GATE EC 2016 Question Paper (31-Jan-2016) (Shift 1)

The value of x for which the matrix = ≤ft[ {*20c 3&2&14\\ 9&7&13\\ - 6& - 4&{ - 9 + } } ] has zero as an eigenvalue is ________

Consider the complex valued function $\mathrm{f}(\mathrm{z})=2{\mathrm{z}}^3+b|z{|}^3$ where $\mathrm{z}$ is a complex variable.

The value of $\mathrm{b}$ for which the function $\mathrm{f}\left(\mathrm{z}\right)$ is analytic is ________

As $\mathrm{x}$ varies from $-1\mathrm{to}+3$, which one of the following describes the behaviour of the function $\mathrm{f}(\mathrm{x})={\mathrm{x}}^3\text{–}3{\mathrm{x}}^2+1$?

How many distinct values of $\mathrm{x}$ satisfy the equation $\sin (\mathrm{x})=x/2$, where $\mathrm{x}$ is in radians?

Consider the time-varying vector $\mathbf{I}=\hat{\mathrm{x}}15\cos \left(\mathrm{wt}\right)+\hat{\mathrm{y}}5$ sin(𝜔𝑡) in Cartesian coordinates, where 𝜔 > 0 is a constant. When the vector magnitude |𝐈| is at its minimum value, the angle 𝜃 that 𝐈 makes with the 𝑥 axis (in degrees, such that 0 ≤ 𝜃 ≤ 180) is ________