WorksheetsNM UNIT 1
Total questions: 25
Worksheet time: 50mins
Rate of convergence of the Newton-Raphson method is generally __________
Rate of convergence of the Newton-Raphson method is generally __________
a) Linear
b) Quadratil
c) Super-linear
d) Cubic
he equation f(x) is given as x3 – x2 + 4x – 4 = 0. Considering the initial approximation at x=2 then the value of next approximation correct upto 2 decimal places is given as __________
a) 0.67
b)1.33
c)1.00
d)1.50
The Newton-Raphson method of finding roots of nonlinear equations falls under the category of which of the following methods?
a) bracketing
b) open
c) random
d) graphical
The Iterative formula for Newton Raphson method is given by __________
a) x1 = x0-f(x0)/f’(x0)
b) x0 = x1-f(x0)/f‘(x0)
c) x0 = x1+f(x0)/f’(x0)
d) x1 = x0+f(x0)/f‘(x0)
In Newton Raphson method if the curve f f(x) is constant then __________
a) f’’(x)=0
b) f(x)=0
c) f’(x)=0
d) f’(x)=c
The equation f(x) is given as x2-4=0. Considering the initial approximation at x=6 then the value of next approximation correct upto 2 decimal places is given as __________
3.33
1.33
2.33
4.33
At which point the iterations in the Newton Raphson method are stopped?
1. a) When the consecutive iterative values of x are not equal
b) When the consecutive iterative values of x differ by 2 decimal places
c) When the consecutive iterative values of x differ by 3 decimal places
d) When the consecutive iterative values of x are equal
The Newton Raphson method fails if __________
a) f’(x0)=0
b) f’’(x0)=0
c) f(x0)=0
d) f’’’(x0)=0
The Newton Raphson method is also called as ____________
a) Tangent method
b) Secant method
c) Chord method
d) Diameter method
For decreasing the number of iterations in Newton Raphson method:
a) The value of f’(x) must be increased
b) The value of f’’(x) must be decreased
c) The value of f’(x) must be decreased
d) The value of f’’(x) must be increased
In Newton Raphson method f’(x) for a given point is given by the formula ____________
a) y/x’
b) y’/x
c) y/x
d) y’/x’
The points where the Newton Raphson method fails are called?
d) stationary
b) continuous
c) non-stationary
d) stationary
1. The convergence of which of the following method depends on initial assumed value?
1. a) False position
b) Gauss Seidel method
c) Newton Raphson method
d) Euler method
The inverse of a matrix exists if and only if it is a non-singular matrix.
a) True
b) False
1. The following system of equation has:
x – y – z = 4
2x – 2y – 2z = 8
5x – 5y – 5z = 20
a)UniqueSolu
b)Nosolution
c)InfinitelymanySolutions
d) Finite solutions
1. The aim of elimination steps in Gauss elimination method is to reduce the coefficient
matrix to ____________
a)diagonal
b)identity
c)lowertriangular
d) upper triangular
In which of the following both sides of equation are multiplied by non-zero constant?
a)Gauss Elimination
b)Gaussian Inconsistentrocedure
c)Gaussian consistent procedur
d) Gaussian substitute procedure
In Gaussian elimination method, original equations are transformed by using _____________
a)Column operations
b)Row Operations
c)Mathematical Operations
d) Subset Operation
The modification of Gauss elimination method is called as ___________
1. a)GaussSeidal
b)GaussJordan
c)Jacobi’sMethod
d) Relaxation Method
Gauss seidal method is similar to which of the following methods?
1. a)Iterationmethod
b)NewtonRaphson
c)Jacobi’smethod
d) Regula-Falsi method
The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite matrices.
a)Positive
b)Negative
c)Zero
d) Equal
Gauss seidal requires less number of iterations than Jacobi’s method.
true
false
The Jacobi iteration converges, if A is strictly dominant.
True
false
In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods.
Slow
Fast
How many assumptions are there in Jacobi’s method?
2
3
1
4
