40 Numerical Methods questions from the Engineering Mathematics bank, written for Indian campus drives and tech interviews. Every question has a verified answer and an AI-tutor explanation on placd.
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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
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2. Which term means: "a bracketing root-finding method that repeatedly halves an interval whose endpoints give opposite signs, converging surely but only linearly"?
Junior
A.Simpson's one-third rule
B.Simpson's three-eighth rule
C.Jacobi method
D.Bisection method
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3. Which statement is correct?
Junior
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
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4. What is Newton-Raphson method?
Junior
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
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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"?
Junior
A.Gauss-Seidel method
B.Newton-Raphson method
C.Euler's method
D.Regula falsi method
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6. Which statement is correct?
Junior
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
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7. What is Regula falsi method?
Junior
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
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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"?
Junior
A.Bisection method
B.Newton-Raphson method
C.Round-off error
D.Regula falsi method
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9. Which statement is correct?
Junior
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
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10. What is Secant method?
Junior
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
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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"?
Junior
A.Secant method
B.Jacobi method
C.Bisection method
D.Simpson's three-eighth rule
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12. Which statement is correct?
Junior
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
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13. What is Trapezoidal rule?
Mid
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
Answer + AI explanation with Pro
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"?
Mid
A.Bisection method
B.Trapezoidal rule
C.Secant method
D.Newton-Raphson method
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15. Which statement is correct?
Mid
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
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16. What is Simpson's one-third rule?
Mid
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
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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"?
Mid
A.Gauss-Seidel method
B.Simpson's one-third rule
C.Fourth-order Runge-Kutta method
D.Round-off error
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18. Which statement is correct?
Mid
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
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19. What is Simpson's three-eighth rule?
Mid
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
Answer + AI explanation with Pro
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"?
Mid
A.Bisection method
B.Simpson's three-eighth rule
C.Gauss-Seidel method
D.Fourth-order Runge-Kutta method
Answer + AI explanation with Pro
21. Which statement is correct?
Mid
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
Answer + AI explanation with Pro
22. What is Euler's method?
Mid
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
Answer + AI explanation with Pro
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"?
Mid
A.Trapezoidal rule
B.Regula falsi method
C.Euler's method
D.Round-off error
Answer + AI explanation with Pro
24. Which statement is correct?
Mid
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
Answer + AI explanation with Pro
25. What is Fourth-order Runge-Kutta method?
Mid
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
Answer + AI explanation with Pro
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"?
Mid
A.Jacobi method
B.Fourth-order Runge-Kutta method
C.Regula falsi method
D.Euler's method
Answer + AI explanation with Pro
27. Which statement is correct?
Mid
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
Answer + AI explanation with Pro
28. What is Gauss-Seidel method?
Senior
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
Answer + AI explanation with Pro
29. Which term means: "an iterative linear solver that immediately reuses each newly computed component within the same sweep, converging for diagonally dominant systems"?
Senior
A.Simpson's three-eighth rule
B.Simpson's one-third rule
C.Gauss-Seidel method
D.Fourth-order Runge-Kutta method
Answer + AI explanation with Pro
30. Which statement is correct?
Senior
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
Answer + AI explanation with Pro
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