Download AKTU B-Tech 3rd Sem 2017-2018 RAS 301 Mathematics Iii Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2017-2018 RAS 301 Mathematics Iii Question Paper

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PaperIDz9019
B.Tech.
(SEM III) THEORY EXAMINATION 2017-18
Mathematics -111
T ime: 3 Hours T and Marks: 70
Note: 1. Attempt all Sections. If require any missing data; then choose suitably.
2. Any special paper specific instruction.
SECTION A
1. Attempt all questions in brief. 2 x 7 = 14
Define analytic function with an example.
Define the Binomial distribution with mean and variance.
Write the normal equation for the curve y = 3+ bx
Give comparison between Regulafalsi method and Newton Raphson method
Write the relation between nth divided difference and nth forward difference.
What do you mean by initial value problem
Find 2-1 ( 5 )
52?1
mwrogcp?s?
SECTION B
2. Attempt any three of the following: 7 x 3 = 21
a. Give an example of a function in which Cauchy Riemann Equations are satis?ed yet
the function is not analytic at the origin. J ustify your answer.
b, Find the measure of Sskewness and kutosis based on moments for the followi
distribution and draw your conclusion
Marks 5?15 15?25 25?35 35?45 45?55
No.0fstudents 1 3 5 7 4
5 ?2 1
Decompose A = [ 7 1 _ 5 ] in the form LU, where L is lower
3 7 4
triangular matrix and U is upper triangular matrix and hence solve the system
ofequations:
5x ? 2y+z = 4
7x +y? 52 = 8
3x+7y+4z= 10.
d. 1 when lesl
Express the function f (X) = as a Fourier Integral.
0 when |x|>1?
00 sin/l cos 1x
? d/l.
Hence evaluate 0 A
e. Given the initial value problem 2?: = x3 ? y3, y(0) = 1.
Find the numerical solution of differential equation atx = 0.6 with h = 0.2 by
using Runge-Kutta method of Fourth order.

SECTION C
3. Attempt any one part of the following: 7 x 1 = 7
(a) Evaluate the integration:f0n sin4 6d9.
(b) __1___ ==1:
State and prove the Cauchy Integral formula. Also evaluatefc (22+4)2 dz 16,,
where C is the circlelz ? iI = 2,
4. Attempt any one part of the following: 7 x 1 = 7
(a)
(b)
5. Attempt any one part of the following:
(a)
(b)
6. Attempt any one part of the following:
(a)
(b)
7. Attempt any one part of the following:
(a)
(b)
1
Find Fourier cosine transform of and hence find Fourier sine transform of
1+x2
x
1+x2' . .
Find the inverse Z-transform of F(z), where F (z) 1s glven by
. z .. 72?1122
(1) (z+2)(z+3) (11) (z?1)(z?2)(z+3)'
7x1=7
In a partially distributed laboratory record of an analysis of a correlation data,
the following result are legible:
Variance of x = 9
Regression equation: 8x ? 10y = 66 = 0,40x ? 18y = 214.
What were (a) the mean of x and y. (b) the standard deviation of y and the
coefficient of x and y:
Find the mean and variance of normal distribution.
7x1=7
Find the real root of the equationx3 ? 2x + 5:0 by method of False positit
correct to three decimal places.
State and prove the Lagrange interpolation formula. Find the interpolating
polynomial by By Lagrange interpolation formula for the given data
x 5 6 9 11
y 12 13 14 16
7x1=7
Apply Simpson?s 3/8 th rule to obtain approximate value of (i)f(;T/2 65m" dx(ii)
0'3 2x ? x2 ?2 dxusing Simpson?s rule with 6 interval.
0
Find x for which y is maximum and find the max value of y
x 1.2 1.3 1.4 1.5 1.6
y 0.9320 0.9636 0.9855 0.9975 0.9996