Class 12th

Indium and other semi conducting materials behaves different characteristic of impurities and pure particle at high temperature zone. Hence in metallurgical process it is refined by the zone refining.

Buna-S required nascent oxygen

Butadiene + styrene $\underset{}{\overset{\left[0\right]}{\to }}$ (Buna-S)

Magnetic field on the axis of a circular coil at distance x from centre, B = $\frac{{\mu }_{0}Ni{r}^2}{2{\left(r^2+x^2\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$ $\frac{{}_{}{}^{}}{{{}^{}{}^{}}^{\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.}}$

$\frac{{\left(r^2+{\left(0.2\right)}^2\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{{\left(r^2+{\left(0.05\right)}^2\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}=8$ $\frac{r^2+{\left(0.2\right)}^2}{r^2+{\left(0.05\right)}^2}=4\Rightarrow r^2=0.01\Rightarrow r=0.1m.$

Number of half lives of Y = 3

Number of half lives of X = 6 [As half life of X is half of that of Y].

$\frac{N_1}{2^6}=\frac{N_2}{2^3}\Rightarrow \frac{N_1}{N_2}=8$

Conversion form

D1 is in forward bias and D2 is in reverse bias.

Current, I $=\frac{5-0.7}{10}=0.43A$

Yes. Determinants can be calculated for any square matrix of n-order, and it is done by expansion of rows and columns. Even in higher dimensions, their job is to define hyper volumes and transformations.

In such cases, the value of determinant turns out to be zero. this is because swapping the values changes the magnitude into the opposite sign (fundamental property of determinants), which results in the final answer being zero.

Yes. Determinants can be fractions and irrational numbers depending on the values of the matrix. This is because the values are calculated as sums and products of the numbers in the matrix which can turn out to be any type of integer.