Class 12th

Cobalt (II) meta borate is a blue colour of Bead.

Here 'X' is the Gypsum (CaSO₄.2H₂O) which is used to enhance the setting of time

In leaching suitable compound is used as solvent.

$A{\mathcal{l}}_2{O}_3+2NaOH+3H_{2}O\to 2Na\left[A\mathcal{l}{\left(OH\right)}_4\right]$

Stannane is the tetrahedral shape of molecule.

Hybridisation is- sp³, shape and structure are tetrahedral

$11\equiv 2mod\left(9\right)$

${\left(11\right)}^{1011}\equiv 2^{1011}mod\left(9\right)$

Again 23 $\equiv$ 1 mod (9)

$\Rightarrow {\left(2^3\right)}^{337}\equiv {\left(-1\right)}^{337}mod\left(9\right)$

$\therefore {\left(11\right)}^{1011}+{\left(1011\right)}^{11}\equiv 8mod\left(9\right)$

$\therefore$ Remainder = 8

f : {1, 3, 5, 7, ….,99} {2, 4, 6, 8, …….100}

$f\left(3\right)\ge f\left(9\right)\ge f\left(15\right)......\ge f\left(99\right)$

$3+\left(n-1\right)6=99\Rightarrow n=17$

cases f (3) > f (9) > f (15) ……. > f (99)

$\therefore$ from the set {2, 4, 6, …., 100}

17 distinct numbers can be selected in 50C17 ways again remaining {1, 5, 7, 11, ….} can map in 33! ways

$\therefore$ total number of such required functions

${=}^{50}{C}_{17}*33!$

$=\frac{50!}{33!17!}*33!{=}^{50}{P}_{33}$

Liquation refining process is applicable for the metal having low m.p, but containing impurities have higher m.p

Higher adsorbtion of gas is corresponds to higher liquefaction and higher liquefaction is directly proportional to the higher critical temperature.

System of equation can be written as

$\left(\begin{array}{ccc}\hfill 2\hfill & \hfill -3\hfill & \hfill 5\hfill \\ \hfill 1\hfill & \hfill 3\hfill & \hfill -1\hfill \\ \hfill 3\hfill & \hfill -1\hfill & \hfill {\lambda }^2-\left|\lambda \right|\hfill \end{array}\right)\left(\begin{array}{l}x\\ y\\ z\end{array}\right)=\left(\begin{array}{l}9\\ -18\\ 16\end{array}\right)$

for no solution

$\frac{9}{10}\left({\lambda }^2-\left|\lambda \right|+3\right)-7=0$

$\Rightarrow 9{\lambda }^2-9\left|\lambda \right|-43=0$

$\Rightarrow \left|\lambda \right|=\frac{9+\sqrt[]{81+36*43}}{18}>0$

$\therefore$ only two possible value of $\lambda$ are there.

$\left|z-3\sqrt[]{2}\right|+\left|z-p\sqrt[]{2}i\right|$ is minimum for z,  $3\sqrt[]{2}\&p\sqrt[]{2}i$ are collinear.

$\iff {\left(3\sqrt[]{2}\right)}^2+{\left(p\sqrt[]{2}\right)}^2={\left(5\sqrt[]{2}\right)}^2$

$\Rightarrow 18+2p^2=50$

$2p^2=32$

$p=\pm 4$