Class 12th

Ceric ammonium nitrate is used to test alcohol while CHCl₃/alc. KOH is used to test 1° amine

Kindly consider the following figure

${\displaystyle \underset{0}{\overset{\pi }{\int }}\left|sin2x\right|dx}$

$=2{\displaystyle \underset{0}{\overset{\pi /2}{\int }}sin2xdx}$ =2 ${\left[\frac{-cos2x}{2}\right]}_0^{\pi /2}$ = $2\left(\frac{1}{2}-\left(-\frac{1}{2}\right)\right)=2$

$y^2=a\left(x+\frac{\sqrt[]{a}}{2}\right),a>0$

2yy1 = a

$y^2=2y{y}_1\left(x+\frac{\sqrt[]{2y{y}_1}}{2}\right)$

$y=2y_{1}x+y_1\sqrt[]{2y{y}_1}$

${\left(y-2y_{1}x\right)}^2=y_1^2.2y{y}_1=2y{y}_1^3$

$\therefore order=1,degree=3$

Hence, degree – order = 3 – 1 = 2

$FeC{l}_3\underset{}{\overset{hydrolysis}{\to }}Fe{\left(OH\right)}_3\downarrow \underset{Adsorption}{\overset{F{e}^{3+}}{\to }}Fe{\left(OH\right)}_3|F{e}^{3+}\left(colloidalparticle\right)$                                                                                               

Caprolactum is monomer of nylon-6

Isoprene is polymer of natural rubber

2 – chloro-1,3-butadiene or chloroprene is the polymer of neoprene which is a synthetic rubber

Acrylonitrite is one of the monomer of Buna-N

Acrylonitrile

$30{}^{30}{C}_0+29{}^{30}{C}_1+.....+2{}^{30}{C}_{28}+1{.}^{30}{C}_{29}=n.2^m$

$\therefore n=15,m=0$

$\therefore n+m=15+30=45$

Kindly consider the following figure

$\left(x-1\right)\left(x^2-x+1\right)=0$

$x=1,x=\frac{1\pm \sqrt[]{3}i}{2}=\frac{1}{2}+\frac{\sqrt[]{3}}{2}i,\frac{1}{2}-\frac{\sqrt[]{3}}{2}i=e^{i\frac{\pi }{3}},e^{-i\frac{\pi }{3}}$

Sum of 162th power of roots = $1+e^{i54\pi }+e^{-i54\pi }=1+1+1=3$