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The data for COMEDK closing ranks for the year 2024 is currently not available for every BTech course at Garden City University. The data that is available shows a small increase in the closing rank in progressing years. However, the available data for COMEDK closing ranks 2023 suggests that a rank of 40,000 is enough to secure admissions into BTech courses at Garden City Unversity. 

TAPMI Manipal offers MBA on the basis of merit and accepted entrance exams. Candidates must meet the eligibility criteria by securing a minimum aggregate in graduation. Furthermore, candidates must secure valid scores in accepted entrance exam and meet the cutoff for final admission. Candidates require to secure valid scores in exams such as XAT, MAT, CAT, NMAT, GMAT, and other equivalent examinations. 

Be the vectors along the diagonals of a parallelogram having are 2.

$\therefore \frac{1}{2}\left|\overrightarrow{a}\times \overrightarrow{b}\right|=2\sqrt[]{2}$

$\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|sin\theta =4\sqrt[]{2}$

$\Rightarrow \left|\overrightarrow{b}\right|sin\theta =4\sqrt[]{2}$ ……. (i)

And

$\Rightarrow \overrightarrow{c}.\overrightarrow{b}=-2{\left|\overrightarrow{b}\right|}^2=-128......(ii)$

$\Rightarrow \left|\overrightarrow{c}\right|=16\sqrt[]{2}.......(iii)$

From (ii) and (iii)

$\left|\overrightarrow{c}\right|\left|\overrightarrow{b}\right|cos\alpha =-128$

$\Rightarrow cos\alpha =\frac{1}{\sqrt[]{2}}$

$\alpha =\frac{3\pi }{4}$

TAPMI Manipal offers admission to various UG and PG level courses. Including merit and entrance based eligibility. Candidates must meet the eligibility criteria and secure valid scores to meet the cutoff for final admission. Furthermore, TAPMI Manipal offers courses such as MBA, BBA, and other PG Diploma courses in full-time mode. Candidates who have applied for courses at TAPMI Manipal are called for the GDPI round and the final shortlist is then created based on various aspects such as academics, entrance scores, and GDPI scores. 

The data on cutoff ranks for the KCET exam 2025 is scheduled to be released on the July 25. The result dates are subject to change and may change depending on specific circumstances. Candidates who appeared for the KCET exam 2025 are advised to regularly check the official website for any news regarding cutoff data. Candidates will need their exam roll no. to see their scorecard when the results are announced.

$L_1:\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{-1}$  

$L_2:\frac{x+3}{2}=\frac{y-6}{1}=\frac{z-5}{3}$               

Now,

$\overrightarrow{p}\times \overrightarrow{q}=\left|\begin{array}{ccc}\hfill \widehat{i}\hfill & \hfill \widehat{j}\hfill & \hfill \widehat{k}\hfill \\ \hfill 2\hfill & \hfill 3\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \end{array}\right|=10\widehat{i}-8\widehat{j}-4\widehat{k}$               

and

  ${\overrightarrow{a}}_2-{\overrightarrow{a}}_1=6\widehat{i}-4\widehat{j}-4\widehat{k}$

  $\therefore S.D=\left|\frac{60+32+16}{\sqrt[]{100+64+16}}\right|=\frac{108}{\sqrt[]{180}}=\frac{18}{\sqrt[]{5}}$      

$L_1:\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{-1}$  

$L_2:\frac{x+3}{2}=\frac{y-6}{1}=\frac{z-5}{3}$               

Now,

$\overrightarrow{p}\times \overrightarrow{q}=\left|\begin{array}{ccc}\hfill \widehat{i}\hfill & \hfill \widehat{j}\hfill & \hfill \widehat{k}\hfill \\ \hfill 2\hfill & \hfill 3\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \end{array}\right|=10\widehat{i}-8\widehat{j}-4\widehat{k}$               

and

  ${\overrightarrow{a}}_2-{\overrightarrow{a}}_1=6\widehat{i}-4\widehat{j}-4\widehat{k}$

  $\therefore S.D=\left|\frac{60+32+16}{\sqrt[]{100+64+16}}\right|=\frac{108}{\sqrt[]{180}}=\frac{18}{\sqrt[]{5}}$                           

TAPMI Manipal offers an MBA for 2 years with an annual intake of 60 students. The Institute offers various specialisations across MBA, such as, Banking and Finacial Services, International Business, HRM, Marketing, Technology Management, and more.

Admission to MBA in Human Resources Management is offered based on Karnataka PGCET, GMAT, XAT, CAT, NMAT and other equivalent examinations. Furthermore, the Institute offers MBA in HR is offered with the tuition fees worth INR 13.02 Lakh. Whereas, the hostel fees is worth INR 3.45 Lacs and one-time payment is around INR 40K, giving a total of INR 16.87 Lacs of course fees for 2 years. 

Yes, K J Somaiya College of Arts and Commerce is a good college. K J Somaiya College of Arts and Commerce is ranked 77th by The Week 2025 under the Accounting & Commerce category, 27th by The Week 2025 under the Humanities & Social Sciences category, and others. The college placements are also very good. 

K J Somaiya College of Arts and Commerce offers PG and UG courses to students. These courses are provided across the Arts,  BCom, and various other streams. At the UG level, the college offers BCom, BA, and other courses to students. At the PG level, the college offers MCom and MA courses to students. The reservation followed by the college for UG students is mentioned below:

• Open and all Reserve Category: 42%
• Gujarati Linguistics: 50%
• Government Others: 3%

TAPMI Manipal offers an MBA for the duration of 2 years as fully residential PG level programme. The programme is spread across various specialisations, such as Banking and Finacial Services, International Business, HRM, Marketing, Technology Management, and more.

Admissions to TAPMI Manipal MBA courses are made based on merit in the qualifying examination and overall student profile. Candidate must have completed graduation in any discipline with a minimum of 50% marks. In case of opting for an MBA in Technology Management, interested candidates must have a minimum of two years of work experience.

C : 4x² + 4y² – 12x + 8y + k = 0

$?\left(1,-\frac{1}{3}\right)$               

Lies on or inside the C then

$4+\frac{4}{9}-12-\frac{8}{3}+k\le 0$

$\Rightarrow k\le \frac{92}{9}$               

Now, circle lies in 4^th quadrant centre

$\equiv \left(\frac{3}{2},-1\right)$               

$\therefore r<1\Rightarrow \sqrt[]{\frac{9}{4}+1-\frac{k}{4}}<1$               

$\Rightarrow \frac{13}{4}-\frac{k}{4}<1$

$\Rightarrow \frac{k}{4}>\frac{9}{4}$

$\Rightarrow k>9$

$\therefore K\in \left(9,\frac{92}{9}\right)$      

Yes, K J Somaiya College of Arts and Commerce is ranked by various ranking bodies. A few of the important K J Somaiya College of Arts and Commerce rankings are mentioned below:

Yes, K J Somaiya College of Arts and Commerce, under the Somaiya, has collaborated with various companies and organisations. The below-mentioned are Somaiya Vidyavihar University collaborations:

Yes, Uka Tarsadia really supports students with placement training. They arrange placement drives and internship chances also. If student use these well then they get more confidence to crack real interviews easy.

Given vertex is  (5, 4) and directrix 3x + y – 29 = 0

Let foot of perpendicular of (5, 4) on directrix be (x₁, y₁)

$\frac{x_1-5}{3}=\frac{y_1-4}{1}=\frac{-\left(-10\right)}{10}$               

$\therefore \left(x_1,y_1\right)=\left(8,5\right)$               

So, focus of parabola will be S = (2, 3)

Let P(x, y) be any point on parabola, then

$\Rightarrow {\left(x-2\right)}^2+{\left(y-3\right)}^2=\frac{{\left(3x+y-29\right)}^2}{10}$               

$\Rightarrow x^2+9y^2-6xy+134x-2y-711=0$               

And given parabola

$x^2+a{y}^2+bxy+cx+dy+k=0$               

$\therefore a=9,b=-6,c=134,d=-2,k=-711$               

$\therefore a+b+c+d+k=576$