40 real Numerical Methods questions from the Engineering Mathematics bank, as asked in Indian campus drives and tech interviews. Every question has a verified answer and an AI-tutor explanation on placd — free to start.
1. What is Bisection method?
Junior
A.numerical integration fitting a cubic over each group of three strips, requiring the number of intervals to be a multiple of three
B.a single-step initial value solver combining four slope evaluations per step with error falling as the fourth power of the step size
C.an open root-finding method using the tangent at the current estimate, converging quadratically near a simple root but failing where the derivative vanishes
D.a bracketing root-finding method that repeatedly halves an interval whose endpoints give opposite signs, converging surely but only linearly
2. Which term means: "a bracketing root-finding method that repeatedly halves an interval whose endpoints give opposite signs, converging surely but only linearly"?
A.Bisection method — a bracketing root-finding method that repeatedly halves an interval whose endpoints give opposite signs, converging surely but only linearly
B.Bisection method — numerical integration fitting a cubic over each group of three strips, requiring the number of intervals to be a multiple of three
C.Bisection method — the error arising from representing numbers in finite precision arithmetic, as distinct from the error of truncating an infinite process
D.Bisection method — a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis
A.an open root-finding method using the tangent at the current estimate, converging quadratically near a simple root but failing where the derivative vanishes
B.an iterative linear solver that immediately reuses each newly computed component within the same sweep, converging for diagonally dominant systems
C.fits a single polynomial through given points using basis polynomials that equal one at their own node and zero at every other, needing no equal spacing
D.the simplest step-by-step solver for an initial value problem, advancing along the tangent at the current point with error proportional to the step size
5. Which term means: "an open root-finding method using the tangent at the current estimate, converging quadratically near a simple root but failing where the derivative vanishes"?
A.Newton-Raphson method — numerical integration fitting a parabola over each pair of strips, requiring an even number of intervals, exact for cubics and with error falling as the fourth power of the step size
B.Newton-Raphson method — an open root-finding method using the tangent at the current estimate, converging quadratically near a simple root but failing where the derivative vanishes
C.Newton-Raphson method — the simplest step-by-step solver for an initial value problem, advancing along the tangent at the current point with error proportional to the step size
D.Newton-Raphson method — a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis
A.the simplest step-by-step solver for an initial value problem, advancing along the tangent at the current point with error proportional to the step size
B.an open root-finding method approximating the derivative by a difference quotient of the two latest estimates, converging at order about one point six one eight
C.an iterative linear solver that computes every component of the new estimate from the previous iterate only, so the sweep order does not matter
D.a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis
8. Which term means: "a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis"?
A.Regula falsi method — a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis
B.Regula falsi method — a bracketing root-finding method that repeatedly halves an interval whose endpoints give opposite signs, converging surely but only linearly
C.Regula falsi method — an open root-finding method approximating the derivative by a difference quotient of the two latest estimates, converging at order about one point six one eight
D.Regula falsi method — numerical integration approximating the curve by straight chords over each strip, exact for linear integrands with error falling as the square of the step size
A.numerical integration approximating the curve by straight chords over each strip, exact for linear integrands with error falling as the square of the step size
B.an open root-finding method approximating the derivative by a difference quotient of the two latest estimates, converging at order about one point six one eight
C.the simplest step-by-step solver for an initial value problem, advancing along the tangent at the current point with error proportional to the step size
D.fits a single polynomial through given points using basis polynomials that equal one at their own node and zero at every other, needing no equal spacing
11. Which term means: "an open root-finding method approximating the derivative by a difference quotient of the two latest estimates, converging at order about one point six one eight"?
A.Secant method — numerical integration approximating the curve by straight chords over each strip, exact for linear integrands with error falling as the square of the step size
B.Secant method — a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis
C.Secant method — fits a single polynomial through given points using basis polynomials that equal one at their own node and zero at every other, needing no equal spacing
D.Secant method — an open root-finding method approximating the derivative by a difference quotient of the two latest estimates, converging at order about one point six one eight
A.an iterative linear solver that computes every component of the new estimate from the previous iterate only, so the sweep order does not matter
B.numerical integration approximating the curve by straight chords over each strip, exact for linear integrands with error falling as the square of the step size
C.numerical integration fitting a cubic over each group of three strips, requiring the number of intervals to be a multiple of three
D.a single-step initial value solver combining four slope evaluations per step with error falling as the fourth power of the step size
14. Which term means: "numerical integration approximating the curve by straight chords over each strip, exact for linear integrands with error falling as the square of the step size"?
A.Trapezoidal rule — numerical integration fitting a parabola over each pair of strips, requiring an even number of intervals, exact for cubics and with error falling as the fourth power of the step size
B.Trapezoidal rule — numerical integration approximating the curve by straight chords over each strip, exact for linear integrands with error falling as the square of the step size
C.Trapezoidal rule — a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis
D.Trapezoidal rule — a single-step initial value solver combining four slope evaluations per step with error falling as the fourth power of the step size
A.a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis
B.an open root-finding method approximating the derivative by a difference quotient of the two latest estimates, converging at order about one point six one eight
C.numerical integration fitting a parabola over each pair of strips, requiring an even number of intervals, exact for cubics and with error falling as the fourth power of the step size
D.a single-step initial value solver combining four slope evaluations per step with error falling as the fourth power of the step size
17. Which term means: "numerical integration fitting a parabola over each pair of strips, requiring an even number of intervals, exact for cubics and with error falling as the fourth power of the step size"?
A.Simpson's one-third rule — a bracketing root-finding method that repeatedly halves an interval whose endpoints give opposite signs, converging surely but only linearly
B.Simpson's one-third rule — an iterative linear solver that computes every component of the new estimate from the previous iterate only, so the sweep order does not matter
C.Simpson's one-third rule — an iterative linear solver that immediately reuses each newly computed component within the same sweep, converging for diagonally dominant systems
D.Simpson's one-third rule — numerical integration fitting a parabola over each pair of strips, requiring an even number of intervals, exact for cubics and with error falling as the fourth power of the step size
A.an iterative linear solver that immediately reuses each newly computed component within the same sweep, converging for diagonally dominant systems
B.numerical integration fitting a parabola over each pair of strips, requiring an even number of intervals, exact for cubics and with error falling as the fourth power of the step size
C.numerical integration fitting a cubic over each group of three strips, requiring the number of intervals to be a multiple of three
D.the simplest step-by-step solver for an initial value problem, advancing along the tangent at the current point with error proportional to the step size
20. Which term means: "numerical integration fitting a cubic over each group of three strips, requiring the number of intervals to be a multiple of three"?
A.Simpson's three-eighth rule — an iterative linear solver that computes every component of the new estimate from the previous iterate only, so the sweep order does not matter
B.Simpson's three-eighth rule — numerical integration fitting a cubic over each group of three strips, requiring the number of intervals to be a multiple of three
C.Simpson's three-eighth rule — an open root-finding method approximating the derivative by a difference quotient of the two latest estimates, converging at order about one point six one eight
D.Simpson's three-eighth rule — a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis
A.the simplest step-by-step solver for an initial value problem, advancing along the tangent at the current point with error proportional to the step size
B.a single-step initial value solver combining four slope evaluations per step with error falling as the fourth power of the step size
C.numerical integration fitting a parabola over each pair of strips, requiring an even number of intervals, exact for cubics and with error falling as the fourth power of the step size
D.an iterative linear solver that computes every component of the new estimate from the previous iterate only, so the sweep order does not matter
23. Which term means: "the simplest step-by-step solver for an initial value problem, advancing along the tangent at the current point with error proportional to the step size"?
A.Euler's method — a single-step initial value solver combining four slope evaluations per step with error falling as the fourth power of the step size
B.Euler's method — the error arising from representing numbers in finite precision arithmetic, as distinct from the error of truncating an infinite process
C.Euler's method — the simplest step-by-step solver for an initial value problem, advancing along the tangent at the current point with error proportional to the step size
D.Euler's method — a bracketing root-finding method that replaces the bisection midpoint by the point where the chord joining the endpoints crosses the axis
A.numerical integration fitting a parabola over each pair of strips, requiring an even number of intervals, exact for cubics and with error falling as the fourth power of the step size
B.numerical integration approximating the curve by straight chords over each strip, exact for linear integrands with error falling as the square of the step size
C.an open root-finding method using the tangent at the current estimate, converging quadratically near a simple root but failing where the derivative vanishes
D.a single-step initial value solver combining four slope evaluations per step with error falling as the fourth power of the step size
26. Which term means: "a single-step initial value solver combining four slope evaluations per step with error falling as the fourth power of the step size"?
A.Fourth-order Runge-Kutta method — a single-step initial value solver combining four slope evaluations per step with error falling as the fourth power of the step size
B.Fourth-order Runge-Kutta method — a bracketing root-finding method that repeatedly halves an interval whose endpoints give opposite signs, converging surely but only linearly
C.Fourth-order Runge-Kutta method — the error arising from representing numbers in finite precision arithmetic, as distinct from the error of truncating an infinite process
D.Fourth-order Runge-Kutta method — an iterative linear solver that immediately reuses each newly computed component within the same sweep, converging for diagonally dominant systems
A.numerical integration fitting a cubic over each group of three strips, requiring the number of intervals to be a multiple of three
B.the error arising from representing numbers in finite precision arithmetic, as distinct from the error of truncating an infinite process
C.numerical integration fitting a parabola over each pair of strips, requiring an even number of intervals, exact for cubics and with error falling as the fourth power of the step size
D.an iterative linear solver that immediately reuses each newly computed component within the same sweep, converging for diagonally dominant systems
29. Which term means: "an iterative linear solver that immediately reuses each newly computed component within the same sweep, converging for diagonally dominant systems"?
A.Gauss-Seidel method — fits a single polynomial through given points using basis polynomials that equal one at their own node and zero at every other, needing no equal spacing
B.Gauss-Seidel method — a bracketing root-finding method that repeatedly halves an interval whose endpoints give opposite signs, converging surely but only linearly
C.Gauss-Seidel method — an iterative linear solver that immediately reuses each newly computed component within the same sweep, converging for diagonally dominant systems
D.Gauss-Seidel method — an iterative linear solver that computes every component of the new estimate from the previous iterate only, so the sweep order does not matter
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