Class 12th

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}LetAbeamatrix\\ \therefore -A=-1.A\\ Hence,negativeofamatrixisobtainedbymultiplyingitby-1.\end{array}$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}LetAandBbeanytwomatrices\\ \therefore Forskewsymmetricmatrices\\ A=-A^{\text{'}}\dots (i)\\ andB=-B^{\text{'}}\dots (ii)\\ Adding(i)and(ii)weget\\ A+B=-A^{\text{'}}-B^{\text{'}}\\ \Rightarrow A+B=-\left(A^{\text{'}}+B^{\text{'}}\right),soA+Bisskewsymmetricmatrix.\\ Hence,thesumoftwoskewsymmetricmatricesisalwaysskewsymmetricmatrices.\end{array}$

Sol. $2\mathrm{P}\mathrm{b}{\left({\mathrm{N}\mathrm{O}}_3\right)}_2\stackrel{\mathrm{\Delta }}{?}2\mathrm{P}\mathrm{b}\mathrm{O}+2{\mathrm{N}\mathrm{O}}_2+{\mathrm{O}}_2$

$2{\mathrm{N}\mathrm{O}}_2?{\mathrm{N}}_2{\mathrm{O}}_4$ colourless

${\mathrm{N}}_2{\mathrm{O}}_4+2\mathrm{N}\mathrm{O}?2{\mathrm{N}}_2{\mathrm{O}}_3$

Oxidation state in ${\mathrm{N}}_2{\mathrm{O}}_3$  is +3

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$Nullmatrixi.e.\left[\begin{array}{cc}\hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill \end{array}\right]or\left[\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \end{array}\right]isbothsymmetricandskewsymmetricmatrix.$

Sol. ${\mathrm{C}\mathrm{r}}^{2+}$ and ${\mathrm{F}\mathrm{e}}^{2+}$  both have 4 unpaired electrons.

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Wehave,\left[\begin{array}{cc}\hfill 4\hfill & \hfill 2\hfill \\ \hfill 3\hfill & \hfill 3\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill 3\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 2\hfill & \hfill 0\hfill \\ \hfill 1\hfill & \hfill 1\hfill \end{array}\right]\\ Usingelementaryrowtransformation{R}_1\to R_1-3R_2,weget\\ \left[\begin{array}{cc}\hfill -5\hfill & \hfill -7\hfill \\ \hfill 3\hfill & \hfill 3\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 1\hfill & \hfill -7\hfill \\ \hfill 0\hfill & \hfill 3\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 2\hfill & \hfill 0\hfill \\ \hfill 1\hfill & \hfill 1\hfill \end{array}\right]\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Giventhat:\left[\begin{array}{cc}\hfill 1\hfill & \hfill -3\hfill \\ \hfill 2\hfill & \hfill 4\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 1\hfill & \hfill -1\hfill \\ \hfill 0\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 3\hfill & \hfill 1\hfill \\ \hfill 2\hfill & \hfill 4\hfill \end{array}\right]\\ Using{C}_2\to C_2-2C_1,weget\\ \left[\begin{array}{cc}\hfill 1\hfill & \hfill -5\hfill \\ \hfill 2\hfill & \hfill 0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 1\hfill & \hfill -1\hfill \\ \hfill 0\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 3\hfill & \hfill -5\hfill \\ \hfill 2\hfill & \hfill 0\hfill \end{array}\right]\\ Hence,thecorrectoptionis\left(d\right).\end{array}$

Sol. Balmer series lies in the visible region.

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}WeknowthatforanytwomtricesAandB,wemayhaveAB=BA,AB\ne BAandAB=0,but\\ itisnotalwaystrue.\\ Hence,thecorrectoptionis\left(d\right).\end{array}$