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

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 _______________ .

Let A = {1, 2, 3} and B = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ________________ .

If R is the largest equivalence relation on a set A and S is any relation on A, then _____________ .

If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by x R y ⇔ y = 3 x, then R = _____________ .

Prove the following result

`cos(sin^-1  3/5+cot^-1  3/2)=6/(5sqrt13)`

Prove the following result-

`tan^-1  63/16 = sin^-1  5/13 + cos^-1  3/5`

If R is a relation on the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3)}, then R is ____________ .

Prove the following result

`sin(cos^-1  3/5+sin^-1  5/13)=63/65`

Solve: `cos(sin^-1x)=1/6`

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

If A = {1, 2, 3}, then a relation R = {(2, 3)} on A is _____________ .