Sets and Relations

The shaded region in the Venn diagram represents

$\begin{aligned} &\begin{aligned} & \text { A, B, C are subsets of the Universal set U } \\ & \text { If } \mathrm{A}=\{x: x \text { is even number, } x \leq 20\} \\ & \mathrm{B}=\{x: x \text { is multiple of } 3, x…

The number of elements in the set $S=\{x \in \mathbb{Z}$ : $x^2-7 x+6 \leq 0$ and $\left.x^2-3 x>0\right\}$ is

In a committee of 25 members, each member is proficient either in Mathematics or in Statistics or in both. If 19 of them are proficient in Mathematics and 16 of them are proficient in Statistics, then the probability…

If set A contains 8 elements then number of subsets of $A$ which contain at least 6 elements is

If $A$ and $B$ are any two events of a sample space, then set-theoretic description for the event: "Exactly one of the events A, B to occur" is (Here $\mathrm{E}^{\mathrm{c}}$ denotes the compliment of the event…

Let $f(x)=|x-3|+|x+5|$ and $A=\left\{a \in \mathbb{R} / \lim _{x \rightarrow a} \frac{f(x)-f(a)}{x-a}\right.$ exists $\}$ Then the number of real numbers which are in $(-\infty,-3)$ $\cup(5, \infty)$ but not in $A$ is

If $A=\{(a, b): 4 a=5 b ; a, b \in\{1,2,3, \ldots 30\}\}$, then the number of such ordered pairs $(a, b)$ is

If a set $A$ has $m$ elements and set $B$ has $n$ elements and the number of injections from $A$ to $B$ is 2520 . Then, $m$ is equal to

Let \(a, b, c\) be real numbers. A set formed with \(a, b, c\) whose order of occurrence is preassigned is called

205 students take an examination of whom 105 pass in English, 70 students pass in Mathematics and 30 students pass in both. How many students fail in both subjects?

$\begin{array}{l} \text { If } \mathrm{A} \text { and } \mathrm{B} \text { are subsets of universal set } \mathrm{X} \text { such that } \mathrm{n}(\mathrm{X})=200, \mathrm{n}(\mathrm{A})=90, \mathrm{n}(\mathrm{B})=80…