NUMERICAL

Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, 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 _____________.

NUMERICAL

For $n \geq 2$, let $S_n$ denote the set of all subsets of $\{1,2, \ldots, n\}$ with no two consecutive numbers. For example $\{1,3,5\} \in S_6$, but $\{1,2,4\} \notin S_6$. Then $n\left(S_5\right)$ is equal to ________

MCQ_SINGLE

Let $A = {(x, y) ∈ R × R : |x + y| ⩾ 3}$ and $B = {(x, y) ∈ R × R : |x| + |y| ≤ 3}$. If $C = {(x, y) ∈ A ∩ B : x = 0$ or $y = 0}$, then $\sum_{(x, y) ∈ C} |x + y|$ is :

NUMERICAL

The number of elements in the set $\left\{n \in \mathbb{N}: 10 \leq n \leq 100\right.$ and $3^{n}-3$ is a multiple of 7$\}$ is ___________.

View All Questions