Numerical Methods - Engineering Mathematics - Mining Engineering Previous Year Questions

1

2007 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2007

The values of \(f(x)\) at \(x_0, x_1\) and \(x_2\) are 9.0, 12.0 and 15.0 respectively. Using the Simpson's \(\frac{1}{3}\) rule, the value of \(\int_{x_0}^{x_2} f(x)\), considering an interval of 0.1 is

A

1.2

B

2.4

C

1.6

D

1.8

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2

2009 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2009

The function \(f(x) = x^2(1 - x)\) is integrated between 0 and 1 (both inclusive) using closed form method and also by Simpson's \(\frac{1}{3}\) rule. The difference in the values obtained from these methods is

A

0

B

\(\frac{1}{480}\)

C

\(\frac{1}{120}\)

D

\(\frac{1}{20}\)

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3

2010 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2010

A person invests Rs.1000 at 10% annual compound interest for 2 years. At the end of two years the whole amount is invested at an annual simple interest of 12% for 5 years. The total value of the investment finally is:

A

1776

B

1760

C

1920

D

1936

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4

2010 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2010

A positive integer m in base 10 when represented in base 2 has the representation p and in base 3 has the representation q. We get p – q = 990 where the subtraction is done in base 10. Which of the following is necessarily true:

A

m ≥ 14

B

9 ≤ m ≤ 13

C

6 ≤ m ≤ 8

D

m < 6

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5

2011 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2011

For the equation \(\frac{dy}{dx} = 2x + 3y\), the value of y at x = 0.1 in one step using Runge-Kutta fourth order method for the condition y = 1 when x = 0, is

A

0.3608

B

1.2508

C

1.3608

D

1.4625

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6

2012 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2012

Assuming sin(1) = 0.841 and sin(3) = 0.141, the Lagrangian linear interpolating polynomial, for the function \(f(x) = \sin(x)\) defined on the interval [1, 3] and passing through the end points of the interval, is

A

-0.35x + 1.19

B

-3.05x + 11.92

C

-35.00x + 119.10

D

-40.50x + 219.19

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7

2020 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2020

The function values at four points of x are shown in the table. The area under the function, using trapezoidal method, is ______ (round off to 1 decimal place).

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8

2021 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2021

The value of the integral \( I = \int_0^4 \sqrt{x} dx \) computed using Simpson's 1/3 rule with 2 subintervals is, ____. [round off to 3 decimal places]

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9

2024 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2024

Magnitude of error in the determination of the integral, \( I \) using Simpson’s 1/3 rule, taking step length as 1.0 is
\( I = \int_{1}^{3} (x^3 + 6) dx \)

A

0

B

1.0

C

1.5

D

2.0

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10

2024 · Mining Engineering · Engineering Mathematics · Numerical Methods

Mining Engineering (MN) 2024

The root of the function, \( f(x) = x^3 - 2x^2 + 3x - 1 \) in the interval [0, 1] using bisection method after two iterations, is ____. (round off up to 2 decimals)

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