The function of leghaemoglobin in the root nodules of legumes is

Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. If the first overtone of $A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B$,the ratio of the lengths of the strings is :

Assertion : $\text{Trans-}2\text{-butene}$ on reaction with $Br_2$ gives $\text{meso-}2,3\text{-dibromobutane}$.
Reason : The reaction involves $\text{syn-addition}$ of bromine.

If $x = 2^{1/3} - 2^{-1/3}$,then $2x^3 + 6x = $

$A$ circular coil of area $200 ~cm^2$ and $50$ turns is rotating about its vertical diameter with an angular speed of $40 ~rad/s$ in a uniform horizontal magnetic field of magnitude $2 \times 10^{-2} ~T$. The maximum emf induced in the coil is (in $~V$)

The solution of $(1+x^2) \frac{dy}{dx} + 2xy - 4x^2 = 0$ is: