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

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)`

The relation 'R' in N × N such that
(a, b) R (c, d) ⇔ a + d = b + c is ______________ .

Evaluate the following:

`cot(cos^-1  3/5)`

If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by 'x is greater than y'. The range of R is ______________ .

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : x R y ⇔ x is relatively prime to y. Then, domain of R is ______________ .

Evaluate the following:

`cos(tan^-1  24/7)`

A relation ϕ from C to R is defined by x ϕ y ⇔ | x | = y. Which one is correct?

Let R be a relation on N defined by x + 2y = 8. The domain of R is _______________ .

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x − 3. Then, R⁻¹ is ______________ .

Prove the following result

`tan(cos^-1  4/5+tan^-1  2/3)=17/6`

Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is _______________ .