NUMERICAL

Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n $\ge$ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 $-$ R2 is _______________.

MCQ_SINGLE

Let $Z$ be the set of integers. If $A = {x \in Z : 2(x + 2) (x^2 - 5x + 6) = 1}$ and $B = {x \in Z : -3 < 2x - 1 < 9}$, then the number of subsets of the set $A \times B$, is

NUMERICAL

Let $A=\{1,2,3, \ldots, 20\}$. Let $R_1$ and $R_2$ two relation on $A$ such that $R_1=\{(a, b): b$ is divisible by $a\}$ $R_2=\{(a, b): a$ is an integral multiple of $b\}$. Then, number of elements in $R_1-R_2$ is equal to _____________.

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 :

NUMERICAL

Let X = {n $ \in $ N : 1 $ \le $ n $ \le $ 50}. If A = {n $ \in $ X: n is a multiple of 2} and B = {n $ \in $ X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.

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