Numerical Methods - Engineering Mathematics - Agricultural Engineering Previous Year Questions

1

2007 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2007

Taking \(y(0) = 0\) and using Euler's method with step size \(h = 0.1\) solution of the differential equation \(\frac{dy}{dx} = 2x y + 1\) gives the value of \(y(0.3)\) as

A

0.3101

B

0.3142

C

0.6202

D

4.080

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2

2007 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2007

Integrating the function \(f(x) = 1 + e^{-x} \sin(4x)\) over the interval \([0,1]\) using Simpson's 1/3rd rule gives

A

1.021

B

1.091

C

1.321

D

2.642

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3

2008 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2008

A function f(x) is evaluated as 1, 1.5, 2.2 and 3.4 at four values of x having intervals of 0.5. The area under the curve f(x) using trapezoidal rule is

A

1.95

B

2.45

C

2.95

D

3.45

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4

2010 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2010

The error in using trapezoidal rule for finding the value of
\( \int_2^3 \frac{dx}{1+x} \) is

A

0.0368

B

0.0468

C

0.0568

D

0.0668

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5

2010 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2010

5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

A

20 days

B

18 days

C

16 days

D

15 days

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6

2011 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2011

The highest order of polynomial integrand for which Simpson's 1/3 rule of integration is exact is

A

first

B

second

C

third

D

fourth

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7

2013 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2013

\(f(x) = e^{-x}\) for \(x = 1.1, 1.2, 1.3, 1.4\) and 1.5, the value of \(\int_{1.1}^{1.5} f(x)dx\) by Simpson's 1/3rd rule is ________

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8

2016 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2016

Integration by trapezoidal method of \(log_{10} (x)\) with lower limit of 1 to upper limit of 3 using seven distinct values (equally covering the whole range) is ______________

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9

2018 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2018

Solution of \(f(x) = x^4 + 2x^3 - 4x^2 + 3x - 1 = 0\) is

A

0.333

B

0.646

C

0.658

D

1.000

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10

2019 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2019

Using trapezoidal rule, the value of \( I = \int_{4.0}^{5.2} \ln(x) \, dx \) (rounded off to three decimal places) is __________.

\( x \)	4.0	4.2	4.4	4.6	4.8	5.0	5.2
\( Y = \ln(x) \)	1.386	1.435	1.482	1.526	1.569	1.609	1.648

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11

2020 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2020

Taking six intervals, each of π/12 and using Simpson's one-third rule, the value of the definite integral ∫₀^{π/2} √cos θ dθ (round off to 3 decimal places) is ________.

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12

2022 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2022

The root of the equation \(\sin x - 4x + 1 = 0\) after its first iteration, using Newton-Raphson method with an initial guess of \(x_0 = 0.2\), is ______. [round off to three decimal places]

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13

2022 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2022

The power consumption readings (in watt) by an instrument at fixed intervals of time (in seconds) are tabulated below:

Time (s)	0.0	0.6	1.2	1.8	2.4	3.0	3.6
Power consumption (W)	8.6	9.2	7.8	6.4	7.2	8.6	11.2

Using Simpson's 1/3ʳᵈ rule, the energy expenditure of the instrument in joule is __________. [round off to two decimal places]

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14

2023 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2023

Given that dy/dx = 2x + y and y = 1, when x = 0. Using Runge-Kutta fourth order method, the value of y at x = 0.2 is __________ (rounded off to 3 decimal places).

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15

2026 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2026

Consider the simultaneous equations
\( 2x + 4y = -7; \quad 3x + 5y = 1 \)
While solving using Gauss elimination without pivoting, after the forward elimination, the diagonal elements of the coefficient matrix are

A

2 and -1

B

3 and 2

C

5 and -2

D

3 and 4

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16

2026 · Agricultural Engineering · Engineering Mathematics · Numerical Methods

Agricultural Engineering (AG) 2026

While solving an equation \(e^{-x} - x = 0\) for \(x\), using Newton-Raphson method with initial guess \(x_0 = 2\), the solution after first iteration (\(x_1\)) is ______. (Rounded off to two decimal places)

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