|
Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts
Numerical Analysis Quiz#4, MCQs
The Timer has started 10:00
-
1)
The Jacobi’s method is A method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.
- A) Jacobi’s method
- B) Newton’s backward difference method
- C) Stirlling formula
- D) Forward difference method
-
2)
The characteristics polynomial of a 3x 3 Identity matrix is __________, if x is the Eigen values of the given 3 x 3 identity matrix. Where symbol ^ shows power.
- A) (X-1)^3
- B) (x+1)^3
- C) X^3-1
- D) X^3+1
-
3)
Regula Falsi means
- A) Method of Correct position
- B) Method of unknown position
- C) Method of false position
- D) Method of known position
-
4)
Eigenvalues of a symmetric matrix are all _________.
- A) Real
- B) Zero
- C) Positive
- D) Negative
-
5)
Newton Raphson method is also known as
- A) Tangent Method
- B) Root method
- C) Open Method
- D) Iterative Method
-
6)
Secant Method uses values for approximation
- A) 1
- B) 2
- C) 3
- D) 4
-
7)
In bisection method the two points between which the root lies are
- A) Similar to each other
- B) Different
- C) Not defined
- D) Opposite
-
8)
Root may be
- A) Complex
- B) Real
- C) Complex or real
- D) None
-
9)
Newton’s divided difference interpolation formula is used when the values of the independent variable are
- A) Equally spaced
- B) Not equally spaced
- C) Constant
- D) None of the above
-
10)
Octal numbers has the base
- A) 10
- B) 8
- C) 6
- D) 2
Numerical Analysis Quiz#3, MCQs
The Timer has started 10:00
-
1)
While solving a system of linear equations, which of the following approach is economical for the computer memory?
- A) Direct
- B) Iterative
- C) Analytical
- D) Graphical
-
2)
The basic idea of relaxation method is to reduce the largest residual to ………….
- A) One
- B) Two
- C) Zero
- D) None of the given choices
-
3)
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.
- A) main diagonal
- B) last column
- C) last row
- D) first row
-
4)
If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.
- A) TRUE
- B) FALSE
-
5)
Gauss - Jordan Method is similar to ……….
- A) Gauss–Seidel method
- B) Iteration’s method
- C) Relaxation Method
- D) Gaussian elimination method
-
6)
While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system; 2x+3y = 1, 3x +2y = - 4 ?
- A) -4
- B) 3
- C) 2
- D) 1
-
7)
The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the eigen values of the given 3 x 3 identity matrix. where symbol ^ shows power.
- A) (x-1)^3
- B) (x+1)^3
- C) x^3-1
- D) x^3+1
-
8)
The linear equation: 2x+0y-2=0 has -------- solution/solutions
- A) Unique
- B) no solution
- C) infinite many
- D) finite many
-
9)
An eigenvector V is said to be normalized if the coordinate of largest magnitude is equal to zero.
- A) TRUE
- B) FALSE
-
10)
When the condition of diagonal dominance becomes true in Jacobi’s Method.Then its means that the method is …………….
- A) Stable
- B) Unstable
- C) Convergent
- D) Divergent
Numerical Analysis Quiz#2, MCQs
The Timer has started 10:00
-
1)
Then the integral of this equation is a curve in
- A) Xt-plane
- B) Yt-plane
- C) Xy-plane
- D) None of the given choices
-
2)
Gauss Elimination method fails if any one of the pivot values becomes
- A) Greater
- B) Small
- C) Zero
- D) None of the given
-
3)
Courts reduction method is also known as Cholesky Reduction method
- A) True
- B) False
-
4)
In Jacobi’s method approximation calculated is used for
- A) Nothing
- B) Calculating the next approximation
- C) Replaced by previous one
- D) All above
-
5)
Power method is applicable for only
- A) Real metrics
- B) Symmetric
- C) Unsymmetrical
- D) Both symmetric and real
-
6)
The process of eliminating value of y for intermediate value of x is know as interpolation
- A) True
- B) False
-
7)
If we retain r+1 terms in Newton’s forward difference formula, we obtain a polynomial of degree ---- agreeing with
- A) r+2
- B) r+1
- C) R
- D) R-1
-
8)
The percentage error in numerical integration is defined as
- A) = (Theoretical Value-Experiment Value)* Experiment Value*100
- B) = (Theoretical Value +Experiment Value)/ Experiment Value*100
- C) = (Theoretical Value-Experiment Value)/ Theoretical Value *100
- D) = (Theoretical Value-Experiment Value)/ Experiment Value*100
-
9)
We prefer ………over the Lagrange’s interpolating method for economy of computation.
- A) Newton’s forward difference method
- B) Newton’s backward difference method
- C) Newton’s divided difference method
- D) None of the given choices
-
10)
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=1
- B) At x=2
- C) At x=3
- D) At x=4
Differential Equations Quiz#4, MCQs
The Timer has started 10:00
-
1)
A set of functions whose wronskian is zero guarantees that set of functions is linearly dependent.
- A) TRUE
- B) FALSE
-
2)
Is homogeneous.
- A) TRUE
- B) FALSE
-
3)
Population dynamics are not practical application of the first order differential equations.
- A) TRUE
- B) FALSE
-
4)
In the homogeneous differential equation after substitution v=y/x the equation reduces to.
- A) Separable differential equation.
- B) Exact differential equation.
- C) Remain homogeneous equation.
- D) None of the other
-
5)
If the Wronskian W of three function f(x),g(x),h(x) is zero, what can be said about the dependency of the functions
- A) May or may not be dependent
- B) Always dependent
- C) Never dependent
- D) None of the other
-
6)
The differential equation
is:
- A) Exact
- B) Linear
- C) Homogenous
- D) Separable
-
7)
The method of undetermined coefficient is limited to homogeneous linear differential equation
- A) TRUE
- B) FALSE
-
8)
Equation of the form
is called
- A) First order linear differential equation
- B) Bernoulli equation
- C) Separable equation
- D) None of the other.
-
9)
Identify the ordinary differential equation
- A) Exact
- B) Linear
- C) Homogenous
- D) Separable
-
10)
A set of functions whose wronskian is zero then set of functions may or may not be dependent.
- A) TRUE
- B) FALSE
Differential Equations Quiz#3, MCQs
The Timer has started 10:00
-
1)
For eigen values λ = 5,5 of a matirx
,there exists ......... eigen vectors.
- A) infinite
- B) one
- C) two
- D) three
-
2)
Singular points of the equation
are
- A) x= -2, 2
- B) x =2
- C) x = - 2
- D) None of them
-
3)
The matrix
has ..............
- A) Real and unequal value
- B) Repeated & real eigenvalue
- C) Complex eigenvalue
- D) None of them
-
4)
Logistics equation is an Example of
- A) Linear
- B) Non linear
- C) Bernoullis
-
5)
The Wronskian of the function
is
- A) 1
- B) 0
- C) -2
- D) None of these
-
6)
Order of the differential equation is the highest order derivative in a differential equation.
- A) TRUE
- B) FALSE
-
7)
Roots of the equation
will be
- A) 0,1,2
- B) 0,+ i , - i
- C) 0,1,i
- D) None of these
-
8)
A differential equation
is called
- A) Initial value problem
- B) Boundary value problem
- C) None of these
-
9)
Order of the differential equation is the highest order derivative in a differential equation.
- A) TRUE
- B) FALSE
-
10)
The given functions
are linearly independent
- A) TRUE
- B) FALSE
Differential Equations Quiz#2, MCQs
The Timer has started 10:00
-
1)
then the order of Matrix AXB is
- A) 2X4
- B) 2X3
- C) 3X3
- D) None of them
-
2)
Suppose that {X1, X2, X3,…,Xn} is a set of n solutions vectors on an interval I, of a homogeneous system X/=AX. The set is said to be a fundamental set of solutions of the system on the interval I if the solution vectors are
- A) Linearly dependent
- B) Linearly independent
- C) Homogeneous
- D) None of them
-
3)
The matrix
has an eigen value of multiplicity
- A) 1
- B) 2
- C) 3
- D) 4
-
4)
The matrix
has eigen values λ = -1,-1,5 where λ = -1 is a
- A) The matrix
- B) Single root of A
- C) triple root of A
- D) double root of A
-
5)
- A) λ = 4 of multiplicity of 1
- B) λ = 4 of multiplicity of 2
- C) λ = 4 of multiplicity of 3
- D) None of them
-
6)
Wronskian of x,x^2 is
- A) x
- B) x^2
- C) x^3
- D) 0
-
7)
If A is a square matrix and its determinant is zero, then
- A) A is singular matrix
- B) A is non-singular matrix.
- C) A is scalar matrix.
- D) A is diagonal matrix.
-
8)
An electronic component of an electronic circuit that has the ability to store charge and opposes any change of voltage in the circuit is called Inductor
- A) Resistor
- B) Capacitor
- C) Transistor
- D) None of them
-
9)
Operator method is the method of the solution of a system of linear homogeneous or linear non-homogeneous differential equations which is based on the process of systematic elimination of the
- A) Dependent variables
- B) Independent variable
- C) Choice variable
- D) None of them
-
10)
Any linear differential equation of the form
is called:
- A) Homogeneous equation
- B) Polar equation
- C) Equi-dimensioanl equation or Cauchy eular
- D) None of them
Numerical Analysis Quiz#1, MCQs
The Timer has started 10:00
-
1)
For the given table of valuesx0.10.20.30.40.50.6f (x)0.4250.4750.4000.4520.5250.575
f / / (0.2), using three-point equation will be calculated as ……
- A) 17.5
- B) 12.5
- C) 7.5
- D) -12.5
-
2)
Simpson’s 1/3 rule, f(x) is of the form
- A) ax + b
- B) ax^2 + bx + c
- C) ax^3 + bx^2 + cx + d
- D) ax^4 + bx^3 + cx^2 + dx + e
-
3)
The basic idea of relaxation method is to reduce the largest residual to ………….
- A) Two
- B) Zero
- C) One
- D) None of the given choices
-
4)
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its
- A) last column
- B) main diagonal
- C) last row
- D) first row
-
5)
A 3 x 3 identity matrix have three and different eigen values.
- A) TRUE
- B) FALSE
-
6)
............lies in the category of iterative method.
- A) Bisection Method
- B) Regula Falsi Method
- C) Secant Method
- D) All of the given choices
-
7)
For the equation x^3 + 3x - 1 = 0 , the root of the equation lies in the interval......
- A) (1, 3)
- B) (1, 2)
- C) (0, 1)
- D) (1, 2)
-
8)
Rate of change of any quantity with respect to another can be modeled by
- A) An ordinary differential equation
- B) A partial differential equation
- C) A polynomial equation
- D) None of the given choices
-
9)
Adam-Moulton P-C method is derived by employing
- A) Newton’s backward difference interpolation formula
- B) Newton’s forward difference interpolation formula
- C) Newton’s divided difference interpolation formula
- D) None of the given choices
-
10)
Direct method consists of method
- A) 2
- B) 3
- C) 4
- D) 5
Differential Equations Quiz#1, MCQs
The Timer has started 10:00
-
1)
The annihilator operator of the function y=e^-6x is
- A)(D-6)^2
- B) (D-6)^3
- C) D-6
- D) D+6
-
2)
After converting the given differential equation
into standard form, the function f(x) is
- A) (Sec3x)/4
- B) Sec3x)/64
- C) None of them
- D) Secx
-
3)
Wronskian of the function
is
- A) 0
- B) 1
- C) 2
- D) 3
-
4)
In the infinite series of (x-a) which can be written as
The number a is called the
- A) Radius of power series
- B) Centre of power series
- C) Base of power series
- D) None of them
-
5)
Suppose that a power series
is represented by a function “f”whose domain is the interval of the convergence of the power series. That function “f” is continuous, differentiable and integrable on
- A) (a + R, a - R)
- B) (R -a, R + a)
- C) (a - R, a + R)
- D) None of them
-
6)
The quantity
is called
- A) Reactance of circuit
- B) Impedance of circuit
- C) Quasi of circuit
- D) None of them
-
7)
The time interval between two successive maxima of
is called
- A) Phase period
- B) Quasi-period
- C) Both the period
- D) None of them
-
8)
The given differential equation
- A) is Over damped
- B) is Critically damped
- C) is Under damped
- D) None of them
-
9)
The standard unit for measurement of inductance is
- A) Volt
- B) Ohms
- C) Henry
- D) None of them
-
10)
Which of the rule in matrices under multiplication does not hold true?
- A) Commutative law
- B) Associative law
- C) Identity law
- D) None of them
Business Math & Stat Quiz#4, MCQs
The Timer has started 10:00
-
1)
How many number of times will the digit ‘7' be written when listing the integers from 1 to 1000?
- A) 271
- B) 300
- C) 252
- D) 304
-
2)
The moving averages represent ------------------
- A) Time series variations
- B) Co-efficient of variations
- C) Statistical Dispersion
- D) Absolute deviation
-
3)
The class frequency is
- A) The number of observations in each class
- B) The difference between consecutive lower class limits
- C) Always contains at least 5 observations
- D) Usually a multiple of the lower limit of the first class
-
4)
If the regression equation is equal to 23.6 - 54.2X, then 23.6 is the _________ while -54.2 is the ________ of the regression line.
- A) slope, intercept
- B) intercept, slope
- C) slope, regression coefficient
- D) radius, intercept
-
5)
If mean scores of midterm and final term of a student is 78% and 80%. Also variances are 106 and 77 then
- A) Midterm has greater variation in marks than Final term
- B) Final term has greater variation in marks than Midterm
- C) No variation in midterm and final term marks
-
6)
The correlation coefficient between x and y shows
- A) Whether y depends on x
- B) Whether y depends on x
- C) whether there is any relation between x and y
- D) whether there is a linear relation between x and y
-
7)
The equation of the regression line is 2y + 5x - 3 = 0. What will be the slope and intercept of the line?
- A) slope = -5, intercept = 3
- B) slope = 5, intercept = -3
- C) slope = -2.5, intercept = 1.5
- D) slope = 2.5, intercept = -1.5
-
8)
Which is incorrect?
- A) The mode is a measurement that records value
- B) A bar graph is same as line graph
- C) A mean may cause distortions
- D) A circle graph is based on 360∞
-
9)
Which one of the following is not a component of the multiplicative time series model
- A) trend
- B) irregular variation
- C) regression trend
- D) seasonality
-
10)
Break Even point is a point at which neither a profit nor ----- is made.
- A) Gain
- B) Loss
- C) Sale
- D) cost
Business Math & Stat Quiz#3, MCQs
The Timer has started 10:00
-
1)
Which one of the following is not a component of the multiplicative time series model?
- A) trend
- B) irregular variation
- C) regression trend
- D) seasonality
-
2)
For graphing univariate data we use
- A) Pie charts,Bar chart
- B) Pareto diagram
- C) Side by side chart
- D) Both (1) & (2)
-
3)
Linear equation: x − y = 0 has the solution only if
- A) x > y
- B) x < y
- C) x = y
- D) x ≠ y
-
4)
For mutually exclusive events A and B
- A) Probability of A intersection B > 0
- B) Probability of A intersection B < 0
- C) Probability of A intersection B = 0
- D) None of these
-
5)
Faulty apple toffees in a production line average out at 6 per box.The management is willing to replace one box in a hundred.What is the number of faulty toffees that this probabilty corresponds to?
- A) 20
- B) 18
- C) 13
- D) None
-
6)
The following formula for probability P(A or B) = P(A) + P(B)-P(A and B) is called
- A) The law of addition
- B) The law of subtraction
- C) The law of multiplication
- D) None of these
-
7)
In the normal distribution curve, peak of the bell-shaped curve gives
- A) Standard deviation
- B) Variance
- C) Mean
- D) Frequency
-
8)
Scatterplots are used only for
- A) quantitative variables
- B) mulivariables
- C) surplus varible
- D) None of these
-
9)
A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
- A) 1260
- B) 210
- C) 210
- D) 10C5 * 6
-
10)
An insurance company wants to predict sales from the amount of money they spend on advertising. Which would be the independent variable?
- A) sales
- B) advertising
- C) insufficient information to decide
- D) (iv) Both (i) and (ii) are correct.
Business Math & Stat Quiz#2, MCQs
The Timer has started 10:00
-
1)
This example returns the present value of an investment that pays Rs. 250 at the end of every month for 2 years. The money paid out will earn 7.5% annually.
- A) PV (7.5%/12, 2*12, 250, 1)
- B) PV (7.5%/12, 2*12, 250, 0)
- C) PV (7.5%/12, 2, 250, 0)
- D) PV (7.5%, 2*12, 250, 1)
-
2)
The algebraic expression of the form ax^2+bx+c is called
- A) monomial
- B) binomial
- C) quadratic equation
- D) trinomial
-
3)
Linear equation: x − y = 0 has the solution only if
- A) x > y
- B) x < y
- C) x = y
- D) x ≠ y
-
4)
Which of the following is linear equation
- A) 2x-3y=-6
- B) x+x+x
- C) 520x²y²
- D) y^2 -3=0
-
5)
If you invest some amount at an interest rate of 8%, then at the end of 9 years. What will be the value of Accumulation Factor?
- A) 12.736
- B) 12.487
- C) 12.965
- D) 12.856
-
6)
The break even point is a point when ----------------------
- A) Revenue is greater than cost.
- B) Revenue is less than cost.
- C) Revenue is exactly equal to cost.
- D) None of the above.
-
7)
Given Old Sale price = $1.95 , Markdown rate =13.6% ,then $Mark down will be
- A) $ 0.27
- B) $ 0.72
- C) $ 0.66
- D) $ 0.92
-
8)
The degree to which numerical data tend to spread about an average is called
- A) The dispersion
- B) Standard deviation
- C) Correlation
- D) None of these
-
9)
If the values of variables are increasing or decreasing in the same direction then such kind of correlation is referred as
- A) Zero Correlation
- B) Perfect Correlation
- C) Positive Correlation
- D) Negative Correlation
-
10)
Identity matrix is also a ……….. matrix
- A) Square
- B) triangular
- C) Diagonal
- D) Both (i)&(iii)