An expression of energy density is given by $u = \frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{kt}\right)$,where $\alpha$ and $\beta$ are constants,$x$ is displacement,$k$ is the Boltzmann constant,and $t$ is the temperature. The dimensions of $\beta$ will be $-$

Which of the following statements is incorrect regarding growth?

The values of a function $f(x)$ at different values of $x$ are given in the table below:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$f(x)$	$2$	$3$	$6$	$11$	$18$	$27$

Then,the approximate area (in square units) bounded by the curve $y=f(x)$ and the $x$-axis between $x=0$ and $x=5$,using the Trapezoidal rule,is

Temperate evergreen forests are found in

$A$ radioactive nucleus $A$ with a half-life $T$ decays into a nucleus $B$. At $t = 0$,there is no nucleus $B$. At some time $t$,the ratio of the number of $B$ nuclei to that of $A$ nuclei is $0.3$. Then,$t$ is given by:

An observer is standing $500 ~m$ away from a vertical hill. Starting between the observer and the hill,a police van sounding a siren of frequency $1000 ~Hz$ moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is $970 ~Hz$,the frequency of the sound heard after reflection from the hill (in $Hz$) is about,(velocity of sound $= 330 ~m/s$):