University: AU(Andhra University)

Valid for: BCA-1st semester

Subject: NSM (Numerical And Statistical Methods)-Important Questions

### UNIT-1

## Solution of equations (Algebraic and Transcendental Equation)

### 1: Bisection Method

Find the root of equation x3-5x+1 using the bisection method in 5 stages?

Find the root of equation x4-8x+1 using the bisection method in 8 stages?

Find a positive root of x3-x-1=0 to correct the 3 decimal place by bisection method?

Find a real root of the equation x3-6x-4=0 by bisection method up to 5 stages?

Find a real oot of x3-5x+3=0 using the bisection method?

Find a real root of the equation x3-x-11=0 by using the bisection method?

### 2: False Position Method

By regular falsi method find the root of equation x3-2x-5=0?

Find the Positive root of equation f(x)=x3-2x-5=0?

Find the root of equation xe2=cosx using the regular falsi method.

Find the root of equation 2x-log10 x=7 which lies b/w 3.5 and 5 by the regular falsi method?

Find the real root of xex= using the regular falsi method.

### 3: Iteration Method

Find the real root of x=1/(x+1)2 by iteration method?

Find the equation sinx=5x-2 by iteration method?

Solve the equation x3-2x-5=0 by iteration method?

Find the positive root of the equation by iteration method 3x=cos x+1.

### 4: Newton-Raphson Method

Using Newton Raphson's method find the root of equation ex-3x that lies between 0 and 1?

Find the root of equation x4-x-10=0 by Newton Raphson method?

Find the root of equation x4-x-9=0 using Newton-Raphson Method.

Find the root of equation x3-x-2=0 using the Newton-Raphson Method?

### 5: Secant Method

Find the real root of the equation x3-2x-5=0 using secant method.

Find the positive oot of x4-x-10=0 by secant method up to 4 stages.

Find the x2-x-1=0 by using secant method?

Find the root x3-x-11=0 by using secant method?

Find the root ex sin x=1=1 by using secant method.

### UNIT -2

## Solution of System of Linear Equations

### 1: Gauss Elimination Method

x1+x2=6;x1+2x2+3x3=14;-x1+x2-x3=-2

x+2y+z=3: 2x+3y+3z=10 3x-y+2z=13

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

2: Gauss- Jordan Method