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Detailed Solution for Test: Counting Theorems - Question 1

Test: Counting Theorems - Question 2

In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?

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Test: Counting Theorems - Question 3

Let A and B be two finite disjoint sets such that n(A ∪ B) = 475 and n(A) = 435, then n(B) is

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Test: Counting Theorems - Question 4

If n(A) + n(B) + n(C) = n(A U B U C) then what are the sets A, B, C are called?

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Test: Counting Theorems - Question 5

If in class XI of a certain school, 24 students got distinction in mathematics, 19 students got distinction in physics and 15 students got distinction in both the subjects, then the number of students in class XI is:

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Test: Counting Theorems - Question 6

There is a group of 80 persons who can drive scooter or car or both. Out of these, 35 can drive scooter and 60 can drive car. Find how many can drive both scooter and car? How many can drive scooter only? How many can drive car only?(Respectively)

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Test: Counting Theorems - Question 7

If P and Q are two sets such that n(P) = 120, n(Q) = 50 and n(P ∪ Q) = 140 then, n(P ∩ Q) is:

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Test: Counting Theorems - Question 8

If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets* A *× *B* and* B *× *A* are

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Test: Counting Theorems - Question 9

If U = 100, n(A) = 30, n(B) = 40, n(A ∩ B) = 10, then n( A' ∩ B' ) =

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Test: Counting Theorems - Question 10

The number of non-empty subsets of the set {1, 2, 3, 4} is

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Test: Counting Theorems - Question 11

A group of 120 students, 90 take mathematics and 72 take economics. If 10 students take neither of the two, how many students take both:

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Test: Counting Theorems - Question 12

In a class of 50 students, 35 students play cricket and 30 students play football; identify the students playing both the games.

Test: Counting Theorems - Question 13

In a class of 40 students 14 take physics and 29 take chemistry. If 5 students take both, how many students take neither of the subjects?

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Test: Counting Theorems - Question 16

A,B,C are three sets such that n(A) = 25, n(B) = 20, n(c) = 27, n(A ∩ B) = 5, n(B ∩ C ) = 7 and A ∩ C = ∅ then n(A ∪ B ∪ C) is equal to

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Test: Counting Theorems - Question 17

In a factory 70% of the workers like oranges and 64% like apples. If x% like both oranges and apples, then

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