$15 \text{ mL}$ of aqueous solution of $Fe^{2+}$ in acidic medium completely reacted with $20 \text{ mL}$ of $0.03 \text{ M}$ aqueous $Cr_2O_7^{2-}$. The molarity of the $Fe^{2+}$ solution is $\times 10^{-2} \text{ M}$ (Round off to the Nearest Integer).

Two point masses of $0.3\, kg$ and $0.7\, kg$ are fixed at the ends of a rod of length $1.4\, m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

For $k=1, 2, 3$, the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1)=\frac{1}{2}$, $P(B_2)=\frac{1}{3}$, and $P(B_3)=\frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box $B_2$ is:

If we remove half of the forest cover of the Earth,the crisis that will occur is:

When a body of mass $1.0 ~kg$ is suspended from a certain light spring hanging vertically,its length increases by $5 ~cm$. By suspending a $2.0 ~kg$ block to the spring,if the block is pulled through $10 ~cm$ and released,the maximum velocity in $m/s$ is: (Acceleration due to gravity $= 10 ~m/s^2$)

All of the following substances react with water. Which pair among them will produce the same gaseous product upon reaction with water?