Download PTU (Punjab Technical University) B.Tech (Bachelor of Technology) / BE (Bachelor of Engineering) 2021 January AE 5th Sem 78226 Numerical Methods Previous Question Paper
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Automobile Engineering) (Sem.?5)
NUMERICAL METHODS
Subject Code : BTAE-502-18
M.Code : 78226
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION-B c ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt any FOUR q ues tions.
3 .
SECT ION-C contains THREE questions carrying T EN marks e ach and s tudents
have to atte mpt any T WO questio ns.
SECTION-A
Write briefly :
1.
State Simpson's three ?Eighth rule
2.
In four tosses of a coin, let x be the number of heads . Calculate the expected value of x.
3.
A sample of 20 items has a mean 42 units and S.D 5 units. Test the hypothesis that it is a
random sample from a normal population with mean 45 units.
4.
Find a real root of the equation x = e?x using Newton Raphson method.
5.
Evaluate tan?1 x
6.
Find positive real root of x3 ? x = 1 by bisection method, correct upto 2 decimal places
between and 2.
7.
State Merit's of Lagrange's formula
8.
Define Spline function.
9.
Define types of numerical instability.
10. Prove that the absolute error in the common logarithm of a number is less than half the
relative error of the given number.
SECTION-B
11. Solve the problem y ? xy2 + y2 = 0. y (0) = 1, y(0) = 0 to evaluate y (0.1) using Taylor's
series methods.
12. Use Gauss elimination method to solve the following system of equations:
2x + y + z = 10, 3x + 2y + 3z = 18, x + 4y + 9z = 16
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13. Fit a poisson distribution to the following data and test the goodness of fit:
x
0
1
2
3
4
f
109
65
22
3
1
dy
14. Use Adam's Moulton-Bashforth method to find y (1.4) given
2
x (1 y ), y (1) = 1,
dx
y (1.1) = 1.233, y (1.2) = 1.548 and y (1.3) = 1.979.
15. a) Compute f (3) from the following table:
x
1
2
4
8
10
F(x)
0
1
5
21
27
b) Given the initial value problem : y = 1 + y2, y(0) = 0, Find y (0.6) by Runge Kutta
fourth order method taking h = 0.2
SECTION-C
16. A river is 80m wide. The depth `y' of the river at a distance `x' from one bank is given
by following table:
x
0
10
20
30
40
50
60
70
80
y
0
4
7
9
12
15
14
8
3
Find the approximate area of cross-section of the river using Simpson's one ? third rule.
17. a) A tank is discharging water through an orifice at a depth of x metre below the surface
of the whose area is A m2. Following are the values of x for the corresponding values
of A.
A
1.257
1.39
1.52
1.65
1.809
1.962
2.123
2.295
2.462
2.650
x
1.5
1.65
1.8
1.95
2.1
2.25
2.4
2.55
2.7
2.85
3.0
Using the formula (0.018) T =
A dx,
calculate T, the time (in seconds) for the
1.5
x
level of the water to drop from 3.0 m to 1.5 m above the orifice.
b) Using Newton's divided difference formula, calculate the value of f(6) from the
following data:
x
4
5
7
10
11
13
F(x)
48
100
294
900
1210
2028
1
18. Find a positive value of
3
(17 )
correct to four decimal places by Newton's Raphson's
method.
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 26 June 2021