PTU Punjab Technical University B-Tech May 2019 Question Papers 2nd Semester Electronic and Communication Engineering (ECE-EIE)
Total No. of Pages : 02
Total No. of Questions : 09
B.Tech. (Electrical Engg./ECE) (2018 Batch) (Sem.?2)
MATHEMATICS-II
Subject Code : BTAM-202-18
M.Code : 76255
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION - B & C have FOUR questions each.
3.
Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4.
Select atleast T WO questions from SECT ION - B & C.
SECTION-A
l.
Answer briefly :
a) Check whether the given equation is exact and obtain the general solution :
(1 +x2)dy + 2xydx = 0
b) Solve the differential equation (x ? a)dy/dx + 3y = 12 (x?a)3 ; x > a > 0.
c) Find the solution of the differential equation y + 2y + 2y = 0.
d) Find a differential equation of the form ay + by + cy = 0, for which e?x and xe?x are
solutions.
e) Solve the differential equation y + 32y + 256y = 0
f) Write a short note on initial value problems.
g) Find the interval in which the root of equation x3 ? x ? 11 = 0 lies.
h) Write a short note on Bisection method.
i) Define transcendental equation.
j) Find the polynomial which takes following data (0, 1), (1, 2) and (2, 1).
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SECTION-B
2.
i) Find the integrating factor and hence solve (5x3 + 12x2 +6y2) dx + 6xy dy = 0
ii) Solve the differential equation dy/dx ? y = y2 (sin x + cos x).
3.
i) Find a homogeneous linear differential equation with real coefficients of lowest order
which has the xe?x + e2x as the particular solution.
ii) Using differential operator, find general solution of (D2 + 9) y = xe2x cosx.
4.
Find the general solution of the equation y+16y = 32 sec 2x, using the method of
variation of parameters.
5.
Find the general solution of the equation x2y+5xy ? 5y = 24xlnx.
SECTION-C
6.
Use Newton iterative method to find the root of equation 3x ? cos(x) + 1, by taking initial
guess 0.6.
7.
Solve the following equations by elimination method 2x + y + z = 10, 3x + 2y + 3z = 18
and x + 4y + 9z = 16.
8.
Using Newton's forward formula, find value of f (1.6), if :
x
1
1.4
1.8
2.2
f(x)
3.49
4.82
5.96
6.5
9.
Using Runge-Kutta method of order 4, find y(0.2) for the equation y = (y ? x)/(y + x)
y(0) = 1, take h = 0.2.
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 04 November 2019