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Last two digit must be in form

$\begin{array}{l}23,4,516\\ 324\\ 32\\ 52\end{array}\}3\times 4=12$

Total number of required number = 12 + 18 = 30

No. Candidates DO NOT need to send “Confirmation Page” printed after completion and submission of online UPTAC application form to the University. However, the candidate should keep the printout of the Confirmation page for record. Candidates are also advised to note down the Application Form Number for any future correspondence.

 $0\le \frac{2+3p}{6}\le 1\Rightarrow p\in \left[-\frac{2}{3},\frac{4}{3}\right],0\le \frac{2-p}{8}\le 1\Rightarrow p\in \left[-6,2\right]and0\le \frac{1-p}{2}\le 1\Rightarrow p\in \left[-1,1\right]$

$0<P\left(E_1\right)+P\left(E_2\right)+P\left(E_3\right)\le 10\le \frac{13}{12}-\frac{p}{8}\le 1\Rightarrow p\in \left[\frac{2}{3},\frac{26}{3}\right]$ Taking intersection to all $p\in \left[\frac{2}{3},1\right]$

$\therefore p_1+p_2=\frac{5}{3}$

Netaji Subhas University of Technology appoints experienced and trained faculty members. NSUT Delhi faculty focuses on theoretical and practical learning. The faculty is committed to helping the students in their career pathways, they engage the students with the latest activities innovative teaching and quality research. 

Yes, internships are a part of BTech curriculum in IIIT Ranchi. Students are required to undergo mandatory internships throughout their BTech course and submit an internship report for gaining the maximum credits for those semesters. 

The normal vector to the plane is $\overline{n_1}\times \overline{n_2}=\left|\begin{array}{ccc}\hfill i\hfill & \hfill 3\hfill & \hfill k\hfill \\ \hfill 1\hfill & \hfill a\hfill & \hfill -1\hfill \\ \hfill -1\hfill & \hfill 1\hfill & \hfill -a\hfill \end{array}\right|=\left(1-a\right)\widehat{i}+\widehat{j}+\widehat{k}$

$\therefore equationofplaneis\left(1-a\right)\left(x-1\right)+\left(y-1\right)+z=0$

(1 – a)x + y + z = 2 – a …… (i)

Now distance from (2, 1, 4) = $\sqrt[]{3}$

$\Rightarrow \sqrt[]{3}=\left|\frac{2\left(1-a\right)+1+4-\left(2-a\right)}{\sqrt[]{{\left(1-a\right)}^2+1+1}}\right|$

$\Rightarrow a^2+2a-8=0\Rightarrow a=-4,2$ the largest value of a = 2.

Netaji Subhas University of Technology admission process begins with an online application. Students applying through JAC Delhi refer to the application process mentioned below:

Follow the steps given below to submit the online application form:

Step 1: Appear for the entrance exam.

Step 2: Apply at DTU/JAC Counselling.

Step 3: JAC Delhi & University Counselling.

Step 4: Document Verification for admission.

SRM IST Vadapalani BTech cutoff for 2025 is mainly decided based on SRMJEEE, which is university's own entrance exam held at a national level. The exam is fully online and takes place in three diffrent phases. Students are ranked according to their performance in the exam, and the cutoff varies for each specialisation and campus. Cutoffs may be higher for popular branches like CSE or AI-ML and slightly lower for others.

Given, mean = np = . and variance = npq = $\frac{\alpha }{3}\Rightarrow q=\frac{1}{3}andp=\frac{2}{3}$

$P\left(X=1\right)=n{p}^1{q}^{n-1}=\frac{4}{243}\Rightarrow n{\left(\frac{2}{3}\right)}^1{\left(\frac{1}{3}\right)}^{n-1}=\frac{4}{243}\Rightarrow n=6$

$P\left(X=4or5\right){=}^6{C}_4{\left(\frac{2}{3}\right)}^4{\left(\frac{1}{3}\right)}^2{+}^6{C}_5{\left(\frac{2}{3}\right)}^5{\left(\frac{1}{3}\right)}^1=\frac{16}{27}$

According to some unofficial sources, the top employers for university graduates are as follows:

• NHS
• Tees, Esk and Wear Valleys
• Amazon
• NHS England
• Middlesbrough College
• Wood
• FUJIFILMSBiotechnologies
• Northumbria University
• GSK 

 $C\subseteq AandC\cap B=\phi$

If C is formed only by {1, 2, 4, 5} total number of subsets of A = 27.

Total number of subsets of {1, 2, 4, 5} = 24

$\therefore$ Number of subsets where $C\cap B\ne \phi$

= 27 – 24 = 112

Atma Ram Sanatan Dharma (ARSD) College has a vibrant campus life with numerous active clubs, societies, and events. Some of the notable ones include the Cultural Society, Nimbus (English Debating Society), Enactus (entrepreneurship and social inclusion), Rangayan (Dramatics Society), and Sarang (Singing Society). The college also hosts events such as TIDE (the annual fest), Aarambh (fresher's party), and various departmental fests and seminars. 

Students should focus on topics based on their Class 12 CBSE syllabus. The entrance test includes questions from Physics, Chemistry, Mathematics or Biology (depending on stream), English, and Aptitude. The test format is multiple-choice and it don't have negative marking. Preparation should start early as the exam can be tricky and competitive. The application fee is INR 1200 per phase, and students can appear in more than one phase if needed to improve their score.

Given : $\overrightarrow{a}=\left(\alpha ,1,-1\right)and\overrightarrow{b}=\left(2,1,-\alpha \right)\overrightarrow{c}=\overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hfill \widehat{i}\hfill & \hfill \widehat{j}\hfill & \hfill \widehat{k}\hfill \\ \hfill \alpha \hfill & \hfill 1\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 1\hfill & \hfill -\alpha \hfill \end{array}\right|$

$=\left(-\alpha +1\right)\widehat{i}+\left({\alpha }^2-2\right)\widehat{j}+\left(\alpha -2\right)\widehat{k}$ Projection of $\overrightarrow{c}$ on $\overrightarrow{d}=-\widehat{i}+2\widehat{j}-2\widehat{k}=\left|\overrightarrow{c}.\frac{\overrightarrow{d}}{\left|\overrightarrow{d}\right|}\right|=30\left\{Given\right\}$

$\Rightarrow \left|\frac{\alpha -1-4+2{\alpha }^2-2\alpha +4}{\sqrt[]{1+4+4}}\right|=30$

On solving $\alpha =\frac{-13}{2}$ (Rejected as > 0) and = 7

Netaji Subhas University of Technology admission is based on merit and entrance. The institute accepts national entrance exams such as JEE Main, JAC Delhi,  CUET, MAT, NATA, CAT,  CMAT, UCEED, and others. The institute admission process begins with an online application. Interested candidates must fill out the online application for the respective course on the official website of the Netaji Subhas University of Technology Delhi. 

 $Area=2{\displaystyle \underset{0}{\overset{\sqrt[]{2}}{\int }}\left(1-\left|x^2-1\right|\right)dx=2\left[{\displaystyle \underset{0}{\overset{1}{\int }}\left(1-\left(1-x^2\right)\right)dx+{\displaystyle \underset{1}{\overset{\sqrt[]{2}}{\int }}\left(2-x^2\right)dx}}\right]}=\frac{8}{3}\left(\sqrt[]{2}-1\right)$

$H_1=\frac{v^2}{R_1}{t}_1=\frac{v^2}{R_1}*20$

H2 $=\frac{v^2}{R_2}*t_2=\frac{v^2}{R_2}*60$

from question,

H1 = H2

$\frac{v^2}{R_1}*20=\frac{v^2}{R_2}*60$

$\frac{R_2}{R_1}=3$

Now connected is parallel

Req = $\frac{R_1{R}_2}{R_1+R_2}$

H = $\left(\frac{v^2}{R_1}+\frac{v^2}{R_2}\right)t\text{'}$

H = $v^2\left[\frac{R_1+R_2}{R_1{R}_2}\right]t\text{'}$

Now, According to question

H = H1 + H2

$v^2\left(\frac{R_1+R_2}{R_1{R}_2}\right)t\text{'}=\frac{v^2}{R_1}*20$

$t\text{'}\left[1+\frac{\frac{R_2}{R_1}}{R_2}\right]=\frac{20}{R_1}$

$t\text{'}\left[1+3\right]=20*3$

$t\text{'}=\frac{60}{4}=15min$