NUMERICAL METHODS AND OPTIMIZTION

Multiple Choice Questions 256 Pages

Savitribai Phule Pune University

Mechanical Engineering

Contributed by

Aarav Patel

12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 1/13
Seat No -
Total number of questions : 60
10520_NUMERICAL METHODS AND OPTIMIZTION
Time : 1hr
Max Marks : 50
N.B
1) All questions are Multiple Choice Questions having single correct option.
2) Attempt any 50 questions out of 60.
3) Use of calculator is allowed.
4) Each question carries 1 Mark.
5) Specially abled students are allowed 20 minutes extra for examination.
6) Do not use pencils to darken answer.
7) Use only black/blue ball point pen to darken the appropriate circle.
8) No change will be allowed once the answer is marked on OMR Sheet.
9) Rough work shall not be done on OMR sheet or on question paper.
10) Darken ONLY ONE CIRCLE for each answer.
Q.no 1. The Newton-Raphson method of finding roots of nonlinear equations falls under the
category of _____________ methods
A : Bracketing
B : Open
C : Random
D : Graphical
Q.no 2. Trapezoidal rule for integration gives exact result when the integrate is a polynomial of
degree
A : 0 but not 1
B : 1 but not 0
C : 0 or 1
D : 2
Page 1
12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 2/13
Q.no 3. The method of finding a specific relation y = f(x) for the data to satisfy as accurately as
possible is called the
A : Curve of least fit
B : Curve of best fit
C : Fitting curves
D : Curve of equation
Q.no 4. Interpolation methods are
A : Linear interpolation
B : Piecewise constant interpolation
C : Polynomial interpolation
D : All of the mentioned
Q.no 5. Trapezoidal method calculate area under the curve is divided into n number of strips,
then is number of interval is
A : Even
B : Multiple of 3
C : Any
D : Multiple of 4
Q.no 6. What is the limitation of Gauss-seidal method?
A : It cannot be used for the matrices with non-zero diagonal elements
B : It is more complex than Jacobi’s method
C : It doesn’t guarantees convergence for each and every matrix
D : It is an iterative technique
Q.no 7. at the optimal solution of maximization problem, the optimal profit must equal to the
worth of
A : used resources
B : unused resources
C : none of the above
Page 2
12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 3/13
D : both a & b
Q.no 8. Which iterative method requires single initial guess root?
A : Bisection method
B : Secant method
C : Method of false position
D : Newton Raphson Method
Q.no 9. The iteration method is a ______ method
A : direct
B : indirect
C : self correcting
D : step by step
Q.no 10. Jacobi iteration method is _____substitution method
A : Indirect
B : Direct
C : Forward
D : Backward
Q.no 11. A partial differential equation requires:
A : Two or more independent variable
B : Exactly one independent variable
C : More than one dependent variable
D : Equal numbers of dependent variable
Q.no 12. Rate of convergence of the Newton-Raphson method is generally __________
A : Linear
B : Quadratic
C : Super-linear
D : Cubic
Page 3
12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 4/13
Q.no 13. The convergence of which of the following method depends on initial assumed value?
A : False position
B : Gauss Seidel method
C : Newton Raphson method
D : Euler method
Q.no 14. The bisection method of finding roots of nonlinear equations falls under the category of
a (an) _________ method.
A : open
B : bracketing
C : random
D : graphical
Q.no 15. Absolute error is defined as
A : Present Approximation – Previous Approximation
B : True Value – Approximate Value
C : abs (True Value – Approximate Value)
D : abs (Present Approximation – Previous Approximation)
Q.no 16. To solve the ordinary differential equation (dy/dx ) - x = y , y(0) = 1 , by Euler’s method,
you need to rewrite the equation as
A : (dy/dx ) - x - y = 0, y(0) = 1
B : (dy/dx ) - y = x , y(0) = 1
C : (dy/dx ) = x/y , y(0) = 1
D : (dy/dx ) = x + y , y(0) = 1
Q.no 17. If y=ae^bx then what is the value of a' & b' respectively.
A : a'=b , b'=log a
B : a'=b , b'= ln a
C : a'=ln a , b'= b
D : a'= log a , b'= b
Page 4
12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 5/13
Q.no 18. An LPP have ____________ optimal solution
A : 1
B : 2
C : 1 or more than 1
D : 2 or more than 2
Q.no 19. Which method has slow convergence?
A : false poison
B : Secant
C : Newton-Raphson
D : Bisection
Q.no 20. The partial differential equation uxx + uyy = 0 is called
A : Wave equation
B : Heat equation
C : Laplace equation
D : Elasticity equation
Q.no 21. The modified Euler method is based on the average of_________________________
A : straight line
B : ellipse
C : chord
D : points
Q.no 22. The process of constructing a sequence of vectors and obtaining the solution of a system
using specified accuracy is called _________
A : Elimination
B : Reduction
C : Iteration
D : Raphson method
Page 5
12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 6/13
Q.no 23. Which of the following is an assumption of Jacobi’s method?
A : The coefficient matrix has no zeros on its main diagonal
B : The rate of convergence is quite slow compared with other methods
C : Iteration involved in Jacobi’s method converges
D : The coefficient matrix has zeroes on its main diagonal
Q.no 24. For partial differential equation, if b² - 4ac < 0 then equation is called
A : Hyperbolic
B : Parabolic
C : Elliptic
D : Circular
Q.no 25. These are essential for solving partial differential equations
A : Algebraic equation
B : Physical principle
C : Mathematical model
D : Boundary condition
Q.no 26. Fourth degree equations are also called _______ equations.
A : quadratic
B : cubic
C : linear
D : bi-quadratic
Q.no 27. In Euler's method: Given initial value problem y'=dy/dx=f(x, y) with y(x0) = y0, then
approximation is given by
A : yn+1=yn+hf(xn-1, yn-1)
B : yn+1=yn+hf(xn-1, yn)
C : yn+1=yn+hf(xn, yn)
D : yn+1=yn+hf(xn, yn-1)
Page 6
12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 7/13
Q.no 28. Newton-Raphson method is applicable the solution of ______.
A : Both algebraic and transcendental equations
B : Both algebraic and transcendental and also used when the roots are complex
C : Algebraic equations only
D : Transcendental equations only
Q.no 29. Maximum value of z=10x+y subjected to x+y≤4; y ≥2
A : 22
B : 33
C : 44
D : 4
Q.no 30. Match the following: A.Newton Raphson 1.Integration B. Runge-kutta 2. Root finding
C.
Gauss-seidel 3. Ordinary Diferential Equations D. Simpson's Rule 4. Solution of system of
Linear Equations Codes:ABCD
A : A. 2341
B : B. 3214
C : C. 1423
D : D. 1243
Q.no 31. Which of the following step is not involved in Gauss Elimination Method?
A : Elimination of unknowns
B : Reduction to an upper triangular system
C : Finding unknowns by back substitution
D : Evaluation of cofactors
Q.no 32. In…… method integral within the limits x0 to xn can be converted to -1 to 1 limits.
A : Guass Legendres 2 point Formula
B : Simpson's 3/8 method
C : Trapezoidal method
Page 7
12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 8/13
D : Simpson's 1/3 method
Q.no 33. The coefficient of a slack variable is _________.
A : 0
B : 1
C : 2
D : -1
Q.no 34. Consider the system of equations x+y=2, 2x+2y=5 This system has
A : one solution
B : No solution
C : infinite solution
D : four solution
Q.no 35. The value of y’/x’ in terms of the angle 0 is given by _____________
A : tanθ
B : secθ
C : cotθ
D : cosecθ
Q.no 36. A system of linear simultaneous equation is given as Ax=B where A=[1 0 1 0; 0 1 0 1; 1 1
0 1; 0 0 0 1] and B=[0; 0; 0; 1] which of following statement is true
A : x is a null vector
B : x is unique
C : x does not exist
D : x has infinitely many values
Q.no 37. Truncation error is caused by approximating
A : irrational numbers
B : fractions
C : rational numbers
Page 8
12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 9/13
D : exact mathematical procedures
Q.no 38. For decreasing the number of iterations in Newton Raphson method:
A : The value of f’(x) must be increased
B : The value of f’’(x) must be decreased
C : The value of f’(x) must be decreased
D : The value of f’’(x) must be increased
Q.no 39. Maximise Z = 3x + 9y subject to the constraints: x + 3y ≤ 60, x + y ≥ 10, x ≤ y & x ≥ 0, y
≥ 0
A : 60
B : 90
C : 180
D : 150
Q.no 40. Maximise Z = 3x + 9y subject to the constraints: x + 3y ≤ 60, x + y ≥ 10, x ≤ y & x ≥ 0, y
≥ 0 Can we get multiple optimal solution if corner points of feasible region are (0, 10), (5, 5),
(15,15)
and (0, 20) respectively.
A : Single Optimal Solution
B : Double Optimal Solution
C : Optimal solution doesn't exist
D : Data is insuficient
Q.no 41. The governing equation for temperature distribution w.r.t distance x in the body is given
by (dT/dX) = -2000/(0.01T + 1) , T(0.2) = 500 and using a step size of h=0.04, the value of T(0.24)
using Euler’s method is most nearly
A : 513.33
B : 486.66
C : 333.33
D : -13.33
Q.no 42. A function is defined as f(x) = x^2 – 3. Between the interval [1,2] find the root of the
function by Bisection Method.
A : 1.7334
Page 9
12/25/2020 https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1
https://sppu.wheebox.com/WAC-3/allqusdownloadhtml.ils?testNo=410&code=1052000&showTest=320&actForm=edit&set=1 10/13
B : 1.7364
C : 1.7354
D : 1.7344
Q.no 43. Solve this system of equations and comment on the nature of the solution using Gauss
Elimination method. x + y + z = 0, -x – y + 3z = 3, -x – y – z = 2
A : Unique Solution
B : No solution
C : Infinitely many Solutions
D : Finite solutions
Q.no 44. The root of x^3 - 2x - 5 = 0 correct to three decimal places by using Newton-Raphson
method is
A : 2946
B : 1404
C : 1.7321
D : 0.7011
Q.no 45. The following system of equation has: x – y – z = 4, 2x – 2y – 2z = 8, 5x – 5y – 5z = 20
A : Unique Solution
B : No solution
C : Infinitely many Solutions
D : Finite solutions
Q.no 46. Solve ut = uxx, 0 < x < 5, t ≥ 0, given that u (x, 0) = 20, u (0, t) = 0, u (5, t) = 100.
Compute u1 for the time-step with h = 1
A : 40
B : 20
C : -40
D : 30
Q.no 47. Using Bisection method find the root of 3*X^2 = 5X+2 in the interval [0,3].
Page 10

NUMERICAL METHODS AND OPTIMIZTION

NUMERICAL METHODS AND OPTIMIZTION

Download this file to view remaining 246 pages