Class 12th

$C=\frac{{\epsilon }_{0}A}{d}\Rightarrow X_C=\frac{1}{C\omega }=\frac{d}{{\epsilon }_{0}A\omega }\Rightarrow l_0=\frac{V_0}{X_C}=\frac{V_0{\epsilon }_{0}A\omega }{d}=\frac{2\pi f{V}_0{\epsilon }_{0}A}{d}$

$\Rightarrow l_0=\frac{2*3.14*50*20*8.85*10^{-12}*1}{2*10^{-3}}=27.79*10^{-6}A=27.79\mu A$              

$R=\frac{\Delta V}{\Delta l}=\frac{0.75-0.70}{\left(5-3\right)*10^{-3}}=\frac{0.05*1000}{2}=25\Omega$

$l=JAcos\theta \Rightarrow 5=J*0.04*cos60°\Rightarrow J=\frac{5}{0.02}=250A/m^2$

$J=\frac{E}{\rho }\Rightarrow E=\rho J=44*10^{-8}*250=11*10^{-5}V/m$              

Power dissipated in cycle = P = $\frac{V_0{l}_0}{2}cos?=\frac{V_0^2}{2z}*\frac{R}{z}=\frac{V_0^{2}R}{2z}$  

For resonance, z = R, so

$\Rightarrow P=\frac{V_0^2}{2R}=\frac{250\sqrt[]{2}*250\sqrt[]{2}}{2*5}=12500Watt=125*10^{2}Watt$        

Let the work function of metal is $?$ , so

$k_1=3V_{0}e=\frac{hc}{\lambda }-?$ . (i)

$K_2=V_{0}e=\frac{hc}{2\lambda }-?$ . (ii)

Doing (i) – 3 X (ii), we have

$0=\frac{hc}{\lambda }-\frac{3hc}{2\lambda }+2?\Rightarrow ?=\frac{hc}{4\lambda }$    

The threshold wavelength = $\frac{hc}{?}=4\lambda$

$A=-\frac{dN}{dt}=\lambda N=\lambda N_0{e}^{-\lambda t}\Rightarrow \lambda \frac{N_0}{16}=\lambda N_0{e}^{-80\lambda }\Rightarrow \frac{1}{16}=e^{-80\lambda }\Rightarrow \frac{1}{16}=e^{-80\lambda }$

$\Rightarrow 80\lambda =\mathcal{l}n\left(16\right)=4\mathcal{l}n\left(2\right)\Rightarrow t_{\frac{1}{2}}=\frac{\mathcal{l}n\left(2\right)}{\lambda }=\frac{80}{4}=20days$

The main idea that the given paragraph shares is that the long-term decline in childhood vaccination rates is a global phenomenon. Only Option A captures this key idea. It also talks about other key ideas stated in the paragraph. Other options are far-fetched as they miss out on some crucial information.

According to the paragraph, the bird species are declining and most of those species come from islands. Statement B uses appropriate keywords and captures all key ideas as well. Other statements are far-fetched and skip a few main ideas shared in the paragraph.

According to the given paragraph, we can realize how the industry revolution introduced new technology which resulted in the emergence of dressmaking shops and how eventually it led to some safety issues. Only, first statement uses all the appropriate keywords and defines the progression of events meaningfully. B and C are far-fetched. D states an irrelevant fact of competition.