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

Sol:

$\begin{array}{l}Givenequationis{x}^2\frac{dy}{dx}=x^2+xy+y^2\\ \Rightarrow \frac{dy}{dx}=\frac{x^2+xy+y^2}{x^2}\\ Puty=vx\left[?Itisahomogeneousdifferentialequation\right]\\ \therefore \frac{dy}{dx}=v+x.\frac{dv}{dx}\\ \therefore v+x.\frac{dv}{dx}=\frac{x^2+v{x}^2+v^2{x}^2}{x^2}\\ \Rightarrow v+x.\frac{dv}{dx}=\frac{x^2\left(1+v+v^2\right)}{x^2}\\ \Rightarrow v+x.\frac{dv}{dx}=1+v+v^2\\ \Rightarrow x.\frac{dv}{dx}=1+v+v^2-v\\ \Rightarrow x.\frac{dv}{dx}=1+v^2\Rightarrow \frac{dv}{1+v^2}=\frac{dx}{x}\\ Integratingbothsidesweget\\ {\displaystyle \int \frac{dv}{1+v^2}}={\displaystyle \int \frac{dx}{x}}\\ \Rightarrow ta{n}^{-1}v=logx+c\Rightarrow ta{n}^{-1}\left(\frac{y}{x}\right)=logx+c\\ Hence,therequiredsolutionista{n}^{-1}\left(\frac{y}{x}\right)=log\left|x\right|+c.\end{array}$

Absolutely, You can definitely appear for many central and state level competitive exams after your BMS graduation. which are:

• UPSC Civil Services (IAS/IPS)
• Banking exams such as IBPS PO, SBI PO, RBI Grade B
• SSC CGL
• State PSC exams
• Railways and Insurance sector jobs
• MBA entrance exams like CAT, XAT, CMAT, MAT

Since BMS is a recognised undergraduate degree it makes you eligible for almost all graduate level government exams in India.

You can go for BCA from Integral University, Lucknow or any colleges.

Yes, you can attempt questions in any sequence in Maharashtra board class 12. Just ensure that while attempting your Maharashtra board exam that you have attempted all the question with a question number written in such a way that examiner can see it properly. And in order to get good marks, it is important to make an impression which can be made by attempting those questions first that you know well. Thus, if you know question no. 12, then instead of 1, 2, attempt those question that you remember properly. 

The BCom specialisations offered by GS College of Commerce are as follows:

Yes, admissions at SCMS School of Engineering and Technology are open now. SCMS SET offers admission to candidates based on entrance exam scores. Aspirants also need to meet the eligibility criteria to apply for a course. Selected candidates are required to keep their educational documents ready for verification purposes.

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

Sol:

$\begin{array}{l}Givenequationis\left(1+x^2\right)\frac{dy}{dx}+2xy=4x^2\\ \Rightarrow \frac{dy}{dx}+\frac{2x}{1+x^2}.y=\frac{4x^2}{1+x^2}\\ \therefore P=\frac{2x}{1+x^2}andQ=\frac{4x^2}{1+x^2}\\ IntegratingfactorI.F=e^{{\displaystyle \int Pdx}}=e^{{\displaystyle \int \frac{2x}{1+x^2}.dx}}=e^{log\left(1+x^2\right)}=1+x^2\\ \therefore Solutionoftheequationis\\ y\times I.F.={\displaystyle \int Q\times I.F.dx+c}\\ \Rightarrow y.\left(1+x^2\right)={\displaystyle \int \frac{4x^2}{1+x^2}\times \left(1+x^2\right)dx+c}\\ \Rightarrow y.\left(1+x^2\right)={\displaystyle \int 4x^{2}dx+c}\\ \Rightarrow y.\left(1+x^2\right)=\frac{4}{3}{x}^3+c\dots \left(i\right)\\ Sincethecurveispassingthroughi.e.,\left(0,0\right)\\ Puty=0andx=0ineqn.\left(i\right)\\ \Rightarrow 0\left(1+0\right)=\frac{4}{3}{\left(0\right)}^3+c\Rightarrow c=0\\ Sotheequationbecomes\\ \therefore y\left(1+x^2\right)=\frac{4}{3}{x}^3\Rightarrow y=\frac{4x^3}{3\left(1+x^2\right)}\\ Hence,therequiredsolutionisy=\frac{4x^3}{3\left(1+x^2\right)}.\end{array}$

The admission process at the PW Institute of Innovation Lucknow includes online application and registration form followed by an entrance exam. Accepted entrance exams include CEE, JEE Main, NEET, CUET and IPMAT. The candidates must also appear for the interview round. Interested candidates can apply online on the official website for the desired course.

Yes, SLS Pandit Deendayal Energy University offers four-year long BBA (Hons) programmes. The mode of study is full-time. Candidates seeking admission have to take the university exam followed by a personal interview round. However, aspirants with a valid SAT India score can also apply for admission. Before the form filling, the aspirants must check out the eligibility requirements. 

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

Sol:

Not exactly the same, but, MSBSHSE can ask questions similar to what were asked in the previous years of Maharashtra HSC exams. Thus, you are advised to download and practice the previous years' question papers thoroughly for better preparation. 

A total of 484 colleges along with, 120 B.Ed. colleges are affiliated with Maharaja Ganga Singh University. These colleges are located all over the Bikaner Division, which includes Bikaner, Sri Ganganagar, Hanumangarh, and Churu districts. Based on student reviews, some of the popular MGSU colleges are:

·      Dr. B R Ambedkar Government PG College, Sri Ganganagar

·      Seth G.L. Bihani S.D. PG College, Sri Ganganagar

·      Government Lohia College, Churu

·      Government Law College, Bikaner

NLU Kolkata admits students to its BA LLB Hons course based on CLAT scores. As per official sources, up till now, the Consortium of NLUs has released the first seat allotment result for 2026. The CLAT 2026 third allotment list is expected to be published on Feb 5, 2026. Once the results are out, students participating in the admission process must go the official website to check it.

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

Sol:

Chances are less for out of syllabus questions in Maharashtra 12th board exam question papers. Maharashtra HSC board exams will be based on Maharashtra HSC syllabus entirely. If any questions are out of syllabus, students will be awarded the marks for it. 

You are advised to go through the Maharashtra HSC 12th syllabus and study all the topics mentioned there.

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

Sol:

$\begin{array}{l}Givenequationis\left(1+t\right)\frac{dy}{dt}-ty=1\\ \Rightarrow \frac{dy}{dt}-\left(\frac{t}{1+t}\right)y=\frac{1}{1+t}\\ \therefore P=-\frac{t}{1+t}andQ=\frac{1}{1+t}\\ IntegratingfactorI.F=e^{{\displaystyle \int Pdt}}=e^{{\displaystyle \int -\frac{t}{1+t}.dt}}=e^{-{\displaystyle \int \frac{1+t-1}{1+t}.dt}}\\ =e^{-{\displaystyle \int \left(1-\frac{1}{1+t}\right).dt}}=e^{-\left[t-log\left(1+t\right)\right]}\\ =e^{-t+log\left(1+t\right)}=e^{-t}.e^{log\left(1+t\right)}=e^{-t}\left(1+t\right)\\ \therefore Solutionoftheequationis\\ y\times I.F.={\displaystyle \int Q.I.F.dt+c}\\ \Rightarrow y.e^{-t}\left(1+t\right)={\displaystyle \int \frac{1}{\left(1+t\right)}.e^{-t}\left(1+t\right)dt+c}\\ \Rightarrow y.e^{-t}\left(1+t\right)={\displaystyle \int e^{-t}dt+c}\\ \Rightarrow y.e^{-t}\left(1+t\right)=-e^{-t}+c\\ Putt=0andy=-1\left[?y\left(0\right)=-1\right]\\ \Rightarrow -1.e^0.1=-e^0+c\\ \Rightarrow -1=-1+c\Rightarrow c=0\\ Sotheequationbecomes\\ \therefore y.e^{-t}\left(1+1\right)=-e^{-t}\\ \Rightarrow 2y=-1\Rightarrow y=-\frac{1}{2}\\ Hence,y\left(1\right)=-\frac{1}{2}isverified.\end{array}$

MGSU Bikaner campus is spread across 1100 acres of land, and is located in Bikaner, Rajasthan. The university consists of 7 faculties, 9 academic centres, 120 B.Ed. colleges and 484 affiliated colleges. MGSU aims to provide an eco-friendly campus and hence, established, a solar plant, oxygen zone, and a green solar corridor. It also provides facilities like Sports Complex, Central Library, Wi-Fi, Cafeteria, ATM, Bank, Post Office, Auditorium, Transportation, etc. MGSU also provides separate hostel facilities for both boys and girls.

Yes, NLU Kolkata BA LLB Hons admissions are open for the academic year 2025-2026. Interested students must visit the official website of the Consortium of NLUs and participate in the counselling process conducted based on CLAT scores. As of now, the official body has released the CLAT second allotment list for 2025.