$A$ $500 \ kg$ car takes a round turn of radius $50 \ m$ with a velocity of $36 \ km/h$. The centripetal force acting on the car is (in $N$)

The area (in sq unit) of the region bounded by the curves $2x = y^2 - 1$ and $x = 0$ is

The differential equation obtained by eliminating the arbitrary constants $a$ and $b$ from $xy = ae^x + be^{-x}$ is

In the figure,the potentiometer wire $AB$ of length $L$ and resistance $9r$ is joined to the cell $D$ of $emf$ $\varepsilon$ and internal resistance $r$. The cell $C$'s $emf$ is $\varepsilon / 2$ and its internal resistance is $2r$. The galvanometer $G$ will show no deflection when the length $AJ$ is

Vitamin $K$ is required for:

Calculate the $emf$ of the cell $Cu_{(s)}|Cu^{2+}_{(aq)}||Ag^{+}_{(aq)}|Ag_{(s)}$. Given: $E_{Cu^{2+} / Cu}^0 = +0.34 \ V$,$E_{Ag^{+} / Ag}^0 = 0.80 \ V$.