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$t_n=\frac{1}{2^n.3^{11-n}}={\left(\frac{1}{3}\right)}^{11}.{\left(\frac{3}{2}\right)}^n$

$S_{10}={\left(\frac{1}{3}\right)}^{11}.\frac{\left(\frac{3}{2}\right).\left({\left(\frac{3}{2}\right)}^{10}-1\right)}{\frac{3}{2}-1}$

$=\frac{1}{3^{10}}.\frac{3^{10}-2^{10}}{2^{10}}$

$=1{+}^{10}{C}_1.2^1{+}^{10}{C}_2.2^2+....{+}^{10}{C}_9.2^9$

k = 21 + 6m ® R = 3

The university graduates work for top sectors such as Operations, Business Development, Sales, Information Technology, and more. Seneca graduates are highly skilled in the following:

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In JEE Advanced chemistry the high weightage chapters include:

1. p-block
2. Chemical bonding
3. Coordination compounds
4. Electrochemistry
5. Ionic & Chemical Equilibrium
6. Electrochemistry & Surface Chemistry
7. Aldehyde & Ketones
8. Polymers
9. Biomolecules

The end date for students who appeared for the ICAR AIEEA PG exam was June 5, 2025, by 5:00 pm. Candidates need to submit the application fee to complete the application process by visiting the official website. 

Official website to download GATE admit card is gate2026.iitg.ac.in. GOAPS portal link is goaps.iitg.ac.in. Candidates must provide their enrollment ID and password to download their hall ticket.

The important topics in JEE Advanced physics are:

1. Waves & Sound
2. Ray & Wave Optics
3. Fluids
4. EM Waves
5. Thermodynamics
6. Modern Physics
7. Kinematics
8. Gravitation
9. Electrostatics

In JEE Advanced maths, the topics that carry high weightage are:

1. Matrix & Determinants
2. Probability
3. Complex Numbers
4. Vector
5. Definite Integration

IIT Guwahati has a decent placement record of placements for courses like BTech, MTech, MBA, BDes, etc. Check out the key highlights of IIT Guwahati placements for the Class of 2024 and 2025 in the table below:

Yes. Candidates who have appeared for JEE Advanced in 2025 and it was there firts attempt, can also attempt JEE Advanced in 2026. However, if JEE Advanced 2025 was your second attempt, then you cannot attempt JEE Advanced in 2026.

The Indian Institute of Technology, Guwahati, will be conducting the GATE 2026 exam. The dates are OUT now. IIT Guwahati last conducted the GATE exam in 2018. Candidates who want to apply for M.Tech or any research programmes can apply for GATE. The application window is available till October 7 without late fees (revised), till October 13 (with late fee) and the exam will be conducted on February 7, 8, 14, and 15. 

The difficulty level of getting into the MBBS course at NTRUHS depends on the cutoff the university releases for each academic year. Check out the cutoff of the university from here: NTRUHS cutoff.

Further, the level of competitiveness and difficulty depends on the affiliated colleges allotted to the students. If the number of seats is limited at any of the affiliated colleges, then there is a chance that the college might have more competition to get them.

= A + B (say)

(1 + x)¹⁵ =

differentiating 15 (1 + x)¹⁴ =   $\sum r{.}^{15}{C}_r{x}^{r-1}$

put  = x = -1

$\Rightarrow 0={-}^{15}{C}_1+2{.}^{15}{C}_2-.......=A$      

  $B{=}^{14}{C}_{13}=2^{13}$            

$\therefore A+B=2^{13}-14$           

$f\left(g\left(x\right)\right)=x\forall x\in R$

$\Rightarrow g\left(x\right)=f^{-1}\left(x\right)$

For y = g (x)

x = y³ + y – 5

$\frac{dx}{dy}=3y^2+1\Rightarrow g\text{'}\left(63\right)=\frac{1}{3\left(16\right)+1}=\frac{1}{49}$

$g\text{'}\left(63\right)=\left(\frac{dy}{dx}\right)$

$\left(\begin{array}{l}x=63\\ y=4\end{array}\right)$

Let direction ratio of the normal to the required plane are l, m, n

$\begin{array}{l}\therefore 3l+m-2n=0\\ \therefore 2l-5m-n=0\\ \therefore \frac{l}{-11}=\frac{m}{-1}=\frac{n}{-17}\end{array}$             

Equation of required plane

11 (x – 1) + 1 (y – 2) + 17 (z + 3) = 0

$\Rightarrow 11x+y+17z+38=0$           

$e^{\left(co{s}^{2}x+co{s}^{4}x+co{s}^{6}x+.....\infty \right)}lo{g}_{e}2$  

$=e^{\frac{co{s}^{2}x}{1-co{s}^{2}x}lo{g}_{e}2}=e^{co{t}^{2}xlo{g}_{e}2}=2^{co{t}^{2}x}$          

t² – 9t + 8 = 0

(t – 8) (t – 1) = 0

$t=2^{co{t}^{2}x}=8=2^3$

$\Rightarrow co{t}^{2}x=3=co{t}^2\frac{\pi }{6}$

$\frac{2sinx}{sinx+\sqrt[]{3}cosx}=\frac{2\times \frac{1}{2}}{\frac{1}{2}+\sqrt[]{3}\times \frac{\sqrt[]{3}}{2}}=\frac{1}{2}$            

In JEE Advanced exam, questions are asked from:

1. Maths
2. Physics
3. Chemistry

There are two papers in the exam and each paper has questions from these three subjects.

Seneca Polytechnic graduates are constantly in high demand all over the world. Seneca graduates work in top sectors that are listed below:

• Operations
• Business Development
• Sales
• Information Technology
• Customer Success and Support