Consider three 4-variable functions f₁, f₂ and f₃, which are expressed in sum-of-minterms as

f₁ = Σ(0, 2, 5, 8, 14),

f₂ = Σ(2, 3, 6, 8, 14, 15),

f₃ = Σ(2, 7, 11, 14)

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

In 16-bit 2's complement representation, the decimal number -28 is :

Let X be a square matrix. Consider the following two statements on X.

I. X is invertible.

II. Determinant of X is non-zero.

Which one of the following is TRUE?

Let G be an undirected complete graph on n vertices, where n > 2. Then, the number of different Hamiltonian cycles in G is equal to