GATE EC 2017 Question Paper (05-Feb-2017) (Shift 2)

The values of the integrals

$\underset{0}{\overset{1}{\int }}\left(\underset{0}{\overset{1}{\int }}\frac{x-y}{\left({\left(x+y\right)}^3\right)}dy\right)dx$

and

$\underset{0}{\overset{1}{\int }}\left(\underset{0}{\overset{1}{\int }}\frac{x-y}{{\left(x+y\right)}^3}dx\right)dy$

are

An integral I over a counterclockwise circle C is given by

I = _C^ {z^2 - 1}{z^2 + 1}e^zdz.

If C is defined as |z| = 3, then the value of I is

If the vector function $\vec{F}=\widehat{a_x}\left(3y-k_{1}z\right)+\widehat{a_y}\left(k_{2}x-2z\right)-\widehat{a_z}\left(k_{3}y+z\right)$ is irrotational, then the values of the constants k₁, k₂ and k₃, respectively, are

Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is 40% chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is ____________.

The minimum value of the function $f\left(x\right)=\frac{1}{3}x\left(x^2-3\right)$ in the interval - 100 ≤ x ≤ 100 occurs at x = __________.