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

The ordinary differential equation $\frac{\mathrm{dy}}{\mathrm{dt}}=-3\mathrm{x}+2,\mathrm{with}\mathrm{x}\left(0\right)=1$

is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is ________.

Suppose C is the closed curve defined as the circle ${\mathrm{x}}^2+{\mathrm{y}}^2=1$ with $\mathrm{C}$ oriented anti-clockwise. The value of ∮(xy^2 dx + x^2y dy) over the curve $\mathrm{C}$ equals ________

Two random variables $\mathrm{X}$ and $\mathrm{Y}$ are distributed according to

{{f_{X,{}}}{≤ft( {,} )}} = ≤ft\{ {*20c {≤ft( {+ } )}&{0 ≤ ≤ 1}&{0 ≤ ≤ 1}\\ 0,&{.}&} .

The probability $(\mathrm{X}+\mathrm{Y}\le 1)$ is ________

The matrix = ≤ft[ {*20c &0&3&7\\ 2&5&1&3\\ 0&0&2&4\\ 0&0&0&} ] has $\det (\mathrm{A})=100$ and $\mathrm{trace}(\mathrm{A})=14$.

The value of $|a-b|$ is ________.

In the given circuit, each resistor has a value equal to 1 Ω.



What is the equivalent resistance across the terminals 𝑎 and 𝑏?