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This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhat:A=\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \end{array}\right]\\ A^2=A.A\\ =\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \end{array}\right]\\ =\left[\begin{array}{ccc}\hfill 1+0+0\hfill & \hfill 0+0-1\hfill & \hfill -1+0-1\hfill \\ \hfill 2+2+0\hfill & \hfill 0+1+3\hfill & \hfill -2+3+3\hfill \\ \hfill 0+2+0\hfill & \hfill 0+1+1\hfill & \hfill 0+3+1\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill 1\hfill & \hfill -1\hfill & \hfill -2\hfill \\ \hfill 4\hfill & \hfill 4\hfill & \hfill 4\hfill \\ \hfill 2\hfill & \hfill 2\hfill & \hfill 4\hfill \end{array}\right]\\ L.H.S.A^2+A=\left[\begin{array}{ccc}\hfill 1\hfill & \hfill -1\hfill & \hfill -2\hfill \\ \hfill 4\hfill & \hfill 4\hfill & \hfill 4\hfill \\ \hfill 2\hfill & \hfill 2\hfill & \hfill 4\hfill \end{array}\right]+\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \end{array}\right]\\ =\left[\begin{array}{ccc}\hfill 1+1\hfill & \hfill -1+0\hfill & \hfill -2-1\hfill \\ \hfill 4+2\hfill & \hfill 4+1\hfill & \hfill 4+3\hfill \\ \hfill 2+0\hfill & \hfill 2+1\hfill & \hfill 4+1\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill 2\hfill & \hfill -1\hfill & \hfill -3\hfill \\ \hfill 6\hfill & \hfill 5\hfill & \hfill 7\hfill \\ \hfill 2\hfill & \hfill 3\hfill & \hfill 5\hfill \end{array}\right]\\ R.H.S.A\left(A+I\right)=\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \end{array}\right]\left[\left(\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \end{array}\right)+\left(\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right)\right]\\ =\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{ccc}\hfill 2\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 2\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 2\hfill \end{array}\right]\\ =\left[\begin{array}{ccc}\hfill 2+0+0\hfill & \hfill 0+0-1\hfill & \hfill -1+0-2\hfill \\ \hfill 4+2+0\hfill & \hfill 0+2+3\hfill & \hfill -2+3+6\hfill \\ \hfill 0+2+0\hfill & \hfill 0+2+1\hfill & \hfill 0+3+2\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill 2\hfill & \hfill -1\hfill & \hfill -3\hfill \\ \hfill 6\hfill & \hfill 5\hfill & \hfill 7\hfill \\ \hfill 2\hfill & \hfill 3\hfill & \hfill 5\hfill \end{array}\right]\\ L.H.S.=R.H.S\\ A^2+A=A\left(A+I\right).Henceverified.\end{array}$

This is a short answer type question as classified in NCERT Exemplar

This is a short answer type question as classified in NCERT Exemplar

Students from all the streams are eligible for admission to the MBA course at Jyothy Institute of Commerce and Management. The selection criteria describes that the students should have passed their UG course with at least 50% aggregate. The university from where students have gained their degree should be recognised.

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhat:P=\left[\begin{array}{ccc}\hfill x\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill y\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill z\hfill \end{array}\right]andQ=\left[\begin{array}{ccc}\hfill a\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill b\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill c\hfill \end{array}\right]\\ PQ=\left[\begin{array}{ccc}\hfill x\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill y\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill z\hfill \end{array}\right]\left[\begin{array}{ccc}\hfill a\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill b\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill c\hfill \end{array}\right]\\ =\left[\begin{array}{ccc}\hfill xa+0+0\hfill & \hfill 0+0+0\hfill & \hfill 0+0+0\hfill \\ \hfill 0+0+0\hfill & \hfill 0+yb+0\hfill & \hfill 0+0+0\hfill \\ \hfill 0+0+0\hfill & \hfill 0+0+0\hfill & \hfill 0+0+zc\hfill \end{array}\right]\\ =\left[\begin{array}{ccc}\hfill xa\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill yb\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill zc\hfill \end{array}\right]\\ Now,QP=\left[\begin{array}{ccc}\hfill a\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill b\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill c\hfill \end{array}\right]\left[\begin{array}{ccc}\hfill x\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill y\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill z\hfill \end{array}\right]\\ =\left[\begin{array}{ccc}\hfill xa+0+0\hfill & \hfill 0+0+0\hfill & \hfill 0+0+0\hfill \\ \hfill 0+0+0\hfill & \hfill 0+yb+0\hfill & \hfill 0+0+0\hfill \\ \hfill 0+0+0\hfill & \hfill 0+0+0\hfill & \hfill 0+0+zc\hfill \end{array}\right]\\ =\left[\begin{array}{ccc}\hfill xa\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill yb\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill zc\hfill \end{array}\right]\\ Hence,PQ=QP.\end{array}$

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}LetA=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill -2\hfill & \hfill 1\hfill \end{array}\right],B=\left[\begin{array}{cc}\hfill 2\hfill & \hfill 3\hfill \\ \hfill 3\hfill & \hfill -4\hfill \end{array}\right]andC=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill -1\hfill & \hfill 0\hfill \end{array}\right]\\ (i)Toverify:\left(AB\right)C=A\left(BC\right)\\ AB=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill -2\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 2\hfill & \hfill 3\hfill \\ \hfill 3\hfill & \hfill -4\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 2+6\hfill & \hfill 3-8\hfill \\ \hfill -4+3\hfill & \hfill -6-4\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 8\hfill & \hfill -5\hfill \\ \hfill -1\hfill & \hfill -10\hfill \end{array}\right]\\ L.H.S.\\ \left(AB\right)C=\left[\begin{array}{cc}\hfill 8\hfill & \hfill -5\hfill \\ \hfill -1\hfill & \hfill -10\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill -1\hfill & \hfill 0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 8+5\hfill & \hfill 0+0\hfill \\ \hfill -1+10\hfill & \hfill 0+0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 13\hfill & \hfill 0\hfill \\ \hfill 9\hfill & \hfill 0\hfill \end{array}\right]\\ BC=\left[\begin{array}{cc}\hfill 2\hfill & \hfill 3\hfill \\ \hfill 3\hfill & \hfill -4\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill -1\hfill & \hfill 0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 2-3\hfill & \hfill 0+0\hfill \\ \hfill 3+4\hfill & \hfill 0+0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill -1\hfill & \hfill 0\hfill \\ \hfill 7\hfill & \hfill 0\hfill \end{array}\right]\\ R.H.S.\\ A\left(BC\right)=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill -2\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{cc}\hfill -1\hfill & \hfill 0\hfill \\ \hfill 7\hfill & \hfill 0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill -1+14\hfill & \hfill 0+0\hfill \\ \hfill 2+7\hfill & \hfill 0+0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 13\hfill & \hfill 0\hfill \\ \hfill 9\hfill & \hfill 0\hfill \end{array}\right]\\ L.H.S.=R.H.S.\\ So,\left(AB\right)C=A\left(BC\right)\\ (ii)Toverify:A\left(B+C\right)=AB+AC\\ B+C=\left[\begin{array}{cc}\hfill 2\hfill & \hfill 3\hfill \\ \hfill 3\hfill & \hfill -4\hfill \end{array}\right]+\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill -1\hfill & \hfill 0\hfill \end{array}\right]\\ =\left[\begin{array}{cc}\hfill 2+1\hfill & \hfill 3+0\hfill \\ \hfill 3-1\hfill & \hfill -4+0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 3\hfill & \hfill 3\hfill \\ \hfill 2\hfill & \hfill -4\hfill \end{array}\right]\\ L.H.S.A\left(B+C\right)=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill -2\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 3\hfill & \hfill 3\hfill \\ \hfill 2\hfill & \hfill -4\hfill \end{array}\right]\\ =\left[\begin{array}{cc}\hfill 3+4\hfill & \hfill 3-8\hfill \\ \hfill -6+2\hfill & \hfill -6-4\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 7\hfill & \hfill -5\hfill \\ \hfill -4\hfill & \hfill -10\hfill \end{array}\right]\\ AB=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill -2\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 2\hfill & \hfill 3\hfill \\ \hfill 3\hfill & \hfill -4\hfill \end{array}\right]\\ =\left[\begin{array}{cc}\hfill 2+6\hfill & \hfill 3-8\hfill \\ \hfill -4+3\hfill & \hfill -6-4\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 8\hfill & \hfill -5\hfill \\ \hfill -1\hfill & \hfill -10\hfill \end{array}\right]\\ AC=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill -2\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill -1\hfill & \hfill 0\hfill \end{array}\right]\\ =\left[\begin{array}{cc}\hfill 1-2\hfill & \hfill 0+0\hfill \\ \hfill -2-1\hfill & \hfill 0+0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill -1\hfill & \hfill 0\hfill \\ \hfill -3\hfill & \hfill 0\hfill \end{array}\right]\\ R.H.S.AB+AC=\left[\begin{array}{cc}\hfill 8\hfill & \hfill -5\hfill \\ \hfill -1\hfill & \hfill -10\hfill \end{array}\right]+\left[\begin{array}{cc}\hfill -1\hfill & \hfill 0\hfill \\ \hfill -3\hfill & \hfill 0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 8-1\hfill & \hfill -5+0\hfill \\ \hfill -1-3\hfill & \hfill -10+0\hfill \end{array}\right]\\ =\left[\begin{array}{cc}\hfill 7\hfill & \hfill -5\hfill \\ \hfill -4\hfill & \hfill -10\hfill \end{array}\right]\\ L.H.S.=R.H.S.\\ Hence,A\left(B+C\right)=AB+AC\end{array}$

In my opinion, Mumbai at present is the best city in India to pursue a Modelling course if it comes within your budget. We all know Mumbai is India's entertainment and fashion hub, and it has the best career and networking options for budding Models. Other than Mumbai, you can also opt for cities like Delhi, Bangalore, and Kolkata with good career options.

There are not many government-recognized colleges or institutes offering full-fledged Modeling courses in India. Though you can opt for options like National Institute of Fashion Technology (NIFT), Film and Television Institute of India (FTII), National School of Drama (NSD), and Satyajit Ray Film and Television Institute (SRFTI). These institutes will offer you courses in related fields like Fashion Design, Film & TV, etc.

Hi, Modelling courses are more about practical learning and a bit of theoretical knowledge. Their curriculum is focused on runway or ramp walking, posing, personal grooming, portfolio building, industry connections, communication skills, and so on. Though it also depends on the course you choose.

Of course not, you are not required to pursue a degree or Diploma in Modelling or any related course to pursue a career path in Modelling. However, it will help you in certain ways, like portfolio building, networking in the industry, makeup & Fashion knowledge, runway techniques learning, etc.

If you want to pursue a short-term Modelling course in India, you can join a Certificate course in Modelling of a 3-6 month duration. Institutes like AAFT, Frankfinn, RK Films & Media Academy, etc., offer such short-term programs.

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l}LetA=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill \end{array}\right],B=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 2\hfill & \hfill 0\hfill \end{array}\right]andC=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 2\hfill & \hfill 2\hfill \end{array}\right]\\ AB=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 2\hfill & \hfill 0\hfill \end{array}\right]\Rightarrow AB=\left[\begin{array}{cc}\hfill 1+0\hfill & \hfill 2+0\hfill \\ \hfill 0+0\hfill & \hfill 0+0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill 0\hfill \end{array}\right]\\ AC=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill \end{array}\right]\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 2\hfill & \hfill 2\hfill \end{array}\right]\Rightarrow AC=\left[\begin{array}{cc}\hfill 1+0\hfill & \hfill 2+0\hfill \\ \hfill 0+0\hfill & \hfill 0+0\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill 0\hfill \end{array}\right]\\ Hence,AB=ACformatrixAisnon-zeroandB\ne C.\end{array}$

The Jyothy Institute of Commerce and Management MBA admission process considers undergraduate academic merit and entrance exam scores. Candidates should apply online through the official website, jyothyicm.org. It should be taken care that the form is filled out accurately and the documents along with the application fee are submitted. A merit list will be released, followed by counseling and document verification based on accepted exam scores. Finally, selected students will have to confirm their admission by paying the admission fee and INR 4 Lacs tuition fee is to be paid in installments.