MCQ_SINGLE

Let $A = {1, 2, 3, …, 10}$ and $B = {\frac{m}{n} : m, n \in A, m < n$ and $gcd(m, n) = 1}$. Then $n(B)$ is equal to :

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 $R = {(P, Q) | P$ and $Q$ are at the same distance from the origin} be a relation, then the equivalence class of $(1, −1)$ is the set :

NUMERICAL

Let A = {n $ \in $ N: n is a 3-digit number} B = {9k + 2: k $ \in $ N} and C = {9k + $l$: k $ \in $ N} for some $l ( 0 < l < 9)$ If the sum of all the elements of the set A $ \cap $ (B $ \cup $ C) is 274 $ \times $ 400, then $l$ is equal to ________.

MCQ_SINGLE

Let $A = {1, 3, 4, 6, 9}$ and $B = {2, 4, 5, 8, 10}$. Let $R$ be a relation defined on $A \times B$ such that $R = {((a_1, b_1), (a_2, b_2)): a_1 \le b_2 \text{ and } b_1 \le a_2}$. Then the number of elements in the set R is :

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