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

Evaluate the following:

`cos^-1{cos  ((4pi)/3)}`

Evaluate the following:

`cos^-1{cos  (13pi)/6}`

Evaluate the following:

`cos^-1(cos3)`

Evaluate the following:

`cos^-1(cos4)`

Evaluate the following:

`cos^-1(cos5)`

Evaluate the following:

`cos^-1(cos12)`

Evaluate the following:

`tan^-1(tan  pi/3)`

Evaluate the following:

`tan^-1(tan  (6pi)/7)`

Evaluate the following:

`tan^-1(tan  (7pi)/6)`

Evaluate the following:

`tan^-1(tan  (9pi)/4)`

Evaluate the following:

`tan^-1(tan1)`

Evaluate the following:

`tan^-1(tan2)`

Evaluate the following:

`tan^-1(tan4)`

Evaluate the following:

`tan^-1(tan12)`

If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?

If A = {1, 2, 3, 4} define relations on A which have properties of being symmetric but neither reflexive nor transitive ?

If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?

Let R be a relation defined on the set of natural numbers N as
R = {(x, y) : x, y ∈ N, 2x + y = 41}
Find the domain and range of R. Also, verify whether R is (i) reflexive, (ii) symmetric (iii) transitive.

Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.

Evaluate the following:

`sec^-1(sec  pi/3)`