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Ptu Maths2 Dec09

This document contains instructions and questions for an engineering mathematics exam. It has 3 sections with a total of 9 questions. Section A contains 8 multiple choice questions worth 2 marks each. Section B contains 2 questions worth 8 marks each. Section C contains 3 questions worth 6 marks each. The exam is worth a total of 60 marks and lasts 3 hours. Candidates must attempt all of Section A and 5 questions total from Sections B and C, selecting at least 2 from each section.

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Shilpa Singh
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109 views3 pages

Ptu Maths2 Dec09

This document contains instructions and questions for an engineering mathematics exam. It has 3 sections with a total of 9 questions. Section A contains 8 multiple choice questions worth 2 marks each. Section B contains 2 questions worth 8 marks each. Section C contains 3 questions worth 6 marks each. The exam is worth a total of 60 marks and lasts 3 hours. Candidates must attempt all of Section A and 5 questions total from Sections B and C, selecting at least 2 from each section.

Uploaded by

Shilpa Singh
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Roll No.

otal No. of Questions : 091 , \ F.| , .^ [Totat No. of Pages: 03


- afu4lLd aa-L'+(u'4' btnt
l/\Tt&1^t
B.Tech. (Sem. - lst | /na)
ENGINEERING MATHEMATICS - II
SUB.IECTCODE: AM - I02 (2k4& Onwards)
PaperID : [A0119]
[Note : Pleasefill subject code and paper ID on OMRI

Time : 03 Hours Maximum Marks : 60


Instruction to Candidates:
1) Section- A is Compulsory.
2) Attempt any Five questionsfrom Section - B & C.
3) SelectatleastTwo questionsfrom Section - B & C.

Section - A
QI) (Marks:2each)
a) What do you understandby complementaryfunction? Explain.
b) Are thesevectorslinearly independent?
x, = (1, 2, l), x, = (2, l, 4), x, = (4, 5, 6), xo = (1,8, -3)
c) StateCayley - Hamilton theorem.
d) Define order and degreeof an ordinary differential equation.
e) Statenecessaryconditionsfor an ordinary differential equation to be
exact.

0 Define directional derivativeof a function.


g) StateType I and Type II errors in sampling.
h) Define Null hypothesisand critical region.
i) StateGaussdivergencetheorem

[-t 2+i s-3il


j) Showthatif A -l Z-i 7 5i thenrA is skewHerrnirian.
-5i l,
[5+3i o2 ]

J-r06eJ8t2el PTO.
Section- B
(Marks : 8 each)

82) (a) Solve the equations:


5-r:+ 3y + 72,=4, 3x + 26y + 22.=9, 7x + 2 y + l l z , - 5

4 3l
f8
A-12' tl
(b) Find the eigcn-valuesand eigenvectorsof
Lr 2 rj

Q3) (a) Prove that the necessaryand sufficient condition for the differential
)nt a//
equationMdx + Ndy = 0, to be exact is -=-.
0y dx
(b) Solve : xdy - ydx = (x2+ Y')dx.

d'y -zdY y=
Q4) (a) Solve : + xe* sinx
dx2 dx

, d.2y d
(b)*2 . .ff+4 = losxsin(logx)
#

QS) (a) If an e.m.f. E sin ot rs applied to L-C-R circuit at time t satisfiesthe

.equatron L+ + n!9*! . If R -zJLc, solvethe


- Es\nan
dt' dt c
differential equationfor q.
(b) A body executesdamped forced vibrations given by the equation

d-:
+ 2Kg + bx2 = s-Kt sinatt.
")r

dt- dt

Solve the equationfor the cases: (1) a2 + b2 - K2 and a)2= b2 - K2 .

J- I 069
Section- C
(Marks : I each)

,)-
dr 11-r lar dzva3rl
Q6) (a) lf / = (a cos/, a sint, at tan a), find _ X ^ andt -, ..t,.?1.
dt dt' I dt dt' dt' I

( b ) P r o v et h a t V x ( Q A ) - Q V x d + Y Q x a .

Q7) (a) Stateand proveStokestheorem.

(b) Use divergence theoremto evaluat"lJ F.rts,F-*3i+y3i+23f, S i,


s
the surfaceof the spherex' + y' * z2= e2,

-
Qq (a) Find mean and varianceof Poissondistribution.
(b) Find a binomial distribution for the following data :
x: 0 1 2 3 4 5
f: 2 14 20 34 22 8

Q9) (a) A sample of 2O items has mean 42 units and S.D. 5 units .test the
hypothesisthat it is a random samplefrom the normal populationwith
mean 45 units given that /0.0,= 2.09, for 19 d.f.
(b) Write a short note on hypothesistesting and its uses.

trntrtI

J-I 069 3

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