question bank nacp

UNIT 1

SN. CAT QUESTIONS LEVEL TYPE MARKS TIME

1 1B1 Find the root of the equation

Xex = cos(x) using the Regula-Falsi method correct to four decimal places. M N 7 15

2 1C1 Solve the equations

10x1 -2x2 -x3 -x4 =3 -2x1 + 10x2 -x3 -x4 =15 M N 7 15

-x1 -x2 +10x3 -2x4 =27 -x1 - x2 -2x3 + 10x4 = -9 by Gauss Seidal iteration method.

3 1C2 Solve by Gauss-Jordan method : M N 7 15

10x -7y+3z+5u =6 -6x+8y-z-4u =5 3x+y+4z+11u=2

5x-9y-2z+4u=7

4 1B2 H T 7 5

5 1C3 Apply Gauss Elimination method to solve the equations : M N 7 15

x+4y-z =-5 x+y-6z = -12 3x-y-z =4

Find the real root of the equation (Using Newton Raphson Method)

Derive the Newton-Raphson formula for the equation f(x)=0. Discuss its geometrical

interpretation.

SEMESTER - 3rd SEM. MECHANICALSUBJECT - NUMERICAL ANALYSIS AND COMP. PROGRAMMING

6 1B3 Find the real root of the equation (Using Newton Raphson Method) H N 7 10

xlog10x-1.2 = 0 correct to five places of decimal.

7 1A1 H N 7 10

8 1B4 H N 7 15

9 1A2 H T 7 1510 1C4 Solve the following equation by Gauss-Jordan method.

2x - 3y + z = -1 x + 4y + 5z = 25 3x - 4y + z = 2

11 1B5 M N 7 15

12 1B6 E N 7 10

13 1B7 H N 7 10

14 1C5 M N 7 15

Find a real root of 2x – 10g10 x = 7 correct to four decimal places using

iteration method.

If u= 4x2y3/z4 and errors in x, y,z be .001, compute the relative maximum

error in u when x=y=z=1.

Find the double root of the equation :

x3 – x

2 –x + 1 = 0

Explain the types of errors in brief. The hypotenuse and side of a right angletriangle are found by

measurement to be 75 and 32 respectively. If the possible error in the hypotenuse is 0.2 and that

in the side is 0.1. Find the possible errors in the computed angle.

Explain the difference between open and bracketing methods of root determination. Determine

the root of the equation, x sin x + x cos x =0, near x = p using Newton-Raphson’s method correct

to three decimal places.Explain, how round off errors can effect the results, determined using elimination method and how the

results can be improved using pivoting.

Solve the following equations by Gauss Elimination method 14 1C5 M N 7 15Solve the following equations by Gauss Elimination method


15 1B8 M N 7 15

correct to three decimal places

16 1B9 H N 7 15

17 1A3 M N 7 10

18 1B10 H N 7 10

19 1B11 H N 7 15

20 1B12 M N 7 15

21 1B13 M N 7 15

22 1C6 M N 7 15

log 1.2 correct to six decimal places.

Find a real root of the equation x3 – 2x – 5 = 0 by the method of false position

-x1 -x2 -2x3 + 10x4 = -9

Find the root of the equation

Xex = cos (x) using the Newton Raphson method correct to four decimal places.

Solve the equations

10x1 – 2x2 –x3 –x4 = 3 -2x1 + 10x2 -x3 –x4 = 15 -x1 –x2 +10x3 -2x4 = 27

Find a real root of 2x - log10 x = 7 correct to four decimal places using

Newton Raphson Method

Determine the number of terms required in the series for log(1+x) to evaluate

2x - log10 x = 7 which lies between 3.5 and 4 by Regula-Falsi method.

2x + y + z = 10 3x + 2y + 3z = 18 x + 4y + 9z = 16

Evaluate 2 g to four decimal places by Newton’s iterative method.

Using Newton-Raphson method find the root of the equation :

x + log10 x = 3.375 correct to four significant figures.

Find the root of the equation :

23 1C7 M N 7 15

24

1B14

H T 7 10

25 1C8 M N 7 15

26 1B15 H N 7 10

27 AB16 M N 7 15

28 1A4 M N 7 10

29 1C9

30

31 1C10 M N 7 15

32 1A5 E T 2 5Define the following : (a) Approximate number (b) Significiant figures ( c) Rounding off

Derive the Newton-Raphson formula for the equation f(x)=0. Discuss its geometrical

interpretation.

Apply Gauss Elimination method to solve the equations :

x+4y-z =-5 x+y-6z = -12 3x-y-z =4

Find e-1

where e=2.71 starting with x0=0.3

Find the real root of the equation x2+4sinx = 0 correct to four places of decimal by using Newton-

Raphson's method.

-x1 -x2 -2x3 + 10x4 = -9

-x1-x2-2x3+10x4=-9

Solve the equation by Gauss-Elimination method :

10x1 -2x2-x3-x4=3 -2x1+10x2-x3-x4=15 -x1-x2+10x3-2x4 = 27

Solve by Gauss-Jordan method :

10x – 7y +3z + 5u = 6 -6x + 8y –z – 4u = 5 3x + y + 4z + 11u = 2

5x -9y -2z + 4u = 7

If R= 4xy2/z3 and errors in x,y,z be 0.001, show that the maximum relative error at x =y=z=1is

0.006.

Solve the equation by Gauss-Seidel method :

28x + 4y-z=32 x+3y+10z=24 2x + 17y+4z=35

32 1A5 E T 2 5Define the following : (a) Approximate number (b) Significiant figures ( c) Rounding off


33 1A6 E T 2 2

34 1B17 M T 5 5

35 1B18 H T 7 5

36 1B19 E T 2 2

37 1B20 H T 7 10

38 1B21 E T 2 2

39 1C11 H T 7 10

40 1C12 H T 7 10

41 1C13 H T 7 10

42 1C14 M N 7 15

43 1B22 M N 7 15

Differentiate between Gauss Elimination & Gauss Jordan method for solving simultaneous

algebric equations.

Differentiate between Gauss Siedel & Gauss Jordan method for solving simultaneous algebric

equation.

Differentiate between Regula Falsi & Secant method.

Write the generalized Newton's method for multiple roots.

Differentiate between Gauss Siedel & Gauss Elimination method for solving simultaneous

algebric equation.

Name the various types of error.

Explain descrete rule of signs.

Differentiate between method of false position & bisection method.

Differentiate between Algebric & Transcedental equation.

x1 + 2x2 + x3 = 8 2x1 + 3x2 + 4x3 =20 4x1 + 3x2 + 2x3 = 16

Find a real root of the polynomial equation :

F(x) = x5 – 34x4 + x3 + 3.76x + 10 = 0 by using Newton-Raphson’s

Solve the equation by the Gauss-Jordan method :

44 1B23 M N 7 15

45 1C15 M N 7 15

46 1C16 M N 7 15

47 1B24 M N 7 15

48 1C17

M N 7 15

49 1B25 M N 7 15

UNIT 2SN. CAT QUESTIONS LEVEL TYPE MARKS TIME

27x + 6y - z = 85 6x + 15y + 2z = 72 x + y + 54z = 110

3x – cos x – 1 = 0 by Newton-Raphson method.

20x + y -2z = 17 3x + 20y – z = -18 2x – 3y + 20 = 25

x = x2 + y

2 y = x

2 – y

2

Apply Gauss-Jordan method to solve the equations :

x + y + z = 9 2x – 3y + 4z = 13 3x + 4y + 5z = 40

Solve the equation :

method :

Solve the following system of equations by Gauss-Seidal iteration

decimal places.

Apply gauss-Seidel iteration method to solve the equations :

Use Newton-Raphson method to solve the equations :

F(x) = x – 34x + x + 3.76x + 10 = 0 by using Newton-Raphson’s

method.

Find the root of the equation x ex = cos x using the secant method, correct to four

SN. CAT QUESTIONS LEVEL TYPE MARKS TIME1 2A1 M N 7 15Use least squares regression to fit a straight line to the following data :


2 2B1 M N 7 15

3 2B2 H N 7 15

4 2B3 M N 7 15

x 0.1 0.15 0.2 0.25 0.3

y = tan x 0.1003 0.1511 0.2027 0.2553 0.3093

5 2A2 M N 7 15

q : 0 0.12 0.49 1.12 2.02 3.2 4.57Calculate the angular velocity and the angular acceleration of the rod when t=0.6 second.

The temperature q of a vessel of cooling water and the time t in minutes

The table below gives the values of tan x for 0.10 x 0.30 :

y(distance) : 10.63 13.03 15.04 16.81 18.42 19.90 12.27Use Newton forward interpolation method.

A rod is rotating in a plane. The following table gives the angle q (radians) through which the rod

has turned for various values of the time t in second.t : 0 0.2 0.4 0.6 0.8 1.0 1.2

y- 4 5 6 5 8 7 6 9 12 11Plot the data and the regression line.The following table gives the distance in nautical miles of the visible horizon for the given heights

in feet above the earth’s surface. Find the values of y when x= 218 ft.x(height) : 100 150 200 250 300 350 400

Find : (i) tan 0.12 (ii)tan 0.26

x- 1 3 5 7 10 12 13 16 18 20

5 2A2 M N 7 15

t : 0 1 2 3 5 7 10 15 20

q : 52.2 48.8 46 43.5 39.7 36.5 33 29 26

6 2B4 M N 7 15

x: 4 5 7 10 11 13

f(x) 48 100 294 900 1210 2028

7 2B5 M N 7 15

X=height 100 150 200 250 300 350 400

Y=distan

ce

10.63 13.03 15.04 16.81 18.42 19.9 21.27

8 2B6 H N 7 15

The table gives the distance in nautical miles of the visible horizon for the

since the begining of observation are connected by the law of the form 8

Find the best values of a, b, c by the method of group averages.

Using Newton’s Divided difference formula, find the values of f(2), f(8)

The temperature q of a vessel of cooling water and the time t in minutes

given heights in feet above the earth’s surface

Find the values of y when : (i) x=218ft (ii) x=410ft

and f(15), given the following table :

Find the values of y when x = 218 ft, and 410 ft.

From the following table of half-yearly premium for policies maturing at different ages, extimate

the premium for policies maturing at age 46and 63 :

q = aebt

+ c. The corresponding values of q and t are given by :-

8 2B6 H N 7 15the premium for policies maturing at age 46and 63 :


Age x 45 50 55 60 65

Premium y 114.84 96.16 83.32 74.48 68.48

9 2A3 E T 2 2

10 2A4 E T 2 2

11 2A5 E T 5 10

12 2A6 M T 7 10

13 2B7 H T 7 10

14 2B8 E T 2 2

15 2B9 E T 2 2

16 2B10 H T 7 15

17 2B11 E T 2 2

18 2B12 E T 2 2

Establish the relationship between the operator :- (a) D = E -1 (b) =1-E-1 c) = E1/2 - E-1/2

(d) µ = 1/2( E1/2 + E-1/2)

Write the general formula for Newton's forward interpolation.

Write the general formula for Newton's backward interpolation.

Differentiate between method of "Group Average" and less square for curve fitting.

Differentiate between forward, backward & central difference table.

What is shift operator.

What is the objective of curve fitting.

What is Avg. operator.

Name the various methods of curve fitting.

Reduce the following equation as linear equation :- (a) y=mxn + c (b) y=axn ( c) y=axn+blogx (d)

y=aebx

(e) xy=ax + by

18 2B12 E T 2 2

19 2B13 M T 5 5

20 2B14 E T 5 10

21 2A7 M N 7 15

x -4 -1 0 2 5

f(x) 1245 33 5 9 1335

22 2B15 M N 7 15

Marks 30-40 40-50 50-60 60-70 70-80

31 42 51 35 31

23 2A8 M N 7 15

x 1 2 3 4 5

y 14 27 40 55 68

24 2A9 H N 7 15

x 2 3 4 5 6

y 144 172.8 207.4 248 298.5

25 2B16 M N 7 15

x 1 1.4 1.8 2.2

Write the general formula for Newton's backward interpolation.

What are the criteria for the right choice of interpolation formula.

Using method of least squares, fit a relation of the form y=abx to the following data

Using Newton’s forward formula, find the value of f(1.6), if :

data :

By the method of least squares, find the straight line that best fits the following

From the ahead table, estimate the number of student who obtained

Marks between 40 and 45 :

Determine f(x) as a polynomial in x for the following data :Enlist the use of Interpolation methods

No. of Students

x 1 1.4 1.8 2.2

y 3.49 4.82 5.96 6.5


26 2B17 M N 7 15

1911 1921 1931 1941 1951 1961

12 15 20 27 39 52

27 2B18 M N 7 15

Years 1946 1948 1950 1952 1954

40 43 48 52 57

28 2B19 H N 7 10

29 2A10 M N 7 15

x 0.1 0.2 0.3 0.4

y=f(x) 1.10517 1.22140 1.34986 1.49182


1 3A1 M N 7 15

The following table gives the population of a town during the last six

censuses. Estimate using interpolation formula, the increase in

population during the period from 1946 to 1948.

Given f(0) = -18, f(1) = 0, f(3) = 0, f(5) = -248, f(6) =0, f(9) =13104, find f(x).

Find the derivative f(x) at x = 1.4 from the following table :

Year

Sales in (1000

The following table gives the sales of a concern for the last five years. Estimate the sales for the

Derive the expression for Simpson’s 1/3rd rule

Population in (thousands)

x : 4.0 4.2 4. 4 4.6 4.8 5.0 5.2

2 3C1 M N 7 15

3 3B1 M N 7 15

4 3B2 M N 7 15

5 3C2 H N 7 15

given that

log x : 1.3863 1.4351 1.4816 1.5261 1.5686 1.6094 1.6487

Solve the differential equation dy/dx = -xy2 with initial, condition y=2 at x=0, by modified

Euler’s method and obtain y at x=0.2 in two steps, correct upto 4 decimal place

Using Runge-Kutta’s 4th

order method determine y for x=0.1,0.2 and 0.3 for the given differential

equation dy/dx = xy + y2 , y(0) = 1.

h=0.2 using Runge-Kutta method of 4th order.

Using modified Euler’s method, find an approximate value of y when x=0.3, given

Given dy/dx = 1+y2, where y=0 when x=0, find y(0.2), y(0.4) and y(0.6), by taking

5 3C2 H N 7 15Using modified Euler’s method, find an approximate value of y when x=0.3, given

that dy/dx = x + y and y = 1 when x = 0.


6 3A2 M N 7 15

7 3C3 H N 7 15

8 3B3 M N 7 15

9 3B4 M N 7 15

10 3C4 H N 7 15

11 3B5 M N 7 15

12 3B6 M N 7 15

13 3B7 H N 7 15

Using Runge-Kutta method of fourth order, solve : dy/dx = y -x /y + x ; with y(0) =1at x=0.2,

0.4.

Using modified Euler's method,find an approximate value of y when x=0.3, given that dy/dx=x+y

and y=1 when x=0.

(i) Trapezoidal rule (ii) Simpson's 1/3 rule

Evaluate dx/1+x2 by using (The value of x ranges from 0 to 6)

Find y(0.8) correct to 4 decimal places if y'=y-x2, y(0.6) = 1.7379 by using Runge-Kutta method

of fourth order.

Given dy/dx = y-x/y+x with initial condition y=1 at x=0; find y for x = 0.1 by Euler's method.Solve the following by Euler modified method : dy/dx=log(x+y),y(0)=2 at x=1.2 and 1.4 with

h=0.2.2 2 2 2

Apply Runge-Kutta method of 4th order to find an approximate value of y for x=0.2 in steps of 0.1

if dy/dx=x+y2, given that y=1at x=0

(iii) Simpson's 3/8 rule and compare the result with its actual value

Using Modified Euler's method, obtain a solution of the equation

dy/dx = x + |y| with initial conditions y=1 at x =0 for the range 0x0.6 in steps of 0.2.

14 3B8 M N 7 15

15 3A3 E T 2 2

16 3A4 M T 5 10

17 3A5 M T 5 10

18 3A6 M T 5 10

19 3A7 H T 7 5

20 3B9 M T 7 5

21 3B10 E T 5 5

22 3B11 E T 2 2

23 3A8

24 3A9 M N 7 15

t 2 4 6 8 10 12 14 16 18 V 10 18 25 29 32 20 11 5 2last value of t and v is 20 and 0 respectively

25 3A10 M N 7 15

Write the general formula for solving ordinary differential equation using Runge-Kutta method..

Develop the Numerical integration formula for Trapezoidal rule.

Evaluate dx/1+x taking 7 ordinates by applying Simpson’s 3/8 rule. Deduce

the value of loge2

. Where 'x' ranges from 0 - 1.

Differentiate between Euler's & modified Euler's method.

Write the general formula for solving ordinary differential equation using Runge method..

Develop the Numerical integration formula for Simpson's 1/3 rule.

Develop the Numerical integration formula for 3/8 rule.

Differentiate Simpson's 1/3 & 3/8 rule.

Write the general formula for Numerical integration.

Calculate the value of sin x dx by Simpson’s 1/3 rule using 11-ordinates

x ranges from 0 - 180 degree

The velocity V (km/min) of a moped which starts from rest, is given at fixed

Interval of time t (min) as follows :

Estimate approximately distance covered in 20 minutes.

Using Runge-kutta method for fourth order, solve : dy/dx=y2-x2/y2+x2 with y(0)=1 at x=0.2,0.4.

the value of loge . Where 'x' ranges from 0 - 1.


26 3B12 M N 7 15

27 3C5 M N 7 15

28 3A11 M N 7 15

S, ft 0 10 20 30 40 50

v, ft/sec. 47 58 64 65 61 52

29 3A12 M N 7 15

30 3B13 H N 7 15

31 3B14 M N 7 15

approximate value of p. where x ranges from 0 to 1

Using Euler’s modified method, find a solution of the equation

dy/dx = x + | y | = f(x,y)

Find the value of log 3 from x2/1+x

3 dx (the value of x ranges from 0 to 1) using Simpson's 1/3

Use Runge-Kutta method to approximate Y, when x=0.1 and x=0.2.

Given that x=0, when y=1 and dy/dx = x + y.

with initial condition y = 1 at x = 0 for the range 0 x -6 in steps of 2.

Evaluate dx/1+x2

by using Simpson’s 3/8 rule. Hence obtain the

Estimate the time taken to travel 60 ft by using Simpson’s 1/3 rule.

Apply Milne’s method to find a solution of the differential equation

y’ =x-y2 in the range 0x1 for the boundary condition y=0 at x=0.

The velocity v of a particle at distance S from a point on its path is given by

the table :

Using Euler’s method, find approximate value of y when x =0.6,

dy/dx = 1-2xy, given that y=0 when x=0 (take h = 0.2).

32 3A13 M N 7 15

33 3B15 Use Runge's method to approximate y when x = 1.1 given y=1.2 at x=1 and dy/dx = 3x + y2M N 7 15

UNIT 4SN. CAT QUESTIONS LEVEL TYPE MARKS TIME1 4A1 E T 2 5

2 4B1 M N 7 15

u7 u4 u1

u8 u5 u2

u9 u6 u3

3 4C1 M N 7 15

Find the value of log 3 from x2/1+x3 dx (the value of x ranges from 0 to 1) using Simpson's 1/3

u(0,t) = u(1,t) = 0 andU(x.0) = 2x for 0x ½

Derive the 5 point standard finite difference scheme for laplace equation

2 u =0

u i,j = ¼ [ u i+1, j + u i-1,j + u i,j+1 + u i,j-1 ] Solve the Poisson’s equation 2 u = 8x2 y2 for the square mesh given below with u(x, y) = 0

Solve the least equation u/ t = 2 u/ x

2 , subject to the condition

U(x.0) = 2x for 0x ½


M N 7 15

4 4B2

8 4B3 M N 7 15

9 4C2 M N 7 15

10 4F1 M N 7 15

11 4C3 M N 7 15

12 4B4 M N 7 15

13 4E1 H N 7 15

x=3=y with u=0 on the boundary and mesh length = 1.

Find the solution of the parabolic equation uxx = 2u, when u(0,t) = u(4,t) = 0

and u(x,0) = x(4-x), taking h=1. Find the values upto t =5.

Solve the equation 2u =-10(x2 + y2 + 10) over the square with sides x=0=y,

Apply relaxation method to solve the equation 2u = - 400, when the region

boundary of the square.

Find the solution of the differential equation d2y/dx

2 + x

2y = 0 with

of u is the square bounded by x = 0, y=0, x=4 and y = 4 and u is 0 on the

Evaluate the pivotal values of the equation uu = 16uxx taking Dx = 1 upto

Solve the equation : 2 u = -10 (x2 + y2 + 10) over the square with sides

x=0=y, x=3=y with u =0 on the boundary and mesh length = 1.

ux (0,t) = 0 U(L,t) = a and initial condition : u(x,0) = u0

t = 1.25. The boundary conditions are u(0,t) = u(5,t) = 0. ut(x,0) =0 and

u(x,0) = x2 (5-x).

Solve the parabolic equation :

k2u/ x2 = u/ t, r <x<t, t>0 with boundary condition :

= 2 (1-x) for 1/2x 1

13 4E1 H N 7 15

14 4F2 H N 7 15

1000

1000 1000 1000 1000

2000 A B 500

2000 C D 0

1000

500 0 0

15 4C4 M N 7 15

16 4C5 M N 7 15

17 4C6 Solve the parabolic equation : M N 7 15

Find the values of u(x,t) satisfying the parabolic equation u/t = 42u/x

2and the boundary

conditions u(0,t)=0=4(8,t) and u(x,0)=4x-1/2x2 at the points x=i : 1,2,…….7 and t=1/8 j : j =

0,1,……..5

Evaluate the pivotal values of the equation uu=16Uxx, taking Dx=1 upto t=1.25. The boundary

conditions are u(0,t) = u(5,t) = 0,ut(x,0)=0 and u(x,0)=x2(5-x)

1000, 625, 875 and 375

by approximating the differential equation with a second order

difference equation.

Solve by Relaxation method. The initial values of U at A,B,C and D are estimated to be

the boundary condition y(0)= 0,y(1) = 1 at the point 0.25, 0.50 and 0.75

Find the solution of the differential equation d2y/dx

2 + x

2y = 0 with

17 4C6 Solve the parabolic equation : M N 7 15


k2u/x2 = u/t 0<x<t, t>0 with boundary condition Ux(0,t) =0 U(l,t)= 9

and initial condition u(x,0) = 40.

18 4B5 Write the general form of Elliptical equation. E T 2 2

19 4B6 Write the general form of Leplace equation. E T 2 2

20 4A2 What is standard 5 point formula. E T 2 2

21 4A3 What is Diagonal 5 point formula. E T 2 2

22 4B7 Differentiate between Jacobi's & Gauss Siedel method for solving partial differential equation H T 7 10

23 4B8 Write the general form of Poisson's equation. E T 2 2

24 4C7 Write the general form of Parabolic equation. E T 2 2

25 4E2 Write the general form of one dimensional heat equation. E T 2 2

26 4E3 Write the general form of Two dimensional heat equation. E T 2 2

27 4A4 Write the general form of Hyperbolic equation. E T 2 2

28 4D1 Write the general form of Wave equation. E T 2 2


1 5A1 H T 2 2State what is wrong in the statement1 5A1 H T 2 2

2 5A2 H T 2 2

3 5A3 H T 2 2

4 5A4 H T 2 2

5 5A5 M T 7 5

}

3 5A6 M T 7 5

printf (“%f” , p );

Find the errors if any in the following program statements :(i) for (i =1, i < = 5 ; i ++ ) for (j =1, j < = 4, j ++ )

sum = sum + x ;count = count + 1 ;

(ii) for ( p = 10; p >0 ; p = p-1 ;

Printf(“% - 10 d % - 15 S ” ,count, city); Find the errors if any in following looping segments. Assume that all the variables have been

declared and assigned values(i) while (count ! = 10);{ count = 1 ;

Printf ( “%-S, %C” \n, city,code); Show the exact output of the following statement Printf (“%2 d \ n% f”, count, price ); Show the exact output of the following statement

State what is wrong in the statement Printf (“% f, %d, %S, price, count, city); State what is wrong in the statement :

for (j =1, j < = 4, j ++ )


4 5D1 H T 7 10

5 5A7 M T 5 5

6 5B1 E T 5 5Explain the various logical operators used in C programming with example.

(ii) power (a, n-1)

(iii) product (m, 10);

(iv) double minimum (float a ; float b;)

{ string [ i ++ ] = i ;

printf (“%S \n” , string [i] ;

State whether the following function headers are valid or invalid and why invalid ?

(i) average (x, y, z) ;

Determine what will be output of the following program segment

(i) for (i = 0 ; string [i] = ‘\0’ ; i ++ ;

printf ( “%d \ n “ string [i] ;

(ii) for ( i = 0 ; i < = strelen [string] ;; )

A [i] [j] = 0 ;(ii) for (i = 4, i >= 0 ; i -- ) for (j = 0 ; j<=4, j++ ) A [i] [j] = B [j] + 1.0 ;

7 5B2 M T 5 5

8 5B3 E T 7 15

9 5C1 H T 7 15

10 5B4 With an example explain the conditional operators available in 'C' Language. M T 5 10

11 5C2 Write a program to store 10 numbers in an array and arrange them in ascending order. H T 7 10

12 5C3 Write a program to generate the pattern H T 7 10

*

**

***

****

*****

14 5B5 Discuss about C constants, C variables and rules for naming C variables. M T 5 5

15 5B6 Discuss about various shorthand assignment operators and relational operators available M T 5 5

(iii) Loops

(iv) Declaration statement

(v) Pointers

Write a C program for solution of ordinary differential equation by Euler’s method.

their syntax and example.

Write notes on the following :

(i) Array

(ii) Break statement

State the various types of logical statements that are used in C programming with

15 5B6 Discuss about various shorthand assignment operators and relational operators available M T 5 5


in C with their symbols.

16 5B7 Write notes on the following : M T 7 15

(i) Functions (ii) Switch Statement (iii) Union (iv) Structure (v) Input/output statement

17 5C4 Write a C program for solution of ordinary differential equation by Runge-Kutta Method H T 7 15

18 Write a C program for solution of algebraic equation by Newton-Raphson method. H T 7 15

19 5B8 Discuss about C constants, C variables and rules for C variables naming. M T 5 10

20 5B9 State the various types of Logical statements that are used in C programming with their syntax M T 5 5

and example.

21 5B10 Write notes on the following : M T 7 10

(i) Array (ii) DO-while (iii) Pointer (iv) Union (v) Structure

22 5B11 Explain various C-expressions with suitable example. M T 5 10

23 5B12 Differentiate one-dimensional arrays and two-dimensional arrays and explain the use of arrays H T 7 10

to solving the problems of Thermal Engineering with suitable examples.

24 5B13 Explain the following termology with suitable program : (i) getchar (ii) Unions M T 7 10

(iii) C-string Library

25 5C5 Write a program to find multiplication of two square matrix. H T 7 15

26 5C6 Write a C program for solution of simultaneous algebrical equation by M T 7 1526 5C6 Write a C program for solution of simultaneous algebrical equation by M T 7 15

Gauss elimination method.

27 5C7 Write a C program to find the values of u(x,t) satisfying the parabolic equation H T 7 15

u/t = 42u/x

2 and the boundary conditions u(0,t)=0=u(8,t)and u(x,0)=

4x - x2/2 at points x=i ; i=0,1,2,……..7 and t=1/8 j , j=0,1,2,……,5.

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