# Statistical and Numerical Methods MCQs Chapter 2

The general problem of finding equations of approximating curves which fit a given
data is called______.

a. curve fitting.
b. approximating curve.
c. empirical relation.
d. linear form.

The best representative curve to the set of point is that for which E the sum of the
squares of the residuals is a minimum. This is known as______.

a. curve fitting.
b. empirical relation.
c. linear form.
d. principles of least squares.

The ______ matrix in the normal equations is symmetric.

a. square.
b. scalar .
c. co-efficient.
d. upper triangular.

In a ordinary differential equations the first category method is______.

a. Taylor Method .
b. Euler Method.
c. Runge-Kutta Method.
d. Pointwise Method.

A _____ of differential equations is a function which satisfies the differential
equations.

a. solution.
b. general solution.
c. particular solution.
d. complete solution.

A _____ of differential equation is a solution got form the general solution by giving particular values to the arbitrary constant.

a. solution.
b. general solution.
c. particular solution.
d. complete solution.

For unequal intervals, we can use _____ to get the derivative value.

a. Newton Forward Interpolation Formula.
b. Newton Backward Interpolation Formula.
c. Newton Forward Difference Formula.
d. LaGrange’s Interpolation Formula.

To find the derivative at the end of the table we use ______ formula.

a. Newton Forward differentiation Formula.
b. Newton Backward differentiation Formula.
c. Newton Forward Difference Formula.
d. LaGrange’s Interpolation Formula.

If the derivative is required at a point to the starting value in the table, we use___ formula.

a.Newton Forward differentiation formula.
b.Newton Backward differentiation Formula.
c.Newton Forward Difference Formula.
d.LaGrange’s Interpolation Formula.

______ rule is derived from Newton’s Cotes Formula.

a. Trapezoidal rule.
b. Simpson’s (1/3)rd rule.
c. Romberg’s Integration.
d. Simpson’s (3/8)th rule.

The degree of y(x) in Trapezoidal Rule is _______.

a. 1.
b. 2.
c. 3.
d. 6.

The degree of y(x) in Simpson’s (1/3)rd Rule is ______.

a. 1.
b. 2.
c. 3.
d. 6.

The degree of y(x) in Simpson’s (3/8)th is________.

a. 1.
b. 2.
c. 3.
d. 6.

Interpolating polynomial is also known as______.

a. smoothing function.
b. interpolating function.
c. collocation polynomial.
d. interpolating formula.

In Lagrange’s interpolation formula, the value of lo(x) = _____.

a. x1  x0 . x  x0
b. x x1 . x0 x1
c. x x1 . x  x0
d. x1 x0 . x2 x0

In Lagrange’s interpolation formula, the value of l1(x1) = _____.

a. 0.
b. 1.
c. 2.
d. 3.

x4 x0

a. h2 { y0 +2(y1+ y2+ y3)+ y4}.
b. h3 { y0 +2(y1+ y2+ y3)+ y4}.
c. h2 { y0 +2y1+ 4(y2+ y3)+ y4}.
d . h2 { y 0 + y 1 + y 2 + y 3 + y 4 } .

Backward substitution method is applied in ______.

a.Gauss-Jordan Method.
b.Gauss-Seidal Method.
c. Newton-Raphson Method.
d. Gauss Elimination Method.

If a set of numerical values of the integral f(x), a single valued function, is applied to b  f (x)dx , then the process is known as_____. a

a. a numerical integration.
c. interpolation.
d. a numerical differentiation.

The Trapezoidal rule for ydx =______.

a. straight line.
b. ellipse.
c. chord.
d. tangent line.

Simpson’s rule will give exact result, if the entire curve y=f(x) is itself a ____.

a. straight line.
b. chord.
c. parabola.
d. tangent line.

Taylors series method will be very useful to give some initial starting values for
powerful methods such as _____.

a. Euler Method.
b. Runge-Kutta Method.
c. Newton-Raphson Method.
d. Gauss Elimination Method.

Each of the mn numbers constituting an m*n matrix is called an _____ of the matrix.

a. square.
b. rectangle.
c. diagonal.
d. element.

The matrix obtained from any given matrix by interchanging its row and column is
called the _____of a matrix.

a. square.
b. rectangle.
c. diagonal.
d. transpose.

A matrix which is not necessarily a square matrix is called a _____matrix.

a. square.
b. rectangular.
c. diagonal.
d. transpose.

In the product AB, the matrix A is called ______.

a. product of the first matrix.
b. product of the second matrix.
c. prefactor.
d. postfactor.

The ______ of a matrix is the largest order of a non-zero minor of the matrix.

a. square.
b. scalar.
c. symmetric.
d. rank.

IfA= 0 1 andB= 1 0

a. 0 1 00
b.1 0 00
c. 1 1 00
d.0 0 00

If A = 2 -1

a. 4.
b.8.
c. 0.
d.-4.

The rank of cd then the determinant of A is ______. 0 0 0 0 then AB=_____.

a. a -b cd
b.a -b -c d
c. d b cd
d. d –b -c a

Inarankmatrix (A)is______.

a.(1) (A)= (m,n).
b.(2) (A)=min (m,n).
c.(3) (A)≤ min (m,n).
d.(4) (A)≥min(m,n).

Every homogeneous system of linear equation is always consistent and this solution is called ____.

a. unique solution.
b. no solution.
c. trivial solution.
d. non-trivial solution.

The number of elements in a square matrix of order n is _______.

a. n.

b. n+2.
c. n-2.
d. n2.

Every square matrix A of order n with entries as real or complex numbers then the number is called_____ of matrix A.

a. rank.
c. inverse.
d. determinant.

If A is of order m*n then AT is of order______.

a. m*n.
b. m/n.
c. n/m.
d. n*m.

If A is any square matrix of order n then kA=______.

a. k A .
b. knA.
c. kAn .
d.kn A.

If the determinant of
0 1 0 x 2 x 13x

a. -2.
b. 1.
c. -1.
d. 2.

The sum of the diagonal elements of a square matrix is called______.

a. scalar matrix.
b. trace.
c. unit matrix.
d. diagonal matrix.

Zero is a characteristic root of a matrix if and only if the matrix is ______.

a. eigen-vector.
b. eigen-value.
c. rank of matrix.
d. singular matrix.

The product of all Eigen values of A is =________.

= 0 then x=________.

b. eigen-vector of A.

c. co-factor of A.
d. determinant of A.

The Eigen value of the matrix
1 -2 -5 4

a. (1,6).
b. (1,-6).
c. (-1,6).
d. (-1,-6).

The inverse of a square matrix can be computed by _________.

a. eigen-vector.
c. eigen-values.
d. Cayley-Hamilton theorem.

The Eigen value of 1 2
4 3 is______.

a. (1,5).
b. (1,-5).
c. (-1,5).
d. (-1,-5).

The latent roots of a ______matrix are just the diagonal elements of the matrix.

a. scalar.
b. diagonal.
c. triangular.
d. singular.

The latent roots of a _____ matrix are of unit modulus.

a. unit.
b. inverse.
c. orthogonal.

______can be determined in two ways by inspection and by grouping methods.

a. range.
b. correlation.
c. mode.
d. regression.

Given observations are arranged in ascending or descending order of magnitude in
_______.

a. arithmetic mean.
b. median.
c. geometric mean.
d. harmonic mean.

______is often computed when quick estimates of average are desired.

a. arithmetic mean.
b. median.
c. geometric mean.
d. harmonic mean.