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BT-301 · Mathematics-III/Unsolved PYQ Paper

BT-301 Mathematics-III - Dec 2025 Question Paper

  1. 7 Marks
    aBy using Newton-Raphon's method find the root of A, which is nearer to 2, correct to three places of decimal.
  2. 7 Marks
    bFind the first term of the series whose second and subsequent terms are 8,3,0,-1,0.
  3. 7 Marks
    aSolve $27x+6y-z=85,\ 6x+15y+2z=72,\ x+y+54z=110$ by Gauss-Seidel iteration method.
  4. 7 Marks
    bCalculate by Simpson's 1/3 rule (up to 3 places of decimal) $\int_{2}^{10} \frac{dx}{1+x}$ by dividing the range in to eight equal parts.
  5. 7 Marks
    aSolve $\frac{dy}{dx} = 1-2xy$ given that $y(0)=0$, by Taylor's method.
  6. 7 Marks
    bSolve the equation $\frac{dy}{dx} = x+y$ , with initial condition $y(0)=1$ by Runge-Kutta method, from $x=0$ to $x=0.2$ with $h=0.1$.
  7. 7 Marks
    aShow that $L\left\{\frac{\cos \sqrt{t}}{\sqrt{t}}\right\} = \sqrt{\frac{\pi}{s}} e^{-\frac{1}{4s}}$
  8. 7 Marks
    bEvaluate $L^{-1}\left\{\frac{6s^{2}+22s+18}{s^{3}+6s^{2}+11s+6}\right\}$.
  9. 7 Marks
    aIf $f(x) = cx^{2}, 0 < x < 1$ , find the value of c and determine the probability that $\frac{1}{3} < x < \frac{1}{2}$.
  10. 7 Marks
    bIn sampling a large number of parts manufactured by a machine, the mean number of defectives in a sample of 20 is 2 out of 1000 such samples, how many would be expected to contain (i) at least 3 defective Parts? (ii) none defective?
  11. 7 Marks
    aFrom the following table, estimate the number of students who obtained marks between 40 and 45.
  12. 7 Marks
    bBy means of Newton's Divided difference formula, find the values of $f(8)$, $f(15)$ from the following table:
  13. 7 Marks
    aState Convolution theorem and hence evaluate $L^{-1}\left\{\frac{s}{(s^{2}+a^{2})^{2}}\right\}$.
  14. 7 Marks
    bSolve $(D^{2}+6D+9)y = \sin x$ given that $y=1,y=0$ when $x=0$.
  15. 7 Marks
    aFind mean of Poisson distribution.
  16. 7 Marks
    bWrite short note on Exponential distribution.
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