GATE Mathematics Practice Quiz

Question 1

Let $A=\begin{pmatrix}1&2&0\0&1&0\0&0&3\end{pmatrix}$. The minimal polynomial of $A$ is

Accepted Answer

$(x-1)^2(x-3)$

Question 2

The value of $\displaystyle \lim_{n\to\infty} n\int_0^1 x^n\log(1+x)\,dx$ is

Accepted Answer

$\log 2$

Question 3

Let $X$ be a continuous random variable with density $f_X(x)=2x$, $0<x<1$, and $0$ otherwise. If $Y=X^2$, then the density of $Y$ on its support is

Accepted Answer

$f_Y(y)=1,\ 0<y<1$

Question 4

The general solution of the differential equation $y''-4y'+4y=e^{2x}$ is

Accepted Answer

$y=(C_1+C_2x)e^{2x}+\frac{x^2}{2}e^{2x}$

Question 5

Let $f(z)=\frac{z^2+1}{z^2(z-1)}$. The residue of $f$ at $z=0$ is

Accepted Answer

$-1$

GATE Mathematics