Week 1 Mathematics 1 Questions | Prasnya

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In a survey among

250

students in Bandipur House of IITM BS degree, the following data were found:

100

students have a Spotify subscription,

110

students have a YouTube Premium subscription,

120

students have an Apple Music membership,

30

students have both Spotify and YouTube Premium subscriptions,

30

students have both Spotify and Apple Music subscriptions, and

40

students subscribe to both YouTube Premium and Apple Music. Assuming that every student has at least one subscription, determine how many students have memberships to all three platforms: Spotify, YouTube Premium, and Apple Music.

Integer answerMARCH 15, 2026

MARCH 15, 2026

R=\{(a,c),(b,c),(d,c),(b,a)\}

be a relation on the set

A=\{a,b,c,d\}

. Determine the correct properties of

R

Multiple correctMARCH 15, 2026

A=\{4,5,6\}

B=\{4,7,8\}

C=\{4,6,7\}

, find the cardinality of

(A-B)\times(B\cap C)

Integer answerMARCH 15, 2026

An online degree programme offers the following courses: Level I: Mathematics, Statistics; Level II: Machine Learning Foundations, Mathematical Thinking; Level III: Deep Learning, Machine Learning Techniques, Advanced Algorithms. Every course in Level I is a prerequisite for every course in Level II, and every course in Level II is a prerequisite for every course in Level III. Let

M

be the set of all these courses and define two relations on

M

R = \{(A, B) \mid A

B

are courses in the same level

\}

S = \{(A, B) \mid A

is a prerequisite for

B\}

. Which of the following statements is/are correct?

Multiple correctOCTOBER 26, 2025

OCTOBER 26, 2025

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?

Integer answerOCTOBER 26, 2025

OCTOBER 26, 2025

S = \{a \mid a \in \mathbb{N},\, a \leq 10\}

R_1

R_2

be relations on

S \times S

R_1 = \{(x, y) \mid x, y \in S,\, y = 3x\}

R_2 = \{(x, y) \mid x, y \in S,\, y = x^2\}

. Find the cardinality of

R_1 \setminus R_2

Integer answerOCTOBER 26, 2025

OCTOBER 26, 2025

A

is the set of odd positive integers less than or equal to 20, and

B

is the set of positive integers less than or equal to 30 which are divisible by 5. Consider the following relation from

A

B

R_1 = \{(a, b) \mid a \in A,\; b \in B,\; a \text{ divides } b\}

Which of the following statements is correct?

Single correctJULY 13, 2025

A group of 500 students went to the college canteen and ordered some items. 285 students ordered ice-cream, 195 students ordered cold coffee, 115 students ordered cold drink, 45 students ordered ice-cream and cold drink, 70 students ordered cold coffee and ice-cream, 50 students ordered cold coffee and cold drink, and 50 students did not order anything. Find the number of students who ordered all three items.

Integer answerJULY 13, 2025

The Cartesian product

A \times A

has 9 elements. Two of the elements of the Cartesian product are

(1, 3)

(3, 7)

. Find the sum of all the elements in set

A

Integer answerFEBRUARY 23, 2025

FEBRUARY 23, 2025

X

be the set of natural numbers divisible by 100,

Y

be the set of natural numbers divisible by 25, and

Z

be the set of natural numbers that are perfect squares. Regions

A, B, C, D, E, F, G

are marked in the Venn diagram (a region can be empty). Which of the following options is/are correct?

Multiple correctFEBRUARY 23, 2025

FEBRUARY 23, 2025

Which of the following option(s) is/are true for the relation

R_1 = \{(x, y) : x, y \in \mathbb{R},\; x^2 + y^2 = 1\}

Single correctFEBRUARY 23, 2025

FEBRUARY 23, 2025

Which of the following relations is/are a one-one function?

Single correctFEBRUARY 23, 2025

FEBRUARY 23, 2025