In which of the following is potassium stored?

If $f: R \rightarrow R$ is defined by $f(x)=x-[x]-\frac{1}{2}$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then $\{x \in R: f(x)=\frac{1}{2}\}$ is equal to :

There are two wires of the same material and same length. If the diameter of the second wire is $2$ times the diameter of the first wire,then the ratio of the extension produced in the wires by applying the same load will be:

If $\frac{x^2+x+1}{x^2+2x+1} = A + \frac{B}{x+1} + \frac{C}{(x+1)^2}$,then $A-B$ is equal to

The solution of $(x^2+y^2) dx = 2xy dy$ is:

If $3 \hat{i}+3 \hat{j}+\sqrt{3} \hat{k}$, $\hat{i}+\hat{k}$, and $\sqrt{3} \hat{i}+\sqrt{3} \hat{j}+\lambda \hat{k}$ are coplanar, then $\lambda$ is equal to