1. What is the main purpose of interpolation?
(A) To find values within a given data range
(B) To estimate values outside the data range
(C) To differentiate a function
(D) To integrate a function
2. Which type of interpolation uses a straight line between two points?
(A) Linear interpolation
(B) Quadratic interpolation
(C) Cubic interpolation
(D) Spline interpolation
3. Quadratic interpolation uses:
(A) Two points
(B) Three points
(C) Four points
(D) Five points
4. Cubic interpolation is preferred when:
(A) Data is linear
(B) Smoothness is required
(C) Only two points are available
(D) Speed is more important than accuracy
5. Lagrange interpolation formula is used for:
(A) Linear approximation only
(B) Polynomial interpolation of any degree
(C) Spline fitting only
(D) Exponential data
6. Which method constructs the interpolating polynomial incrementally?
(A) Lagrange method
(B) Newton’s divided difference method
(C) Linear interpolation
(D) Cubic spline
7. Which type of interpolation ensures continuous first and second derivatives?
(A) Linear
(B) Quadratic
(C) Cubic spline
(D) Newton’s method
8. Runge’s phenomenon is associated with:
(A) Low-degree polynomials
(B) High-degree polynomial interpolation
(C) Linear interpolation
(D) Spline interpolation
9. Which method is more stable for high-degree interpolation?
(A) Lagrange polynomial
(B) Newton’s divided differences
(C) Cubic spline
(D) Linear interpolation
10. Curve fitting is mainly used to:
(A) Approximate a smooth function through data
(B) Find derivatives
(C) Find integrals
(D) Solve linear equations
11. Least squares method is commonly used for:
(A) Interpolation
(B) Curve fitting
(C) Numerical integration
(D) Numerical differentiation
12. In linear curve fitting, the relationship between variables is assumed to be:
(A) Linear
(B) Quadratic
(C) Exponential
(D) Logarithmic
13. Exponential curve fitting is used when:
(A) Data follows a straight line
(B) Data grows or decays exponentially
(C) Data is random
(D) Only two points are available
14. Polynomial curve fitting can be unstable if:
(A) Degree is too high
(B) Degree is too low
(C) Data points are few
(D) Both B and C
15. The sum of squared errors is minimized in:
(A) Interpolation
(B) Least squares curve fitting
(C) Linear approximation
(D) Cubic spline interpolation
16. Linear interpolation can cause errors if:
(A) Data is highly nonlinear
(B) Data is evenly spaced
(C) Only two points are used
(D) Step size is small
17. Newton’s forward difference is suitable for:
(A) Equally spaced data
(B) Unequally spaced data
(C) Random data
(D) None of the above
18. Newton’s backward difference is mainly used for:
(A) Starting points
(B) End points of data
(C) Random points
(D) Midpoints
19. Which method reduces oscillations in polynomial interpolation?
(A) Lagrange polynomial
(B) High-degree polynomial
(C) Cubic spline
(D) Linear interpolation
20. Curve fitting is necessary when:
(A) Exact function is unknown
(B) Data contains noise
(C) Prediction is required
(D) All of the above
21. Interpolation passes:
(A) Through all data points
(B) Near the data points
(C) Only through first and last points
(D) None of the above
22. In least squares fitting, the curve:
(A) Passes exactly through all points
(B) Minimizes the distance to points
(C) Ignores some points
(D) Passes only through first and last points
23. Which method is computationally simple and fast for small datasets?
(A) Linear interpolation
(B) Cubic spline
(C) Lagrange polynomial of high degree
(D) Newton’s method
24. Which method is preferred for large datasets requiring smooth curves?
(A) Linear interpolation
(B) Cubic spline
(C) High-degree polynomial interpolation
(D) Exponential fitting
25. In curve fitting, overfitting occurs when:
(A) Degree of polynomial is too high
(B) Degree of polynomial is too low
(C) Step size is small
(D) Data is evenly spaced
26. Linear regression is a type of:
(A) Interpolation
(B) Curve fitting
(C) Differentiation
(D) Integration
27. Newton’s divided difference method can handle:
(A) Equally spaced data only
(B) Unequally spaced data
(C) Random data only
(D) None of the above
28. Lagrange interpolation is easy to implement but:
(A) Computationally expensive for many points
(B) Less accurate for small data
(C) Only works for linear data
(D) Not used in EE
29. Cubic spline interpolation ensures:
(A) Continuous first derivative
(B) Continuous second derivative
(C) Both first and second derivatives continuous
(D) No derivative continuity
30. The main difference between interpolation and curve fitting is:
(A) Interpolation passes through all points, curve fitting approximates
(B) Curve fitting passes through all points, interpolation approximates
(C) Both are the same
(D) None of the above