Sets

Let S be the set of the first 11 natural numbers. Then the number of elements in A = \B S : n(B) 2 and the product of all elements of B is even\ is .

Let A = \x : |x2 - 10| 6\ and B = \x : |x - 2| > 1\. Then

1. A B = (- , 1] (2, )
2. B - A = (- , -4) (-2, 1) (4, )
3. A - B = [2, 3)
4. A B = [-4, -2] [3, 4]

Let A = \( , ) R R : | - 1| 4 and | - 5| 6\ and B = \( , ) R R : 16( - 2)2 + 9( - 6)2 144\. Then

1. A B
2. B A
3. neither A B nor B A
4. A B = \(x, y) : -4 x 4, -1 y 11\

Let A = \1, 6, 11, 16, \ and B = \9, 16, 23, 30, \ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then n(A B) is

1. 3814
2. 4003
3. 4027
4. 3761

Let A=\(x,y) :|x+y| 3\ and B=\(x,y) :|x|+|y| 3\. If C=\(x,y) :x=0 or y=0\, then (x,y) |x+y| is :

1. 18
2. 24
3. 15
4. 12

Let A=\1,2,3, ,10\ and B= \ mn:m,n A, m<n and (m,n)=1 \. Then n(B) is equal to :

1. 29
2. 31
3. 37
4. 36