In the circuit shown,the current in the $1\,\Omega$ resistor is

Four resistors $A, B, C$ and $D$ form a Wheatstone bridge. The bridge is balanced when $C = 100 \ \Omega$. If $A$ and $B$ are interchanged,the bridge balances for $C = 121 \ \Omega$. The value of $D$ is (in $\Omega$)

For the reaction $A + B \rightarrow C$,experiments were performed in the presence of a large amount of $B$ to measure the initial reaction rate $(V_f)$ as a function of the initial concentration of $A ([A]_0)$. The data from the experiments are plotted as shown below. The order of the reaction with respect to $A$ is $.....$

If $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$ such that $\min f(x) > \max g(x)$,then the relation between $b$ and $c$ is:

$A$ converging beam of rays is incident on a diverging lens. Having passed through the lens,the rays intersect at a point $15 \, cm$ from the lens on the opposite side. If the lens is removed,the point where the rays meet will move $5 \, cm$ closer to the lens. The focal length of the lens is.....$cm$

The resistance across $M$ and $N$ in the given figure is