Class 12th

If n₂ -> n₁ in H (Z = 1) gives $\lambda$ then $z{n}_2\to z{n}_1$  give same $\lambda$  H-like ion for He⁺ ion (z = 2)

  $\frac{P}{Q}=\frac{R}{X}{X}_{max}=\frac{R_{max}.Q_{max}}{P_{min}}$

$=9000*\frac{1000}{10}=9*10^{5}ohm$

$x_{min}=\frac{R_{min}.Q_{min}}{P_{max}}=100*\frac{10}{1000}=1ohm$  

$R=8\mathrm{c}\mathrm{m},A=2{\mathrm{m}\mathrm{m}}^2,B_0=0$  at   $t=0\mathrm{s}\mathrm{e}\mathrm{c}$ $$

$$ $B=2$  Tat $$ $t=0.2\mathrm{s}\mathrm{e}\mathrm{c}$

$$ $\left|\epsilon \right|=\frac{2-0}{0.2}\pi *64*{10}^{-4}$  volts

$\frac{}{}$ $i=\frac{\left|\epsilon \right|}{r}=\frac{64\pi *{10}^{-3}}{5*{10}^{-3}}$  ampere

$$ $i=\frac{64\pi }{5}$  ampere

$$ $dF=idlB=$  magnetic force

$dm{\omega }^{2}R=$ centrifugal force

$\begin{array}{ll}\therefore & idlB=dm{\omega }^{2}R\\ \Rightarrow & idl\cdot B=\frac{m}{2\pi R}\cdot dl{\omega }^{2}R\\ \Rightarrow & \omega =\sqrt[]{\frac{2\pi iB}{m}}=\sqrt[]{\frac{2\pi *64\pi *1}{5*9*{10}^{-3}}}\\ & \omega =\frac{16\pi }{3}*10\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}\mathrm{e}\mathrm{c}=170\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}\mathrm{e}\mathrm{c}\end{array}$

c = -5, a = 2, b = 1

1 + x? - x? = a? (1+x)? + a? (1+x) + a? (1+x)² . + a? (1+x)?
Differentiate
4x³ - 5x? = a? + 2a? (1+x) + 3a? (1+x)².
12x² - 20x³ = 2a? + 6a? (1+x).
Put x = -1
12 + 20 = 2a? ⇒ a? = 16

A² - 4A + 4I = 0
(A - 2I)² = 0 ⇒ A-2I ≠ 0
B = 297A - 594I
= 297 (A - 2I)

? C? +? C? =? C?
Σ (from r=0 to 3)? C? =? C? +? C? +? C? +? C?
=? C? +? C? +? C? +? C?
= ¹²C? = (12*11*10)/6 = 220

From Guass's Law

${\displaystyle ?\overrightarrow{E}.\overrightarrow{dA}=\frac{q_{in}}{{\in }_0}}$            

$E.4\pi r^2=\frac{{\displaystyle \underset{0}{\overset{r}{\int }}\left(4\pi r^2.dr\right)\left(\alpha r\right)}}{{\in }_0}$            

$E=\left(\frac{\alpha r^2}{4{\in }_0}\right)$            

Biomolecules in class 12 Chemistry include the following important topics: classification and structure of carbohydrates, amino acids, and proteins, enzymes and their characteristics, nucleic acids (DNA and RNA structure and components), and vitamins.

You must also prepare the following topics that are frequently asked in exams: zwitterion structure in amino acids, enzyme action mechanisms, and differences between DNA and RNA.

∫ (from 0 to π/2) (x/2)|cos (2x)|dx
∫ (from 0 to π/4) (x/2)cos (2x)dx - ∫ (from π/4 to π/2) (x/2)cos (2x)dx
= [x sin (2x)/4 - ∫sin (2x)/4 dx] (from 0 to π/4) - [x sin (2x)/4 - ∫sin (2x)/4 dx] (from π/4 to π/2)
= [x sin (2x)/4 + cos (2x)/8] (from 0 to π/4) - [x sin (2x)/4 + cos (2x)/8] (from π/4 to π/2)
= (π/16 - 1/8) - (-1/8 - π/16) = π/8