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

Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, add a minimum number of ordered pairs so that the enlarged relation is symmeteric, transitive and reflexive.

Let A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A.

Let A = {a, b, c} and the relation R be defined on A as follows: R = {(a, a), (b, c), (a, b)}. Then, write minimum number of ordered pairs to be added in R to make it reflexive and transitive.

Defines a relation on N :
  x > y, x, y ∈  N

Determine the above relation is reflexive, symmetric and transitive.

Evaluate the following:

`\text(cosec)^-1(\text{cosec}  pi/4)`

Evaluate the following:

`cosec^-1(cosec  (3pi)/4)`

Evaluate the following:

`cosec^-1(cosec  (6pi)/5)`

Defines a relation on N :

x + y = 10, x, y∈ N

Determine the above relation is reflexive, symmetric and transitive.

Evaluate the following:

`cosec^-1(cosec  (11pi)/6)`

Defines a relation on N:

xy is square of an integer, x, y ∈ N

Determine the above relation is reflexive, symmetric and transitive.

Evaluate the following:

`cosec^-1(cosec  (13pi)/6)`

Defines a relation on N:

x + 4y = 10, x, y ∈ N

Determine the above relation is reflexive, symmetric and transitive.

Evaluate the following:

`cosec^-1{cosec  (-(9pi)/4)}`

Evaluate the following:

`cot^-1(cot  pi/3)`

Evaluate the following:

`cot^-1(cot  (4pi)/3)`

Evaluate the following:

`cot^-1(cot  (9pi)/4)`

Show that the relation R defined by R = {(a, b) : a – b is divisible by 3; a, b ∈ Z} is an equivalence relation.

Evaluate the following:

`cot^-1(cot  (19pi)/6)`

Evaluate the following:

`cot^-1{cot (-(8pi)/3)}`

Evaluate the following:

`cot^-1{cot  ((21pi)/4)}`