Consider three sets X, Y and Z having 6, 5 and 4 elements respectively. All these 15 elements are distinct. Let S = (X - Y) ∪ Z. How many proper subsets does S have?

Consider the following statements in respect of relations and functions:

1. All relations are functions but all functions are not relations.

2. A relation from A to B is a subset of Cartesian product A × B.

3. A relation in A is a subset of Cartesian product A × A.

Which of the above statements are correct?

If log10 2 log₂ 10 + log₁₀(10^x) = 2, then what is the value of x?

Let ABC be a triangle. If cos2A + cos2B + cos2C = -1 then which one of the following is correct?