dy/dx - = 1 - y,y(0) = 0 is an example of

[zaasmi]

To evaluate a definite integral of tabular function f(x), piecewise linear approximation led to ---------.

Select correct option:
Trapezoidal Method
Simpson’s 1/3 Rule
Simpson’s 3/8 Rule
Romberg’s Method

[zaasmi]

In Simpson’s rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into an ………… number n of subintervals of equal length.

Select correct option:
Odd
**Even **
Prime
None of the given choices

[zaasmi]

At which of the following point the derivatives or slopes the functions f(x) = x – 2 and g(x) = x + 2 may differ?

Select correct option:
differ for every value of ‘x’
does not differ for any value of ‘x’
x = 2
x = -2

[zaasmi]

Which of the following is the Cote’s number (weighting coefficient) for the function: f(x) = x+1 in the interval [0,1]?

Select correct option:
3/2
-3/2
1/2
-1/2

[zaasmi]

Simpson’s 3/8 rule represents the area between the curve y = f(x) in the interval say [a,b] above x-axis by approximating the given curve by the ----------.

Select correct option:
Cubic curve through one point
Cubic curve through two points
Cubic curve through three points
Cubic curve through four points

[zaasmi]

Zero-th order divided difference is defined as

Select correct option:
y[x0]=x0
y[x0]=y1
y[x0]=y0
None of the given choices

[zaasmi]

Which of the following is the Global Error for Simpson’s 3/8 Rule while integrating ‘f(x) = Cosx’ in the interval of [0,pi] of equally spaced subinterval of width ‘h =pi/6’and intermediate point x = pi/2?

Select correct option:
-pi/80
pi/800
0
1

[zaasmi]

If f(x) = 2x, then which of the following is will be derivative of f(x) at x = 0.2?

Select correct option:
0.2
0.4
2
-2

[zaasmi]

If f(x) = 2x, then which of the following is will be derivative of f(x) at x = 0.2?

Select correct option:
0.2
0.4
2
-2

[zaasmi]

If f(x) = 2x, then which of the following is will be derivative of f(x) at x = 0.2?

Select correct option:
0.2
0.4
2
-2

[zaasmi]

The determinant of a diagonal matrix is the product of the diagonal elements.

[zaasmi]

@zaasmi said in mth603 final term solved papers by moaaz:

The determinant of a diagonal matrix is the product of the diagonal elements.

True
In a diagonal matrix, all non-diagonal elements are zero, and the determinant is calculated by multiplying the diagonal elements.

[zaasmi]

Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.

[zaasmi]

@zaasmi said in mth603 final term solved papers by moaaz:

Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.

True
The power method is used to find the dominant eigenvalue of a matrix and requires linearly independent eigenvectors for convergence.

[zaasmi]

A 3 x 3 identity matrix have three and different eigen values.

[zaasmi]

@zaasmi said in mth603 final term solved papers by moaaz:

A 3 x 3 identity matrix have three and different eigen values.

True
An identity matrix has diagonal elements as 1 and all other elements as 0, resulting in three distinct eigenvalues.