MEHRAN UNIVERSITY OF ENGINEERING & TECHNOLOGY FIRST TERM THIRD YEAR (5TH TERM) 12-BATCH OF B.E.(MECHANICAL) REGULAR PRACTICAL EXAMINATION 2014 NUMERICAL ANALYSIS & COMPUTER SUBJECT:ID.NO. APPLICATIONS Dated: 18-05-2014 Time Allowed: 30 Minutes Max. Marks:- 15 Marks Obtained:1. Internal Examiner -------------------In Words --------------------------------

Signature 2. External Examiner --------------------

Q. No.

Determine whether the following statements are True/ False:

(1) In C++, header file ‘’ can be included instead of ‘ for real valued computations’. (2) If approximate value is 3.56 and actual value is 3.58; then 0.0056 is the relative error. (3) Picard’s method is analytical method for solving differential equation of 1st order. (4) Newton Raphson method converges more rapidly than fixed point method. (5) In C++, x10  7 y 3 can be written as: pow(x-10*y,3). (6) Simpson’s 1/3 rule can be used when number of sub intervals is odd, a multiple of three and of four. (7) Lagrange’s Interpolation is used only for non – equally spaced data. (8) To calculate norm of a vector in Dev C++; complex.h header file is needed to be included. (9) Newton’s divided difference interpolation is only used for equally spaced data. (10) f  x  5h   f  x  5h   f  x  4h  Fill in the blanks:

(13)

In C++, ‘\t’ stands for ----------------------------If interpolating polynomial is of third order then number of non-zero difference columns in difference table will be ________. A symmetric square matrix can be decomposed by cholesky’s method if it is _________.

(14)

Numerically largest eigenvalue of A  

(15) (16)

Relation between “E” and “  ” is given by _______________. If y0  2, y1  8, and y2  18 then 2 y2  __________________________.

(17)

In C++, f  x   cos x  1/ x can be written as ____________________.

(18) (19) (20)

The way one can define f  x   tan 1 x  1 in C++ is _______________ Newton Raphson method fails if ________________. for (int i=0; i
(11) (12)

2 0   is ______________. 3  1  





Cont’d on P/-2…

(-2-) Choose the best possible choice in the following questions: (21)

Number of iterations required by Bisection method is _________ if pre-specified error tolerance is 0.01% for a function defined on [0, 1]. i. 20 (ii) 10 (iii) 50 (iv) none of these

(22)

Result found in numerical analysis may be i. Approximate and Stable ii. Exact

(23)

If f (x) is a real continuous function in [a, b] , and f (a) f b  0 , then for f x   0 , there is (are) ____________ in the domain [a, b] . i. one root

(24)

iii. Inaccurate

ii. an undeterminable number of roots

The closing brace of structure is followed by (A) Comma (B) full-stop

iii. no root

(C)

iv. at least one root

semi-colon

(D)

colon

(25)

The Newton-Raphson method of finding roots of nonlinear equations falls under the category of _____________ methods.

(A)

bracketing

(26)

(B)

open

(C)

random

(D)

graphical

x6  4 y can be written as: In C++, 3 (A) (x*x/3)-(4*y*y) (B) pow(3,x) - pow(3,y) (C) pow(x,6)/3+4*sqroot(y) (D) Both “A” and “B” (E) None of these

(27)

If f ( x0 )  f ( x1 ) then ________________ is better Initial Guess for Newton-Raphson method. (A) x0 (B) x1 (C) f(x0) (D) f(x1)

(28)

The process of finding the value of function corresponding to any value of xr where x0
(29)

The method which utilizes most recent values as soon as they are available is: (A) Gauss-Jordon (B) Jacobi’s method (C) Relaxation method (D) Gauss-Seidel (E) Gauss-Elimination

(30)

What is the order of convergence of Regula Falsi Method?

(A) 4

(B)

2

(C)

1

(D)

1.618

------------------THE END------------------