Ask & Answer: India's Largest Education Community

$dm=\left(\frac{m}{L}\right)dx$

$\therefore T=\frac{m{\omega }^2}{2L}\left(L^2-x^2\right)$

$\therefore ?L={\int }_0^L\frac{m{\omega }^2}{2L\pi r^{2}Y}\left(L^2-x^2\right)dx$

$=?L=\frac{m{\omega }^2{L}^2}{3\pi r^{2}Y}$

$i=\frac{v_0}{R}\left(1-e^{\frac{tR}{L}}\right)$

$U=\frac{1}{2}L{i}^2$

$\frac{dU}{dt}=Li\frac{di}{dt}$

$2L\times \frac{R}{L}\times \frac{v_0^2}{R^2}\left(1-e^{\frac{tR}{L}}\right)e^{\frac{tR}{L}}=\frac{v_0^2}{R}\left(1-e^{\frac{tR}{L}}\right)$

$t=\frac{L}{R}In2$

The GATE 2026 exam pattern for CS, EC, EE, and ME can be checked below. The general aptitude section (GA) carries 15 marks, while the subject-based questions carries 85 marks, out of which engineering mathematics section consists of 13 marks. The GATE question paper will be in English language and the time duration is three hours. 

Number of moles of C = Number of moles of CO₂ = $\frac{330}{44}$ moles

Number of moles of H = 2 × no. of moles of H₂O = $\left(\frac{270}{18}\times 2\right)$ moles

 Mass of C = $\frac{330}{44}\times 12$ gm = 90 gm

 Mass of H = $\frac{270}{18}\times 2\times 1gm=30gm$

$\begin{array}{l}\mathrm{\%}ofC=\frac{90}{120}\times 100\mathrm{\%}=75\mathrm{\%}\\ \mathrm{\%}ofH=\frac{30}{120}\times 100\mathrm{\%}=25\mathrm{\%}\end{array}$  

$y=A\sin ?\frac{2\pi t}{T}$

$t_2-t_1=\frac{T}{2\pi }\left. [{\sin }^{-1}?\frac{x_1}{A}-{\sin }^{-1}?\frac{x_2}{A}\right]$

Deformation energy per unit volume,

$U=\int dU=\int \frac{P^2}{2B}Ady$

$=\int \frac{{\rho }^2{g}^{2}y}{2B}Ady$

$U=\frac{{\rho }^2{g}^2}{2B}\frac{h^3}{3}A$

$=\frac{{\rho }^2{g}^2{h}^2}{6B}\left(volume\right)$

$=1.5\mu J$

The time duration of the GATE exam 2026 is three hours. This year, IIT Guwahati is conducting the exam. Candidates appearing for the exam must download their admit card from the website. The details regarding the GATE question paper time limit is available in the information brochure. 

The students will have to submit the WBJEE 2026 application form before the final date, which is expected to be in the last week of February 2026. After the final date, the authorities will not accept any registrations for the entrance examination.

WBJEE OMR sheets will be available after the provisional answer key is released. The responses recorded in the entrance examination will be available through the OMR sheets. Students can check the OMR sheets to know which options they had marked in the examination.

The official WBJEE 2026 exam date has not been announced yet. However, it is expected to be held in the fourth week of April 2026. The authorities will announce the official dates online. Students are advised to refer to the WBJEE dates so that they do not miss any important event.

WBJEE 2026 seat allotment dates have not been announced yet. Students will have to log in to check their allotment status and to download the allocation letter for the admission process. Separate allotment results will be announced for the different rounds of counselling.

$U=a{P}^4$

$\frac{PV}{\gamma -1}=a{P}^4$

$P^{-3}V=a\left(\gamma -1\right)$

$P{V}^{-1/3}=constant$

$ComparingwithP{V}^x=constant$

$x=-\frac{1}{3}$

$C=\frac{R}{\gamma -1}+\frac{R}{1-x}=\frac{R}{\frac{5}{3}-1}+\frac{R}{1+\frac{1}{3}}=\frac{3R}{2}+\frac{3R}{4}$

$C=\frac{9R}{4}$

WBJEE 2026 application form is expected to be released in January 2026. The link to register for WBJEE 2026 will be available at the official website. The students will have to fill out the form with the required information and pay the application fee.

The GATE 2026 exam pattern of Life Sciences (XL) is as follows -

• General aptitude  - 15 marks
• B1 section (reasoning and comprehension) carries 16 questions of 25 marks
• Optional section from C1 to C6 carries 39 questions of 60 marks. 

Candidates must go through the GATE pattern and marking scheme before attempting the questions. 

$b=a\sqrt[]{1-e^2}$

$\frac{dA}{dt}=\frac{L}{2m}$

$\frac{A}{T}=\frac{L}{2m}$

$T=\frac{2mA}{L}=\frac{2m\pi ab}{L}=\frac{2m\pi a^2\sqrt[]{1-e^2}}{L}$

The GATE paper code of Engineering Sciences is XE. This year, IIT Guwahati has introduced a new sectional paper under XE, naming Energy Science (XE-I). The optional section (where the applicant has to choose any two) carries 70 marks. The GATE optional sections are as follows -

• Fluid Mechanics
• Materials Science
• Solid Mechanics
• Thermodynamics
• Polymer Science and Engineering
• Food Technology
• Atmospheric and Oceanic Sciences
• Energy Science

Yes, GATE has negative marking for MCQs only. There is no negative marking for MSQs and NATs. For 1 mark question, 1/3rd marks is deducted for incorrect response and for 2 marks, 2/3rd mark is deducted for incorrect response. Candidates who are appearing for the exam this year, must be aware of the exam pattern and marking scheme. 

$f\left(A,B\right)=\frac{1-sinB+sinA-sinAsinB+cosAcosB}{cosA\left(1-sinB\right)}$

$\begin{array}{l}\Rightarrow f\left(A,B\right)\left(cosA-cosAsinB-cosB+sinAcosB\right)\\ =2sinA-2sinB\end{array}$

$\Rightarrow f\left(A,B\right)=\frac{2\left(sinA-sinB\right)}{cosA-cosB+sin\left(A-B\right)}=2g\left(A,B\right)$