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This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Thegivendifferentialequationis\\ \frac{dy}{dx}-y=1\\ Here,P=-1andQ=1\\ So,\text{integrating\hspace{0.17em}}factor=e^{{\displaystyle \int Pdx}}=e^{{\displaystyle \int -1dx}}=e^{-x}\\ So,thesolutionis\\ y\times I.F={\displaystyle \int Q\times I.F.dx+c}\\ \Rightarrow y\times e^{-x}={\displaystyle \int 1.e^{-x}.dx+c}\\ \Rightarrow y.e^{-x}=-e^{-x}+c\\ Putx=0,y=1\\ \Rightarrow 1.e^0=-e^0+c\\ \Rightarrow 1=-1+c\therefore c=2\\ So,theequationisy.e^{-x}=-e^{-x}+2\\ \Rightarrow y=-1+2e^x=2e^x-1\\ Hence,thecorrectoptionis\left(d\right).\end{array}$

Gateway Institute of Engineering and Technology BBA fees are to be paid at certain time-intervals such as annually or semesterly, as per the university. The Gateway Institute of Engineering and Technology BBA course fees include different aspects such as the tuition fees, hostel charges, and other deposits. The total tuition expense for the study of BBA course at Gateway Institute of Engineering and Technology is INR 2.26 Lakh.

Note: The above information about Gateway Education course fees, is taken from the official website and might be subject to revision and hence, indicative.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Thegivendifferentialequationis\\ x\frac{dy}{dx}-y=x^4-3x\\ \frac{dy}{dx}-\frac{y}{x}=x^3-3\\ Here,P=-\frac{1}{x}andQ=x^3-3\\ So,\text{\hspace{0.17em}integrating}factor=e^{{\displaystyle \int Pdx}}=e^{{\displaystyle \int -\frac{1}{x}dx}}=e^{-logx}=e^{log\frac{1}{x}}=\frac{1}{x}\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

Yes, an MBA programme is offered through RGU’s International College via the Navitas pathways. This is ideal for the international students who need pre-session preparation. There are three programs under this MBA which are in the fields of Business & Management, Accounting & Finance, and Creative and Cultural Business. The estimated tuition fee is £18,000 per year (INR 18–21? L).

The MSc admissions process at Surana College Post Graduate Departments indicates that admission is determined based on the marks obtained in the last qualifying exam. Interested students will need to apply through the official website. In order to confirm their seat, the applicants will need to submit the relevant documents and the admission fee.

The fees for Surana College Post Graduate Department MSc for two years are INR 2.2 lakh. The total course fee includes tuition fees and other fees. Additionally, the admission fee, security fee, and other one-time fee payments are made only once. Hence, to confirm their admission for the MSc programme, candidates are required to submit the applicable course fee.

NOTE: The aforementioned fee is taken from the official website/sanctioning body. It is still subject to change and, hence, is indicative.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Givenequationisy=Ax+A^3\\ Differentiatingbothsides,weget\\ \frac{dy}{dx}=Awhichhas\text{\hspace{0.17em}degree}1.\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Thegivendifferentialequationis\\ tanyse{c}^{2}xdx+tanxse{c}^{2}ydy=0\\ \Rightarrow tanxse{c}^{2}ydy=-tanyse{c}^{2}xdx\\ \Rightarrow \frac{se{c}^{2}y}{tany}.dy=\frac{-se{c}^{2}x}{tanx}.dx\\ Integratingbothsides,weget\\ \Rightarrow {\displaystyle \int \frac{se{c}^{2}y}{tany}.dy={\displaystyle \int \frac{-se{c}^{2}x}{tanx}.dx}}\\ \Rightarrow log\left|tany\right|=-log\left|tanx\right|+logc\\ \Rightarrow log\left|tany\right|+log\left|tanx\right|=logc\\ \Rightarrow log\left|tanx.tany\right|=logc\\ \Rightarrow tanx.tany=k\left[?logc=k\right]\\ Hence,thecorrectoptionis\left(d\right).\end{array}$

KD Dental College and Hospital follows an entrance-based admission process and to apply for the courses candidates must follow the application process: 

Step 1: Visit the official website of the institute.

Step 2: Go to the apply now section.

Step 3: Fill out the form with accurate details. 

Step 4: Pay the application fee and download the form for future use. 

Gateway Institute of Engineering and Technology BBA course is delivered by the university in the full-time mode. The study duration of the BBA course lasts for three years which is further divided into six semesters. Admission into the BBA course is subject to result of personal interview conducted by the institute. The admission is mostly merit-based. Satisfying eligibility criteria is crucial for admission.

Yes, candidates can apply for more than one BSc specialisation at Remo International College. They are required to submit a separate application form and required documents and must pay an application fee according to the course. Moreover, the confirmation of which course a student will get depends on the merit list or major selected by them in the application form.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Givendifferentialequationis\\ cosx.\frac{dy}{dx}+ysinx=1\\ \Rightarrow \frac{dy}{dx}+\frac{sinx}{cosx}y=\frac{1}{cosx}\Rightarrow \frac{dy}{dx}+tanxy=secx\\ Here,P=tanxandQ=secx\\ Integratingfactor=e^{{\displaystyle \int Pdx}}=e^{{\displaystyle \int tanxdx}}=e^{logsecx}=secx\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

There are 5 MSc courses offered at International College at Robert Gordon University in fields such as Business & Management, Accounting & Finance, Engineering, Creative & Cultural Business, and Computing. These courses are offered as the pathway programs at the International College at Robert Gordon.

Yes, BBA application process at Sasurie College of Arts and Science with the help of Sunstone is completely online. The applicants should head to the official webpage and register by providing academic information and documents. On successful screening, those who pass through the Sunstone screening process are put in the merit list. The application is validated with the payment of fee.

Sasurie College of Arts and Science run by Sunstone has a selection procedure which involves Sunstone screening test and an interview. In this process students are shortlisted according to their performance. Admission of a final nature may follow only after verifying the eligibility and passing the screening. The result list in the form of a merit list is issued prior to confirmation of seat.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Givendifferentialequationis\\ xdy-ydx=0\\ \Rightarrow \frac{dy}{dx}=\frac{y}{x}\Rightarrow \frac{dy}{y}=\frac{dx}{x}\\ Integratingbothsides,weget\\ {\displaystyle \int \frac{dy}{y}={\displaystyle \int \frac{dx}{x}}}\\ \Rightarrow logy=logx+logc\\ \Rightarrow logy=logxc\\ \Rightarrow y=xcwhichisastraightline\text{passing\hspace{0.17em}}throughtheorigin.\\ Hence,thecorrectoptionis\left(c\right).\end{array}$