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This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}{}_{15}{C}_8+{}_{15}{C}_9-{}_{15}{C}_6-{}_{15}{C}_7={}_{15}{C}_{15-8}+{}_{15}{C}_{15-9}-{}_{15}{C}_6-{}_{15}{C}_7\left[?{}_n{C}_r={}_n{C}_{n-r}\right]\\ ={}_{15}{C}_7+{}_{15}{C}_6-{}_{15}{C}_6-{}_{15}{C}_7=0\\ Hence,thevalueofthefilleris0.\end{array}$

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}ThegivenseriesisA.P.whosefirsttermisaandcommondifferenceisd.\\ \therefore S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]=q{n}^2\\ \Rightarrow =2a+\left(n-1\right)d=2qn\dots \left(i\right)\\ S_m=\frac{m}{2}\left[2a+\left(m-1\right)d\right]=q{m}^2\\ \Rightarrow =2a+\left(m-1\right)d=2qm\dots \left(ii\right)\\ Solvingeqn.\left(i\right)andeqn.\left(ii\right)weget\\ 2a+\left(m-1\right)d=2qm\\ \underset{\_}{2a+\left(n-1\right)d=2qn}\\ \left(-\right)\left(-\right)\left(-\right)\\ \left(m-n\right)d=2qm-2qn\\ \left(m-n\right)d=2q\left(m-n\right)\\ \therefore d=2q\\ Puttingthevalueofdfromeqn.\left(ii\right),weget\\ 2a+\left(m-1\right).2q=2qm\Rightarrow 2a=2qm-\left(m-1\right)2q\\ \Rightarrow 2a=2q\left(m-m+1\right)\Rightarrow 2a=2q\Rightarrow a=q\\ \therefore S_q=\frac{q}{2}\left[2a+\left(q-1\right)d\right]=\frac{q}{2}\left[2q+\left(q-1\right)2q\right]\\ =\frac{q}{2}\left[2q+2q^2-2q\right]=\frac{q}{2}\times 2q^2=q^3\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

The cut-off ranks for BSc courses at Elphinstone College for the year 2024 stood at 95.2% for candidates in the general category and 75.80% for candidates in the EWS category. There are also individual cut-off ranks for each specialisation, which candidates are advised to check on the official website of Elphinstone College.

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Giventhat{}_n{P}_r=840and{}_n{C}_r=35\\ \Rightarrow \frac{n!}{\left(n-r\right)!}=840\dots \left(i\right)and\frac{n!}{r!\left(n-r\right)!}=35\dots \left(ii\right)\\ Dividingeqn.\left(i\right)by\left(ii\right)weget\\ \frac{\frac{n!}{\left(n-r\right)!}}{\frac{n!}{r!\left(n-r\right)!}}=\frac{840}{35}\Rightarrow \frac{n!}{\left(n-r\right)!}\times \frac{r!\left(n-r\right)!}{n!}=24\\ \Rightarrow r!=24\Rightarrow r!=4\times 3\times 2\times 1\\ \Rightarrow r!=4!\therefore r=4\\ Hence,thevalueofthefilleris4.\end{array}$

Alva's Law College offers a variety of popular programmes in the field of Law. Students can opt for the BA LLB, BCom LLB, BBA LLB, or the regular LLB program. These courses are offered in various specializations to students. The integrated courses like BA LLB provides students with a harmonious knowledge of Law and Humanities/Commerce/Management.

The CDS 2 2025 admit card has been released on the official website. Eligible candidates can download their e-admit card from the official website by using their login credentials. The UPSC CDS 2 2025 exam is scheduled to be conducted on September 14, 2025.

After doing BBA, one can seek out for employment in share trading, business corporations, industries, print media, and so on. They can also work in Government sector or in IT industries. The main advantage of the BBA programme from Ahmedabad Institute of Business Management is that aspirants can pursue the MBA programme after completing the same. They can specialize in their desired disciplines while pursuing the MBA programme.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Sincex,2y,3zareinA.P.\\ \therefore 2y-x=3z-2y\\ \Rightarrow 4y=x+3z\dots \left(i\right)\\ Nowx,y,zareinG.P.\\ \therefore Commonratior=\frac{y}{x}=\frac{z}{y}\dots \left(ii\right)\\ \therefore y^2=xz\\ Puttingthevalueofxfromeqn.\left(i\right),weget\\ y^2=\left(4y-3z\right)z\Rightarrow y^2=4yz-3z^2\\ \Rightarrow 3z^2-4yz+y^2=0\Rightarrow 3z^2-3yz-yz+y^2=0\\ \Rightarrow 3z\left(z-y\right)-y\left(z-y\right)=0\Rightarrow \left(3z-y\right)\left(z-y\right)=0\\ \Rightarrow 3z-y=0andz-y=0\\ \Rightarrow 3z=yandz\ne y\left[?zandyaredistinctnumbers\right]\\ \Rightarrow \frac{z}{y}=\frac{1}{3}\Rightarrow r=\frac{1}{3}\left[?Fromeqn.\left(ii\right)\right]\\ Hence,thecorrectoptionis\left(b\right).\end{array}$

No, Elphinstone College is not a private college. Elphinstone College is a government college that is affiliated with the Homi Bhabha State University of Maharashtra and is subject to all policies of the Homi Bhabha State University and the government of Maharashtra.

The good attempts refer to the number of questions candidates should ideally attempt in the exam with accuracy inorder to be considered for the next round of selection process. The good attempts vary based on the difficulty level and previous year trends.

Since the admission process of Jyothy Institute of Commerce and Management BBA course is split into various steps, and each step is carried out at different time intervals. Therefore, for staying updated with the process and not losing out on any important timeframe, admission dates are important.

Madras University uses a merit-based admission process for its M.Sc. Medical Microbiology program, based on marks in the qualifying undergraduate degree. While the university doesn't have a specific entrance exam for this program, it does use entrance exams like TANCET for other courses such as MBA and MCA. For M.Sc. Medical Microbiology, admission is based on the marks obtained in the bachelor's degree. 

Yes, CMJ University offers three BBA programmes. The available courses are BBA (general), BBA in Hospitality and Hotel Management, and Retail Operations. CMJ University BBA admission is granted on a merit-basis. Thus, the applicants performance in Class 12 or equivalent exam is evaluated. 

At Elphinstone College, the seat allocation is done entirely through a merit-based procedure. The marks obtained by a candidate during their Class 12 board examinations, along with the availability of a seat for the chosen course, will be the metrics used for seat allocation.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhat{T}_n=a+\left(n-1\right)d\\ \therefore T_9=a+\left(9-1\right)d\Rightarrow T_9=a+8d\\ and{T}_{13}=a+12d\\ Asperthegivencondition\\ 9\left[a+8d\right]=13\left[a+12d\right]\\ \Rightarrow 9a+72d=13a+156d\Rightarrow -4a=84d\\ \Rightarrow a=-21d\dots \left(i\right)\\ Now,T_{22}=a+21d=-21d+21d=0\left[Fromeqn.\left(i\right)\right]\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhat{T}_3=4\\ \Rightarrow a{r}^{3-1}=4\left[?T_n=a{r}^{n-1}\right]\\ \Rightarrow a{r}^2=4\\ Productoffirst5terms=a.ar.a{r}^2.a{r}^3.a{r}^4=a^5{r}^{10}={\left(a{r}^2\right)}^5={\left(4\right)}^5\\ Hence,thecorrectoptionis\left(c\right).\end{array}$