In which of the following is lead sulfate $(PbSO_4)$ soluble?

If the axes are rotated through an angle $45^{\circ}$ in the positive direction without changing the origin,then the coordinates of the point $(\sqrt{2}, 4)$ in the old system are

Let $f: R \rightarrow R$ be a function such that $f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+6, x \in R$,then $f(2)$ equals

$A$ uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series,the effective resistance of all the pieces is

$A$ body of mass $m = 10^{-2} \; kg$ is moving in a medium and experiences a frictional force $F = -kv^2$. Its initial speed is $v_0 = 10 \; m/s$. If,after $10 \; s$,its energy is $\frac{1}{8} mv_0^2$,the value of $k$ will be:

In the given figures,which path is the shortest?