GATE EC 2015 Question Paper (31-Jan-2015) (Shift 1)

Consider a system of linear equations, $\mathrm{x}-2\mathrm{y}+3\mathrm{z}=-1$, $\mathrm{x}-3\mathrm{y}+4\mathrm{z}=1$ and

$-2\mathrm{x}+4\mathrm{y}-6\mathrm{z}=\mathrm{k}.$ The value of k for which the system has infinitely many solutions is______.

A function f(x) = 1 - x² + x³ is defined in the closed interval [-1, 1]. The value of x, in the open interval (-1, 1) for which the mean value theorem is satisfied, is

Suppose A and B are two independent events with probabilities $\mathrm{P}\left(\mathrm{A}\right)\ne 0$ and $\mathrm{P}\left(\mathrm{B}\right)\ne 0$. Let $\bar{\mathrm{A}}$ and $\bar{\mathrm{B}}$ be their complements. Which one of the following statements is False?

Let z = x + iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is Not True?

The value of p such that the vector ≤ft[ {*20c 1\\ 2\\ 3 } ] is an eigenvector of the matrix ≤ft[ {*20c 4&1&2\\ &2&1\\ 14& - 4&10 } ] is __________.