Let $z=x+iy$ be a complex number where $x$ and $y$ are integers. Then the area of the rectangle whose vertices are the roots of the equation $z\bar{z}^3+\bar{z}z^3=350$ is

Two positively charged particles $m_{1}$ and $m_{2}$ have been accelerated across the same potential difference of $200 \ keV$ as shown below. Given mass of $m_{1} = 1 \ amu$ and $m_{2} = 4 \ amu$. The de Broglie wavelength of $m_{1}$ will be $x$ times that of $m_{2}$. The value of $x$ is . . . . . . . (nearest integer)

Name the method of asexual reproduction in lichens.

If $\sin ^{-1}\left(\frac{3}{x}\right)+\sin ^{-1}\left(\frac{4}{x}\right)=\frac{\pi}{2}$,then $x$ is equal to

What type of glycosidic linkages are present in cellulose?

If $\int \frac{dx}{(1+\sqrt{x}) \sqrt{x-x^2}} = \frac{A \sqrt{x}}{\sqrt{1-x}} + \frac{B}{\sqrt{1-x}} + C$,where $C$ is a real constant,then $A+B$ equals to