Class 12th

A ring magnet is a type of strong and permanent magnet which is made from the alloy of iron, boron and neodymium. These are the part of rare-earth magnet family which is the reason behind their the strongest magnetic properties amongst all other permanent magents.

A U-shaped magnet is another type of bar magnet. This is known as a horseshoe magnet since its shapes resembles the object called horseshoe. The two ends of this U-shaped magnet are its magnetic poles. Configration of these magnetic poles creates a concentrated magnetic field. This concentrated magnetic field makes it much more stronger than a simple and straight bar magnet.

Kindly go through the solution

Based on theory.

$\frac{l_1}{l_2}=\frac{4}{1}$                

$\Rightarrow l_{max}={\left(\sqrt[]{l_1}+\sqrt[]{l_2}\right)}^2=l_1+l_2+2\sqrt[]{l_1{l}_2}$

$\Rightarrow \frac{l_{max}+l_{min}}{l_{max}-l_{min}}=\frac{5}{x}$

$\Rightarrow \frac{1}{2}*\frac{l_2\left(1+\frac{l_1}{l_2}\right)}{\sqrt[]{l_1{l}_2}}=\frac{5}{x}$

$\Rightarrow \frac{1}{2}\frac{1}{\sqrt[]{4}}=\frac{1}{x}\Rightarrow x=4$               

When electric field vector is completely removed and incident on Brewster's angle then only refraction takes place.

The two points in a bar magnet are its North pole and South pole. A bar magnet has magnetic field lines around it. These points give these field lines a travelling direction. For example, the magnetic field lines emerge form the North pole of the bar magnet and then they curve toward South pole. This makes a complete loop of magnetic field lines around the bar magnet.

we know,   $C=\frac{1}{\sqrt[]{{\mu }_0\in o}}=3*10^8,Given,{\in }_r=1$

$v=\frac{1}{\sqrt[]{{\mu }_0{\in }_r{\in }_o{\mu }_r}}=2*10^8$            

$\Rightarrow \frac{3*10^8}{2*10^8}=\sqrt[]{{\in }_r{\mu }_r}$               

$={\left(1.5\right)}^2={\in }_r{\mu }_r$              

${\mu }_r=2.25$               

Number of solution of the equation |cos x| = sin x for $x\in \left[-4\pi ,4\pi \right]$ $$ will be equal to 4 times the number of solutions of the same equation for $x\in \left[0,2\pi \right]$ $$

Graphs of y = |cos x| and y = sin x are as shown below.

Hence, two solutions of given equation in [0, 2]

$$ $\Rightarrow$  total of 8 solutions in [4, 4]

V = 210 sin 3000 t

$\omega$ = 3000

$X_L=\omega L=30$                

$X_C=\frac{1}{\omega c}=\frac{40}{3}$                

$tan?=\frac{V_L-V_C}{V_R}=\frac{X_L-X_C}{R}$                

$\begin{array}{l}tan?=0.17\\ ?=ta{n}^{-1}\left(0.17\right)\end{array}$                

For $x^2+\alpha x=\beta >0\forall x\in R$  to hold, we should have   ${\alpha }^2-4\beta <0$

If $\alpha =1,\beta$  can be 1, 2, 3, 4, 5, 6 i.e., 6 choices

If a  = 4, b can be 5 or 6 i.e., 2 choices

hence total favourable outcomes

= 6 + 5 + 4 + 2 + 0 + 0 = 17

Required probability =  $\frac{17}{36}$

If n is number of trials, p is probability of success and q is probability of unsuccess then,

Mean = np and variance = npq.

Here np + npq = 24         …. (i)

np. npq = 128                   …. (ii)

and q = 1 – p                    …… (iii)

From eq. (i), (ii) and (iii) :

$=\left(32+\frac{32*31}{2}\right).\frac{1}{2^{32}}$      

$=\frac{33}{2^{28}}$