Advertisements
Advertisements
प्रश्न
If n(A ∪ B ∪ C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ∩ C) = 15, n(A ∩ C) = 25 and n(A ∩ B ∩ C) = 10, then the value of x is
विकल्प
10
15
25
30
Advertisements
उत्तर
15
Explanation;
Hint:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)
100 = 4x + 6x + 5x – 20 – 15 – 25 + 10
100 = 15x – 50
⇒ 150 = 15x
⇒ x = `150/15`
= 10
APPEARS IN
संबंधित प्रश्न
Write the cardinal number of the following set:
A = {0, 1, 2, 4}
Write the cardinal number of the following set:
F = {Whole numbers from 8 to 14}
Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.
Find: n(A ∪ D)
State true or false for the following. Correct the wrong statement.
If A = {0}, then n(A) = 0
In an examination 50% of the students passed in Mathematics and 70% of students passed in Science while 10% students failed in both subjects. 300 students passed in both the subjects. Find the total number of students who appeared in the examination, if they took examination in only two subjects
In a colony, 275 families buy Tamil newspaper, 150 families buy English newspaper, 45 families buy Hindi newspaper, 125 families buy Tamil and English newspaper, 17 families buy English and Hindi newspapers, 5 families buy Tamil and Hindi newspaper and 3 families buy all the three newspaper. If each family buy atleast one of these newspaper then find Number of families buy only one newspaper
In a colony, 275 families buy Tamil newspaper, 150 families buy English newspaper, 45 families buy Hindi newspaper, 125 families buy Tamil and English newspaper, 17 families buy English and Hindi newspapers, 5 families buy Tamil and Hindi newspaper and 3 families buy all the three newspaper. If each family buy atleast one of these newspaper then find Number of families buy atleast two newspaper
A survey of 1000 farmers found that 600 grew paddy, 350 grew ragi, 280 grew corn, 120 grew paddy and ragi, 100 grew ragi and corn, 80 grew paddy and corn. If each farmer grew atleast anyone of the above three, then find the number of farmers who grew all the three.
Each student in a class of 35 plays atleast one game among chess, carrom and table tennis. 22 play chess, 21 play carrom, 15 play table tennis, 10 play chess and table tennis, 8 play carrom and table tennis and 6 play all the three games. Find the number of students who play chess and carrom but not table tennis (Hint: Use Venn diagram)
Which symbol is used to denote the cardinality of a set A?
