Mechanical Engineering

Section 1:
Linear Algebra
Matrix
Algebra Systems of linear equations, eigenvalues and eigenvectors.
Calculus
Functions of single variable, Limit, Continuity and differentiability, Mean value theorems, Indeterminate forms, Evaluation of definite and improper integrals, Double and triple integrals, Partial derivatives, Total derivative, Taylor Series (in one and two variables), Maxima and minima, Fourier series, Gradient, divergence and curl, Vector identities, Directional derivatives, Line, surface and volume integrals, Applications of Gauss, Stokes and Greens theorems.
Differential equations
First order equations (linear and non-linear) higher order linear differential equations with constant coefficients, Euler-Cauchy equation, Initial and boundary value problems, Laplace transforms, Solutions of heat, wave and Laplace's equations.
Complex variables
Analytic functions, Cauchy-Riemann equations, Cauchy's integral theorem and integral formula, and Taylor and Laurent series.
Probability and Statistics
Definitions of probability, sampling theorems, conditional probabilityMean, median, mode and standard deviation; random variables, binomial, Poisson and normal distributions.
Numerical Methods
Numerical solutions of linear and non-linear algebraic equations, Integration by trapezoidal and Simpsons rules, and Single and multi-step methods for differential equations.

You will get mechanical branch in VIT, Vellore but in second or third category (i. e. you have to pay more for that desired branch). Let me explain you the admission system here. Rank in VIT to get admission should be 90,000, so you can get admission in VIT from the 6th category as well. There are various categories as well. With each category admission, fees go high. First category closed till 15,000 rank, and you can get Mechanical till 16000 rank but there are 2nd category as well, if you want mechanical, but you have to pay more for that. Additional Information: Predict engineering colleges you can get on the basis of your JEE Rank: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_campaign=8321427.