Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (ECE)-Electronics And Communications Engineering 2020 December 2nd Sem 76255 Mathematics Ii Previous Question Paper
Roll No.
Total No. of Pages : 03
Total No. of Questions : 18
B.Tech. (Electrical Engg./ECE) (2018 & Onwards) (Sem.?2)
MATHEMATICS-II
Subject Code : BTAM-202-18
M.Code : 76255
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 have FOUR questio ns eac h.
3 .
Attempt any FIVE questions from SECT ION B & C carrying EIGHT marks eac h.
4 .
Select atleast T WO que stions from SECT ION - B & C.
SECTION-A
Answer briefly :
3
2
4
d y
dy
1)
Is this differential equation 2
4
x
y
y 0
linear?
2
dx
dx
2)
Is this differential equation (ey + 1) cos x dx + ey sin xdy = 0 exact?
3)
Write the solution of the Clairaut's equation y = px + cos?1 (p + 1).
2
2
2
z
z
z
4)
Find complete solution of
4
4
0.
2
2
x
x
y
y
2
2
2
z
z
z
5)
Find particular integral of
7
12
x y
e
.
2
2
x
x
y
y
6)
Give geometric interpretation of Newton Raphson method.
7)
Give the Gauss's forward interpolation formula.
3
8)
Write the formula for Simpson's rule.
8
9)
Give the Adam's predictor corrector formula.
10) Write the one dimensional heat equation.
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SECTION-B
11) Solve :
2
dy
2xy cos x 2xy 1
a)
.
2
2
dx
x sin x 3
dy
b) tan y
+ tan x = cos y cos2x.
dx
12) a) Solve (x2D2 ? 2xD ? 4) y = x4.
2
3x
d y
dy
e
b) Solve using method of variation of parameters
6
9 y
.
2
2
dx
dx
x
13) Solve a) yzp + zxq = xy.
2
2
2
z
z
z
b)
6
cos (3x y).
2
2
x
x
y
y
14) a) Solve the PDE (D + D ? 1) (D + 2D ? 3) z = 4 + 3x + 6y.
u
u
b) Using method of separation of variables, solve 3
2
0 with u (x, 0) = 4e?x.
x
y
SECTION-C
15) a) Find a root of cos x = xex using regula falsi method correct upto three decimal places.
b) Using interpolation, find missing values in the following table :
x
45
50
55
60
65
y
3.0
-
2.0
-
-2.4
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16) a) Estimate f (38), using Gauss backward difference formula :
x
20
25
30
35
40
45
f (x)
354
332
291
260
231
204
2
b) Estimate
x
e dx,
using Trapezoidal rule by taking 10 intervals.
0
17) a) Use Taylor's series method to find the value of y at x = 0.2 upto 3 decimals, where y
dy
(0) = 0,
1 2xy.
dx
b) Use Runge-Kutta method of order 4 to find the value of y at x = 0.1 upto 3 decimals,
dy
where y (0) = 1,
x y .
dx
2
f
f
18) Using Crank-Nicholson method, solve the PDE 2
; 0 < t < 1.5, 0 < x < 4
2
x
t
subject to conditions f (x, 0) = 50 (4 ? x), f (0, t) = 0, f (4, t) = 0.
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 13 February 2021