PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Let R = {(a, a³) : a is a prime number less than 5} be a relation. Find the range of R.

Let R be the equivalence relation on the set Z of the integers given by R = { (a, b) : 2 divides a - b }.

Write the equivalence class [0].

For the set A = {1, 2, 3}, define a relation R on the set A as follows:
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Write the ordered pairs to be added to R to make the smallest equivalence relation.

Let A = {0, 1, 2, 3} and R be a relation on A defined as
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}
Is R reflexive? symmetric? transitive?

Evaluate the following:

`sin(tan^-1  24/7)`

Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : | a²- b² | < 8}. Write R as a set of ordered pairs.

Let the relation R be defined on N by aRb iff 2a + 3b = 30. Then write R as a set of ordered pairs

Write the smallest equivalence relation on the set A = {1, 2, 3} ?

Let R be a relation on the set N given by
R = {(a, b) : a = b − 2, b > 6}. Then,

Evaluate the following:

`sin(sec^-1  17/8)`

If a relation R is defined on the set Z of integers as follows:
(a, b) ∈ R ⇔ a² + b² = 25. Then, domain (R) is ___________

R is a relation on the set Z of integers and it is given by
(x, y) ∈ R ⇔ | x − y | ≤ 1. Then, R is ______________ .

The relation R defined on the set A = {1, 2, 3, 4, 5} by
R = {(a, b) : | a² − b² | < 16} is given by ______________ .

Evaluate the following:

`cosec(cos^-1  3/5)`

Let R be the relation over the set of all straight lines in a plane such that  l₁ R l₂ ⇔ l ₁⊥ l₂. Then, R is _____________ .

Evaluate the following:

`sec(sin^-1  12/13)`

If A = {a, b, c}, then the relation R = {(b, c)} on A is _______________ .

Let A = {2, 3, 4, 5, ..., 17, 18}. Let '≃' be the equivalence relation on A × A, cartesian product of Awith itself, defined by (a, b) ≃ (c, d) if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is _______________ .

Let A = {1, 2, 3}. Then, the number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is ______.

Evaluate the following:

`tan(cos^-1  8/17)`