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

Write the following in the simplest form:

`sin{2tan^-1sqrt((1-x)/(1+x))}`

Write the domain of the relation R defined on the set Z of integers as follows:-
(a, b) ∈ R ⇔ a² + b² = 25

If R = {(x, y) : x² + y² ≤ 4; x, y ∈ Z} is a relation on Z, write the domain of R.

Write the identity relation on set A = {a, b, c}.

Write the smallest reflexive relation on set A = {1, 2, 3, 4}.

If R = {(x, y) : x + 2y = 8} is a relation on N by, then write the range of R.

If R is a symmetric relation on a set A, then write a relation between R and R⁻¹.

Let R = {(x, y) : |x² − y²| <1) be a relation on set A = {1, 2, 3, 4, 5}. Write R as a set of ordered pairs.

If A = {2, 3, 4}, B = {1, 3, 7} and R = {(x, y) : x ∈ A, y ∈ B and x < y} is a relation from A to B, then write R⁻¹.

Let A = {3, 5, 7}, B = {2, 6, 10} and R be a relation from A to B defined by R = {(x, y) : x and y are relatively prime}. Then, write R and R⁻¹.

Define a reflexive relation ?

Define a symmetric relation ?

Define a transitive relation ?

Evaluate the following:

`sin(sin^-1  7/25)`

Define an equivalence relation ?

If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.

A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x, y) : y is one half of x; x, y ∈ A} is a relation on A, then write R as a set of ordered pairs.

Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b if "a is a divisor of b". Write R as a set of ordered pairs.

Evaluate the following:

`sin(cos^-1  5/13)`

State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive ?