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BT-401 · Mathematics-III/Unsolved PYQ Paper

BT-401 Mathematics - III - Nov 2022 Question Paper

  1. 7 Marks
    aBy using Newton Raphson method, find the root of $x^4-x-10=0$. Which is nearer to $x = 2$, correct to three places of decimals.
  2. 7 Marks
    bProve that: $(I + \Delta)(I - \nabla) \equiv \Delta\nabla$
  3. 7 Marks
    aFind the value of $f(5)$ from the following table.
  4. 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.
  5. 7 Marks
    aGiven following data, find the value of the following integral using simpson's 1/3 rule and compare it with the actual value. $$\int_0^4 e^x dx$$ $[e^0=1, e^1=2.72, e^2=7.39, e^3=20.09, e^4=54.60]$
  6. 7 Marks
    bUsing Simpson's 3/8 rule to solve the integral $$\int_4^{5.2} \log_e x dx$$
  7. 7 Marks
    aSolve by Jacobi's iteration method, the equations $$20x+y-2z = 17$$ $$3x+20y-z = -18$$ $$2x-3y+20z = 25$$
  8. 7 Marks
    bEvaluate by Simpson's Rule $\int_0^1 e^{-x^2} dx$
  9. 7 Marks
    aFind $y(4.2)$ by Euler's modified method taking $h = 0.1$, from $\frac{dy}{dx} = \frac{2-y}{4x}$, taking $y = 1$ when $x = 4$.
  10. 7 Marks
    bFind $y(1.05)$ using the Runge-Kutta Fourth order method from $$\frac{dy}{dx} = x^2 + y^2, y(1) = 1.2, h = 0.05.$$
  11. 7 Marks
    aUse Euler's method to solve $\frac{dy}{dx} = \frac{y^2-x}{y^2+x}, x = 0, y = 1$. Compute $y(0.1), y(0.2)$.
  12. 7 Marks
    bUse Euler's Modified method to solve the equation $\frac{dy}{dx} = x + \sqrt{y}, y(2) = 4, h = 0.2$, compute $y(2.4)$.
  13. 7 Marks
    aEvaluate $$L(e^{3t} \cos 2t)$$
  14. 7 Marks
    bEvaluate $$L^{-1}\left[\frac{s+7}{s^2+4s+8}\right]$$
  15. 7 Marks
    aFind mean of the Binomial distribution.
  16. 7 Marks
    bSuppose a machine produces on an average 80% good pieces, find the probability that out of 5 pieces produced by this machine 3 pieces will be good.
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