Recent questions in Mathematics Foundation

$\lim _{x \rightarrow 0} \frac{x^{2}}{\sin x}=$$0$ $1$$2$$-1$

The ordinary differential equation\[\frac{d y}{d x}=x^{2} y\]has $y$ as the dependent variable and $x$ as the independent variable. Which of the following classification(...

A biased die has six faces numbered as $k=1,2,3,4,5$, and $6$. On rolling the die, the probability of the number k appearing is proportional to $k^{2}$. What is the proba...

Consider a function $y=f(x)$ which satisfies the following equation:$\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0$ As $x \rightarrow-\infty, y=1$, and at $x=0, y=2$.The valu...

A student reported following arsenic concentrations in water samples:$$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text{Arsenic concentration (mg/L)} & 0.10 & 0.12 & 0.20 & 0...

$\mathrm{X}$ is normally distributed with following data $(25.8,36.6,26.3,21.8,27.2)$. Select the correct statement about $X\left(\mathrm{t}_{\text {crit }, \alpha}=0.05,...

Given $\mathbf{P}$ is $m \times n$ matrix, $\mathbf{Q}$ is $n \times l$ matrix, $\mathbf{R}$ and $\mathbf{S}$ are $n \times n$ matrices, and superscript $\mathrm{T}$ deno...

Ten litres of the sample was filtered through a membrane filter and the filter was transferred to solid agar media which supports growth of coliform organisms. After incu...

$\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-1}{x}$ is (rounded off to one decimal place)

Given, $y=f(x) ; \frac{d^{2} y}{d x^{2}}+4 y=0 ; y(0)=0 ; \frac{d y}{d x}(0)=1$. The problem is a/aninitial value problem having solution $\mathrm{y}=x$boundary value pro...

Eigen values of the matrix $\left[\begin{array}{cc}0 & 1 \\ -2 & 3\end{array}\right]$ are$1$ and $2$$1$ and $3$$1$ and $-2$$0$ and $3$

An individual has four different email accounts. $60 \%$ of emails come into his corporate account, $30 \%$ come into his gmail account and remaining $10 \%$ are equally ...

The area of the region (rounded off to one decimal place) enclosed between the curves $y=x$ and $y=3 \sqrt{x}$ and between the lines $x=0$ and $x=1$ is ________ units.