List of practice Questions

Let the sets A and B denote the domain and range respectively of the function \(f(x)=\frac{1}{\sqrt[x]-x}\) where [x] denotes the smallest integer greater than or equal to x . Then among the statements 
(S1) : A ∩ B = (1, ∞) – N and  
(S2) : A ∪ B = (1, ∞) 

Which of the following statement is a tautology?

Let S = {E₁, E₂, ……………., E₈} be a sample space of a random experiment such that \(P(E_n) = \frac{n}{36}\) for every n = 1, 2, ………, 8. Then the number of elements in the set\(\{ A \subseteq S : P(A) \geq \frac{4}{5} \}\) is_________.

The number of elements in the set S= {x∈R : 2cos⁡\((\frac{x_2+x}{6})\)=\(4^x+4^{-x}\)}

Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$Then $R$ is