GATE EC 2014 Question Paper (15-Feb-2014) (Shift 1)

For matrices of the same dimension M, N, and scalar c, which one of these properties DOES NOT ALWAYS hold?

In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is _____

C is a closed path in the z-plane given by |z| = 3. The value of the integral _C^ ≤ft( {{z^2 - z + 4j}z + 2j} )dz is

A real (4 × 4) matrix A satisfies the equation A² = I, where I is a (4 × 4) identity matrix. The positive eigenvalue of A is ________.

Let X₁, X${}_{2,}$ and X₃ be independent and identically distributed random variables with uniform distribution on {0, 1}. The probability P(X₁ is the largest) is _______.