Numerical Methods and Interpolation Questions and Answers

Q: If a monotonic and continuous function \(y = f(x)\) has only one root in the interval \(x_{1} \lt x \lt x_{2}\), then

The condition is \(f(x_{1})f(x_{2}) \lt 0\).A continuous monotonic function with exactly one root strictly between \(x_{1}\) and \(x_{2}\) crosses zero once there, so it has one sign at \(x_{1}\) and the opposite sign at \(x_{2}\). The product of two numbers of opposite sign is negative. This is the condition used to bracket a root in the bisection and false-position methods.A positive product would mean the same sign at both ends, so a monotonic function would have no root between them. A zero product would put the root at an end point, not inside the interval. \(f(x_{1}) = f(x_{2})\) is impossible for a strictly monotonic function on distinct points.

______ is a method of constructing new data points within a range of discrete set of known data points.

A.Interpolation
B.Isolation
C.Integration
D.Limit

Exam Year(s)

DSSSB TGT - 2023,

Answer: A

Interpolation is a method of constructing new data points within the range of a discrete set of known data points. Isolation means keeping something apart, integration finds the area under a curve or sums small parts, and a limit is the value that a function approaches, so none of these three estimates values between known points. An example is estimating the temperature at noon from readings taken at 11 am and 1 pm.

Discuss in Forum

Which of the given options best describes the truthfulness of the following statements? i) Interpolation is a statistical method by which related known values are used to estimate an unknown value or set of values. ii) In the Inverse Distance Weighted (IDW) interpolation method, estimation of cell values is done by averaging values of sample data points in the neighbourhood of each processing cell.

A.i-True, ii-True
B.i-False, ii-True
C.i-True, ii-False
D.i-False, ii-False

Exam Year(s)

DSSSB TGT - 2023,

Answer: A

Both statements are true. Interpolation is a statistical method by which related known values are used to estimate an unknown value or set of values. In the Inverse Distance Weighted method the cell values are estimated by averaging the values of sample data points in the neighbourhood of each processing cell, with nearer points given more weight. So the first option is correct. In IDW a point close to the cell has more influence on its value than a point far away.

Discuss in Forum

If a monotonic and continuous function \(y = f(x)\) has only one root in the interval \(x_{1} \lt x \lt x_{2}\), then

A.\(f(x_{1})f(x_{2}) \gt 0\)
B.\(f(x_{1})f(x_{2}) = 0\)
C.\(f(x_{1})f(x_{2}) \lt 0\)
D.\(f(x_{1}) - f(x_{2}) = 0\)

Exam Year(s)

GATE AE - 2023,

Answer: C

The condition is \(f(x_{1})f(x_{2}) \lt 0\).

A continuous monotonic function with exactly one root strictly between \(x_{1}\) and \(x_{2}\) crosses zero once there, so it has one sign at \(x_{1}\) and the opposite sign at \(x_{2}\). The product of two numbers of opposite sign is negative. This is the condition used to bracket a root in the bisection and false-position methods.

A positive product would mean the same sign at both ends, so a monotonic function would have no root between them. A zero product would put the root at an end point, not inside the interval. \(f(x_{1}) = f(x_{2})\) is impossible for a strictly monotonic function on distinct points.

Discuss in Forum

Loading…

Topics

Other Subjects

Tags: Numerical Methods and Interpolation Questions and Answers || Numerical Methods and Interpolation MCQ Questions and Answers || Numerical Methods and Interpolation GK Questions and Answers || Numerical Methods and Interpolation GK MCQ Questions || Numerical Methods and Interpolation Multiple Choice Questions and Answers || Numerical Methods and Interpolation GK || GK on Numerical Methods and Interpolation || Engineering Mathematics Questions and Answers || Engineering Mathematics MCQ Questions and Answers || Engineering Mathematics GK Questions and Answers || GK on Engineering Mathematics

Numerical Methods and Interpolation Questions and Answers

Topics

Other Subjects

About Us

Stay informed about all important Dates & Notifications