In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

 chapter 1 miscellaneous sets ncert cbse

13. In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many
students were taking neither tea nor coffee?

 

let A =set of students taking tea

B = set of students taking coffee

U = universal set 

n(U) =600

n(A)  = 150

n(B) =225

n(A intersection B) =100

n(A union B) = n(A) + n(B) - n(A intersection B) 

                    = 150 + 225 -100 =275

 

number of students were taking neither tea nor coffee

= n(U)  - n(A union B)

= 600 -275

=325 

14. In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

let A = set of students who know hindi

B = set of students who know english

n(A) =100

n(B) = 50

n(A intersection B) =25

 

n(A union B) = n(A) + n(B) - n(A intersection B) 

 =100 + 50 -25 = 125

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 chapter 1 miscellaneous sets ncert cbse

13. In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many
students were taking neither tea nor coffee?

solution

 

14. In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group? 

solution

11th cbse ncert chapter 2 relations and functions miscellaneous exercise

 

12. Let A = {9,10,11,12,13} and let f : A → N be defined by f (n) = the highest prime factor of n. Find the range of f.

solution

 

11. Let f be the subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a
function from Z to  Z? Justify your answer.

solution

 

10. Let A ={1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5), (2,9), (3,1), (4,5), (2,11)}
Are the following true?
(i) f is a relation from A to B
(ii) f is a function from A to B.
Justify your answer in each case.

solution 

 

9. Let R be a relation from N to N defined by

 R = {(a, b) : a, b ∈ N and a = (b^2) }. 

Are the following true?
(i) (a,a) ∈ R, for all a ∈ N
(ii) (a,b) ∈ R, implies (b,a) ∈ R
(iii) (a,b) ∈ R, (b,c) ∈ R implies (a,c) ∈ R.

 solution 

 

 8. Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by
f(x) = ax + b, for some integers a, b. Determine a, b.

solution  

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