In a certain test there are $n$ questions. In the test,${2^{n - i}}$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, \dots, n$. If the total number of wrong answers given is $2047$,then $n$ is equal to:

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered $1$ to $6$) and let $E_k = \{(a, b) \in S : ab = k\}$ for $k \geq 1$. If $p_k = P(E_k)$ for $k \geq 1$,then which of the following is correct?

Which of the following is not a chromophore?

$\frac{1}{1 \cdot 3} + \frac{1}{2 \cdot 5} + \frac{1}{3 \cdot 7} + \frac{1}{4 \cdot 9} + \ldots$ is equal to

$A$ wall is made up of two layers $A$ and $B$. The thickness of the two layers is the same,but materials are different. The thermal conductivity of $A$ is double than that of $B$. In thermal equilibrium,the temperature difference between the two ends is $36\,^{\circ}C$. Then the difference of temperature at the two surfaces of $A$ will be......... $^{\circ}C$