CAT 2025 Lesson : Class Discussion: Modern Maths - Set Theory: 1 to 8

Class Discussion: Set theory

Question 1

The set {1, 4} is equal to which of the following?

(a) {

|x| : x^{2} – 3x – 4 = 0

, x ɛ R}
(b) {

x : x^{2} + 5x + 4 = 0,

x ɛ R}
(c) {

x^{2} : x < 3,

x ɛ N}

		a only
		a & b only
		a & c only
		b & c only

Question 2

The sum of each of the elements of the set {

x^{2} – 5 : x^{2} + x – 20 = 0

, x ɛ N} is

		5
		11
		31
		45

Question 3

How many integers exist between 1 and 200 (both inclusive) which are not multiples of 3 or 5?

Answer: 107

Question 4

How many integers exist between 1 and 200 (both inclusive) which are not multiples of 3, 5 or 7?

Answer: 92

Question 5

In a class, 88% of the students play cricket, 42% play hockey and 62% play football. If every student plays at least one sport and 76% of the students play at least 2 games, then what percentage of the students play all 3 sports?

Answer: 16

Question 6

In a class, 88% of the students play cricket, 42% play hockey and 62% play football. If 24% of the students play exactly 1 sport, then what is the maximum possible percentage of students who can play all 3 sports?

Answer: 40

Question 7

Three-fourth of the students in a class passed in maths, while 40% of them passed in science. If one-fourth of those who failed in science also failed in maths, then what percentage of the students who passed in maths also passed in science?

		20%
		25%
		30%
		40%

Question 8

In a class of 150 students, 140 have visited Europe, 125 have visited Africa, 110 have visited South America, 130 have visited North America and 120 have visited Australia. The minimum number of students in the class who must have visited all 5 of these continents is

Answer: 25

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