Sets

Let A = {1, 2, 3, 4, 5, 6, 7}. Define B = $B=\left\{T\subseteq A:either1\notin Tor2\in T\right\}$ and $C=\left\{T\subseteq A:TthesumofalltheelementsofTisaprimenumber\right\}.$ Then the number of elements in the set $B\cup C$ is

Let A = $\left\{z\in C:1\le |z-\left(1+i\right)\le 2\right\}$ and B = $\left\{z\in A:|z-\left(1-i\right)|=1\right\}$ . Then, B :

Let the image of the point P(1, 2, 3) in the line $L:\frac{x-6}{3}=\frac{y-1}{2}=\frac{z-2}{3}$  be Q $LetR\left(\alpha ,\beta ,\gamma \right)$ .  be a point that divides internally the line segment PQ in the ration 1 : 3. Then the value of $22\left(\alpha +\beta +\gamma \right)$  is equal to………….

The sum of the cubes of all the roots of the equation $x^4-3x^3-2x^2+3x+1=0$ is

Let f : R R satisfy $f\left(x+y\right)=2^{x}f\left(y\right)+4^{y}f\left(x\right),\forall x,y\in \text{?}R\text{?}.$ ${}^{}{}^{}$ If f(2) = 3, then $14.\frac{f\text{'}\left(4\right)}{f\text{'}\left(2\right)}$ $\frac{}{}$ is equal to……….

The number of elements in the set

$S=\left\{\theta \in \left[-4\pi ,4\pi \right]:3co{s}^{2}2\theta +6cos2\theta -10co{s}^2\theta +5=0\right\}$ is…………….

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

Let $S=[-\pi ,\frac{\pi }{2})-\left\{-\frac{\pi }{2},-\frac{\pi }{4},-\frac{3\pi }{4},\frac{\pi }{4}\right\}.$ Then the number of elements in the set $|A=\left\{\theta \in S:tan\theta \left(1+\sqrt[]{5}tan\left(2\theta \right)\right)=\sqrt[]{5}-tan\left(2\theta \right)\right\}$ is……….

Let S = $\left\{x\in \left[-6,3\right]-\left\{-2,2\right\}:\frac{\left|x+3\right|-1}{\left|x\right|-2}\ge 0\right\}$ and T = $\left\{x\in Z:x^2-7\left|x\right|+9\le 0\right\}.$ Then the number of element is $S\cap T$ is :

A survey shows that $63\mathrm{\%}$ of the people in a city read newspaper $A$ whereas $76\mathrm{\%}$ read newspaper $B$ . if $x\mathrm{\%}$ of the people read both the newspapers, then a possible value of $x$ can be: