The equation of the pair of straight lines parallel to the $X$-axis and touching the circle $x^2+y^2-6x-4y-12=0$ is:

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?

$A$ force $F = -K(y\hat{i} + x\hat{j})$ (where $K$ is a positive constant) acts on a particle moving in the $xy$-plane. Starting from the origin,the particle is taken along the positive $x$-axis to the point $(a, 0)$ and then parallel to the $y$-axis to the point $(a, a)$. The total work done by the force $F$ on the particle is:

The coconut water and the edible part of coconut are equivalent to:

An important evidence in favour of organic evolution is the occurrence of

Two capillaries of the same material but of different radii are dipped in a liquid. In one of the capillaries,the liquid rises to a height of $22 \ cm$ and in the other to $66 \ cm$. The ratio of their radii is