Sets

If tan(π/9), x, tan(7π/18) are in arithmetic progression and tan(π/9), y, tan(5π/18) are also in arithmetic progression, then |x - 2y| is equal to :
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In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?
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A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:
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Let U(i=1 to n)Xᵢ = U(i=1 to 50)Yᵢ = T, where each Xᵢ contains 10 elements and each Yᵢ contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xᵢ 's and exactly 6 of sets Yᵢ 's then n is equal to:

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

Let     A = <!-- [if gte mso 9]><xml> </xml><![endif]-->  $\left\{n\in N:nisa3-digitnumber\right\}$

B = <!-- [if gte mso 9]><xml> </xml><![endif]-->  $\left\{9k+2:k\in N\right\}$

And     C = $\left\{9k+\mathcal{l}:k\in N\right\}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> for some <!-- [if gte mso 9]><xml> </xml><![endif]-->  $\mathcal{l}\left(0<\mathcal{l}<9\right)$

If the sum of all the elements of the set <!-- [if gte mso 9]><xml> </xml><![endif]-->  $A\cap \left(B\cup C\right)$ is 274 × 400, then $\mathcal{l}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> is equal to___________.

The sum of all the elements in the set $\left\{n\in \left\{1,2,......,100\right\}|H.C.F.ofnand2040is1\right\}$ is equal to………

The numbers of elements in the set $\left\{n\in \left\{1,2,3,....100\right\}|{\left(11\right)}^n>{\left(10\right)}^n+{\left(9\right)}^n\right\}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> is………….