## Answer & Solution

**Option C**

1.

What is the cube root of 1468 to 3 decimal places?

2.

Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson's rule is

Angle (degree) | 0 | 60 | 120 | 180 | 240 | 300 | 360 |

Torque (Nm) | 0 | 1066 | -323 | 0 | 323 | -355 | 0 |

3.

Roots of the algebraic equation x^{3} + x^{2} + x + 1 = 0 are

4.

In the Newton-Raphson method, an initial guess of x_{0} = 2 is made and the sequence x_{0}, x_{1}, x_{2} ... is obtained for the function 0.75x^{3} - 2x^{2} - 2x + 4 = 0

Consider the statements

I. x_{3} = 0.

II. The method converges to a solution in a finite number of iterations.

Which of the following is TRUE?

Consider the statements

I. x

II. The method converges to a solution in a finite number of iterations.

Which of the following is TRUE?

5.

While numerically solving the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{x}}{{\text{y}}^2} = 0,\,{\text{y}}\left( 0 \right) = 1$$ using Euler's predictor-corrector (improved Euler-Cauchy) with a step size of 0.2, the value of y after the first step is

6.

The Newton-Raphson iteration $${{\text{x}}_{{\text{n}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{n}}} + \frac{{\text{R}}}{{{{\text{x}}_{\text{n}}}}}} \right)$$ can be used to compute the

7.

When the Newton-Raphson method is applied to solve the equation f(x) = x^{3} + 2x - 1 = 0, the solution at the end of the first iteration with the initial guess value as x_{0} = 1.2 is

8.

The matrix \[\left[ {\text{A}} \right] = \left[ {\begin{array}{*{20}{c}}
2&1 \\
4&{ - 1}
\end{array}} \right]\] is decomposed into a product of a lower triangular matrix x[L] and an
upper triangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are

9.

Consider a differential equation $$\frac{{{\text{dy}}\left( {\text{x}} \right)}}{{{\text{dx}}}} - {\text{y}}\left( {\text{x}} \right) = {\text{x}}$$ with the initial condition y(0) = 0. Using Euler's first order method with a step size of 0.1, the value of y(0.3) is

10.

Consider an ordinary differential equation $$\frac{{{\text{dx}}}}{{{\text{dt}}}} = 4{\text{t}} + 4.$$ If x = x_{0} at t = 0, the increment in x calculated using Runge-Kutta fourth order multistep method with a step size of Δt = 0.2 is