\[\begin{gathered} Which\,of\,the\,following\,method\,can\,be\,used\,for\,{\text{interpolation}}\,for\,the\,given\,values\,of\,x\,and\,y? \hfill \\ \begin{array}{*{20}{c}} x&{0.3}&{0.7}&{0.9} \\\ y&{0.067}&{0.248}&{0.518} \end{array} \hfill \\\ \end{gathered} \]

• A) Newton’s backward difference formula
• B) Newton’s forward difference formula
• C) Newton’s interpolation formula
• D) Lagrange’s interpolation formula

Trapezoidal rule of integration of a definite integral is of…………

• A) O(h3)
• B) None of the given choices
• C) O(h2)
• D) O(h4)

\[The\,first\,divide\,difference\,y[{x_0},{x_1}]\,can\,be\,given\,as\,\]

• A) \[\frac{{{y_1} - {y_0}}}{{{x_1} - {x_0}}}\]
• B) All
• C) \[\frac{{\nabla {y_1}}}{h}\]
• D) \[\frac{{\Delta {y_0}}}{h}\]

What will be the value of first order divided difference f[1,5]for the following data x:0 1 5 y:2 1 5

• A) 2
• B) 0
• C) 3
• D) 1

Let f(x,y) = 2{x^3} + 6{y^3} + 9xy For x=0, 1,2,3,4, and y=0, 1,2,3,4 Then computing the value of f(2.5,3.5) is an example of .......

• A) Interpolation in three dimensions
• B) Interpolation in two dimensions
• C) Interpolation in four dimensions
• D) Interpolation in one dimension

We can improve the accuracy of trapezoidal and Simpson’s rules using ……

• A) Simpson’s 1/3 rule
• B) None of the given choices
• C) Simpson’s 3/8 rule
• D) Richardson’s extrapolation method

In Lagrange’s interpolation, for n values of y corresponding to n values of x, we can represent the function f (x) by a polynomial of degree

• A) n+1
• B) n-1
• C) n
• D) n+2

For\,the\,given\,data\,{\text{points}}\,(2,0.3),\,(4,1),\,and\,(6,1.2)\,\,the\,divide\,difference\,table\,will\,be\,given\,as

• A) \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{0.3}&{0.1}&{} \\\ 4&1&{ - 0.0625}&{0.35} \\\ 6&{1.2}&{}&{} \end{array}
• B) \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{0.3}&{ - 0.0625}&{} \\\ 4&1&{0.1}&{0.35} \\\ 6&{1.2}&{}&{} \end{array}
• C) \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{0.3}&{0.35}&{} \\\ 4&1&{0.1}&{ - 0.0625} \\\ 6&{1.2}&{}&{} \end{array}
• D) \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{0.3}&{ - 0.0625}&{} \\\ 4&1&{0.35}&{0.1} \\\ 6&{1.2}&{}&{} \end{array}

Newton’s divided difference interpolation formula is used when the values of the independent variable are

• A) None
• B) Equally spaced
• C) Not equally spaced
• D) Constant

In double integration, we keep one variable say x fixed and ……………

• A) Varying the other variable y
• B) Reliable the other variable y
• C)
• D)

Given the following data x:1 2 5 y:1 4 10 Value of 1st order divided difference f[2 , 5] is

• A) 2
• B) 1
• C) 0
• D) -2

Given the following data x: 1 3 -7 f(x): 3 -6 -2 Which formula is useful in finding the interpolating polynomial?

• A) Newton’s backward difference formula
• B) None of the given choices
• C) Newton’s forward difference formula
• D) Lagrange’s interpolation formula

x: 1 3 7 10 f(x): -3 10 3 13 Which formula is useful in finding the interpolating polynomial?

• A) Lagrange’s interpolation formula
• B) (viii) None of the given choices
• C) Newton’s backward difference formula
• D) Newton’s forward difference formula

Trapezoidal and Simpson’s integrations are just a linear combination of values of the
given function at different values of the …………variable.

• A) Dependent
• B) Independent
• C) Arbitrary
• D) None of the given choices

If f(x) = 2{x^3} - 5{x^2} + 9x - 6 , then its------derivative is zero for all x.

• A) 2nd
• B) 4th
• C) 5th
• D) 3rd

\begin{gathered} Which\,of\,the\,following\,method\,can\,be\,used\,for\,{\text{interpolation}}\,for\,the\,given\,values\,of\,x\,and\,y? \hfill \\ \begin{array}{*{20}{c}} x&{0.3}&{0.7}&{0.9} \\\ y&{0.067}&{0.248}&{0.518} \end{array} \hfill \\\ \end{gathered}

• A) Newton’s interpolation formula
• B) Newton’s forward difference formula
• C) Lagrange’s interpolation formula
• D) Newton’s backward difference formula

For\,the\,given\,data\,{\text{points}}\,(4,1.3),\,(8,1.5),\,and\,(12,1.9)\,\,the\,divide\,difference\,table\,will\,be\,given\,as

• A) \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{1.3}&{0.05}&{} \\\ 8&{1.5}&{0.1}&{0.0062} \\\ {12}&{1.9}&{}&{} \end{array}
• B) \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{1.3}&{0.0062}&{} \\\ 8&{1.5}&{0.1}&{0.05} \\\ {12}&{1.9}&{}&{} \end{array}
• C) \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{1.3}&{0.1}&{} \\\ 8&{1.5}&{0.35}&{0.0062} \\\ {12}&{1.9}&{}&{} \end{array}
• D) \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{1.3}&{0.1}&{} \\\ 8&{1.5}&{0.0062}&{0.05} \\\ {12}&{1.9}&{}&{} \end{array}

\[For\,the\,given\,data\,{\text{points}}\,({x_{0,}}{y_0}),\,({x_1}{y_1}),\,({x_2}{y_2}),\,and\,({x_{3,}}{y_3})\,\,the\,first - order\,divide\,difference\,will\,be\,given\,as\]

• A) \[y[{y_0},{y_1},{y_2}]\]
• B) \[y[{x_0},{x_1}]\]
• C) \[y[{x_0}]\]
• D) \[y[{x_0},{x_1},{x_2}]\]

Given the following data x: 0 1 2 4 y: 1 1 2 6 Value of 1st order divided difference f[2,4] is

• A) 2
• B) 0
• C) 1
• D) -2

For\,the\,given\,data\,{\text{points}}\,(1, - 3),\,(2,0),\,and\,(3,15),\,the\,zero - order\,divide\,difference\,will\,be\,

• A) 0
• B) -1
• C) -3
• D) -2