Class 12th

From option let it be isosceles where AB = AC then

$x=\sqrt[]{r^2-{\left(h-r\right)}^2}$            

 =   $\sqrt[]{r^2-h^2-r^2+2rh}$

$x=\sqrt[]{2hr-h^2}........\left(i\right)$        

Now ar $\left(\Delta ABC\right)=\Delta =\frac{1}{2}BC*AL$

$\Delta =\frac{1}{2}*2\sqrt[]{2hr-a^2}*h$       

then   $x=\sqrt[]{2*\frac{3r}{2}*r-\frac{9r^2}{4}}=\frac{\sqrt[]{3}}{2}rfrom\left(i\right)$

$\Rightarrow BC=\sqrt[]{3}r$      

So . $AB=\sqrt[]{h^2+x^2}=\sqrt[]{\frac{9r^2}{4}+\frac{3r^2}{4}}=\sqrt[]{3}r$

Hence $\Delta$ be equilateral having each side of length $\sqrt[]{3}r.$  

Sphalerite is ore of zinc consists of ZnS during its concentration group 1 cyanides are used as depressants like NaCN

Major components of gun metal are Cu, Sn and Zn

${?}_1=\frac{3}{5}{E}_0\left(0.2\right)N{m}^2{C}^{-1},and{?}_2=\frac{4}{5}{E}_0\left(0.3\right)N{m}^2{C}^{-1}$

$\Rightarrow \frac{{?}_1}{{?}_2}=\frac{3*0.2*5}{5*0.3*4}=\frac{1}{2}$

It depends on the frequency of the wave. Rays such as Gamma rays, X-Rays etc. have higher frequencies which can lead to harmful impacts if exposed to the human body. These kind of rays cannot be even produced easily unlike low frequency rays.

$A_1+A_2={\displaystyle {\int }_0^{\pi /2}cosxdx}$           

$={\left(Sinx\right)}_0^{\pi /2}=1$           

$A_1={\displaystyle {\int }_0^{\pi /4}\left(cosx-sinx\right)dx={\left(sinx+cosx\right)}_0^{\pi /4}}$           

$=\frac{2}{\sqrt[]{2}}-1=\sqrt[]{2}-1$

$So{A}_2=1-\left(\sqrt[]{2}-1\right)=2-\sqrt[]{2}=\sqrt[]{2}\left(\sqrt[]{2}-1\right)$

$Now\frac{A_1}{A_2}=\frac{1}{\sqrt[]{2}}$

The following are the topics covered in this chapter: Electric Field and Field Lines, Gauss's Law, Electric Dipole, Conductors and Insulators, and Electric Flux. 

$L\frac{di}{dt}=V\Rightarrow 2di=3tdt\Rightarrow 2{\displaystyle \underset{0}{\overset{i}{\int }}di=3}{\displaystyle \underset{0}{\overset{4}{\int }}tdt\Rightarrow i=12A}$

$U=\frac{1}{2}L{i}^2=\frac{1}{2}*2*12^2=144J$

For JEE Main exam, the Electric Charges and Fields is an important chapter. It is a part of Electrostatics unit. The weightage of this unit is around 6-9% of the total Physics section. You should expect around 3-5 questions in this unit including the questions from the class 12 physics chapter 1.

$L\frac{di}{dt}=V?2di=3tdt?2{\displaystyle \underset{0}{\overset{i}{?}}di=3}{\displaystyle \underset{0}{\overset{4}{?}}tdt?i=12A}$

$U=\frac{1}{2}L{i}^2=\frac{1}{2}*2*12^2=144J$