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BT-401 · Mathematics-III/Unsolved PYQ Paper

BT-401 Mathematics - III - Jun 2023 Question Paper

  1. 7 Marks
    aFind the real root of the equation $x^3-3x-5=0$ correct to four places of decimals by Newton Raphson method.
  2. 7 Marks
    bEvaluate $$\Delta^6(ax-1)(bx^2-1)(cx^3-1); h=1$$
  3. 7 Marks
    aUsing Newton's divided difference formula, find $f(8)$ and $f(15)$ from the following table.
  4. 7 Marks
    bFind the real root of the equation $xe^x-3=0$ correct to three decimal places by Regula Falsi method.
  5. 7 Marks
    aUse Simpson's 1/3 and 3/8 rule to evaluate the following. $$\int_0^1 \frac{dx}{1+x^2}$$ Hence obtain the approximate value of $\pi$ in each case.
  6. 7 Marks
    bCompute the value of the following integral by trapezoidal Rule. $$\int_{0.2}^{1.4}(Sinx-\log_e x+e^x)dx$$
  7. 7 Marks
    aSolve the following system by Gauss Siedel iteration method. $$27x+6y-z=85$$ $$6x+15y+2z=72$$ $$x+y+54z=110$$
  8. 7 Marks
    bUse Simpson's rule to find approximate value of the following integral. $$\int_1^2 \frac{dx}{x}$$
  9. 7 Marks
    aUse Euler's method compute the solution of $\frac{dy}{dx}=y^2-x^2$ with $y(0)=1$ at $x=0.1$.
  10. 7 Marks
    bUse Euler's Modified method to solve the equation $\frac{dy}{dx}=x+y$, $y(0)=1$, $h=0.2$ compute $y(1)$
  11. 7 Marks
    aUse Laplace transform to solve the Initial Value Problem. $$y'+2y=26\sin 3t,\: y(0)=3$$
  12. 7 Marks
    bEvaluate $$L(t \cos at)$$
  13. 7 Marks
    aEvaluate $$L^{-1}\left[\frac{1}{(1+s)^3}\right]$$
  14. 7 Marks
    bEvaluate $$L\{t^2e^{-3t}\}$$
  15. 7 Marks
    aFind mean of Poisson distribution.
  16. 7 Marks
    bWrite Short note on Exponential Distribution.
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