Class 11th

Equation of required circle

$C:{\left(x-2\right)}^2+{\left(y-1\right)}^2+\lambda \left(2y-x\right)=0..........\left(i\right)$              

Intersect C₁x² + y² + 2y – 5 = 0 .(ii)

$\therefore$ Equation of radical axis

    $-4x-4y+10+\lambda \left(2y-x\right)=0..........\left(ii\right)$          

Centre of C₁ (0, -1) lies on .(ii)

$\Rightarrow 4+10-2\lambda =0\Rightarrow \lambda =7$        

Equation of circle C is

$x^2+y^2-11x+12y+5=0$       

Diameter = $\sqrt[]{245}=7\sqrt[]{5}$  

  $F-Be-F$   $\mu =0$ $$

BF3 $\mu =0$

H2O $\mu \ne 0$ $$

NH3 $\mu \ne 0$ $$

CCl4 $\mu =0$ $$

HCl $\mu \ne 0$ $$

$T_1=27°C=300K$ T2 = 45° C = 45 + 273 = 318 K

P1 = 30 atmP2 =?

V is constant due to rigid tank\

$\therefore \frac{P_1}{T_1}=\frac{P_2}{T_2}$

$\frac{30}{300}=\frac{P_2}{318}\therefore P_2=\frac{1}{10}*318=31.8atm\approx 32atm$

A beat wave arises due to constructive and destructive interference between two sound waves. These two frequencies have nearly equal frequencies but never the same. The resulting amplitude envelope oscillates at the beat frequency.  

Beats form when two harmonic waves of nearly equal frequencies and identical amplitudes travel in the same direction, whic allows the superposition of waves. 

Beat frequency is the rate of amplitude modulation we hear when two wave frequencies, f1 and f2 interfere. It's given by |f1-f2|. It represents how fast the loudness oscillates over time. 

$\frac{a}{1-r}=15,\frac{a^2}{1-r^2}=150$

$\Rightarrow r=\frac{1}{5},a=12\Rightarrow \frac{a{r}^2}{1-r^2}=\frac{1}{2}$

Line BM : 2x + y = 3 Þ M (0, 3)

Line CD : 7x – 4y = 1 Þ C (3, 5)

Mirror image of A (-3, 1) in the line CD is $\left(\frac{13}{5},\frac{-11}{5}\right)$  and it will lie on BC.

Slope of AC is 2/3

Slope of BC is 18.

$tan\theta =\frac{18-\frac{2}{3}}{1+18\left(\frac{2}{3}\right)}=\frac{4}{3}$   

 where θ = $\angle ACB$  

$\sum X=200$

$\sum x^2=2125$

For new data

$\sum x=200-25+35=210$

$\overline{x}=10.5$

$\sum x^2=2725$

${\sigma }^2=\frac{2725}{20}-{\left(10.5\right)}^2=26$

Kindly consider the following figure