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EE & EEE MATH QUESTION FOR 2015-19 BATCH MATH -4
MODULE 1 FOR PRACTICE BY MATH-DEPARTMENT GEC
MATHEMATICS 3
MULTIPLE CHOICE
QUESTION’s answer
1. WHAT IS THE RELATION BETWEEN Ea
(ABSOLUTE ERROR ) AND Er (RELATIVE ERROR)
a)Ea= Er/T b) Er=Ea/T c)
Er=Ea ×100 d) none of these
2. What is the maximum order of R.K
method
a)1 b) 2
c) 4 d) none of these
3. If there are 4 points then maximum
degree of the polynomial is
a)3 b)4 c)2 d)none
of these
4. What is the approximate value of π up
to 5 significant digit?
a)3.1415 b)3.1416 c)3.1412 d)none
of these
5. Newton’s divided difference formula
is applicable for
a)arbitrary
spaced point
b)equally spaced point c)fixed
point d)none of these
6. To find f(1) and f(7) for
the data X 2 4 6 Is known as
F(X) 8
20 40
a)inter polation b)intra
polation c)extension d)none
of these
7. To find f (3) & f (8) for the data X 2
5 9 10 is known as;
F(X) 17 35 59 65
a)intra polation b)extra polation c)inclumion d)none of these
8. Test the nature of the following function f (z)= z’ (Z bar)
a)analytic b)not analitic
c)harmonic d)
none of these
9 .Test the nature of real part of f (z) = 1/z
a)harmonic b)not
harmonic c)analytic d)none of these
10. If a function is analytic in a domain D then
a)differentiable outside of
domain
b)continuous outside of domain
c)differentiable
inside of domain
d)none of these
SHORT
QUESTIONS
1. Round of the following number to 3 significant
digits.
a) 2.0065 b) 0.0125
a) 2.0065 b) 0.0125
2. Round of the following numbers up to
4 decimal places.
a) 1.32655 b)2.96785
a) 1.32655 b)2.96785
3. If 5/6 in approximated by 0.8333 ,
then find relative error.
4. If value of sin x is approximate by
1.0021 at x=π/2 ,then find out the percentage error ?
5. Write down the formula for Newton’s
Divided difference for x,x1,x2,x3
6. Write down the formula for Newton’s
forward interpolation for three points x0,x1,x2
7. write down the formula for Lagrange’s
interpolation for (n+1) points , x0,x1,………..,xn
8. Write down the formula for Newton’s
Backward interpolation for 4 points x0,x1,x2,x3.
9. State Trapezoid’s rule for 10
intervals.
10.
State
Simpson’s 1/3 rule for 10 intervals.
11.
State
Simpson’s 3/8 rule for 10 intervals.
12.
State
Euler’s formula for ordinary differential equation ?
13.
State
Euler modified formula for ordinary differential equation ?
14.
State
R.K 2nd order method ?
15.
State
R.K 3rd order method ?
16.
What
do you mean by predictor and corrector method ?
17.
Write
down the formula for Adams-Barb forth method ?
18.
Write
down the formula for Millen’s method ?
19.
Define
interpolation ?
20.
Define
extrapolation ?
21.
Define
analytic function ?
22.
State
Cauchy Riemann equation in Cartesian form ?
23.
State
Cauchy Riemann equation in polar form ?
24.
How
the error is propagated ?
LONG TYPE
1. Find y(0.1) and y(0.2) using Euler’s method dy/dx= xy ,y(0)=1
2. Find y(4.1) using Euler’s modified
method for dy/dx = x2+xy ,
y(4)=3
3. Find y(2.1) and y(2.2) using R.K 2nd
order method for dy/dx = x+y , y(2)=3.14
4. Test analyticity f(z) = 1/z4
5. Test harmonicity v = x/x2+y2 and find
the corresponding analytic function .
6. Find the value of the analytic
function for v = e-xsiny
7. Find a & b such that v = ax3+by3
is harmonic and hence find the corresponding analytic function.
8. Derive Newton’s divided difference
polynomial for the data (0,0) ,(2,2) ,(5,20),(6,30)
9. Evaluate 1
∫dx/1+x2
using trapezoidal rule by taking 10 interval
0
10.
Evaluate 3
∫ln x dx using
Simpson’s 1/3rd rule by taking
n=8
1
11.
Evaluate 4
∫e(x)2 . dx using
Simson’s 3/8th rule by taking n = 10
2
12.
Evaluate 2
∫x2 dx
using 3- point Gauss Legendre rule.
1
13.
Derive
the Lagrange’s inter polation polynomial for the data
X 0 1 3 6
F(X) 2 3 11 38
14.
Find
out the value of f(2) from the data
F(X) 0 26 124 342
15.
Find
out the value of f(8) from the data
F(X) 3 29 127 345
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