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${\left(2x^r+\frac{1}{x^2}\right)}^{10}$

Let the constant term is (k + 1)^th term.

${\therefore }^{10}{C}_k{\left(2x^r\right)}^{10-k}.x^{-2k}$              

${=}^{10}{C}_k{2}^{10-k}.x^{10r-rk-2k}$              

              For constant term 10r – rk – 2k = 0.

$\therefore k=\frac{10r}{r+2}k\in I$              

$\therefore r=3,k=6andr=8,k=8$               

For k = 6

For k = 8  

$\therefore r=8$

Yes, to get admission for the BVoc or Certificate course at Zee Institute of Creative Art, Delhi, candidates must meet the eligibility criteria set by the college. Candidates must pass Class 12 as their basic eligibility. The selection criteria are based on merit. 

The fee structure for BDS courses at Manipal College of Dental Sciences, Mangalore follows an per annum model. The feestructure is comprised of the tuition fee for the BDS course and other recurring fees. In the first year, candidates are also required to pay caution deposit of around INR 10,000. Candidates can check the tuition fee structure of Manipal College of Dental Sciences, Mangalore BDS courses on the official website. 

The average age of n men is X year. Total age is given by N years

$\begin{array}{l}Newaverageage =\frac{NX+X-1+X+1+X+2}{N+3}\\ =\frac{NX+3X+2}{N+3}\\ =\frac{X[N+3]}{N+3}+\frac{2}{N+3}\\ \Rightarrow X+\frac{2}{N+3}\end{array}$

The DAV School of Business Management BBA course helps students build a foundation in various domains of Management. However, in today's job market, having only theoretical knowledge might not be enough to sustain and land a dream job. Nowadays, many students pursue additional skill-based courses to get a competitive edge and gain industry-relevant skills. Listed below are some of the courses that can help BBA graduates land a dream job:

• Strategising in Business
• Marketing Management
• Digital Marketing
• HR Analytics
• Risk Management
• Financial Analysis
• Power BI
• Advanced Excel

Yes, United Group of Institutions provide merit-based scholarship to BBA students. The scholarship amount depends upon the candidates Class 12 scores. To avail it, the aspirants have to submit the relevant documents as well for verification. Mentioned below is the UGI Greater Noida BBA scholarship criteria:

• 90% and above - INR 20,000
• 85% to 89.99% - INR 15,000
• 75% to 84.99% - INR 10,000

REVA University admissions are open for 2026 session. Candidates are offered admission to most of the programmes based on REVA CET score. The university also accepts other national or state-level entrance exam scores. Interested candidates can apply online or offline for the preferred course.

At DAV School of Business Management, students can pursue a BBA Hons course that runs for a duration of three years. The total fees to pursue this programme amount to INR 5.75 lakh. This fee is a combination of two components: tuition fees and hostel fees. To know more, students can check out the below table:

Note: The above-mentioned fee is as per the official sources. However, it is indicative and subject to change.

According to the available data on the Manipal College of Dental Sciences, Mangalore BDS course fees, the total BDS fees at Manipal College of Dental Sciences, Mangalore is slightly higher than the average BDS course fees at other similar institutes. The BDS course fees at Manipal College of Dental Sciences, Mangalore in 2025 is INR 22.1 lakh. The average BDS course fees is somewhere around INR 20 lakh.

The admission process starts with the registration for AITAM and Andhra Pradesh ICET. After Andhra Pradesh ICET registration, a correction window is usually opened for students to make changes to their application. The Andhra Pradesh ICET exam is generally held in May, with results declared in the same month. Following this, the counselling process for seat allotment begins a around July. Once seats are allocated, the university conducts an orientation session. 

1^st position can be filled in 4 ways as zero cannot appear in 1^st position.

2^nd position can be filled in 4 ways and so on.

Total cases = 4 * 4 * 3 * 2 * 1 = 96

The application fee charged by DAV School of Business Management for BBA admission is INR 500. Students who wish to apply for the course must pay this fees. Other than this, it is also important to note that this fee is nonrefundable under any circumstances.

Note: The above-mentioned fees is as per official sources. However, it is subject to change.

Yes, DAV School of Business Management does provide the option of applying offline for the BBA course. To apply offline, students are required to visit the admissions office at the institute's campus with educational documents. Students will be provided with an application form, which is to be submitted on the spot, along with the application fees.

Yes, the caution deposit submitted by candidates at the time of admission by candidates is refundable. The caution deposit is only refundable if the candidates complete their BDS course with Manipal College of Dental Sciences, Mangalore. The amount ofcaution deposit that is refundable is unknown. The caution deposit for BDS courses at Manipal College of Dental Sciences, Mangalore is INR 10,000. 

Total time = 182s

2 + 4 + 6 + 8 +……………+ n terms = 182

i.e. n=13

Total distance covered = 2* [1² + 2 ²+ 3² +……. …………. + 13²]

= 2 * 13 * 14 * $\frac{27}{6}$  = 9 * 13 * 14m

Average speed = 9 * 13 * $\frac{4}{182}$ = 9m/s

$A={\left(\begin{array}{ccc}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right)}_{3\times 3}$

 B is a matrix of same order with entries from {1,2,3,4,5}. and satisfying AB = BA.

$LetB=\left(\begin{array}{ccc}\hfill a_{11}\hfill & \hfill a_{12}\hfill & \hfill a_{13}\hfill \\ \hfill a_{21}\hfill & \hfill a_{22}\hfill & \hfill a_{23}\hfill \\ \hfill a_{31}\hfill & \hfill a_{32}\hfill & \hfill a_{33}\hfill \end{array}\right)$           

$\therefore \left(\begin{array}{ccc}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right)\left(\begin{array}{ccc}\hfill a_{11}\hfill & \hfill a_{12}\hfill & \hfill a_{13}\hfill \\ \hfill a_{21}\hfill & \hfill a_{22}\hfill & \hfill a_{23}\hfill \\ \hfill a_{31}\hfill & \hfill a_{32}\hfill & \hfill a_{33}\hfill \end{array}\right)=\left(\begin{array}{ccc}\hfill a_{11}\hfill & \hfill a_{12}\hfill & \hfill a_{13}\hfill \\ \hfill a_{21}\hfill & \hfill a_{22}\hfill & \hfill a_{23}\hfill \\ \hfill a_{31}\hfill & \hfill a_{32}\hfill & \hfill a_{33}\hfill \end{array}\right)\left(\begin{array}{ccc}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right)$

$a_{21}=a_{12},a_{22}=a_{11},a_{23}=a_{13},a_{31}=a_{32}$

$\therefore$ there exist only 5 distinct entries in the matrix B so that possible case = 5⁵ = 3125