Relations and F...

Let n (A) = m, and n (B) = n. Then the total number of non-empty relations that can be defined from A to B is

If \([x]^2\) – 5 [x] + 6 = 0, where [ . ] denote the greatest integer function, then

Range of f (x) = \(\frac{1}{1 - 2cosx}\) is

Let f (x) = \(\sqrt{1 + x^2}\), then

Domain of \(\sqrt{a^2 - x^2}(a > 0)\) is

If f (x) = ax + b, where a and b are integers, f (–1) = – 5 and f (3) = 3, then a and b are equal to

The domain of the function f defined by f (x) = \(\sqrt{4 - x} + \frac{1}{\sqrt{x^2 - 1}}\) is equal to

The domain and range of the real function f defined by f (x) = \(\frac{4 - x}{x - 4}\) is given by

The domain and range of real function f defined by f (x) = \(\sqrt{x - 1}\) is given by

The domain of the function f given by f(x) = \(\frac{x^2 + 2x + 1}{x^2 - x - 6}\)

The domain and range of the function f given by f (x) = 2 – |x - 5| is

The domain for which the functions defined by f (x) = \(3x^2\) – 1 and g (x) = 3 + x are equal is

If A = {1,2,3,4} and B = {5,6,7} then number of relations from A to B is equal to

For a set A, consider the following statements 

I. A ∪ P(A) = P(A) 

II. {A} ∩ P(A) = A

III. P (A) - {A} = P(A)

Where P denotes power set. Which of the statements given above is/are correct? 

Consider the universal set S = {0,1,2,3,4,5,6,7,8,9} and A = { 1,2,3,4 }, B = {2, 3, 5,6}, C = {2, 3, 7}, then

The value of B′ − A′ is