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Rajasthan PTET 2025 Counselling schedule was announced on July 4, 2025. Candidates who have cleared the PTET exam are eligible to register for the counselling process. They must pay 5000 Rs. as the initial amount during the counselling registration and the remaining amount of Rs. 22,000 until July 30. The college reporting date after the Phase 1 seat allotment round is July 31, 2025.

$\begin{array}{l}Giventhat:A=\left\{1,3,5\right\},B=\left\{2,4,6\right\}andC=\left\{0,2,4,6,8\right\}\\ \therefore Universalsetofallthegivensetsis\\ U=\left\{0,1,2,3,4,5,6,8\right\}\\ Hence,thefilleris\left\{0,1,2,3,4,5,6,8\right\}.\end{array}$

Once Takshashila University closes the application portal for BTech courses, the admissions committee reviews all the applications. Students who have a good academic background and satisfy the eligibility criteria are shortlisted for further process. Students may be required to take an entrance exam or appear for an interview round. Students who are required to take the test are informed timely.

MSc Nursing itself is a very good option for Nurses who want to gain expertise in a specific department. However, some specializations hold significant value due to their high demand, well-paying career options, etc. Among these MSc Nursing specializations, Obstetrics and Gynaecological Nursing, Child Health (Paediatric) Nursing, Mental Health (Psychiatric) Nursing, Medical-Surgical Nursing, and Community Health Nursing are the most popular and the most sough-after areas.

IIT Jodhpur offers various UG & PG courses in the streams of Management, Engineering and Science. The IIT Jodhpur fee is made up of a number of different elements, including the tuition, security deposit, and hostel fee. There are two types of IIT Jodhpur fee components: refundable and non-refundable. To confirm their seat, candidates who made through the shortlist via the IIT Jodhpur admission process must pay the course fee. The Institute fee structure includes tuition fees varying from INR 26 K to INR 9 Lakh. Considering the other institutes' fee range, IIT Jodhpur offers courses at an affordable price. 

$\begin{array}{l}PowersetofA=P\left(A\right)=\left\{\left\{1\right\},\left\{2\right\},\left\{1,2\right\},?\right\}\\ Hence,thefilleris\left\{\left\{1\right\},\left\{2\right\},\left\{1,2\right\},?\right\}.\end{array}$

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

$\begin{array}{l}Giventhat:f\left(x\right)=2x+1andg\left(x\right)=4x-7\\ \left(i\right)Forf\left(x\right)=g\left(x\right),weget\\ 2x+1=4x-7\Rightarrow 2x-4x=-7-1\\ \Rightarrow -2x=-8\\ \Rightarrow x=4.Hence,therequiredrealnumberis4.\\ \left(ii\right)Forf\left(x\right)<g\left(x\right),weget\\ 2x+1<4x-7\Rightarrow 2x-4x<-7-1\\ \Rightarrow -2x<-8\\ \Rightarrow x>4.Hence,therequiredrealnumberisx>4.\end{array}$

Some the top recruiters for Amrita Vishwa Vidyapeetham placement are listed below:

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhat:tan\theta +sin\theta =mandtan\theta -sin\theta =n\\ L.H.S.m^2-n^2=\left(m+n\right)\left(m-n\right)\\ =\left[\left(tan\theta +sin\theta \right)+\left(tan\theta -sin\theta \right)\right].\left[\left(tan\theta +sin\theta \right)-\left(tan\theta -sin\theta \right)\right]\\ =\left[tan\theta +sin\theta +tan\theta -sin\theta \right].\left[tan\theta +sin\theta -tan\theta +sin\theta \right]\\ =2tan\theta .2sin\theta =4sin\theta tan\theta R.H.S.\\ L.H.S.=R.H.S.Henceproved.\end{array}$

$\begin{array}{l}FromthevenndiagramitisclearthatA-B=A\cap B\text{'}\\ Hence,thefillerisA\cap B\text{'}.\end{array}$

$\begin{array}{l}SinceA\subset B\therefore n\left(A\cup B\right)=n\left(B\right)\\ Hence,thefillerisn\left(B\right).\end{array}$

Yes, during the final stage of BTech admissions at Takshashila University, students who are offered admission must pay the first installment of the first-year fees. In general, at this stage, students are required to pay admission fees and some part of the tuition fees. For more information, students can visit the official website of the university.

$\begin{array}{l}Here,A=?\therefore n\left(A\right)=0\\ ?n\left[P\left(A\right)\right]=2^{n\left(A\right)}=2^0=1\\ Hence,thefilleris1.\end{array}$

Both colleges offer several specialisations in BE/ BTech courses. Moreover, the total number of seats offered in the BTech course at R.V. College of Engineering is around 1,555. Moreover, the number of seats offered in BTech at Ramaiah Institute of Technology is around 1,401. Therefore, RVCE offers a larger number of seats in undergraduate engineering courses compared to Ramaiah Institute of Technology. Moreover, the admission process for BE/ BTech courses is almost similar at both institutes. 

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

$\begin{array}{l}Giventhat:f\left(x\right)=x^2+7andg\left(x\right)=3x+5\\ \left(i\right)f\left(3\right)+g\left(-5\right)=\left[{\left(3\right)}^2+7\right]+\left[3\left(-5\right)+5\right]\\ =\left(9+7\right)+\left(-15+5\right)=16-10=6\\ Hence,f\left(3\right)+g\left(-5\right)=6\\ \left(ii\right)f\left(\frac{1}{2}\right)\times g\left(14\right)=\left[{\left(\frac{1}{2}\right)}^2+7\right]\times \left[3\times 14+5\right]\\ =\left(\frac{1}{4}+7\right)\times \left(42+5\right)=\frac{29}{4}\times 47=\frac{1363}{4}\\ Hence,f\left(\frac{1}{2}\right)\times g\left(14\right)=\frac{1363}{4}\\ \left(iii\right)f\left(-2\right)+g\left(-1\right)=\left[{\left(-2\right)}^2+7\right]+\left[3\left(-1\right)+5\right]\\ =\left(4+7\right)+\left(-3+5\right)=11+2=13\\ Hence,f\left(-2\right)+g\left(-1\right)=13\\ \left(iv\right)f\left(t\right)-f\left(-2\right)=\left(t^2+7\right)-\left[{\left(-2\right)}^2+7\right]=t^2+7-11\\ =t^2-4\\ Hence,f\left(t\right)-f\left(-2\right)=t^2-4.\\ \left(v\right)\frac{f\left(t\right)-f\left(5\right)}{t-5},t\ne 5=\frac{\left(t^2+7\right)-\left[{\left(5\right)}^2+7\right]}{t-5}\\ =\frac{t^2+7-32}{t-5}=\frac{t^2-25}{t-5}=t+5\\ Hence,\frac{f\left(t\right)-f\left(5\right)}{t-5},t\ne 5=t+5.\end{array}$

You can take admission in BS or BSc degree at IIT Jodhpur. There's a qualifier test to get into it. 

$\begin{array}{l}Theset\left\{x\in R:1\le x<2\right\}canbewrittenas\left[1,2\right)\\ Hence,thefilleris\left[1,2\right).\end{array}$