List of top Mathematics Questions on types of sets

Let S be the set of values of λ, for which the system of equations  
6λx – 3y + 3z = 4λ2 ,  
2x + 6ly + 4z = 1, 
3x + 2y + 3λz = l has no solution. Then  12∑λ∈S ∑ _{λ ∈ S} | λ | 12 ∑ λ ∈ | λ |  is equal to ________ .
The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is
Two sets AA and BB are as under: A={(a,b)∈R×R:∣a−5∣<1A = \{(a, b) \in R \times R : |a - 5| < 1 and ∣b−5∣<1}|b - 5| < 1\} ; B={(a,b)∈R×R:4(a−6)2+9(b−5)2≤36}B = \{(a, b) \in R \times R : 4(a - 6)2 + 9(b - 5)^2 \leq 36\}. Then
The number of all three elements subsets of the set {a1,a2,a3...an}\{a_1, a_2, a_3 . . . a_n\} which contain a3a_3 is
The number of proper subsets of a set having n+1n + 1 elements is
The number of subsets of {1,2,3,............,9}\{1, 2, 3 ,............,9\} containing at least one odd number is
The number of subsets of {1,2,3,…,9}\{1,2,3, \ldots, 9\} containing at least one odd number is
The number of the proper subset of {a, b, c} is:
The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects ?