Let $f(x)$ be a continuous and differentiable function for all real numbers such that $f(x + y) = f(x) - 3xy + f(y)$. If $\lim_{h \to 0} \frac{f(h)}{h} = 7$,then the value of $f'(x)$ is:

$A$ circular disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is

In $Fe(CO)_5$,the $Fe-C$ bond possesses

The coiling of garden pea tendrils around a support is an example of which phenomenon?

$A$ particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $V$. When it moves from one point to a diametrically opposite point,its

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 $= 330 ~m/s$):