GATE Engineering Sciences Practice Quiz

Question 1

Let $A=\begin{bmatrix}2&1\0&2\end{bmatrix}$. The value of $e^{At}$ is

Accepted Answer

$e^{2t}\begin{bmatrix}1&t\0&1\end{bmatrix}$

Question 2

For the function $f(z)=\frac{e^z}{z^2(z-1)}$, the residue at $z=0$ is

Accepted Answer

$-2$

Question 3

A tank contains an incompressible liquid of density $\rho$. The pressure at a depth $h$ below the free surface open to atmosphere is $p$. Which of the following is correct for gauge pressure?

Accepted Answer

$p=\rho gh$

Question 4

For steady, fully developed, laminar flow of a Newtonian fluid in a circular pipe of radius $R$, the axial velocity profile is $u(r)=u_{max}\left(1-\frac{r^2}{R^2}\right)$. The ratio $\frac{u_{avg}}{u_{max}}$ is

Accepted Answer

$\frac{1}{2}$

Question 5

For a closed, simple compressible system undergoing a reversible adiabatic process, which one of the following statements is correct?

Accepted Answer

$\Delta S=0$

GATE Engineering Sciences

Practice Quizzes

GATE Engineering Sciences Practice Quiz

Vector differentiation identities Fundamentals | GATE Engineering Sciences