Advertisements
Advertisements
Question
In a class of 200 students who appeared in certain examinations, 35 students failed in CET, 40 in NEET and 40 in JEE, 20 failed in CET and NEET, 17 in NEET and JEE, 15 in CET and JEE, and 5 failed in all three examinations. Find how many students, did not fail in any examination.
Solution
Let A = set of students who failed in CET
B = set of students who failed in NEET
C = set of students who failed in JEE
X = set of all students
∴ n(X) = 200, n(A) = 35, n(B) = 40, n(C) = 40, n(A ∩ B) = 20, n(B ∩ C) = 17, n(A ∩ C) = 15 and n(A ∩ B ∩ C) n = 5
n(A ∪ B ∪ C)
= n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C)
= 35 + 40 + 40 − 20 − 17 − 15 + 5
= 68
∴ No. of students who did not fail in any exam
= n(X) − n(A ∪ B ∪ C)
= 200 − 68
= 132
APPEARS IN
RELATED QUESTIONS
Identify whether the following is set or not? Justify your answer.
The collection of all even integers.
Write the following set in the set-builder form:
{3, 6, 9, 12}
List all the elements of the following set:
C = {x : x is an integer, x2 ≤ 4}
Which of the following collection are sets? Justify your answer:
The collection of difficult topics in mathematics.
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:
−2 ...... A
Describe the following sets in Roster form:
{x : x is a letter before e in the English alphabet}
Describe the following sets in set-builder form:
B={1,1/2 ,1/3, 1/4,1/5,...........};
Describe the following sets in set-builder form:
C = {0, 3, 6, 9, 12, ...}
Describe the following sets in set-builder form:
D = {10, 11, 12, 13, 14, 15};
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ b, c \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \in A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[a \in A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\phi \in A\]
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[\phi \in A\]
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[\phi \in A\]
Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true?
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
0 ____ A
Describe the following set in Roster form
A = {x/x is a letter of the word 'MOVEMENT'}
Describe the following set in Roster form
C = {x/x = 2n + 1, n ∈ N}
Describe the following set in Set-Builder form
{0}
Describe the following set in Set-Builder form
{0, ±1, ±2, ±3}
Describe the following set in Set-Builder form
{0, –1, 2, –3, 4, –5, 6, ...}
If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∪ B ∪ C).
In a class of 200 students who appeared in certain examinations, 35 students failed in CET, 40 in NEET and 40 in JEE, 20 failed in CET and NEET, 17 in NEET and JEE, 15 in CET and JEE, and 5 failed in all three examinations. Find how many students, failed in NEET or JEE entrance
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 neither Marathi and English newspaper
Answer the following:
Write down the following set in set-builder form
{a, e, i, o, u)
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 n + 1
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 Mathematics and Science but not in English
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 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 at least one of the three languages
In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Then, the number of students who play neither is ______.
