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This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Thegivendifferentialequationis\frac{d^{2}y}{d{x}^2}-2\frac{dy}{dx}+y=0\\ \text{\hspace{0.17em}Since}theaboveequationisoforderandfirst\\ \therefore D^{2}y-2Dy+y=0,whereD=\frac{d}{dx}\\ \Rightarrow \left(D^2-2D+1\right)=0\\ \therefore auxiliaryequationis{m}^2-2m+1=0\\ \Rightarrow {\left(m-1\right)}^2=0\Rightarrow m=1,1\\ IftherootsofAuxiliaryequationarerealandequalsay\left(m\right)then,\\ CF=\left(c_{1}x+c_2\right).e^{mx}\\ \therefore CF=\left(Ax+B\right).e^x\\ So,y=\left(Ax+B\right).e^x\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

Candidates who have completed a bachelor's degree with at least 55% aggregate in any discipline are eligible to apply for MBA at KL Business School. Aspirants must have relevant documents to prove their eligibility at the time of admission. Besides, aspirants should have a valid score in CAT, MAT, ICET, XAT or KLMAT for admission to MBA programme.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Thegivenequationoffamilyofcurvesis\\ y^2=4a\left(x+a\right)\\ \Rightarrow y^2=4ax+4a^2\dots \left(i\right)\\ Differentiatingbothsides,w.r.t.x,weget\\ 2y.\frac{dy}{dx}=4a\\ \Rightarrow y.\frac{dy}{dx}=2a\Rightarrow \frac{y}{2}.\frac{dy}{dx}=a\\ Now,puttingthevalueofaineqn.\left(i\right)weget\\ y^2=4x\left(\frac{y}{2}.\frac{dy}{dx}\right)+4{\left(\frac{y}{2}.\frac{dy}{dx}\right)}^2\\ \Rightarrow y^2=2xy\frac{dy}{dx}+y^2{\left(\frac{dy}{dx}\right)}^2\\ \Rightarrow y=2x\frac{dy}{dx}+y{\left(\frac{dy}{dx}\right)}^2\\ \Rightarrow 2x.\frac{dy}{dx}+y.{\left(\frac{dy}{dx}\right)}^2-y=0\\ Hence,thecorrectoptionis\left(d\right).\end{array}$

Students must remember to carry the Maharashtra SSC admit card 2026 along with the stationery like pens, pencils, ruler, geometry box etc. It is important that they do not forget the Maharashtra Board hall ticket 2026 otherwise they will not be allowed to write the exam. 

Maharashtra SSC exams 2026 will be conducted between February 20 and March 18, 2026 in pen and paper format. 

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Thegivendifferentialequationis\\ \left[1+{\left(\frac{dy}{dx}\right)}^2\right]=\frac{d^{2}y}{d{x}^2}\\ Here,thehighestderivativeis2,\\ \therefore order=2\\ andthepowerofthehighestderivativeis1\\ \therefore \text{\hspace{0.17em}degree}=1\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

The total tuition fee for MBA at KL Business School ranges between INR 6.7 lakh and INR 11 lakh. This information is sourced from official website/ sanctioning body and is subject to change. The total fee of MBA is a cumulative of components such as caution deposit, tuition fee, exam fee, etc. Aspirants have to deposit some part of the fee at the time of admission to confirm their seat.

In case you find any mistakes in the Maharashtra SSC admit card, you must contact your school officials to get it corrected. 

Collect the Maharashtra Hall Ticket from school and carry it on all exam days, otherwise you will not be allowed to write the exam.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Thegivendifferentialequationis\\ {\left[\frac{d^{3}y}{d{x}^3}\right]}^2-3\frac{d^{2}y}{d{x}^2}+2{\left(\frac{dy}{dx}\right)}^4=y^4\\ Here,thehighestderivativeis\frac{d^{3}y}{d{x}^3}.\\ \therefore orderofthedifferentialequationis3\\ andthepowerofthehighestderivativeis2\\ \therefore its\text{\hspace{0.17em}degreeis}2\\ Hence,thecorrectoptionis\left(d\right).\end{array}$

Yes, candidates need to have a valid score in ICET, CAT, MAT or XAT for admission to MBA programme. Those who have not appeared for any of the accepted exam can appear for KLMAT conducted by the university. Selected candidates have to further pass a personal interview round for admission. Once selected, aspirants have to pay the course fee to confirm their seat.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$Thegivendifferentialequationis\\ \frac{dy}{dx}+y=e^{-x}Since$
$\begin{array}{l}\mathrm{it}islineardifferentialequationwhereP=1andQ=e^{-x}\\ \therefore I.F.=e^{{\displaystyle \int P.dx}}=e^{{\displaystyle \int 1.dx}}=e^x\\ So,thesolutionis\\ y\times I.F.={\displaystyle \int Q\times }I.F.dx+c\Rightarrow y\times e^x={\displaystyle \int e^{-x}}.e^{x}dx+c\\ \Rightarrow y\times e^x={\displaystyle \int e^0.}dx+c\Rightarrow y.e^x={\displaystyle \int 1.}dx+c\\ \Rightarrow y.e^x=x+c\\ Puty=0andx=0\\ \therefore 0=\left(0+c\right)\therefore c=0\\ \therefore equationisy.e^x=x\\ So,y=x.e^{-x}\\ Hence,thecorrectoptionis\left(d\right).\end{array}$

Yes, students must solve the Maharashtra SSC sample papers or previous years' question papers within the time provided as this will help them with time management. This practice will let them know which questions to answer first and those that can be attempted later. This way, students can attempt the questions they definitely know the answer to and score full marks. Thereafter, they can attempt other questions in the time left. 

The total tuition fee for BBA at KL Business School ranges between INR 6.8 Lacs and INR 7.3 lakh. This information is sourced from official website/ sanctioning body and is subject to change. Candidates who are selected for admission have to deposit some part of the fee to confirm their seat. The total fee includes various components such as caution deposit, tuition fee, exam fee, etc.

No, Maharashtra board has not yet released the Maharashtra SSC sample papers 2026. Once released, students will be able to download and practice them by clicking on the link - Maharashtra SSC saple papers.

It is advised that students practice the Maharashtra Class 10 question papers 2026 for better preperation of the examinations. They make one familiar with the exam pattern, marking scheme, different types of questions asked in the exam and more. 

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Thegivenequationisy=acosx+bsinx\\ \therefore \frac{dy}{dx}=-asinx+bcosx\\ \Rightarrow \frac{d^{2}y}{d{x}^2}=-acosx-bsinx\\ \Rightarrow \frac{d^{2}y}{d{x}^2}=-\left(acosx+bsinx\right)\\ \Rightarrow \frac{d^{2}y}{d{x}^2}=-y\Rightarrow \frac{d^{2}y}{d{x}^2}+y=0\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

Candidates who have passed Class 12 or equivalent examination with 55% aggregate and above are eligible to apply for BBA at KL Business School. Aspirants must hold the documents proving their eligibility for verification at the time of admission. Besides, aspirants also need to appear for a written test conducted by KL University for admission.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Thegivendifferentialequationis\\ \left(2y-1\right)dx-\left(2x+3\right)dy=0\\ \Rightarrow \left(2x+3\right)dy=\left(2y-1\right)dx\\ \Rightarrow \frac{dy}{2y-1}=\frac{dx}{2x+3}\\ Integratingbothsides,weget\\ {\displaystyle \int \frac{dy}{2y-1}={\displaystyle \int \frac{dx}{2x+3}}}\\ \Rightarrow \frac{1}{2}log\left|2y-1\right|=\frac{1}{2}log\left|2x+3\right|+logc\\ \Rightarrow log\left|2y-1\right|=log\left|2x+3\right|+2logc\\ \Rightarrow log\left|2y-1\right|-log\left|2x+3\right|=log{c}^2\\ \Rightarrow log\left|\frac{2y-1}{2x+3}\right|=log{c}^2\\ \Rightarrow \frac{2y-1}{2x+3}=c^2\Rightarrow \frac{2x+3}{2y-1}=\frac{1}{c^2}\\ \Rightarrow \frac{2x+3}{2y-1}=k,wherek=\frac{1}{c^2}\\ Hence,thecorrectoptionis\left(c\right).\end{array}$