In the circuit shown in the figure,the power developed across the $1 \Omega$,$2 \Omega$,and $3 \Omega$ resistors are in the ratio of:

$\frac{(1+i)^{2011}}{(1-i)^{2009}}$ is equal to

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=2x+3$ and $g(x)=x^2+7$,then the values of $x$ such that $g(f(x))=8$ are

If $\theta$ is the angle between the curves $xy=2$ and $x^2+4y=0$, then $\tan \theta$ is equal to:

The line $2x + \sqrt{6}y = 2$ is a tangent to the curve $x^2 - 2y^2 = 4$. The point of contact is

$A$ ray of light of intensity $I$ is incident on a parallel glass slab at point $A$ as shown in the diagram. It undergoes partial reflection and refraction. At each reflection, $25\%$ of incident energy is reflected. The rays $AB$ and $A'B'$ undergo interference. The ratio of $I_{max}$ and $I_{min}$ is (in $: 1$)