Maharashtra State Board of Technical Education 2008 Diploma Electrical and Electronics Applied Mathematics Electronics Group - Question Paper
Sample Question Paper - I
9030- Electronics Group
Course Name Course code Semester Subject Duration
- EE/EP/ET/EN/EX/IE/IS/IC/DE/EV/MU/ED/EI
- Third
- Applied Mathematics
- 3 hours Marks: 80
Instructions: 1) All the questions are compulsory
2) Figures to the right indicate full marks
3) Assume suitable additional data if necessary
4) Use of pocket calculator is permissible
Q. 1 Attempt any eight of the following
(16)
a) Integrate w.r.t. x 1
5x
-+e
1 + x2
b) Integrate w.r.t. x
2
c) Integrate w.r.t. x
xe
d)
dx
Evaluate
f-5
J x2 + 4
e) Find the order and degree of the differential equation
d2x ( dx
+ 1 I = 5
dt 2 I dt
f) Solve the differential equation
dy a x- y = 0 dx
g) Find the equation of the curve whose slope is (x-3) and which passes through (2,0)
h) Find l(2 + 3t - e-t)
i) Find L(t2 e3)
25 - 3
Q. 2 Attempt any three (12)
a) Form the differential equation if
y = Ae3 + Be "3x
b) Solve the differential equation
dy = x2 + y2 dx 2xy
c) Solve
x log x + y = 2log x dx
d) A particle starting with velocity 6m/sec has an acceleration
(1 -,2) m/ sec2. When does it first come to rest? How far has it then traveled?
Q.3 Attempt any three (12)
a) Find L[sin4t cos2t ]
b) Find L[e ~2t (3cos4t - 2sin3t)]
+1
-1
c) Find L
d) Solve by using L.T.
3 + 2 x = e3t if x(0) = 1 dt
Q. 4 Attempt any four (16)
a) Integrate w.r.t. x
(Sin _1 x)3
x)
x2
b) Integrate w.r.t. x 1
(x + 1)(x + 2)(x + 3)
dx
c) Evaluate jj
V x2 - 6 x +13
n/2 I
Vcos x
d) Evaluate J . ' dx
o Vcos Wsin x
e) Find the area of circle x2 + y2 = r2 by integration
f) Find R.M.S. value of an alternating current I = 10 sin 100 nt
a) Obtain Fourier series for
f(x) = x in the internal (-n,n)
b) Using Bisection method find the approximate root of the equation x3 - x - 4 = 0 (carry out three iterations only)
c) Find a root of the equation
x3 - 2x - 5 = 0 using regular falsi method (up to 3 iterations)
d) Using Newton Raphson method to evaluate V10 correct to three decimal places
a) Obtain the half range cosine series for f(x) = x over (0,n)
b) Solve the following equations by Gauss Elimination method 2x + 3y + z = 13, x + y - 2z = -1,3x - 4y + 4z = 15
c) Solve the following equation by Jacobis method
10 x + y + 2 z = 13,3x +10 y + z = 14,2 x + 3 y +10 z = 15
d) Solve the following equations by Gauss - Seidal method 6 x + y + z = 105,4 x + 8 y + 3z = 155,5x + 4 y -10 z = 65
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| Earning: Approval pending. |
