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BT-401 · Mathematics-III/Unsolved PYQ Paper

BT-401 Mathematics III - Jun 2024 Question Paper

  1. 7 Marks
    aIf the equation $f(x)$ is given as $x^3 - x^2 + 4x - 4 = 0$. Considering the initial approximation at $x = 2$ then find the value of next approximation correct upto 2 decimal places.
  2. 7 Marks
    bWhat is the rate of convergence of Newton Raphson method?
  3. 7 Marks
    aFind i) $\Delta e^{ax}$ ii) $\Delta^2 e^x$ iii) $\Delta \log x$
  4. 7 Marks
    bProve that $f(4) = f(3) + \Delta f(2) + \Delta^2 f(1) + \Delta^3 f(1)$ taking '1' as the interval of differencing.
  5. 7 Marks
    aUsing Simpson's 3/8 rule to solve the integral $$\int_{4}^{5.2} \log_e x \, dx$$
  6. 7 Marks
    bFind $f(0.18)$ from the following table using Newton's Forward interpolation formula.
  7. 7 Marks
    aApply Gauss Elimination method to solve the following equations : $$2x - y + 3z = 9$$ $$x + y + z = 6$$ $$x - y + z = 2$$
  8. 7 Marks
    bFind missing values in the following table:
  9. 7 Marks
    aUse Runge-Kutta method to approximate $y$, when $x = 0.1$ and $x = 0.2$, given that $x = 0$ when $y = 1$ and $\frac{dy}{dx} = x + y$.
  10. 7 Marks
    bUse Milne's method to solve $\frac{dy}{dx} = x + y$ with initial condition $y(0) = 1$, from $x = 0.20$ to $x = 0.30$.
  11. 7 Marks
    aFind the value of $f(5)$ from the following table.
  12. 7 Marks
    bFind the real root of the equation $x \log_{10} x - 1.2 = 0$ correct to five places of decimal by Regula Falsi Method.
  13. 7 Marks
    aFind the inverse Laplace transform of $\frac{2s+1}{s(s-1)}$.
  14. 7 Marks
    bState convolution theorem and hence evaluate $$L^{-1}\left[\frac{s}{(s^2+1)(s^2+4)}\right].$$
  15. 7 Marks
    aA binomial variable $X$ satisfies the relation $9P(X = 4) = P(X = 2)$ when $n = 6$. Find the value of the parameter $p$ and $P(X = 1)$.
  16. 7 Marks
    bA large number of measurement is normally distributed with a mean $65.5$" and S.D. of $6.2$". Find the percentage of measurements that fall between $54.8$" and $68.8$".
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