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BT-301 · Mathematics-III/Unsolved PYQ Paper

BT-301 Mathematics - III - Jun 2023 Question Paper

  1. 7 Marks
    aFind Solution using Newton's Divided Difference Interpolation formula. | $x$ | 300 | 304 | 305 | 307 | |---|---|---|---|---| | $F(x)$ | 2.4771 | 2.4829 | 2.4843 | 2.4871 |
  2. 7 Marks
    bUsing Newton Raphson Method, find the real root of the equation $3x = \cos x + 1$.
  3. 7 Marks
    aFind the first and second derivatives at $x = 1.1$ from the following table | $x$ | 1 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 | |---|---|---|---|---|---|---| | $F(x)$ | 0 | .1280 | .5440 | 1.2960 | 2.4320 | 4.00 |
  4. 7 Marks
    bFind Solution using Simpson's 3/8 rule. | $x$ | 0 | 0.1 | 0.2 | 0.3 | 0.4 | |---|---|---|---|---|---| | $y$ | 1 | 0.9975 | 0.99 | 0.9776 | 0.8604 |
  5. 7 Marks
    aApply Runge-kutta method of fourth order to solve $$10 \frac{dy}{dx} = x^2 + y^2 ; y(0) = 1 \text{ for } x = 0.1$$
  6. 7 Marks
    bUse Milne's method to find the solution of differential equation $\frac{dy}{dx} = x - y^2$; given that $y = 0$ when $x = 0$ for $0 < x < 1$.
  7. 7 Marks
    aFind Laplace transform of the following data
  8. 7 Marks
    bSolve : $(D^2 + 1) y = t \cos 2t, y(0) = 0 = y'(0), t > 0$.
  9. 7 Marks
    aFind the Mean and Variance of the Poisson distribution.
  10. 7 Marks
    bA fair coin is tossed 10 times, what are the probability of getting exactly 6 heads and at least six heads.
  11. 7 Marks
    aUse Taylor series method to obtain the value of $y$ at $x = 0.1$, For the differential equation $\frac{dy}{dx} = x + y; y(0) = 1$.
  12. 7 Marks
    bSolve the following equation by Gauss-Seidel method $$\begin{aligned} 20x + y - 2z &= 17 \\ 3x + 20y - z &= -18 \\ 2x - 3y + 20z &= 25 \end{aligned}$$
  13. 7 Marks
    aSolve the following system of equation by Crout's method $$\begin{aligned} 2x + 3y - z &= 5 \\ 3x + 2y + z &= 10 \\ x - 5y + 3z &= 0 \end{aligned}$$
  14. 7 Marks
    bFind the Fourier Cosine Transform of $e^{-x}$
  15. 7 Marks
    aFind $y(0.2)$ by Euler's modified method $$\frac{dy}{dx} = \log_{10} (x + y), y(0) = 1$$
  16. 7 Marks
    bFind the root of the equation $x^3 - 9x + 1 = 0$ between $x = 2$ and $x = 4$ by the method of bisection.
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