Mathematics-3
Previous year question paper with solutions for Mathematics-3
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- Find the Laplace transform of, et 5t
- State Dirichlet’s conditions for the Fourier expansion of f(x) in (0,2)
- Form a partial differential equation from, z = axy + b where a and b are arbitrary constants.
- Define an analytic function and give an example.
- Define the term “an eigen vector” as applied to a square matrix.
- State Runga-Kutta method of order 4
- State any two assumptions for the Poisson distribution.
- What is type-I error?
- Write a short note on “confidence interval estimation”
- State and prove the first shifting property of Laplace transforms.
- Explain the Dirichlet’s conditions for the existence of Fourier series of a function f(x).
- Give any four differences between Gauss Elimination and Gauss-Seidel methods
- Why Modified Euler method is better than Euler?
- What is the mean, median and mode of a normal distribution?
- Find the probability of number 4 turning up at least once in two tosses of a fair dice
- What is Central Limit Theorem?
- What is the mean, median and mode of a normal distribution?
- What is Central Limit Theorem?
- Find the probability of number 4 turning up at least once in two tosses of a fair dice.
- Find the Laplace transform of t.sin at
- Form the partial differential equation by eliminating the functions
- from the relation z = f(x + 4t) + g(x - 4t)
- Prove that the function sinhz is analytic and find its derivatives
- Define partial pivoting with example.
- If the mean of a binomial distribution is 3 and the variance is 3/2, find the probability of obtaining at least 4 success.
- Suppose that X has Poisson distribution. If P(X = 2) = (2/3)P(X = 1) then find P(X = 0)