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BT-401 · Mathematics-III/Unsolved PYQ Paper

BT-401 Mathematics III - Dec 2024 Question Paper

  1. 7 Marks
    aUsing Newton-Raphson method find the real root of the equation $3x = \cos x + 1$ correct to five decimal places.
  2. 7 Marks
    bFind $f(g)$ from the following table
  3. 7 Marks
    aApply the Simpson's $\frac{3}{8}$ rule to evaluate the following integral for six digit $\int_{1.0}^{1.30} \sqrt{x} \cdot dx$.
  4. 7 Marks
    bSolve the following system of equation using Gauss-Seidel method. $$27x + 6y - z = 85$$ $$6x + 15y + 2z = 72$$ $$x + y + 54z = 110$$
  5. 7 Marks
    aUsing Runge-Kutta method of fourth order solve $\frac{dy}{dx} = \frac{y^2 - x^2}{y^2 + x^2}$, $y(0) = 1$ at $x = 0.4$ in step of $0.2$
  6. 7 Marks
    bFind $y(2.2)$ using Euler's method for $\frac{dy}{dx} = -xy^2$ where $y(2) = 1$.
  7. 7 Marks
    aFind the Inverse Laplace transform of $\frac{1}{p^3\left(p^2 + a^2\right)}$.
  8. 7 Marks
    bUsing Laplace transform solve the differential equation $\frac{d^3y}{dt^3} + 2\frac{d^2y}{dt^2} - \frac{dy}{dt} - 2y = 0$ Where $y = 1, \frac{dy}{dt} = 2, \frac{d^2y}{dt^2} = 2$ at $t = 0$.
  9. 7 Marks
    aFit a Poisson distribution to the following.
  10. 7 Marks
    bCalculate the mean and standard deviation of Binomial Distribution.
  11. 7 Marks
    aFind $\frac{dy}{dx}$ at $x = 1.5$ from the following table
  12. 7 Marks
    bEvaluate $\int_{0}^{\infty} \frac{e^{-t} \cdot \sin t}{t} dt$
  13. 7 Marks
    aShow that Newton Raphson method is quadratic convergent.
  14. 7 Marks
    bDrive Newton forward interpolation formula and use it to estimate the value of $f(1.25)$ from the following table
  15. 7 Marks
    aSolve the system of equations $$3x + y - z = 3$$ $$2x - 8y + z = -5$$ $$x - 2y + 9z = 8$$ Using Gauss elimination method.
  16. 7 Marks
    bFind Fourier sine transform of $\frac{1}{x}$.
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