PYQs Based Test - 10 : Engineering Mathematics

The value of the integral 1/2π i _C^ {z^2 + 1}{z^2 - 1}dz where z is a complex number and C is a unit circle with centre at 1 + 0j in the complex plane is __________ .

The magnitude of the directional derivative of the function f(x, y) = x² + 3y² in a direction normal to the circle x² + y² = 2, at the point (1, 1), is

Consider the sequence xₙ= 0.5xₙ₋₁ + 1, n = 1, 2, ... ... with x₀ = 0. Then $\underset{n\to \infty }{\lim }{x}_n$

Consider that X and Y are independent continuous valued random variables with uniform PDF given by X ~ U(2, 3) and Y ~ U(1, 4). Then P(Y ≤ X) is equal to __________ (rounded off to two decimal places).

Consider the matrix M = ≤ft[ {*20c 1& - 1&0\\ 1& - 2&1\\ 0& - 1&1 } ]. One of the eigenvectors of M is