The eccentricity of the ellipse $x^2+4y^2+2x+16y+13=0$ is

$15 \text{ mL}$ 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).

An object with a mass $10 \ kg$ moves at a constant velocity of $10 \ m/s$. $A$ constant force then acts for $4 \ s$ on the object and gives it a speed of $2 \ m/s$ in the opposite direction. The impulse acting on the object is ........ $N \cdot s$.

If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 80$,then the least value of $n$ is

When a current of $2\, A$ flows in a battery from negative to positive terminal,the potential difference across it is $12\, V$. If a current of $3\, A$ flows in the opposite direction,the potential difference across the terminals of the battery is $15\, V$. The $emf$ of the battery is ................ $V$.

When a current of $2\, A$ flows in a battery from negative to positive terminal, the potential difference across it is $12\, V$. If a current of $3\, A$ flows in the opposite direction, the potential difference across the terminals of the battery is $15\, V$. The $emf$ of the battery is ............... $V$.