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BT-401 · Mathematics-III/Unsolved PYQ Paper

BT-401 Mathematics III - Jun 2025 Question Paper

  1. 7 Marks
    aFind the real root of equation $f(x) = x^3 - x - 10$ by using Newton Raphson method correct up to 4 decimal places.
  2. 7 Marks
    bFind solution $y(301)$ using Newton Divided difference interpolation formula
  3. 7 Marks
    aEvaluate the following using Simpson's 3/8 rule.
  4. 7 Marks
    bSolve the given set of equations by using Gauss elimination method: $$x + y + z = 4$$ $$x - 4y + 3z = 8$$ $$x + 6y + 2z = 6$$
  5. 7 Marks
    aUsing modified Euler's method, find an approximate value of $Y$, when $x = 0.3$. Given that $\frac{dy}{dx} = x + y$ and $y = 1$, when $x = 0$.
  6. 7 Marks
    bConsider an ordinary differential equation $\frac{dy}{dx} = x^2 + y^2, y(1) = 1.2$. Find $y(1.05)$ using the fourth order Runge-Kutta method.
  7. 7 Marks
    aFind the inverse Laplace transform of the following functions. $$F(s) = \frac{1}{(s+1)(s^2+1)}$$
  8. 7 Marks
    bSuppose that the function $y(t)$ satisfies the DE $y'' - 2y' - y = 1$, with initial values, $y(0) = -1, y'(0) = 1$. Find the laplace transform of $y(t)$.
  9. 7 Marks
    aA device is used to measure the speed of cars on a highway. The speed is normally distributed with a $90$ km/hr mean and a standard deviation of $10$. What is the probability that the car picked was travelling at more than $100$ km/hr?
  10. 7 Marks
    bThe mean and the standard deviation of a binomial distribution are $100$ and $5$. Find the binomial distribution.
  11. 7 Marks
    aIn a normal distribution, $10.03\%$ of the items are under $25$ kg. weight and $89.97\%$ of the items are under $70$ kg. weight. What are the mean and standard deviation of the distribution?
  12. 7 Marks
    bFind Solution using Lagrange's Interpolation formula.
  13. 7 Marks
    aFind the Laplace transform of the following function i) $L(t^2 e^{-t} \cosh 2t)$ ii) $L(e^{3t} \sin^2 4t)$
  14. 7 Marks
    bUsing Milne's method find $y(4.4.)$ given $5xy + y^2 - 2 = 0$ Given $y(4) = 1, y(4.1) = 1.0049, y(4.2) = 1.0097$ and $y(4.3) = 1.0143$.
  15. 7 Marks
    aFind mean of Poisson distribution.
  16. 7 Marks
    bWrite short note on Exponential distribution.
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