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ASCO does conduct its own written test followed by a personal interview but, if the candidate's previous academic performance is strong enough, then direct admission may be granted. This totally depends on the university. It is mandatory to clear the PI in case direct admission is not granted.

This is a True or False type Questions as classified in NCERT Exemplar

Sol: 

$\begin{array}{l}Giventhat\left|\overrightarrow{a}+\overrightarrow{b}\right|=\left|\overrightarrow{a}-\overrightarrow{b}\right|\\ Squaringbothsides,weget\\ {\left|\overrightarrow{a}+\overrightarrow{b}\right|}^2={\left|\overrightarrow{a}-\overrightarrow{b}\right|}^2\\ \Rightarrow {\left|\overrightarrow{a}\right|}^2+{\left|\overrightarrow{b}\right|}^2+2\overrightarrow{a}.\overrightarrow{b}={\left|\overrightarrow{a}\right|}^2+{\left|\overrightarrow{b}\right|}^2-2\overrightarrow{a}.\overrightarrow{b}\\ \Rightarrow 2\overrightarrow{a}.\overrightarrow{b}=-2\overrightarrow{a}.\overrightarrow{b}\\ \Rightarrow \overrightarrow{a}.\overrightarrow{b}=-\overrightarrow{a}.\overrightarrow{b}\\ \Rightarrow 2\overrightarrow{a}.\overrightarrow{b}=0\Rightarrow \overrightarrow{a}.\overrightarrow{b}=0\\ whichimpliesthat\overrightarrow{a}and\overrightarrow{b}areorthogonal.\\ HencethegivenstatementisTrue.\end{array}$

This is a True or False type Questions as classified in NCERT Exemplar

Sol:  $True.$

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

$\begin{array}{l}Thegivenplanesare\\ P_1:5x+3y+6z+8=0\\ P_2:x+2y+3z-4=0\\ P_3:2x+y-z+5=0\\ Equationsoftheplanepassingthroughthelineofintersectionof{P}_{2}and{P}_{3}is\\ \left(x+2y+3z-4\right)+\lambda \left(2x+y-z+5\right)=0\\ \Rightarrow \left(1+2\lambda \right)x+\left(2+\lambda \right)y+\left(3-\lambda \right)z-4+5\lambda =0\dots \left(i\right)\\ Plane\left(i\right)isperpendicularto{P}_1,then\\ 5\left(1+2\lambda \right)+3\left(2+\lambda \right)+6\left(3-\lambda \right)=0\\ \Rightarrow 5+10\lambda +6+3\lambda +18-6\lambda =0\\ \Rightarrow 7\lambda +29=0\Rightarrow \lambda =\frac{-29}{7}\\ Puttingthevalueof\lambda ineq.\left(i\right),weget\\ \left[1+2\left(\frac{-29}{7}\right)\right]x+\left[2-\frac{29}{7}\right]y+\left[3+\frac{29}{7}\right]z-4+5\left(\frac{-29}{7}\right)=0\\ \Rightarrow \frac{-15}{7}x-\frac{15}{7}y+\frac{50}{7}z-4-\frac{145}{7}=0\\ \Rightarrow -15x-15y+50z-28-145=0\\ \Rightarrow -15x-15y+50z-173=0\Rightarrow 15x+15y-50z+173=0\end{array}$

The course fee for the MBA programme at ICRI Bangalore is INR 1.8 lakh. Candidates who clear the admission process for the course can pay the course fee and secure their seat in the programme. Candidates must appear for the required entrance in order to get the call for the GDPI round. 

This is a True or False type Questions as classified in NCERT Exemplar

Sol:         

$\begin{array}{l}If\left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right|then\overrightarrow{a}=\pm \overrightarrow{b}whichistrue.\\ HencethegivenstatementisTrue.\end{array}$

On- admission scholarships for the UG students includes 100% scholarships for candidates with 95% Aggregate and above in (CBSE/ISC) Board of 12 (2025/2024). There are scholarships based on CUET UG, which provides 100% scholarship. Other types of scholarships include sports and martyrs.

For MAT CBT July 2025, the registration window is open from June 18 to July 14, 2025. The admit card will be released on July 17, 2025, and the exam will be held on July 20, 2025. The result will be declared on July 24, 2025. These dates are crucial for Silver Oak University MBA aspirants applying through MAT.

Yes, Amity School of Communication offers scholarships for all courses. However, it totally depends on the qualifications and approval of higher authorities. As of today, Amity School of Communication Noida, has offered scholarships to over 50,000 meritorious students.  

The UChicago cost of attendance for undergrads and grads both, is given below:

Undergraduate Cost of Attendance:

Graduate Cost of Attendance:

1 USD = INR 85.53 

Silver Oak University accepts scores from popular management entrance exams such as MAT, CAT, and CMAT for its MBA admission. Candidates must perform well in any of these exams and meet the academic eligibility criteria. Final selection is based on entrance test scores, merit, and availability of seats.

Yes, ASCO offers various kinds of scholarships to the candidates which includes on- admission, CUET based, CAT based, Ssports, martyr's scholarships, etc. Candidates can apply for the same in the admission process and if the scholarship committee agrees it will be granted.

Yes, admissions for the MBA programme at Silver Oak University for the 2025 academic year are currently open. Interested candidates should apply early, meet the eligibility criteria, and appear for one of the accepted entrance exams like MAT, CAT, or CMAT. Visit the official Silver Oak University website to fill out the application form and track updates.

Atmiya University provides good placements to its graduating students.However, the institution has not released the placement report as of yet. In the meantime, check out the table below to know the median package recorded during Atmiya University placements 2024:

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

$\begin{array}{l}Givenequationsoflinesare\\ \overrightarrow{r}=\left(8+3\lambda \right)\widehat{i}-\left(9+16\lambda \right)\widehat{j}+\left(10+7\lambda \right)\widehat{k}\dots \left(i\right)\\ and\overrightarrow{r}=15\widehat{i}-29\widehat{j}+5\widehat{k}+\mu \left(3\widehat{i}+8\widehat{j}-5\widehat{k}\right)\dots \left(ii\right)\\ Equation\left(i\right)canbere-writtenas\\ \overrightarrow{r}=8\widehat{i}-9\widehat{j}+10\widehat{k}+\lambda \left(3\widehat{i}-16\widehat{j}+7\widehat{k}\right)\dots \left(iii\right)\\ Here,\overrightarrow{a_1}=8\widehat{i}-9\widehat{j}+10\widehat{k}and\overrightarrow{a_2}=15\widehat{i}-29\widehat{j}+5\widehat{k}\\ \overrightarrow{b_1}=3\widehat{i}-16\widehat{j}+7\widehat{k}and\overrightarrow{b_2}=3\widehat{i}+8\widehat{j}-5\widehat{k}\\ \overrightarrow{a_2}-\overrightarrow{a_1}=7\widehat{i}+38\widehat{j}-5\widehat{k}\\ \overrightarrow{b_1}\times \overrightarrow{b_2}=\left|\begin{array}{ccc}\hfill \widehat{i}\hfill & \hfill \widehat{j}\hfill & \hfill \widehat{k}\hfill \\ \hfill 3\hfill & \hfill -16\hfill & \hfill 7\hfill \\ \hfill 3\hfill & \hfill 8\hfill & \hfill -5\hfill \end{array}\right|\\ =\widehat{i}\left(80-56\right)-\widehat{j}\left(-15-21\right)+\widehat{k}\left(24+48\right)\\ =24\widehat{i}+36\widehat{j}+72\widehat{k}\\ \therefore Shortestdistance,SD=\left|\frac{\left(\overrightarrow{a_2}-\overrightarrow{a_1}\right).\left(\overrightarrow{b_1}\times \overrightarrow{b_2}\right)}{\left|\overrightarrow{b_1}\times \overrightarrow{b_2}\right|}\right|=\left|\frac{\left(7\widehat{i}+38\widehat{j}-5\widehat{k}\right).\left(24\widehat{i}+36\widehat{j}+72\widehat{k}\right)}{\sqrt[]{{\left(24\right)}^2+{\left(36\right)}^2+{\left(72\right)}^2}}\right|\\ =\left|\frac{168+1368-360}{\sqrt[]{576+1296+5184}}\right|=\left|\frac{168+1008}{\sqrt[]{7056}}\right|=\frac{1176}{84}=14units\\ Hence,therequireddistanceis14units.\end{array}$

This is a Fill in the blanks type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Let\overrightarrow{a}=a_1\widehat{i}+a_2\widehat{j}+a_3\widehat{k}\\ \therefore \overrightarrow{a}.\widehat{i}=\left(a_1\widehat{i}+a_2\widehat{j}+a_3\widehat{k}\right).\widehat{i}\\ =a_1\\ Similarly,\overrightarrow{a}.\widehat{j}=a_{2}and\overrightarrow{a}.\widehat{k}=a_3\\ \therefore \left(\overrightarrow{a}.\widehat{i}\right).\widehat{i}+\left(\overrightarrow{a}.\widehat{j}\right).\widehat{j}+\left(\overrightarrow{a}.\widehat{k}\right).\widehat{k}=a_1\widehat{i}+a_2\widehat{j}+a_3\widehat{k}=\overrightarrow{a}\\ Hence,thevalueofthefilleris\overrightarrow{a}.\end{array}$

The MBA specialisations offered by ICRI Bangalore - Institute of Clinical Research India Bangalore are as follows: 

Atmiya University provides good placements to its graduating students. The students are given excellent placement support every year placing them in top companies. Check out the table below to know the key highlights of the Atmiya University placements 2024: