MCQ_SINGLE

Define a relation R on the interval $[0, π/2)$ by $x$ R $y$ if and only if $\sec^2x - \tan^2y = 1$. Then R is :

MCQ_SINGLE

Let $\bigcup_{i=1}^{50} X_i = \bigcup_{i=1}^{n} Y_i = T$ where each $X_i$ contains $10$ elements and each $Y_i$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_i$'s and exactly $6$ of sets $Y_i$'s, then $n$ is equal to:

MCQ_SINGLE

Let $S = {1, 2, 3, …, 10}$. Suppose $M$ is the set of all the subsets of $S$, then the relation $R = {(A, B) : A ∩ B ≠ 𝜙; A, B ∈ M}$ is :

MCQ_SINGLE

Let $S = \mathbb{N} \cup \{0\}$. Define a relation R from S to $\mathbb{R}$ by: $R = \{(x, y) : \log_e y = x \log_e (\frac{2}{5}), x \in S, y \in \mathbb{R}\}$. Then, the sum of all the elements in the range of $R$ is equal to:

MCQ_SINGLE

Let $A$ be the set of all functions $f: Z \rightarrow Z$ and $R$ be a relation on $A$ such that $R = {(f, g): f(0) = g(1) \text{ and } f(1) = g(0)}$. Then $R$ is :

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