Which of the following is known as the $ \text{Christmas Tree} $?

If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle of $\frac{3 \pi}{4}$ with the positive $X$-axis,then the value of $f^{\prime}(3)$ is

The function of leghaemoglobin in the root nodules of legumes is

In which of the following compounds,the transition metal is in oxidation state of zero?

$(a)$ Show that for every natural number $n$ relatively prime to $10$,there exists a natural number $m$ consisting only of digits $1$ such that $n$ divides $m$.
$(b)$ Hence or otherwise,show that every positive rational number can be expressed in the form $\frac{a}{10^b(10^c-1)}$ for some natural numbers $a, b, c$.

Three concentric metallic spherical shells of radii $R, 2R, 3R$ are given charges $Q_1, Q_2, Q_3$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then,the ratio of the charges given to the shells,$Q_1 : Q_2 : Q_3$ is