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This is a Long Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l}LetusconsiderthatthecompanyincreasestheannualsubscriptionbyRs.x\\ So,xisthenumberofsubscriberswhodiscontinuetheservices.\\ \therefore Totalrevenue,R\left(x\right)=\left(500-x\right)\left(300+x\right)\\ =150000+500x-300x-x^2\\ =-x^2+200x+150000\\ Differentiatingbothsidesw.r.t.x,weget{R}^{\text{'}}\left(x\right)=-2x+200\\ Forlocalmaximaandlocalminima,R^{\text{'}}\left(x\right)=0\\ -2x+200=0\Rightarrow x=100\\ R^{\text{'}\text{'}}\left(x\right)=-2<0Maxima\\ So,R\left(x\right)ismaximumatx=100\\ Hence,inordertogetmaximumprofit,thecompanyshouldincreaseitsannualsubscription\\ byRs.100.\end{array}$

To get admission to Backstage Pass Institute of Gaming and Technology, students need to fulfil the basic educational requirements and qualify for the defined admission criteria for differrent courses. Check below the detailed information:

Candidates are selected for IIAD UG and PG programmes on the basis of the following:

• Performance in the IIAD Design Aptitude Test (iDAT) or iMAT (for management programmes)
• Performance in the Studio Test/Personal Interview
• Portfolio review (for some programmes)

This is a Long Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=x^5-5x^4+5x^3-1\\ f^{\text{'}}\left(x\right)=5x^4-20x^3+15x^2\\ Forlocalmaximaandlocalminima,f^{\text{'}}\left(x\right)=0\\ \therefore 5x^4-20x^3+15x^2=0\Rightarrow 5x^2\left(x^2-4x+3\right)=0\\ \Rightarrow 5x^2\left(x^2-3x-x+3\right)=0\Rightarrow x^2\left(x-3\right)\left(x-1\right)=0\\ \therefore x=0,x=1andx=3\\ Now{f}^{\text{'}\text{'}}\left(x\right)=20x^3-60x^2+30x\\ \Rightarrow f^{\text{'}\text{'}}{\left(x\right)}_{atx=0}=20{\left(0\right)}^3-60{\left(0\right)}^2+30\left(0\right)=0whichisneitherMaximanorMinima.\\ \therefore f\left(x\right)hasthepointofinflextionatx=0\\ \Rightarrow f^{\text{'}\text{'}}{\left(x\right)}_{atx=1}=20{\left(1\right)}^3-60{\left(1\right)}^2+30\left(1\right)\\ =20-60+30=-10<0Maxima\\ \Rightarrow f^{\text{'}\text{'}}{\left(x\right)}_{atx=3}=20{\left(3\right)}^3-60{\left(3\right)}^2+30\left(3\right)\\ =540-540+90=90>0Minima\\ Themaximumvalueofthefunctionatx=1\\ f\left(x\right)={\left(1\right)}^5-5{\left(1\right)}^4+5{\left(1\right)}^3-1\\ =1-5+5-1=0\\ Theminimumvalueofthefunctionatx=3\\ f\left(x\right)={\left(3\right)}^5-5{\left(3\right)}^4+5{\left(3\right)}^3-1\\ \text{\&thins}\end{array}$

IME IIT Kanpur provides great placements to its students. Check out the table below to know about the IME IIT Kanpur placement statistics 2024:

Yes, BSEB 12th books are enough for board exams as they are designed by subject experts according to the syllabus. They cover all the topics in a simple and clear manner. Most of the exam questions come directly from these textbooks. However, for better understanding and practice, you can also refer to sample papers, previous year papers, and guidebooks. Focus on solving textbook exercises and important examples regularly.

The placement rate for IME IIT Kanpur in 2024 stood at 100% Take a look at the table below that presents the IME IIT Kanpur placement highlights for 2024:

You can get the official BSEB 12th books from your school or download them from the Bihar Board's official website – biharboardonline.bihar.gov.in. The books are also available on the Bihar State Textbook Publishing Corporation's website. Many educational apps and platforms also provide free PDFs of these books. These books follow the BSEB syllabus and are important for exam preparation. Always use the latest edition for accurate study content.

This is a Long Answer Type Question as classified in NCERT Exemplar

Sol:

The highest package offered during IME IIT Kanpur placements 2024 stood at INR 24 LPA. The table below presents the same:

Institute of Management Studies, BHU is located as part of the Faculty of Management Studies at Benaras Hindu University. The institute offers MBA course in the General as well as International Business streams. The tuition fees for the General MBA course is INR 1.06 lakhs, while for MBA International Business it is INR 99.31 thousands. Students can choose to explore the various scholarship initiatives at Institute of Management Studies, BHU.

The eligibility for OET at home is same as other test formats under Occupational English Test (OET on Paper, OET on Computer at a venue). We have mentioned few of them here:

• You must be a healthcare professional (or nearing completion of your qualification).
• For Indian test-takers, a valid, original passport is mandatory.
• There's no specific age restriction to take the test.
• OET does not set a minimum English proficiency level to register for the test, but the test itself is designed for intermediate to advanced English users.
• You don't need a job offer or university admission to be eligible to take the OET.

The placements at IME IIT Kanpur are good. The following table presents the placement statistics for IME IIT Kanpur: