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RGPV JUN 2020 SOLUTIONS
NEW
Q.1 Express f(x)=x as a half range sine series in 0 < x < 2
Q.2 Obtain the Fourier series for the function f(x)=x2 in -Π < x < Π ( -Pai < x < Pai)
Q.3 Find the Fourier sine transform of f(x) = 1 / x .
Q. 4 : Find a root of the equation x
3
-4x-9=0 using bisection method correct to three decimal places.
RGPV DEC 2018
Q. 5: Using Newton-Raphson method, find the real root of the equation 3x=cos x+1.
RGPV DEC 2018
Q. 6: Find the cubic polynomial which takes the following values-
RGPV DEC 2018
Q. 7 : By means of Newton's divided difference formula, find f(8) and f(9) from the following data-
RGPV DEC 2018
Q. 8: Using Simpson's 1/3 rule, obtain by taking sevan ordinates. Compare it with exact values.
RGPV DEC 2018
Q. 9 : Solve the following system by Gauss elimination method- 6x + 3y + 2z = 6
RGPV DEC 2018
Q. 10 : Solve the following system of equations using Gauss-Seidel method- 27x + 6y - z = 85
RGPV DEC 2018
Q. 11 : Using Lagrange's interpolation formula, find the cubic polynomial that takes the following values.
RGPV DEC 2018
Q. 12 : Using Runge-Kutta method of fourth order solve the differential equation- dy / dx = xy for x = 1.2
RGPV DEC 2018
Q. 13 : Using Picard's method find y for x = 0.1 Given that
RGPV DEC 2018
Q. 14 : Solve the given equation for y(1.1) using Taylor series method-
RGPV DEC 2018
Q. 15 : Find the followings- (i) L{t^2 sin at}
RGPV DEC 2018
Q. 16 : Using convolution theorem find L
-1
{1 / (s-1)(s+2)}.
RGPV DEC 2018
Q. 17 : Using Laplace transform, solve equation (D
2
+ 2D +1) y=t. Given that y(0) = -3, y(1) =1.
RGPV DEC 2018
Q. 18 : Find the probability that at most 5 defective fuses will be found in a box of 200 fuses if experience shows that 2% of such fuses are defective.
RGPV DEC 2018
Q. 19 : Find mean and variance of Binomial distribution.
RGPV DEC 2018
Q. 20 : Find a root of following equation using bisection method correct to three places of decimal f(x)=x^3-3x-5.
RGPV MAY 2019
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