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.
Answer: A


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.
Answer: D


The ______ matrix in the normal equations is symmetric.

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


In a ordinary differential equations the first category method is______.

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


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

a. solution.
b. general solution.
c. particular solution.
d. complete solution.
Answer: A


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.
Answer: C


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.
Answer: D


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.
Answer: B


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.
Answer: A


______ 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.
Answer: A


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

a. 1.
b. 2.
c. 3.
d. 6.
Answer: A


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

a. 1.
b. 2.
c. 3.
d. 6.
Answer: B


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

a. 1.
b. 2.
c. 3.
d. 6.
Answer: C


Interpolating polynomial is also known as______.

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

Answer: C


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
Answer: B


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

a. 0.
b. 1.
c. 2.
d. 3.
Answer: B


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 } .
Answer: A


Backward substitution method is applied in ______.

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


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.
b. quadrate.
c. interpolation.
d. a numerical differentiation.
Answer: A


The Trapezoidal rule for ydx =______.

a. straight line.
b. ellipse.
c. chord.
d. tangent line.
Answer: C


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.
Answer: C


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.
Answer: B


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

a. square.
b. rectangle.
c. diagonal.
d. element.
Answer: D


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.
Answer: D


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

a. square.
b. rectangular.
c. diagonal.
d. transpose.
Answer: B


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.
Answer: C


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

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

Answer: D


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.
Answer: C


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
Answer: D


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).
Answer: C


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.

Answer: C


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

a. n.

b. n+2.
c. n-2.
d. n2.
Answer: D


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

a. rank.
b. adjoint.
c. inverse.
d. determinant.
Answer: D


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

a. m*n.
b. m/n.
c. n/m.
d. n*m.
Answer: D


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

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

Answer: D


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

a. -2.
b. 1.
c. -1.
d. 2.
Answer: B


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

a. scalar matrix.
b. trace.
c. unit matrix.
d. diagonal matrix.
Answer: B


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.
Answer: D


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

a. adjoint of A.
= 0 then x=________.

b. eigen-vector of A.

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

Answer: D


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

a. (1,6).
b. (1,-6).
c. (-1,6).
d. (-1,-6).
Answer: C


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

a. eigen-vector.
b. adjoint of a matrix.
c. eigen-values.
d. Cayley-Hamilton theorem.

Answer: D


The Eigen value of 1 2
4 3 is______.

a. (1,5).
b. (1,-5).
c. (-1,5).
d. (-1,-5).
Answer: C


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

a. scalar.
b. diagonal.
c. triangular.
d. singular.
Answer: C


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

a. unit.
b. inverse.
c. orthogonal.
d. adjoint.
Answer: C


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

a. range.
b. correlation.
c. mode.
d. regression.
Answer: C


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

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

Answer: B


______is often computed when quick estimates of average are desired.

a. arithmetic mean.
b. median.
c. geometric mean.
d. harmonic mean.
Answer: B


______ is used in the construction of index numbers.

a. arithmetic mean.
b. median.
c. geometric mean.
d. harmonic mean.
Answer: C

Scroll to Top