Class 12th

 $g_{\left(ath\right)}=g_{\left(atdepth\alpha h\right)}$ h << R

$\Rightarrow g\left(1-\frac{2h}{R}\right)=g\left(1-\frac{\alpha h}{R}\right)$

$\begin{array}{l}1-\frac{2h}{R}=1-\frac{\alpha h}{R}\Rightarrow \frac{2h}{R}=\alpha \frac{h}{R}\\ \alpha =2\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}False.\\ SinceAB\ne BAifABandBAarewelldefined.\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}True.\\ IfA,BandCarethematricesofadditionthen\\ A+\left(B+C\right)=\left(A+B\right)+C\left(associative\right)\\ A+B=B+A\left(commutative\right)\end{array}$

 $R=\frac{u^{2}sin\left(2*45°\right)}{g}=\frac{u^2}{g}$

$\frac{R}{2}=\frac{u^2}{2g}=\frac{u^{2}sin20}{g}$

$sin2\theta =\frac{1}{2}$

$\Rightarrow 2\theta =30°\Rightarrow \theta =15°$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}True.\\ Foradditionandsubtraction,theorderoftwomatricesshouldbesame.\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}False.\\ Thetwomatricesaresaidtobeequaliftheircorrespondingelementsaresame.\end{array}$

Sol. A - B has the lowest potential energy and it means it has stronger bond.

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}False.\\ Amatrixisanarrayofelements,numbersorfunctionshavingrowsandcolumns.\end{array}$

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

$\begin{array}{l}{A}^{-1}doesnotexistifweapplyoneormorerowoperationswhilefinding{A}^{-1}byelementaryrow\\ operations,obtainallzeroesinoneormorerows.\end{array}$

Sol. ${\mathrm{O}}^{2-}>{\mathrm{F}}^{-}>{\mathrm{N}\mathrm{a}}^{+}>{\mathrm{M}\mathrm{g}}^{2+}$ . Greater the Zeff, smaller is size.