Sets

The number of elements in the set $\left\{z=a+ib\in C:a,b\in Zand1<\left|z-3+2i\right|<4\right\}$  is……….

The number of elements in the set $\left\{z=a+ib\in C:a,b\in Zand1<\left|z-3+2i\right|<4\right\}$  is……….

Let A = $\left\{1,a_1,a_2....a_{18},77\right\}$  be a set of integers with 1 < a₁ < a₂ < … < a₁₈ < 77. Let the set A + A = $\left\{x+y:x,y\in A\right\}$  contains exactly 39 elements. Then, the value of a₁ + a₂ +…. + a₁₈ is equal to…………

If f(A, B) = $\frac{1+sinA}{cosA}+\frac{cosB}{1-sinB}$ and g(A, B) = $\frac{\left(sinA-sinB\right)}{sin\left(A-B\right)+cosA-cosB}$ and h(A,B) = $\frac{f(A,B)}{g(A,B)}$ then the value of $h\left(18°,36°\right).$  (wherever defined)

If n(A U B U C) + n((A U B U C)') = 50, n(A)=10, n(B)=15, n(C)=20, n(A∩B)=5, n(B∩C)=6, n(C∩A)=10, n(A∩B∩C)=5, then the value of n(A U B U C)'

There are two sets A = {a: a ∈ N and –3 ≤ a ≤ 5} and B = {b: b ∈ Z and 0 ≤ b ≤ 4}. The number of elements common in A * B and B * A are

If the number of distinct positive rational numbers $\frac{p}{q}$  smaller than 1, where p, q $\in \{1,2,3......,6\}$  is k then k is

The number of elements in the set {(a,b) : 2a² + 3b² = 35, a,b ∈ Z}, where Z is the set of all integers, is :

Let     A = $\left\{n\in N:nisa3-digitnumber\right\}$

B =  $\left\{9k+2:k\in N\right\}$

And     C = $\left\{9k+\mathcal{l}:k\in N\right\}$  for some   $\mathcal{l}\left(0<\mathcal{l}<9\right)$

If the sum of all the elements of the set  $A\cap \left(B\cup C\right)$  is 274 * 400, then $\mathcal{l}$  is equal to___________.

Let A = {n∈N|n² ≤ n + 10,000}, B = {3k + 1|k ∈ N} and C = {2k|k∈ N}, then the sum of all the elements of the set A ∩ (B-C) is equal to……