NRI INSTITUTE OF TECHNOLOGY
Visadala Road, Perecherla (P.O), Guntur District
Subject: MM
Marks : 15
I B. Tech I Semester I Mid Question Paper
Each question carries equal marks:
UNIT – I
1. a) Find the positive real root of the equation x 3  4 x  9  0 by bisection method correct to 3
places of decimal places.
b) Find a real root of the equation by using bisection method cos 2x  x  0 .
2. a) Find a positive root of the equation by Iteration method 2x  3  cos x .
b) Find approximate value of the real root of x log 10 x  1.2 using third approximation by false
position method.
3. a) Find approximate value of the real root of xe x  2 using Regula-Falsi method..
b) Find the real root of the equations x 3  x  2  0 correct to three decimal places by
Newton - Raphson method.
4. a) Using Newton-Raphson method, find 23 .
b) Using Iteration method find a root of equation x 3  x  10  0 perform 5 iterations using
x0  0.
5. a) Using Newton-Raphson Method find Reciprocal of a number.
b) Derive a formula to find the cube root of N using Newton-Raphson Method hence find the
cube root of 15.
UNIT – II
1
6.a) Evaluate f x if f x   2
at h=1.
x  5x  6
b) Verify that the value of y when x=10 is 920 of y  x 3  x 2  x  10 and only six values of y
corresponding to 1,2,3,4,5,6 are used.
7.a) Find the missing term in the following:
X
logx
100
2.0000
101
2.0043
102
-
103
2.0128
104
2.0170
b) Prove that          2  2 E 1
8.a)The values of f(x) for x=0,1,2,……,6 are given by
x
0
1
2
3
4
5
6
F(x)
1
3
11
31
69
131
223
Estimate the value of f(3.4) using only four of the given values by using Newton’s forward.
x
b) Certain values of x and log 10
are (300, 2.4771), (304, 2.4829), (305, 2.4843), (307, 2.4871).
301
Find log 10
9.a) Apply Gauss’s forward formula to find the value of u 9 , if u 0  14 , u4  24 u8  32 u12  35
u16  40 .
b) Prove that 1   2  2  1 
2
2
10.a) Given the values
x
3
5
7
9
11
f(x)
6
24
58
108
74
Using Lagrange’s formula for interpolation find the value of f(6).
b) Given u1=22, u2=30, u4=82, u7=106, u8=206, find u6. Using Lagrange’s formula for
interpolation
UNIT – III
11. Apply Taylor’s method to obtain approximate value of y(1.1) and y(1.2) correct to three
1
3
decimal places for the differential equation y  xy , y 1  1
12. Solve by Euler’s method, y '  x  y , y(0) = 1 and find y(0.3) taking step side h = 0.1
Compare the result obtained by this method with the result obtained by analytical method.
dy
 xy  y 2 , y 0   1 for y0.1, y0.2.
13. Use Runge-kutta method to solve
dx
dy
 x 2  y 2 , y 0   1 by using Picard’s method
14. Solve
dx
15. Compute y at y = 1.5 in steps of 0.25 by Euler’s modified method given
y '  xy  2, y1  1
'
***********