Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
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 Mathematics only, c = 3.
APPEARS IN
संबंधित प्रश्न
Identify whether the following is set or not? Justify your answer.
The collection of all even integers.
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:
{2, 4, 6, …}
List all the elements of the following set:
D = {x : x is a letter in the word “LOYAL”}
Which of the following collection are sets? Justify your answer:
The collection of all girls in your class.
Which of the following collection are sets? Justify your answer:
A collection of novels written by Munshi Prem Chand.
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:
−4 ...... A
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:
9 ...... A
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:
0 ...... A
Describe the following sets in Roster form:
{x ∈ N : x = 2n, n ∈ N};
Write the set of all vowels in the English alphabet which precede q.
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.
\[a \in {\left\{ a \right\}, b}\]
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\phi \subset \left\{ a, b, c \right\}\]
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?
\[\left\{ a, b, c \right\} \subset A\]
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[1 \in A\]
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? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
Prove that:
\[A \subseteq B, B \subseteq C \text{ and } C \subseteq A \Rightarrow A = C .\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
8 ____ A
Describe the following set in Set-Builder form
{0, ±1, ±2, ±3}
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
In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take bot tea and coffee, 8 students take both milk and coffee. None of them take tea and milk both and everyone takes at least one beverage, find the total number of students in the hostel.
Write the following interval in Set-Builder form
`(-∞, 5]`
State which of the following statement are true and which are false. Justify your answer.
37 ∉ {x | x has exactly two positive factors}
Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n + 5 = 8
Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n is greater than 4
Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}
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 and Science but not in English
Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then ______.
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 ______.
Let S = {x | x is a positive multiple of 3 less than 100}
P = {x | x is a prime number less than 20}. Then n(S) + n(P) is ______.
If A and B are any two sets, then A – B is equal to ______.
Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.
