$\frac{1}{2}-\frac{1}{2 \cdot 2^2}+\frac{1}{3 \cdot 2^3}-\frac{1}{4 \cdot 2^4}+\ldots$ is equal to

Silver ions are added to a solution with $[Br^{-}] = [Cl^{-}] = [CO_3^{2-}] = [AsO_4^{3-}] = 0.1 \ M$. Which compound will precipitate with the lowest $[Ag^{+}]$ concentration?

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $(4/5) \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $(3/5) \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,its time period (in $seconds$) is

If the radius of the earth were to shrink by $1\%$ and its mass remained the same,the acceleration due to gravity on the earth's surface would

If $A = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$,then $AA' = $

Give signs used for floral formula.