From which plant is palm oil obtained?

$\cos \left[\cos ^{-1}\left(-\frac{1}{7}\right)+\sin ^{-1}\left(-\frac{1}{7}\right)\right]$ is equal to

$A$ metal wire $PQ$ slides on parallel metallic rails having separation $0.25 \ m,$ each having negligible resistance. There is a $2 \ \Omega$ resistor and $10 \ V$ battery as shown in the figure. There is a uniform magnetic field directed into the plane of the paper of magnitude $0.5 \ T.$ $A$ force of $0.5 \ N$ to the left is required to keep the wire $PQ$ moving with constant speed to the right. With what speed is the wire $PQ$ moving? (Neglect self-inductance of the loop).

At $80\,^oC$,the vapour pressure of pure liquid $A$ is $520\,mmHg$ and that of pure liquid $B$ is $1000\,mmHg$. If a mixture of $A$ and $B$ boils at $80\,^oC$ and $1\,atm$ pressure,the amount of $A$ in the mixture is $........$ $mol\,\%$.

Which of the following metals is present in Vitamin $B_{12}$?

If the area of the auxiliary circle of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ $(a>b)$ is twice the area of the ellipse,then the eccentricity of the ellipse is