Class 12th

$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$

$\Rightarrow \frac{1}{2}=\frac{1}{3}+\frac{1}{5}-P\left(A\cap B\right)$

$P\left(\frac{A}{B\text{'}}\right)+P\left(\frac{B}{A\text{'}}\right)$

$=\frac{P\left(A\right)-P\left(A\cap B\right)}{1-P\left(B\right)}+\frac{P\left(B\right)-P\left(A\cap B\right)}{1-P\left(A\right)}=\frac{5}{8}$

Following are the $\Delta H°$  hydration of given ions

Cr²⁺ - 1926 KJ/mole

Mn²⁺ - 1860 KJ/mole

Fe²⁺ - 2000 KJ/mole

Co²⁺ - 2078 KJ/mole

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.