BT-301 · Mathematics-III/Unsolved PYQ Paper
BT-301 Mathematics - III - Nov 2022 Question Paper
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7 MarksaFind a positive root of the equation by iteration method $3x = \cos x + 1$.
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7 MarksbUsing Lagrange's interpolation formula, find $y(6)$ from the following data: | X | 3 | 5 | 7 | 9 | 11 | |---|---|---|---|---|---| | Y | 6 | 24 | 58 | 108 | 74 |
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7 MarksaEvaluate $\int_{0}^{\pi} \sin x \, dx$ by dividing the range into 10 equal parts using: i) Trapezoidal rule ii) Simpson's 1/3 rule
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7 MarksbUsing Gauss-Seidel iteration method to solve the system. $$10x + y + z = 12, \quad 2x + 10y + z = 13, \quad 2x + 2y + 10z = 14.$$
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7 MarksaGiven that $\sin 45 = 0.7071$, $\sin 50 = 0.7660$, $\sin 55 = 0.8192$, $\sin 60 = 0.8660$. Then find the $\sin 58$ by using Newton's backward interpolation formula.
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7 MarksbUsing Simpson's 3/8 rule, evaluate $\int_{0}^{6} \frac{dx}{1+x^2}$ by dividing the range into 6 equal parts.
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14 MarksGiven $\frac{dy}{dx} = x + \sin y$ and $y(0) = 1$. Compute $y(0.2)$ and $y(0.4)$ with $h = 0.2$ using Euler's modified method.
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7 MarksaUsing Laplace Transform, Evaluate $\int_{0}^{\infty} \frac{\cos at - \cos bt}{t} \, dt$.
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7 MarksbFind $$L^{-1} = \left\{ \frac{s^2}{(s^2 + a^2)^2} \right\}$$
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14 MarksUsing Laplace Transform, Solve $(D^2 + 2D + 5)y = e^{-t} \sin t$, given that $y(0) = 0, y'(0) = 1$.
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7 Marksa20% of items produced from a factory are defective. Find the probability that in a sample of 5 chosen at random. i) None is Defective ii) One is Defective iii) $P(1 < x < 4)$.
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7 MarksbIf a random variable has a Poisson distribution such that $P(1) = P(2)$. Find out i) Mean of the distribution ii) $P(x \geq 1)$ iii) $P(1 < x < 4)$
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7 MarksaDerive Mean of the Normal Distribution.
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7 MarksbUsing Runge-Kutta method of fourth order solve $y' = xy$, $y(1) = 2$ at $x = 1.2$ with $h = 0.2$.
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