NUMERICAL

Let A = {n $\in$ N | n2 $\le$ n + 10,000}, B = {3k + 1 | k$\in$ N} an dC = {2k | k$\in$N}, then the sum of all the elements of the set A $\cap$(B $-$ C) is equal to _____________.

MCQ_SINGLE

If $R = {(x, y) : x, y \in Z, x^2 + 3y^2 \le 8}$ is a relation on the set of integers $Z$, then the domain of $R^{-1}$ is :

NUMERICAL

Let $A=\{1,2,3,4,5,6,7\}$ and $B=\{3,6,7,9\}$. Then the number of elements in the set $\{C \subseteq A: C \cap B \neq \phi\}$ is ___________.

MCQ_SINGLE

Let $R$ be the set of real numbers. Statement I: $A = \{(x, y) \in R \times R: y - x \text{ is an integer }\}$ is an equivalence relation on $R$. Statement II: $B = \{(x,y) \in R \times R: x = \alpha y \text{ for some rational number } \alpha\}$ is an equivalence relation on $R$.

MCQ_SINGLE

Let $S = {1, 2, 3, … , 100}$. The number of non-empty subsets A of S such that the product of elements in A is even is :

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