Question

Of the members of three athletic teams in a school, $$21$$ are in the cricket team, $$26$$ are in the hockey team and $$29$$ are in the football team. Among them, $$14$$ play hockey and cricket, $$15$$ play hockey and football, and $$12$$ play football and cricket. Eight play all the three games. The total number of members in the three athletic teams is :

A. $$43$$  
B. $$76$$
C. $$49$$
D. none of these
Answer :   $$43$$
Solution :
$$\eqalign{ & n(C) = 21,\,\,n(H) = 26,\,\,n(F) = 29,\,\,n\left( {H \cap C} \right) = 14, \cr & n(H \cap F) = 15,\,\,n(F \cap C) = 12,\,\,n(C \cap H \cap F) = 8 \cr & \therefore n(C \cup H \cup F) = n(C) + n(H) + n(F) - n(H \cap C) - n(H \cap F) - n(F \cap C) + n(C \cap H \cap F) \cr & = 21 + 26 + 29 - 14 - 15 - 12 + 8 \cr & = 43. \cr} $$

Releted MCQ Question on
Calculus >> Sets and Relations

Releted Question 1

If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$   equals.

A. $$X$$
B. $$Y$$
C. $$\phi $$
D. None of these
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Releted Question 2

The expression $$\frac{{12}}{{3 + \sqrt 5 + 2\sqrt 2 }}$$    is equal to

A. $$1 - \sqrt 5 + \sqrt 2 + \sqrt {10} $$
B. $$1 + \sqrt 5 + \sqrt 2 - \sqrt {10} $$
C. $$1 + \sqrt 5 - \sqrt 2 + \sqrt {10} $$
D. $$1 - \sqrt 5 - \sqrt 2 + \sqrt {10} $$
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Releted Question 3

If $${x_1},{x_2},.....,{x_n}$$    are any real numbers and $$n$$ is any positive integer, then

A. $$n\sum\limits_{i = 1}^n {{x_i}^2 < {{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$
B. $$\sum\limits_{i = 1}^n {{x_i}^2 \geqslant {{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$
C. $$\sum\limits_{i = 1}^n {{x_i}^2 \geqslant n{{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$
D. none of these
View Answer
Releted Question 4

Let $$S$$ = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of $$S$$ is equal to

A. 25
B. 34
C. 42
D. 41
View Answer

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Sets and Relations

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