An element playing an important role in nitrogen fixation is

The energy of a photon is equal to the kinetic energy of a proton. If $\lambda_1$ is the de-Broglie wavelength of a proton and $\lambda_2$ is the wavelength associated with the photon,and if the energy of the photon is $E$,then $(\lambda_1 / \lambda_2)$ is proportional to

The major product of the following reaction is

$P$ is a point on the segment joining the feet of two vertical poles of heights $a$ and $b$. The angles of elevation of the tops of the poles from $P$ are $45^{\circ}$ each. Then,the square of the distance between the tops of the poles is

The biquadratic equation,two of whose roots are $1+i$ and $1-\sqrt{2}$,is

The area (in sq units) of the quadrilateral formed by two pairs of lines $\lambda^2 x^2 - m^2 y^2 - n(\lambda x + m y) = 0$ and $\lambda^2 x^2 - m^2 y^2 + n(\lambda x + m y) = 0$ is: