Let, the length of train is x meter and the velocity of the train is v km/hr.

According to first condition,$\frac{x}{(v-4.5){\displaystyle \frac{5}{18}}}=8.4.............\left(i\right) [\because \frac{Dis\tan ce}{Velocity}=Time]$

According to second condition,$\frac{x}{(v-5.4){\displaystyle \frac{5}{18}}}=8.5............\left(ii\right)$

From equation (i) $\frac{x}{(v-4.5){\displaystyle \frac{5}{18}}}=8.4$

$$\begin{gathered} =x=(v-4.5)\times \frac{5}{18}\times 8.4 \\ =x=(v-4.5)\times \frac{42}{18} \\ =x=\frac{7(v-4.5)}{3} \\ =3x=7v-314.5 \\ =18x=42v-182............\left(iii\right) \\ From Equation \left(ii\right)\frac{x}{(v-5.4){\displaystyle \frac{5}{18}}}=8.5 \\ =x=8.5\times \frac{5}{18}(v-5.4) \\ =18x=42.5v-229.5..........\left(iv\right) \\ Subtracting equation \left(iii\right) from equation \left(iv\right) \\ \frac{18x=42.5v-229.5 \\ 18x=42v-189}{0=0.5v-40.5} \\ =0.5v=40.5 \\ \therefore v=\frac{40.5}{0.5}=81 \\ \therefore The velocity of the train is 81kmph. \left(answer\right) \end{gathered}$$

Let, the container primarily contains 7x and 5x of mixtures A and B respetively.

Now, after drawing off 9 litres of mixtures

The quantity of A left in the mixture = $7x-\frac{7\times 9}{5+7}=7x-\frac{63}{12}=7x-\frac{21}{4}$ litres.

And the quantity of B left in the mixture = $5x-\frac{5\times 9}{5+7}=5x-\frac{45}{12}-\frac{15}{4} litres.$

According to question, $\frac{7x-{\displaystyle \frac{21}{4}}}{5x-{\displaystyle \frac{15}{4}}+9}=\frac{7}{9}$

$$\begin{gathered} =\frac{{\displaystyle \frac{28x-21}{4}}}{{\displaystyle \frac{20x-15+36}{4}}}=\frac{7}{9} \\ =\frac{28x-21}{4}\times \frac{4}{20x+21}=\frac{7}{9} \\ =\frac{28x-21}{20x+21}=\frac{7}{9} \\ =252x-189=140x+147 \\ =112x=336 \\ \therefore x=\frac{336}{112}=3 \\ \therefore The container contained = 7\times 3=21 litres of A. \end{gathered}$$

In bag 1: There are 5 red balls and 3 green balls.

In bag 2: There are 4 red balls and 6 green balls.

Now,

In case 1, the probability of getting red ball from bag I and green ball from bag

$2=\frac{5}{5+3}\times \frac{6}{4+6}=\frac{5}{6}\times \frac{6}{10}=\frac{30}{60}$

And, In case 2, the probability of getting green ball from bag I and red ball from bag

$2=\frac{3}{8}\times \frac{4}{10}=\frac{12}{80}$

$\therefore$Probability of getting 1 red ball and 1 green ball = $\frac{30}{80}+\frac{12}{80}=\frac{30+12}{80}=\frac{42}{80}=\frac{21}{40}$ (answer).

Let us depict a picture according to question

Now, let one ship is x meter away and another ship is y meter away from the lighthouse.

Here, AD = 100 meter = height of lighthouse

$\angle$ABD = 45$°$ and $\angle$ACD = 30$°$

From $∆$ADC.

tanθ = $\frac{AD}{DC}$

= tan 30$°$ = $\frac{100}{x}$

$$\begin{gathered} =\frac{1}{\sqrt{3}}=\frac{100}{x} \\ \therefore x=100\sqrt{3} \\ Again, from ∆ABD \\ \tan \theta =\frac{AD}{BD} \\ =\tan 45°=\frac{100}{y} \\ =1=\frac{100}{y} \\ \therefore y=100 \\ \because The dis\tan ce between the two ships will be =x+y \\ =100\sqrt{3}+100=100(1.73+1)=100(2.73)=273 \left(answer\right) \end{gathered}$$

Given, $\frac{x^2+xy+y^2}{x^2-xy+y^2}$

$$\begin{gathered} \therefore x+y=\frac{\sqrt{5}+1}{\sqrt{5}-1}+\frac{\sqrt{5}-1}{\sqrt{5}+1}=\frac{{(\sqrt{5}+1)}^2+{(\sqrt{5}-1)}^2}{(\sqrt{5}-1) (\sqrt{5}+1)}=\frac{{\left(\sqrt{5}\right)}^2+2\times \sqrt{5}\times 1+1^2+{\left(\sqrt{5}\right)}^2-2\times \sqrt{5}\times 1+1^2}{{\left(\sqrt{5}\right)}^2-\left(1\right)} \\ =\frac{5+2\sqrt{5}+1+5-2\sqrt{5}+1}{5-1}=\frac{12}{4}=3 \\ And, xy =\frac{\sqrt{5}+1}{\sqrt{5}-1}\times \frac{\sqrt{5}-1}{\sqrt{5}+1}=1 \\ Now, x^2+xy+y^2=x^2+2xy+y^2-xy={(x+y)}^2-xy=3^2-1=9-1=8 \\ And, x^2-xy+y^2=x^2+2xy+y^2-3xy={(x+y)}^2-3xy=3^2-(3\times 1)=9-3=6 \\ \therefore \frac{x^2+xy+y^2}{x^2-xy+y^2}=\frac{8}{6}=\frac{4}{3} \end{gathered}$$

Given that, ab+bc+ca=0

$$\begin{gathered} \therefore ab+bc=-ca \therefore ca=-(ab+bc) \\ =ab+ca=-bc \therefore =bc=-(ab+ca) \\ =bc+ca=-ab \therefore =ab=-(bc+ca) \\ Again given that, \frac{1}{a^2-bc}+\frac{1}{b^2-ac}+\frac{1}{c^2-ab} \\ =\frac{1}{a^2+ab+ca}+\frac{1}{b^2+ab+bc}+\frac{1}{c^2+bc+ca}=\frac{1}{a(a+b+c)}+\frac{1}{b(b+a+c)}+\frac{1}{c(c+b+a)} \\ =\frac{1}{a(a+b+c)}+\frac{1}{b(a+b+c)}+\frac{1}{c(a+b+c)}=\frac{1}{a(a+b+c)}\times (\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=\frac{1}{a+b+c}\times \frac{(bc+ca+ab)}{abc} \\ =\frac{ab+bc+ca}{abc(a+b+c)}=\frac{0}{abc(a+b+c)}=0 \end{gathered}$$

Convection currents are the loops of moving water or air which transfer energy from one place to another place.

Convection currents influence the weather creating wind that blows clouds carrying precipitation from one place to another place.

As mountains are in high position, it gets heat faster. So, the air of mountains is warm. This warm air rises and the cooler air in the valley rushes to the mountains to replace the rising air.

Local winds stay in a smaller area whereas global winds cover larger areas.

                                                                                                                      Impact of television on social value

Television is one of the most popular devices that are used for entertainment all over the world. It has become quite common nowadays and almost every household has one television set at their place. 

With the invention of television, the craze allured many people to spend all their time watching TV. People started considering it detrimental as it attracted the kids the most. In other words, kids spent most of their time watching television and not studying. However, as times passed, the channels of television changed. More and more channels were broadcasted with different specialties. Thus, it gave us knowledge too along with entertainment. 

The impact of television on social values are numerous and definitely vary in positive and negative ways. Since television was first introduced it has been a very large part of our society. Television started as a form of entertainment that would be watched by the family for an hour a night as a relaxing way of getting away from the stresses of real life. Television has now turned into one of the biggest industries in the world, and has more influence than anyone could have imagined. Many people view television as a very positive form of entertainment, as it is without a doubt the most popular kind in the world. 

Television can expose children to situations that they should definitely not view at young ages. Everywhere you look on television there is a sex scene or a love scene. Many parents are very anxious that their children should not be viewing this material, and at this point there are not many good ways to keep them from watching it. Television now uses a rating system for all of its shows, but that is ignored by a good percent of the population. Television also takes all people away from reading and other activities that could be done in place of the 5 hours that is spent in front of the television every afternoon and night. The majority of household women can be seen as lazy or indolent because they pass most of their time watching serials. It is seen in the present time parents are callous to their children as they are busy in Indian TV serials. Conjugal relationships have been tremendously hampered due to some particular programs telecast by some television channel as husbands or wives cannot act according to the TV programs.

Today, television is very much popular for some particular programs. In our Bangladesh, television is being watched for news and some serials telecast from foreign channels. We are Bangladeshi and our culture is totally different from others. So importing some foreign channels will destabilize our values as those programs are not suitable for our society. The way of acting, romanticism, dialogues etc that are shown on that channels, sometimes go against our values. For this reason, we are losing our values and morals as we are trying to imitate those cultures. Thus, television impacts immensely on the social values of young generation.

২৩-১১-২০১৯
বরাবর 
চেয়ারম্যান 
জেলা পরিষদ, মানিকগঞ্জ 

বিষয়: শিবালয় উপজেলাধীন দশচিড়া ও চারিপাড়া গ্রামের মধ্যে ব্রিজ নির্মাণের আবেদন। 

জনাব, 
যথাবিহীত সম্মান প্রদর্শনপূর্বক আমরা দশচিড়া ও চারিপাড়া গ্রামের অধিবাসীরা জানাচ্ছি যে শিবালয় উপজেলাধীন উপরিউক্ত ঐ দুই গ্রামের মধ্য দিয়ে বয়ে চলছে ইছামতি নদীর একটি প্রধান অংশ। এই দুই গ্রামে বসবাসরত প্রায় ৮ হাজার অধিবাসীকে প্রায় প্রতিদিনই নৌকাযোগে এই ছোট নদীটি পার হতে হয়। স্কুল, কলেজ ও মাদ্রাসাসহ বেশ কয়েকটি শিক্ষা প্রতিষ্ঠানে গমনের জন্য প্রতিনিয়তই এই সকল কোমলমতি শিক্ষার্থীদের চরম দুর্ভোগ পোহাতে হয়। এছাড়া নদীতে সর্বদা খেয়া না থাকায় অসুস্থ রোগীদের পারাপারে মারাত্মক অসুবিধার সৃষ্টি হয়। কিন্তু এই দুই গ্রামের মধ্যে একটি সংযোগ ব্রীজ স্থাপিত হলে উভয় গ্রামের মানুষের মধ্যে নেমে আসবে স্বস্তির নিঃশ্বাস। 

অতএব, জনাবের নিকট বিনীত নিবেদন এই যে, আমাদের দুই গ্রামের মধ্যে সংযোগকারী একটি ব্রীজ নির্মাণ করে এলাকাবাসী কৃতজ্ঞতা পাশে থেকে বাধিত করবেন। 

বিনীত নিবেদক 
মোঃ ইসমাইল হোসেন। 
টেপড়া, শিবালয়, মানিকগঞ্জ-১৮৫০।