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IIM shortlist of top IIMs is released in the first week of January soon after CAT result declaration. All IIMs release their shortlist one by one after that in the same month. By the end of January, all 21 IIMs release their MBA/PGP shortlist. The WAT-PI shortlists for admission is released individually by the institutes but for the CAP participating IIMs. For them, the CAP conducting IIM releases the PI shortlist form and guidelines on behalf of rest of them. 

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

As the size of metal ions increases, the stability of peroxides and superoxides increases. Peroxide and superoxide ions combine with a large size of alkali metals. Lithium forms monoxide, sodium forms peroxide and potassium, rubidium and caesium forms superoxide.

Li+O₂→Li₂O

Na+O₂→Na₂O₂

 K+O₂→KO₂

Given,  $f(x)=\left[\begin{array}{ccc}\hfill cosx\hfill & \hfill -sinx\hfill & \hfill 0\hfill \\ \hfill sinx\hfill & \hfill cosx\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill \end{array}\right]$

So, F (y) $=\left[\begin{array}{ccc}\hfill cosy\hfill & \hfill -siny\hfill & \hfill 0\hfill \\ \hfill siny\hfill & \hfill cosy\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill \end{array}\right]$

$\therefore f(x)f(y)=\left[\begin{array}{ccc}\hfill cosx\hfill & \hfill -sinx\hfill & \hfill 0\hfill \\ \hfill sinx\hfill & \hfill cosx\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill \end{array}\right]\left[\begin{array}{ccc}\hfill cosx\hfill & \hfill -sinx\hfill & \hfill 0\hfill \\ \hfill sinx\hfill & \hfill cosx\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill \end{array}\right]$

IIM shortlist is the list of CAT test takers who make it to the second phase of IIM admission process, which is Written Ability Test (WAT) and Personal Interview (PI). The IIM shortlist is the list of candidates who are eligible to participate in the WAT-PI rounds of IIMs for MBA admission.

Given,  $x\left[\begin{array}{ll}x\hfill & y\hfill \\ z\hfill & w\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill x\hfill & \hfill 6\hfill \\ \hfill -1\hfill & \hfill 2w\hfill \end{array}\right]+\left[\begin{array}{cc}\hfill 4\hfill & \hfill x+y\hfill \\ \hfill z+w\hfill & \hfill 3\hfill \end{array}\right].$

$(B)\Rightarrow \left[\begin{array}{cc}\hfill 3x\hfill & \hfill 3y\hfill \\ \hfill 3z\hfill & \hfill 3w\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill x+4\hfill & \hfill 6+x+y\hfill \\ \hfill -1+2+w\hfill & \hfill 2w+3\hfill \end{array}\right]$

CAT is an annual exam, thus one can appear for it only once in same academic year. However, one can appear for it any number of times over several years. There is no cap on number of appearance. There is no age limit either. Many candidates appear for the CAT two-three times to achieve their desired percentile. 

Yes, you are eligible. Candidates with bachelor's degree in any subject is eligible for CAT exam. However, it must be from a UGU recognised university and the candidate must meet the minimum aggregate score criteria for CAT, which is 50 per cent for General category and 45 per cent for SC/ST category students. 

3x + y = 5 _____ (ii)

Adding (i) and (i) we get,

2x - y + 3x + y = 10 + 5.

5x = 15

$\Rightarrow x=\frac{15}{5}$ => x = 3

5x = 15

$\Rightarrow x=\frac{15}{5}$ => x = 3

Putting x = 3 in (i) we gel,

2 × 3 - y = 10

6 - 10 = y

y = -4

PSIT College of Higher Education NIRF report 2025 is released. According to the report, the key highlights of UG 3-year (BCA and BBA) placements over the past three years are presented below:

No, CAT eligibility criteria and MBA eligibility criteria are same i.e. graduation. However, the minimum marks criteria may vary from institute to institute. Also, in case of stream specific MBA courses such as MBA in Pharma or MBA in Agri-Management etc., the requirement is graduation in specific subject. 

Yes, you can apply for CAT 2025, but you will have to get high marks in final year so that average score of graduation is minimum 50% (45% for reserved category students).

PSIT College of Higher Education NIRF report 2025 is released. According to the report, the key highlights of UG 3-year (BBA and BCA) placements over the past three years are presented below:

$\begin{array}{l}\\ 2\left[\begin{array}{ll}x\hfill & z\hfill \\ y\hfill & t\hfill \end{array}\right]+3\left[\begin{array}{cc}\hfill 1\hfill & \hfill -1\hfill \\ \hfill 0\hfill & \hfill 2\hfill \end{array}\right]=3\left[\begin{array}{ll}3\hfill & 5\hfill \\ 4\hfill & 6\hfill \end{array}\right]\end{array}$

$\Rightarrow \left[\begin{array}{cc}\hfill 2\times x\hfill & \hfill 2\times 2\hfill \\ \hfill 2\times y\hfill & \hfill 2\times t\hfill \end{array}\right]+\left[\begin{array}{cc}\hfill 3\times 1\hfill & \hfill 3\times (-1)\hfill \\ \hfill 3\times 0\hfill & \hfill 3\times 2\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 3\times 3\hfill & \hfill 3\times 5\hfill \\ \hfill 3\times 4\hfill & \hfill 3\times 6\hfill \end{array}\right]$

$$ $\Rightarrow \left[\begin{array}{cc}\hfill 2x\hfill & \hfill 2z\hfill \\ \hfill 2y\hfill & \hfill 21\hfill \end{array}\right]+\left[\begin{array}{cc}\hfill 3\hfill & \hfill -3\hfill \\ \hfill 0\hfill & \hfill 6\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 9\hfill & \hfill 15\hfill \\ \hfill 12\hfill & \hfill 18\hfill \end{array}\right].$

$\Rightarrow \left[\begin{array}{cc}\hfill 2x+3\hfill & \hfill 2z-3\hfill \\ \hfill 2y+0\hfill & \hfill 21+6\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 9\hfill & \hfill 15\hfill \\ \hfill 12\hfill & \hfill 18\hfill \end{array}\right]$

Equating the corresponding elements of the matrices $u$ get,

2x + 3 = 9

2x = 9 - 3

$\Rightarrow x=\frac{6}{2}$

x = 3

2z - 3 = 15

2z = 15 + 3

$\Rightarrow z=\frac{18}{2}$

z = 9

2y = 12

$\Rightarrow y=\frac{12}{2}$ => y = 6

2t + 6 = 18

2t = 18 - 6

2t = 12 => t = $\frac{12}{2}$ t = 6