While using the Composite Trapezoidal form for integrating y = f(x) in [0,10] which is subdivided in equally spaced interval of width ‘h =2’, then which of the following is the area of associated trapezoidal strip over subinterval:[2,4] ?

• A) (y2 – y4)/2
• B) (y2 – y4)
• C) (y2 + y4)
• D) (y2 + y4)/2

To improve the accuracy of the derivative of the function, which of the following method is more helpful?

• A) Divided Difference
• B) Interpolation
• C) Central Difference
• D) Extrapolation

$$\begin{gathered} For\,the\,given\,divide\,difference\,table \hfill \\ \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 2&{2.2}&{0.325}&{} \\\ 6&{3.5}&{0.15}&{ - 0.0219} \\\ {10}&{4.1}&{}&{} \end{array} \hfill \\ the\,Newton's\,divide\,difference\,\,{\text{interpolation}}\,formula\,will\,be \hfill \\\ \end{gathered}$$

• A) $$y = f(x) = 2.2 + (x - 2)((x - 6)(0.325) + (x - 2)( - 0.0219)$$
• B) $$y = f(x) = 2.2 + (x - 6)(0.325) + (x - 12)((x - 6)( - 0.0219)$$
• C) $$y = f(x) = 2.2 + (x - 2)(0.325) + (x - 2)((x - 6)( - 0.0219)$$
• D) $$y = f(x) = 2.2 + (x - 12)(0.325) + (x - 6)((x - 2)( - 0.0219)$$

At which of the following points the Maximum value of 2nd derivative of function
f(x) = -(2/x) in the interval:[1,4] exits?

• A) At x=4
• B) At x=1
• C) At x=2
• D) At x=3

1st ordered divided difference formula is defined as

• A) y[x0,x1]=(y1+y0)/(x1-x0)
• B) None of the given choices
• C) y[x0,x1]=(y1-y0)/(x1+x0)
• D) y[x0,x1]=(y1-y0)/(x1-x0)

To take the derivative of f(x) = 2x in the interval [-3,3], which of the following partition of subintervals will be suitable?

• A) Unequally spaced
• B) Equally spaced
• C) Any arbitrary partition will work
• D) Union of equally spaced and unequally spaced intervals.

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

• A) 4th
• B) 5th
• C) 2nd
• D) 3rd

$$\begin{gathered} What\,will\,be\,the\,value\,of\,'a'\,in\,the\,given\,divide\,difference\,table? \hfill \\ \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 3&{0.4}&{}&{} \\\ 6&{0.9}&{0.1667}&{} \\\ 9&{1.7}&{0.2667}&a \end{array} \hfill \\\ \end{gathered}$$

• A) 0.0254
• B) 0.0349
• C) 0.0211
• D) 0.0167

Integration is a ………………process.

• A) None of the given choices
• B) Subtracting
• C) Summing
• D) Dividing

Geometrically, in Simpson’s 1/3 Rule, we find the area of -------- strip/strips at time under a curve of given function.

• A) one
• B) two
• C) five
• D) three

In the process of Numerical Differentiation, we differentiate an interpolating polynomial in place of ------------.

• A) actual function
• B) Lagrange’s polynomial
• C) Newton’s Divided Difference Interpolating polynomial
• D) extrapolating polynomial

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

In Simpson’s rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into an ………… number n of subintervals of equal length.

• A) None of the given choices
• B) Prime
• C) Odd
• D) Even

In Simpson’s 3/8 rule, the global error is of ………………

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

Simpson’s 1/3 rule is based on fitting three points with a ………………

• A) Quadratic
• B) Cubic
• C)
• D)

Which of the following is the Cote’s number (weighting coefficient) for the function:
f(x) = x+1 in the interval [0,1]?

• A) -1/2
• B) -3/2
• C) 3/2
• D) 1/2

In Simpson’s rule, we can estimate the integral by …………the areas under the parabolic arcs through three successive points.

• A) Subtracting
• B) None of the given choices
• C) Adding
• D) Multiplying

Which of the following is the Global Error for Trapezoidal’s Rule while integrating
f(x) = x^2 in the interval of [0,2] of equally spaced subinterval of width h =1 and intermediate point x=1?

• A) -1/2
• B) 1/3
• C) 1/2
• D) -1/3

If f(x) = 2x, then which of the following is will be derivative of f(x) at x = 0.2?

• A) 2
• B) 0.4
• C) 0.2
• D) -2

If y(x) is approximated by a polynomial ${P_n}(x)$ of degree n then the error is given by

• A) $$\varepsilon (x) = y(x) - {P_n}(x)$$
• B) $$\varepsilon (x) = y(x)\,\, \times \,\,{P_n}(x)$$
• C) $$\varepsilon (x) = y(x)\,\, \div \,\,\,{P_n}(x)$$
• D) $$\varepsilon (x) = y(x) + {P_n}(x)$$