GATE IN 2018 Question Paper (04-Feb-2018) (Shift 2)

Let 𝑁 be a 3 by 3 matrix with real number entries. The matrix 𝑁 is such that 𝑁² = 0. The eigen values of N are

Let 𝑓₁(𝑧) = 𝑧² and 𝑓₂(𝑧) = z̅ be two complex variable functions. Here z̅ is the complex conjugate of z. Choose the correct answer.

𝑋 and 𝑌 are two independent random variables with variances 1 and 2, respectively. Let 𝑍 = 𝑋 − 𝑌. The variance of 𝑍 is

Consider two functions f(x) = (x - 2)² and g(x) = 2x - 1, where x is real. The smallest value of x for which f(x) = g(x) is ________.

Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. The probability of getting the head for the third time in the fifth toss is