An aqueous solution of sodium carbonate is alkaline. This is because sodium carbonate is a salt of which of the following?

The solution of $\frac{dx}{dy} + \frac{x}{y} = x^2$ is:

If $a$ stands for the edge length of the cubic systems: simple cubic,body-centered cubic,and face-centered cubic,then the ratio of radii of the spheres in these systems will be respectively:

An oil drop having a mass $4.8 \times 10^{-13} ~kg$ and charge $2.4 \times 10^{-18} ~C$ stands still between two charged horizontal plates separated by a distance of $1 ~cm$. If now the polarity of the plates is changed,the instantaneous acceleration of the drop is: $(g = 10 ~ms^{-2})$ (in $~ms^{-2}$)

Four particles $A, B, C$ and $D$ of equal mass $m$ are placed at the four corners of a square. They move with equal uniform speed $v$ towards the intersection of the diagonals. After the collision,particle $A$ comes to rest,particle $B$ traces its path back with the same speed $v$,and particles $C$ and $D$ move with equal speeds $v'$. What is the velocity of particle $C$ after the collision?

In the triangle with vertices at $A(6, 3), B(-6, 3)$ and $C(-6, -3)$,the median through $A$ meets $BC$ at $P$,the line $AC$ meets the $x$-axis at $Q$,while $R$ and $S$ respectively denote the orthocentre and centroid of the triangle. Then the correct matching of the coordinates of points in List-$I$ to List-$II$ is

List-$I$	List-$II$
$(i) P$	$(A) (0, 0)$
$(ii) Q$	$(B) (6, 0)$
$(iii) R$	$(C) (-2, 1)$
$(iv) S$	$(D) (-6, 0)$
	$(E) (-6, -3)$
	$(F) (-6, 3)$

$(i) (ii) (iii) (iv)$