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$\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]=0$

$\left|\begin{array}{ccc}\hfill 1\hfill & \hfill 6\hfill & \hfill 3\hfill \\ \hfill 3\hfill & \hfill 2\hfill & \hfill 1\hfill \\ \hfill \alpha +1\hfill & \hfill \beta -1\hfill & \hfill 1\hfill \end{array}\right|=0$

$8\beta -24=0\Rightarrow \beta =3$

$\left|\overrightarrow{c}\right|=\sqrt[]{6}$

${\left(\alpha +1\right)}^2+{\left(\beta -1\right)}^2+1=6\Rightarrow {\left(\alpha +1\right)}^2=1$

a = 1 = 1, 1 $\Rightarrow \alpha =-2,0$ $$

+ = 1, 3

The order of stability of resonating structures: carrying no charge $>$  carrying minimum charge and each atom having octet complete.

The COMEDK UGET counselling registration fee is Rs 2000 and is a non-refundable charge.

Variance of 2001, 2003, 2006, 2007, 2009, 2010 is same as variance of 1, 3, 6, 7, 9, 10

mean =  $\frac{1+3+6+7+9+10}{6}=6$

var (x) =  $\frac{1^2+3^2+6^2+7^2+9^2+10^2}{6}?36$

var (x) = 10

There are two types of seat categories in COMEDK counselling 2025- GM and KKR. The government has reserved 70% of the seats in colleges located in Kalyana Karnataka area in favour of locals and 8% of the seats are reserved for locals of the Kalyana Karnataka Region located outside the said region. The Kalyana Karnataka Region comprises of Kalaburagi, Yadgir, Bidar, Koppal, Raichur, Ballari and Vijayanagara districts.

  $\sim \left(p\to q\right)=p\wedge \sim q$

A quadrilateral is a square and it is not a rhombus

If the test centre cancels your GRE booking, then you will get a 100% refund or a free reschedule from ETS. They will inform you about this on your Email.  Check your email for options and act quickly to secure a new preferred date.

$f\left(x\right)=[\begin{array}{l}-\frac{1}{x}x\in \left(-\infty ,-1\right)\\ a{x}^2+bx\in \left(-1,1\right)\\ \frac{1}{x}x\in \left[1,\infty \right)\end{array}$

cont at x = 1, a + b = 1

diff at x = 1, 2a = 1 $\Rightarrow a=-\frac{1}{2}\Rightarrow b=\frac{3}{2}$

area of quad PACB = LR = 8

$P=1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+...+\infty$

$\frac{P}{3}=\frac{1}{3}=\frac{2}{3^2}+\frac{6}{3^3}+\frac{10}{3^4}+...+\infty$

$\frac{2P}{3}=1+\frac{1}{3}+\left[\frac{4}{3^2}+\frac{4}{3^3}+\frac{4}{3^4}+...+\infty \right]$

$\frac{2P}{3}=\frac{\frac{4}{3}}{1-\frac{1}{3}}\Rightarrow P=3$

$f\left(x\right)=x^2+x+\left(\frac{\lambda +1}{\lambda }\right)$

$f\left(1\right)<0\Rightarrow 2+\left(\frac{\lambda +1}{\lambda }\right)<0$

$\frac{3\lambda +1}{\lambda }<0\Rightarrow \lambda \in \left(-\frac{1}{3},0\right)$

WBJEE cutoff is released online. It is prepared after checking different exam and admission related factors. Some important factors that are considered to determine cutoff are entrance exam difficulty level, previous years' cutoff trends, number of seats for admission, total number of applicants and more.

After the seats are allotted, students will have to pay seat acceptance fee of INR 5000 online to download allotment letter. Next, they will have to report to their respective college for document verification and tuition fee payment.

WBJEEB conducts the WBJEE counselling process online. All qualified candidates have to register for the counselling and fill out their choice of colleges and courses. The counselling fee also has to be paid online, i.e., through net banking/credit card/debit card. No offline counselling will be held.

$3-2^x-2^{1-x}\ge 0put{2}^x=t$

$3-t-\frac{2}{t}\ge 0\Rightarrow t^2-3t+2\le 0$

$\left(t-1\right)\left(t-2\right)\le 0\Rightarrow t\in \left[1,2\right]$

WBJEEB will announce WBJEE 2026 toppers. Highest scoring students will be given top ranks in WBJEE 2026. In previous year, Aniruddha Chakrabarti secured first rank in WBJEE, followed by Samyajyoti Biswas and Dishaanth Basu in second and third rank. List of the top 10 rankers in WBJEE 2026 will be released by authorities.

To register for the COMEDK counselling candidates have to log in to the candidate portal at comedk.org fill in their details and pay the counselling fee.