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This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}LetthethirdpHvaluebex.\\ GiventhatfirstpHvalue=8.48\\ andsecondpHvalue=8.35\\ \therefore AveragevalueofpH=\frac{8.48+8.35+x}{3}\\ ButaveragevalueofpHliesbetween8.2and8.5\\ \therefore 8.2<\frac{8.48+8.35+x}{3}<8.5\\ \Rightarrow 24.6<16.83+x<25.5\\ \Rightarrow 24.6-16.83<x<25.5-16.83\\ \Rightarrow 7.77<x<8.67\\ Hence,thethirdpHvalueliesbetween7.77and8.67.\end{array}$

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhat:Costfunction,C\left(x\right)=26,000+30x\\ andrevenuefunctionR\left(x\right)=43x\\ NowforprofitP\left(x\right),R\left(x\right)>C\left(x\right)\\ \Rightarrow 43x>26000+30x\Rightarrow 26000+30x<43x\\ \Rightarrow 30x-43x<26000\Rightarrow -13x<-26000\\ \Rightarrow 13x>26000\Rightarrow x>2000\\ Hence,numberofcassettestobemanufacturedforsomeprofitmustbemorethan2000.\end{array}$

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhat4x+3\ge 2x+17\dots \left(i\right)\\ 3x-5<-2\dots \left(ii\right)\\ Fromeqn.\left(i\right)weget\\ 4x+3\ge 2x+17\Rightarrow 4x-2x\ge 17-3\\ \Rightarrow 2x\ge 14\Rightarrow x\ge 7\\ Fromeqn.\left(ii\right)weget\\ \Rightarrow 3x-5<-2\Rightarrow 3x<3\\ \Rightarrow x<1\\ Wesetthatthesolutionx\ge 7andx<1isnotpossible.Hencetherewillbenosolutionofx.\end{array}$

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhat-5\le \frac{2-3x}{4}\le 9\\ \Rightarrow -20\le 2-3x\le 36\Rightarrow -22\le -3x\le 34\\ \Rightarrow 22\ge 3x\ge -34\\ \Rightarrow \frac{22}{3}\ge x\ge \frac{-34}{3}\\ Hencex\in \left[\frac{-34}{3},\frac{22}{3}\right]\end{array}$

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhat\left|x-1\right|\le 5and\left|x\right|\ge 2\\ \Rightarrow -5\le x-1\le 5andx\le -2orx\ge 2\\ \Rightarrow -5+1\le x\le 5+1andx\le -2orx\ge 2\\ \Rightarrow -4\le x\le 6andx\le -2orx\ge 2\\ Hencex<\left[-4,-2\right]\cup \left[2,6\right]\end{array}$

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhat\frac{1}{\left|x\right|-3}\le \frac{1}{2}\\ \Rightarrow \left|x\right|-3\ge 2\left[?\frac{1}{x}<\frac{1}{y}\Rightarrow x>y\right]\\ \Rightarrow \left|x\right|\ge 5\\ \Rightarrow \left|x\right|\le -5or\left|x\right|\ge 5\\ So,x\in \left(-\infty ,-5\right]\cup \left[5,\infty \right)\dots \left(i\right)\\ Here,\left|x\right|-3\ne 0\\ \Rightarrow \left|x\right|-3<0or\left|x\right|-3>0\\ \Rightarrow \left|x\right|<3or\left|x\right|>3\\ \Rightarrow -3<x<3orx<-3orx>3\dots \left(ii\right)\\ Fromineqn.\left(i\right)and\left(ii\right)weget\\ x\in \left(-\infty ,-5\right]\cup \left(-3,3\right)\cup \left[5,\infty \right)\end{array}$

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhat\frac{\left|x-2\right|-1}{\left|x-2\right|-2}\le 0\\ Put\left|x-2\right|=y\\ \therefore \frac{y-1}{y+2}\le 0\\ \Rightarrow y-1>0,y-2<0\Rightarrow y>1,y<2\\ \Rightarrow 1<y<2\Rightarrow 1<\left|x-2\right|<2\\ \Rightarrow 1<\left|x-2\right|,\left|x-2\right|<2\\ \Rightarrow x-2<-1orx-2>1and-2<x-2<2\\ \Rightarrow x<1orx>3and-2+2<x<2+2\\ \Rightarrow x<1orx>3and0<x<4\\ Hence,thesolutionis\left(0,1\right)\cup \left(3,4\right).\end{array}$

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhat\frac{4}{x+1}\le 3\le \frac{6}{x+1},x>0\\ \Rightarrow 4\le 3\left(x+1\right)\le 6\Rightarrow 4\le 3x+3\le 6\\ \Rightarrow 4-3\le 3x\le 6-3\Rightarrow 1\le 3x\le 3\\ \Rightarrow \frac{1}{3}\le x\le 1\\ Hence,thesolutionis\frac{1}{3}\le x\le 1.\end{array}$

Kerala Agricultural University offers various specialisations spread across different fields of agriculture and allied sciences. At the time of application, students must choose their choice of specialisation. Mentioned below are the specialisations offered by the university:

• Forestry
• Agriculture 
• Climate Change and Environmental Science, etc. 

In India, government jobs are preferred by job seekers over private jobs. This happens because government jobs provide many benefits, such as tax deductions, good pay, job stability, incentives, and more. This attracts a lot of competition and thus, getting a government job is not easy. However, a BSc degree helps students develop skills required to combat the competition. Some of the jobs that BSc graduates can pursue are tabulated below:

The basic eligibility requirement to get admission into BSc courses at UAS Dharwad and Kerala Agricultural University is almost similar, in which candidates are required to qualify for their Class 12 from a relevant stream with a minimum aggregate of 50%. Further, for the selection process, KAU accepts relevant ICAR CUET/ KEAM scores. On the other hand, UAS Dharwad accepts relevant scores of ICAR CUET/ KCET. Hence, the only difference is the type of entrance exam accepted for the BSc course. Candidates can choose any of them that align with their career choices, location preferences and affordability. 

The total tuition fee for the BSc course at TNAU ranges from INR 36,000 - INR 2 lakh, and the tuition fee for KAU BSc courses ranges from INR 71,700 to INR 71,900. Therefore, there might be a possibility that some of the BSc courses offered at TNAU are more affordable than the KAU BSc courses. However, TNAU fee ranges last till INR 2 lakh, and KAU fee ranges from INR 71,700 to 71,900. Thus, the tuition fee for KAU BSc courses is more affordable than TNAU BSc courses. The fee amount mentioned is sourced from the official website/sanctioning body and is subject to change. Therefore, it is indicative. 

With a rank of 5700 in EWS (female) category in 2025, you have a real chance of receiving a free or significantly subsidized seat in government colleges in Visakhapatnam. One very strong option would be Visakha Government Degree College for Women. They offer various undergraduate programs and support EWS candidates through scholarships and fee exemptions. Admission is merit-based and category-based, your rank should be competitive enough to get a seat in popular courses such as, B.A., B.Com., or B.Sc. It is important to check the admission counselling rounds, and apply early to have the best chances.

Hanyang University is one of the most prominent universities for higher education in South Korea. Hanyang University placement rate attracts international students the most. The university graduates are in high demand all over the world. Hanyang University placement rate stands at 94.1%, and the graduates are employed within 6 months of graduation. According to unofficial sources, the average salary of Hanyang University graduates KRW 70,140,803 (INR 44.20 L), annually. The university graduates work for top companies such as SK Hynix, Samsung SDI, Coupang, Deloitte, Accenture, Google, and more.