Class 12th

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.

Viscosity of the hydrophilic sol is always higher than H₂O, because dispersed phase particle attracted by dispersion medium.

Side band frequencies are 1 MHz $\pm$ $$ 1 kHz

$\frac{l_{max}}{l_{min}}=\frac{{\left(\sqrt[]{\frac{l_1}{l_2}}+1\right)}^2}{{\left(\sqrt[]{\frac{l_1}{l_2}}-1\right)}^2}\Rightarrow \frac{l_{max}-l_{min}}{l_{max}+l_{min}}=\frac{2.\sqrt[]{\frac{l_1}{l_2}}}{\frac{l_1}{l_2}+1}=\frac{2\sqrt[]{2x}}{2x+1}$

$\overrightarrow{AB}+\overrightarrow{AH}=\overrightarrow{AO}$

$\overrightarrow{AC}+\overrightarrow{AG}=2\overrightarrow{AO}$

$\overrightarrow{AD}+\overrightarrow{AF}=3\overrightarrow{AO}$

$\overrightarrow{AE}=2\overrightarrow{AO}$

Adding All,  

$\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}+\overrightarrow{AG}+\overrightarrow{AH}=8\overrightarrow{AO}=16\widehat{i}+24\widehat{j}-32\widehat{k}$

At t = 0, no current flows through inductor.

$i=\frac{E}{\frac{6*9}{6+9}}=\frac{5E}{18}$

At t = $\infty$ $$ , current flows through circuit as if inductor is shorted.

$i=\frac{E}{\frac{5}{2}+\frac{4}{5}}=\frac{10E}{33}$

Key is open.

$i_{rms}=\frac{15}{60}=\frac{1}{4}A$

$20=\frac{1}{4}*100*L\Rightarrow L=0.8H$

$10=\frac{1}{4}.\frac{1}{100C}\Rightarrow C=2.5*10^{-4}F=250\mu F$