LIST-I LIST-II A. Gauss Seidel method I. Interpolation B. Forward Newton method II. Non-linear Differential equation C. Runge Kutta method III. Numerical Integration D. Trapezoidal rule IV. Linear algebraic equations
Choose the correct answer from the options given below:
Gauss Seidel Method for Linear Algebraic Equations
The Gauss Seidel method is an iterative algorithm primarily utilized to solve systems of linear algebraic equations. It refines the solution iteratively, using the most recently computed values of the variables in each step, which generally leads to faster convergence for certain types of systems.
Forward Newton Method in Interpolation
The Forward Newton method, often referred to as Newton's forward difference formula, is a technique used in numerical analysis for interpolation. This method constructs a polynomial that passes exactly through a given set of data points, enabling estimation of function values at intermediate points.
Runge Kutta Method for Differential Equations
The Runge Kutta method encompasses a family of powerful numerical techniques used for approximating solutions to ordinary differential equations (ODEs). It is particularly effective for problems involving non-linear differential equations, where finding exact analytical solutions can be challenging.
Trapezoidal Rule in Numerical Integration
The Trapezoidal rule is a widely applied method for approximating the value of a definite integral, falling under the umbrella of numerical integration. It approximates the area under a curve by dividing the integration interval into smaller segments and treating each segment as a trapezoid.
Summary of Method Matching
Below is a breakdown matching the methods presented in LIST-I with their corresponding applications in LIST-II:
| LIST-I Method | LIST-II Application | Key Purpose |
|---|---|---|
| A. Gauss Seidel method | IV. Linear algebraic equations | Iterative solution for linear systems. |
| B. Forward Newton method | I. Interpolation | Polynomial interpolation using differences. |
| C. Runge Kutta method | II. Non-linear Differential equation | Numerical approximation for ODEs. |
| D. Trapezoidal rule | III. Numerical Integration | Approximation of definite integrals. |
Important Questions from Mixed Topic (CUET PG)
- Who was the founder of Bolshevik Communist party?
- What is the key guide to statecraft in the realist tradition?
- Chronologically arrange the events in the Cold War period.
A. Berlin Wall is constructed
B. Communist China joins the UN
C. Soviet invasion of Czechoslovakia
D. Berlin Blockade
Choose the correct answer from the options given below: Morgenthau's principles of political realism are:
A. Politics is rooted in permanent and unchanging human nature which is basically self centred, self-regarding and self-interested
B. Politics is an autonomous sphere of action and cannot therefore be reduced to morals
C. International Politics is an arena of conflicting self-interests
D. The ethics of international relations is situational ethics which is very different from private morality
Choose the correct answer from the options given below:Who among the following political thinkers consider the anarchical self help system to be a compelling factor for States to maximise their relative power positions?
