Advertisements
Advertisements
Question
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in more than one subject only
Advertisements
Solution
Let the number of students passed in Mathematics M, E be in English and S be in Science.
Then n(U) = 100
n(M) = 12
n(E) = 15
n(S) = 8
n(E ∩ M) = 6
n(M ∩ S) = 7
n(E ∩ S) = 4
And n(E ∩ M ∩ S) = 4
Let us draw a Venn diagram.
According to the Venn diagram, we get
a + b + d + e = 15 ......(i)
b + c + e + f = 12 ......(ii)
d + e + f + g = 8 .....(iii)
n(E ∩ M) = 6
∴ b + e = 6 ......(iv)
n(M ∩ S) = 7
∴ e + f = 7 ......(v)
n(E ∩ S) = 4
∴ d + e = 4 ......(vi)
And n(E ∩ M ∩ S) = 4
∴ e = 4 ......(vii)
From equation (iv) and (vii)
We get b + 4 = 6
∴ b = 2
From equation (v) and (vii)
We get 4 + f = 7
∴ f = 3
From equation (vi) and (vii)
We get d + 4 = 4
∴ d = 0
From equation (i) we get
a + b + d + e = 15
⇒ a + 2 + 0 + 4 = 15
⇒ a = 9
From equation (ii)
b + c + e + f = 12
⇒ 2 + c + 4 + 3 = 12
⇒ c = 3
From equation (iii)
d + e + f + g = 8
⇒ 0 + 4 + 3 + g = 8
⇒ g = 1
∴ Number of students who passed in more than one subject = b + e + d + f = 2 + 4 + 0 + 3 = 9.
APPEARS IN
RELATED QUESTIONS
Identify whether the following is set or not? Justify your answer.
A collection of novels written by the writer Munshi Prem Chand.
Identify whether the following is set or not? Justify your answer.
The collection of questions in this Chapter.
Write the following set in roster form:
A = {x : x is an integer and –3 ≤ x < 7}
Write the following set in the set-builder form:
{5, 25, 125, 625}
List all the elements of the following set:
F = {x : x is a consonant in the English alphabet which precedes k}.
Which of the following collection are sets? Justify your answer:
A collection of novels written by Munshi Prem Chand.
Which of the following collection are sets? Justify your answer:
The collection of all question in this chapter.
If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space:
12 ...... A
Describe the following sets in Roster form:
{x ∈ R : x > x}.
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]
Which of the following statements are correct?
Write a correct form of each of the incorrect statement.
\[a \in {\left\{ a \right\}, b}\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \subset A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\phi \in A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\phi \in A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
Let \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\] Which of the following are true? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
Write down all possible proper subsets each of the following set:
{1, 2},
Write down all possible proper subsets each of the following set:
{1, 2, 3}
Prove that:
\[A \subseteq B, B \subseteq C \text{ and } C \subseteq A \Rightarrow A = C .\]
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, = {2, 4, 6, 8} and C = {3, 4, 5, 6}.
Find \[\left( A \cap C \right)'\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
0 ____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
2 _____ A
Describe the following set in Set-Builder form
{0}
From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read Only one of the newspapers
Write the following interval in Set-Builder form.
(2, 5]
A college awarded 38 medals in volleyball, 15 in football, and 20 in basketball. The medals awarded to a total of 58 players and only 3 players got medals in all three sports. How many received medals in exactly two of the three sports?
Answer the following:
In a survey of 425 students in a school, it was found that 115 drink apple juice, 160 drink orange juice, and 80 drink both apple as well as orange juice. How many drinks neither apple juice nor orange juice?
Given that E = {2, 4, 6, 8, 10}. If n represents any member of E, then, write the following sets containing all numbers represented by n2
Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}
Write the following sets in the roaster form:
F = {x | x4 – 5x2 + 6 = 0, x ∈ R}
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in English and Mathematics but not in Science.
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in Mathematics only
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study English only
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study French and Sanskrit but not English
A survey shows that 63% of the people watch a News Channel whereas 76% watch another channel. If x% of the people watch both channel, then ______.
Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.
