PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.

The relation f is defined by f(x) = `{(x^2,0<=x<=3),(3x,3<=x<=10):}`

The relation g is defined by  g(x) = `{(x^2, 0 <= x <= 2),(3x,2<= x <= 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)}. Is the following true?

f is a relation from A to B

Justify your answer in case.

Which of the following collection are sets? Justify your answer:

 The collection of all girls in your class.

Which of the following collection is set? Justify your answer: 

The collection of ten most talented writers of India.

Which of the following collection are sets? Justify your answer: 

 The collection of difficult topics in mathematics.

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.

Which of the following collection are sets? Justify your answer:  

The collection of prime integers.

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: 

−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

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 Roster form: 

{x ∈ N : x² < 25}; 

Describe the following sets in Roster form: 

{x ∈ N : x is a prime number, 10 < x < 20};

Describe the following sets in Roster form: 

 {x ∈ N : x = 2n, n ∈ N};

Describe the following sets in Roster form: 

 {x ∈ R : x > x}.