If $z=x+iy$ is a complex number satisfying $\left|z+\frac{i}{2}\right|^2=\left|z-\frac{i}{2}\right|^2$,then the locus of $z$ is

If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $(x_i, y_i)$,for $i=1, 2, 3, 4$,then $y_1+y_2+y_3+y_4$ equals

The angle between the straight lines represented by $(x^2+y^2) \sin^2 \alpha = (x \cos \alpha - y \sin \alpha)^2$ is

The value of $\{x \in R \mid \log_{10} ((1.6)^{1-x^2} - (0.625)^{6(1+x)}) \in R\}$ is

If the electric flux entering and leaving a closed surface are $\phi_1$ and $\phi_2$ respectively,then the electric charge inside the surface will be:

On addition of $1 \ mL$ solution of $10 \% \ NaCl$ to $10 \ mL$ gold sol in the presence of $0.025 \ g$ of starch,the coagulation is just prevented. What is the gold number of starch?