpendicular lines and distance statements

Q69MSQ3 Marks·Choose all correct options
Qualifier · May 2023Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Q70MCQ3 Marks·Choose one option
Qualifier · September 2023Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q71
Q71MCQ3 Marks·Choose one option
Qualifier · September 2023Key ↓
Which of the following options is true?
1. A
2. B
3. C
4. D

Type 18 · asked 3 times · Functions, exponentials & logarithms

Analyse a function with |x| terms (one-one, onto, range)

Q72MCQ4 Marks·Choose one option
Qualifier · September 2023Key ↓
1. A
2. B
3. C
4. D
Q73MSQ5 Marks·Choose all correct options
Qualifier · January 2024Key ↓
1. A
2. B
3. C
4. D
Q74MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 19 · asked 3 times · Sequences & limits

Limit of a_n = c + (-1)^n / n^k

Read the passage below, then answer Q75
Q75NAT2 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Enter your answer correctly to two decimal places.
Your answer:
Read the passage below, then answer Q76
Q76NAT3 Marks·Write the number
End Term · 13 Apr 2025 (AN)Key ↓
Your answer:
Read the passage below, then answer Q77
Based on the above data, answer the subquestions.
Q77NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:

Type 20 · asked 3 times · Continuity & differentiability

Find constants that make a piecewise function differentiable

Q78MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q79
Based on the above data, answer the given subquestions.
Q79NAT3 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:
Useful Reference Data for this Paper
Q80MCQ4 Marks·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D

Type 21 · asked 2 times · Sets & Venn diagram counting

Two-set Venn diagram: find people in only one set

Read the passage below, then answer Q81
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
Q81NAT2 Marks·Write the number
Qualifier · September 2023Key ↓
If there are 10 people who don’t like both games, then what is the number of people who like only cricket?
Your answer:
Useful Reference Data for this Paper
Q82NAT4 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
In an online degree program, it was found that in one term, 72 students took Mathematics, 85 students took Statistics, and 30 students took both Mathematics and Statistics. How many students took only one of the two subjects?
Your answer:

Type 22 · asked 2 times · Quadratic functions

Pick the quadratic function that matches a given graph

Q83MSQ5 Marks·Choose all correct options
Qualifier · January 2023Key ↓
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
Q84MSQ3 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
Which of the following functions have graphs as in Figure 2?
1. A
2. B
3. C
4. D

Type 23 · asked 2 times · Relations & functions basics

True/false: cardinality of S x S, parabola vertex, slope of a line

Q85MSQ4 Marks·Choose all correct options
Qualifier · September 2023Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Q86MSQ3 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
Which of the following options is / are true ?
1. A
2. B
3. C
4. D

Type 24 · asked 2 times · Polynomials & their graphs

Compare p(x) = -x^5+5x^4-7x-2 and q(x) = -x^5+5x^4-x^2-2

Q87MSQ5 Marks·Choose all correct options
Qualifier · January 2024Key ↓
1. A
2. B
3. C
4. D
Useful Reference Data for this Paper
Q88MSQ4 Marks·Choose all correct options
Quiz 1 · 26 Oct 2025 (AN)Key ↓
1. A
2. B
3. C
4. D

Type 25 · asked 2 times · Polynomials & their graphs

Degree of sum/product and remainder degree of polynomials

Read the passage below, then answer Q89
Q89MSQ3 Marks·Choose all correct options
Qualifier · September 2023Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q90
Q90MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D

Type 26 · asked 2 times · Relations & functions basics

Decide which relations are functions, one-one or onto

Q91MSQ5 Marks·Choose all correct options
Qualifier · January 2023Key ↓
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
Read the passage below, then answer Q92
Q92MCQ4 Marks·Choose one option
Qualifier · September 2023Key ↓
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.

Type 27 · asked 2 times · Coordinate geometry & straight lines

Find tan of the angle between two lines

Read the passage below, then answer Q93
Q93MCQ3 Marks·Choose one option
Qualifier · January 2024Key ↓
If θ is the angle between L₁ and L₂, then tan θ is equal to
1. A
2. B
3. C
4. D
Read the passage below, then answer Q94
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.
Q94MCQ4 Marks·Choose one option
Qualifier · May 2024Key ↓
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
1. A
2. B
3. C
4. D

Type 28 · asked 2 times · Coordinate geometry & straight lines

Find the intersection point of two lines from given conditions

Read the passage below, then answer Q95
Q95MCQ3 Marks·Choose one option
Qualifier · January 2024Key ↓
Choose the point where L₁ and L₂ intersect.
1. A(10, 18)
2. B(5, 8)
3. C(−10,−18)
4. D(6, 6)
Read the passage below, then answer Q96
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.
Q96MCQ4 Marks·Choose one option
Qualifier · May 2024Key ↓
1. A
2. B
3. C
4. D

Type 29 · asked 2 times · Coordinate geometry & straight lines

Use the section formula for a point dividing a segment in a ratio

Q97NAT5 Marks·Write the number
Qualifier · May 2023Key ↓
Your answer:
Useful Reference Data for this Paper
Q98NAT4 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 30 · asked 2 times · Quadratic functions

Find the quantity that maximises a quadratic profit or amount

Read the passage below, then answer Q99
Q99NAT2 Marks·Write the number
Qualifier · May 2023Key ↓
Find the quantity of the raw material such that the company has the maximum profit.
Your answer:
Q100NAT4 Marks·Write the number
Qualifier · September 2023Key ↓
Your answer:

Type 31 · asked 2 times · Derivatives, tangents & extrema

Find the derivative value f'(1) of a given function

Read the passage below, then answer Q101
Based on the above data, answer the given subquestions.
Q101NAT2 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Your answer:
Read the passage below, then answer Q102
Q102NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 32 · asked 2 times · Shortest paths & spanning trees

Find the cost of a minimum spanning tree

Q103NAT5 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Your answer:
Q104NAT4 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 33 · asked 2 times · Shortest paths & spanning trees

True/false about Prim's algorithm and MST cost

Q105MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (AN)Key ↓
Which of the following options is true?
1. AThe cost of the spanning tree obtained by Prim’s Algorithm is the same as obtained by Kruskal’s Algorithm.
2. BThe minimum cost-spanning tree obtained by Prim’s Algorithm is the same as obtained by Kruskal’s Algorithm.
3. CThe minimum cost-spanning tree is not a tree.
4. DIf the weight of each edge in a graph is equal, then the total cost of the graph is equal to the cost of the minimum cost-spanning tree.
Q106MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (FN)Key ↓
Which of the following options is true?
1. AThe minimum cost-spanning tree obtained by Prim’s Algorithm is always the same as obtained by Kruskal’s Algorithm.
2. BThe minimum cost-spanning tree is not a tree.
3. CThe cost of the spanning tree obtained by Prim’s Algorithm is the same as obtained by Kruskal’s Algorithm.
4. DIf the weight of each edge in a graph is equal, then the total cost of the graph is equal to the cost of the minimum cost-spanning tree.

Type 34 · asked 2 times · Shortest paths & spanning trees

Find possible missing edge weights x, y for a given MST

Read the passage below, then answer Q107
Based on the above data, answer the given subquestions.
Q107MSQ4 Marks·Choose all correct options
End Term · 13 Apr 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q108
Suppose Nitya wishes to find the minimum cost spanning tree of the graph given below. While finding the minimum cost spanning tree she finds that a few edge weights are missing (x and y) but she is sure that the weight of the minimum cost spanning tree is 15 in the graph.
Based on the above data, answer the given subquestions.
Q108MSQ4 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)Key ↓
Which of the following are possible values for x and y?
1. Ax = 2, y = 6.
2. Bx= 4, y = 3.
3. Cx = 3, y = 4.
4. Dx = 1, y = 6.

Type 35 · asked 2 times · Graphs: BFS, DFS, colouring & covers

Maximum independent set and minimum vertex cover of a graph

Q109MSQ4 Marks·Choose all correct options
End Term · 13 Apr 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Q110MSQ4 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 36 · asked 2 times · Graphs: BFS, DFS, colouring & covers

Check possible BFS/DFS visit orders of a graph

Q111MSQ4 Marks·Choose all correct options
End Term · 13 Apr 2025 (AN)Key ↓
1. AIf we perform Breadth-First Search at node 0, then one of the possible orders in which the nodes will be visited is 01246573.
2. BIf we perform Depth First Search at node 7, then one of the possible order in which the nodes will be visited is 74356012
3. CIf we perform Breadth-First Search at node 0, then one of the possible orders in which the nodes will be visited is 01264537.
4. DIf we perform Depth First Search at node 0, then one of the possible orders in which the nodes will be visited is 76435012.
Q112MSQ4 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)Key ↓
1. AIf we perform Breadth-First Search at node 0, then one of the possible orders in which the nodes will be visited is 01423567.
2. BIf we perform Depth First Search at node 0, then one of the possible order in which the nodes will be visited is 04123576
3. CIf we perform Breadth-First Search at node 0, then one of the possible orders in which the nodes will be visited is 01423765.
4. DIf we perform Depth First Search at node 0, then one of the possible orders in which the nodes will be visited is 04132567.

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1245

Q2A, B

Q3A, D

Q4A, C, D

Q5B, D

Q6A, D

Q72

Q8B, C

Q9A, D

Q10B

Q11A

Q12-2

Q1311

Q1417

Q1515

Q162

Q174

Q180

Q190

Q20C

Q213

Q222

Q23B

Q24A

Q25A, D

Q26A, B

Q27A, C, D

Q2820

Q29325

Q3011

Q31325

Q3226

Q3310

Q3423

Q3520

Q36A, B, D

Q37A, D

Q38B, C

Q39B, C

Q406

Q4117

Q42A

Q4313 to 14

Q445

Q45C

Q46C

Q47D

Q48A

Q49-6

Q50A, C

Q51A, C

Q521

Q531

Q54B

Q557.7 to 7.9

Q563

Q574

Q584

Q593

Q60B, C, D

Q61A, B, D

Q62A, D

Q63A, C, D

Q64B, D

Q65A

Q6620

Q671

Q682

Q69C, D

Q70B

Q71A

Q72B

Q73A, C

Q74B, C

Q750.12 to 0.13

Q760.1 to 0.3

Q770.11 to 0.13

Q78A

Q796

Q80C

Q8160

Q8297

Q83A, D

Q84A, D

Q85B, C

Q86A, C

Q87B, C, D

Q88A, D

Q89B, C

Q90D

Q91B, D

Q92B

Q93A

Q94B

Q95C

Q96D

Q973

Q981.3 to 1.4

Q992

Q100165

Q10114

Q10211

Q10323

Q10413

Q105A

Q106C

Q107B, C

Q108A, C

Q109B, C

Q110A, D

Q111B, C

Q112A, D

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.